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Characterization of the Fraser fault, Southwestern British Columbia, and surrounding geology through… Perz, Michael J. 1993

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CHARACTERIZATION OF THE FRASER FAULT, SOUTHWESTERNBRITISH COLUMBIA, AND SURROUNDING GEOLOGY THROUGHREPROCESSING OF SEISMIC REFLECTION DATAbyMichael J. PerzB.Sc.(Hons.) (Physics), Toronto, 1990A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF GEOPHYSICS AND ASTRONOMYWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJuly 1993© Michael J. Perz, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department of  C:-E Of is /Yr/ Glfr A,vp 4..C711 AA el"(The University of British ColumbiaVancouver, CanadaDate  act,^ 943DE-6 (2/88)ABSTRACTSeismic reflection data were acquired in 1988 along a 70 km profile crossing theFraser fault, a major dextral strike-slip boundary between the Eastern Coast and Inter-montane belts of the southern Canadian Cordillera. Preliminary processing by industrycontract and subsequent interpretation revealed several interesting tectonic features; how-ever, the subsurface position and depth extent of the fault were ambiguous. The presentstudy involves reprocessing of these data in an effort to provide an improved subsurfaceimage, and hence a better understanding of the local tectonic regime.Severe crookedness of the line necessitated the implementation of unconventionalprocessing techniques, including creation of several "mini-profiles" which cut throughthe scatter of source-receiver midpoints near the fault zone, and application of a first-order correction for effects of reflector crossdip (i.e., the crossline component of reflectordip). A method for estimating the optimum crossdip correction parameter was developed.Although it demonstrated promise when applied to synthetic data, disappointing resultswere obtained with the field data. Refraction-based statics were computed using a two-step procedure consisting of initial identification and correction of systematic errors in thepicked first break traveltimes, and subsequent application of a conventional 2—D staticsalgorithm. Dip moveout correction (DMO) was applied to the upper 5.0 s of data toenhance the image of steeply dipping features.Significant aspects of the interpretation of the reprocessed dataset include: (i)evidence of deep crustal extent (or possible crustal penetration) for the Fraser fault;(ii) correlation of two northeast-dipping reflectors (not visible on the contract-processedsections) with southwest-directed thrusting along the Pasayten fault; and (iii) correlationof two east-dipping events near the western edge of the profile with deep roots of theCoast Belt Thrust System.iiContents ABSTRACT ^List of TablesList of Figures ^AcknowledgementsINTRODUCTION ^ 1Background and research motivation ^ 1Tectonic setting ^ 5Thesis outline 13ACQUISITION AND INITIAL PROCESSING ^ 16Acquisition details ^ 16Processing system 18Initial processing steps ^ 20Data quality ^ 21Deconvolution 23Deconvolution theory ^ 25The convolutional model 25The wavelet ^ 26Statistical deconvolution ^ 26Phase considerations 27Predictive vs spiking deconvolution ^ 32Synthetic tests ^ 33Deconvolution in practice^ 36Chapter 11.11.21.3Chapter 22.12.22.32.42.52.5.12.5.1.12.5.1.22.5.1.32.5.1.42.5.1.52.5.22.5.3Ill^2.6^Spatial resolution ^  39Chapter 3^STATIC CORRECTIONS ^ 423.1^The shortcomings of the residual statics method ^ 423.2^Refraction statics^  433.2.1^The REFSTAT2 model 443.2.2^The REFSTAT2 algorithm ^ 453.3^Systematic errors ^ 483.3.1^The surface stacking chart as a diagnostic tool in theanalysis of systematic error^  493.3.2^The residual traveltime  503.3.3^The reciprocal difference time^  513.3.4^Sources of systematic error  513.3.5^The residual and reciprocal difference plotting algorithms ^ 533.3.6^Result presentation and discussion ^ 543.4^Elevation correction ^ 633.5^Data results after statics application—stacked sections ^ 66Chapter 4^DIP MOVEOUT CORRECTION AND VELOCITYANALYSIS ^  694.1^DMO theory  694.2^DMO—practical considerations ^  714.2.1^The time-variant DMO impulse response: synthetic tests ^ 714.2.2^Spatial aliasing considerations ^  734.2.3^The partial stack ^ 774.2.4^DMO and velocity analysis^  80iv^4.3^The DMO/velocity analysis processing stream ^ 844.4^Data results—stacked sections after DMO^ 85Chapter 5^CROSSDIP CORRECTION^ 885.1^Introduction ^  885.2^The 3—D CMP bin traveltime equation for a uniform dipping5.2.1layer over a halfspace   88Applying DMO before crossdip correction: synthetic tests ^ 945.3 Crossdip parameter estimation ^ 955.3.1 Algorithm testing ^ 1005.4 The crossdip correction processing stream ^ 1045.5 Data results—stacked sections after crossdip correction 107Chapter 6 PROCESSING NEAR THE FRASER CANYON ^ 1096.1 Introduction ^ 1096.2 CMP binning 1096.3 Static and crossdip effects ^ 1106.3.1 Cascading crossdip and residual statics corrections . . . 1196.4 Summary of processing stream and data results ^ 122Chapter 7 FINAL PROCESSING AND RESULT PRESENTATION . 1287.1 Data merging ^ 1287.2 Coherency filtering 1287.3 Migration ^ 1297.4 Result presentation ^ 131Chapter 8^INTERPRETATION ^  148^8.1^Introduction ^  1488.2^Surface geology  1488.3^Result interpretation ^  151Chapter 9^SUMMARY AND FINAL DISCUSSION ^ 1689.1^Crooked line processing ^  1689.2^Interpretation ^  170Appendix A^Derivation of the 3—D CMP bin reflection traveltimeexpression (equation (5.7)) ^  178Appendix B^Demonstration that the crossdip-corrected zero-offsetsection effectively images the inline component of dip ^ 190viList of Tables2.1 Acquisition parameters ^  18viiList of Figures1.1 Location map showing SBC18 and other regional seismic profiles . . . . 21.2 Terrane map of the Canadian Cordillera ^  61.3 Geological map of southeastern Coast belt displaying the Coast BeltThrust System ^  91.4 SBC18 profile superimposed atop local geology map ^ 111.5 Flowchart of SBC18 processing stream ^  142.1 SBC18 acquisition geometry^  172.2 Acquisition near the Fraser Canyon ^  192.3 The CMP binning process ^ 222.4 Common shot gather contaminated by ground roll ^ 242.5 The Klauder wavelet for SBC18^ 302.6 Comparison of predictive deconvolution and spiking deconvolution followedby phase correction ^ 342.7 Autocorrelogram for CSG 773^ 372.8 Common shot gather before deconvolution ^  392.9 Predictive deconvolution comparison 403.1 Earth model used in refraction statics computation ^ 453.2 The surface stacking chart ^  503.3 Plotting convention for reciprocal difference plots ^  553.4 Residual traveltime plot for VPs 27-199 and reciprocal difference time plotfor VPs near Fraser Canyon ^ 563.5 Residual traveltime and reciprocal difference time plots for VPs 400-641 ^ 593.6 Expanded view of zoom box shown in Fig. 3.5c ^  623.7 Residual plot for VPs 721-800 ^ 64viii3.8 Residual plot for VPs 1000-1050^ 653.9. Relationship between the datum plane and the refraction statics model. ^ 663.10 Comparison of stacked sections after application of statics ^ 684.1. The earth model assumed in deriving dip moveout equation (4.2). .. 704.2. Data volume plot in midpoint-offset-time space^ 724.3. Elimination of reflector point dispersal by application of DMO ^ 724.4 DMO impulse response testing ^  744.5 Testing DMO antialiasing properties  784.6 The partial stacking procedure ^  814.7 Velocity analysis flow charts  834.8 Comparison of stacked sections with and without DMO processing .. 875.1 The crossdip correction ^  895.2 Earth model assumed in deriving equation (5.7) ^  925.3 Covariance analysis for a synthetic CMP gather  1025.4 Stacked sections from N-S mini-profile before and after crossdipcorrection ^  1035.5 Covariance analysis—real data example 1 ^  1055.6 Covariance analysis—real data example 2  1065.7 Comparison of stacked sections before and after crossdip correction ^ 1086.1 Main slalom line across Fraser Canyon ^  1116.2 Slalom line—west side of canyon  1126.3 Slalom line—east side of canyon ^  1136.4 Southern slalom line—undershoot  1146.5 Central slalom line—undershoot ^  1156.6 Northern slalom line—undershoot  1166.7 Slalom line in NW-SE direction—undershoot^  117ix6.8 Brute stack for CMP bin map shown in Fig. 6.2^  1206.9 Stacked section (CMP bin map in Fig. 6.2) after application of 3–Drefraction statics ^  1216.10 Processing sequence used in the vicinity of the Fraser Canyon . . . ^ 1236.11 Stacked section (CMP bin map in Fig. 6.2) after cascaded application ofcrossdip correction and residual statics^  1246.12 Composite stacked section near Fraser Canyon (after reprocessing) ^ 1256.13 Composite stacked section near Fraser Canyon (original processing) 1267.1 Station elevation and stacking velocity information ^ 1347.2 SBC18 final zero-offset stacked section ^  1367.3 Coherency-filtered version of SBC18 final zero-offset stacked section ^ 1387.4 SBC18 migrated section ^  1407.5 Migration using a reduced velocity profile ^  1427.6 Final zero-offset stacked sections—Fraser Canyon ^ 1447.7 Final zero-offset stacked sections after coherency filtering—FraserCanyon^  1468.1 SBC18 original interpretation ^  149Geological cross-section of Coast Belt Thrust System and interpretation ofwestern portion of SBC18—before and after reprocessing ^ 1508.3 Reproduction of Fig. 1  4^   1528.4 SBC18 revised interpretation based on reprocessing—migrated section 1548.5 SBC18 revised interpretation based on reprocessing—zero-offset stackedsection ^  1568.6 Expanded view of sections near Pasayten fault ^  163A.1 3–D model consisting of a single dipping layer over a halfspace . . . ^ 179A.2 Introduction of a new source-receiver pair to the model in Fig. A.1 ^ 180A.3 Display of an arbitrary vector in both rotated and unrotated coordinatesystems ^  184A.4 Definition of angles of crossdip and inline dip ^  186A.5 Hypothetical common midpoint scatter plot  189xiAcknowledgementsTo my grandparents...I would like to thank my supervisor Dr. R. M. Clowes for his guidance, encourage-ment and friendship over the past three years. Thanks are also due to Drs. R. D. Russell,T. J. Ulrych and M. J. Yedlin for critically reviewing this thesis. I benefitted from con-versations, insightful/stimulating or otherwise, with many friends at the department, afew of whom deserve special mention: Dave Aldridge, Dave Dalton, Barry Curtis Zelt,Rob Luzitano, Zhiyi Z,hang, Taimi Mulder, Costas Karavas, Brad Isbell, Skagway, JohnHole, Guy Cross and Deirdre O'Leary. Special thanks are in order to Brian Tjeng forassistance rendered in collating the thesis copies. John Amor demonstrated remarkablepatience in providing assistance in all matters computational. I thank my parents fortheir support, and my dog Riley—well just for being there (maybe you're right Riley,the Fraser fault is a processing artifact).Sonix Exploration Limited acquired the data and Western Geophysical carried outthe original processing. The quality of their efforts is very much appreciated. Iam grateful to Hampson-Russell Software Services for donating their 3–D refractionstatics software. Funding for Lithoprobe reflection experiments is provided by both anNSERC Collaborative Special Project and Program grant in support of Lithoprobe aswell as by the Geological Survey of Canada. Additional funds for reprocessing werederived from NSERC Research and Infrastructure grants to R. M. Clowes. Personalsupport was provided in part by student scholarships donated by Shell Canada Limited,Commonwealth Geophysical Ltd., and Western Geophysical/UNOCAL Canada Limited.xiiChapter 1INTRODUCTION1.1 Background and research motivationThe Lithoprobe Southern Cordillera transect was established in an effort to provide adetailed characterization of the Cordilleran orogeny, and to thereby elucidate the tectonicprocesses which contributed to the westward growth of North America in the past, aswell as those which continue today to shape the western edge of the continent. As partof the transect, several seismic reflection profiles were run in 1988 across southwest andsouth-central British Columbia (Figure 1.1). Profile SBC18 crosses the Fraser fault, amajor Eocene strike-slip feature that has accommodated more than 100 km of right-lateraldisplacement. The fault marks the boundary between the Eastern Coast and Intermontanebelts of the southern Canadian Cordillera. Restricted road access has resulted in a severelycrooked survey line; although the profile is nominally oriented perpendicular to thenorthwest-southeast direction of regional strike, its easternmost half trends principallynorth-south.Contract processing of the SBC18 dataset by Western Geophysical and subsequentinterpretation (Varsek et al., 1993; Monger and Journeay, 1992) revealed, in the wordsof Varsek et al. (1993), "one of the most complex patterns of dip domains observedon any Lithoprobe seismic data across the southern Canadian Cordillera". In particular,the subsurface position and depth extent of the Fraser fault were ambiguous. Theseconsiderations provided the original motivation for both careful reprocessing of the datasetand subsequent interpretation, which together constitute the essence or this thesis.The thesis is founded upon two principal objectives: (i) a more detailed subsurfacecharacterization along the entire profile, placing particular emphasis on structure near1Figure 1.1. Location map showing Lithoprobe reflection profiles in southwesternBritish Columbia (see legend), Consortium for Continental Reflection Profiling(COCORP) reflection profile W7 in northwestern Washington state, andSouthern Cordillera Refraction Experiment (SCoRE) lines 3 and 10 (boldfacedotted lines) (following page). Figure is adapted from Varsek et al. (1993).Major tectonic units are also displayed in the figure. The five morphogeologicalbelts of the Cordillera are displayed in the inset. Abbreviations: Cascademetamorphic core (CMC), Central Nicola horst (CNH), Mount Lytton complex(MLC), Northwest Cascade system (NWCS), Okanogan plutonic complex (OPC),Ashlu Creek fault (ACF), Ashcroft fault system (AF), Bralorne fault system (BF),Beaufort Range fault (BRF), Central Coast Belt detachment (CCBF), CowichanLake fault (CF), Castle Pass fault (CPF), Chuwanten fault (ChwF), Crescent fault(CrF), Coldwater fault (CWF), Duffy Lake fault (DLF), Fraser fault (FF), Hozameenfault (HF), Harrison Creek fault (HCF), Jack Mountain fault (JMF), Kwoiek Creekfault (KF), Marshall Creek fault (MCF), Miller Creek fault (MIF), Mocassin Lakefault (MLF), Mission Ridge fault (MRF), Methow River fault (MtF), OkanaganValley fault (OVF), Owl Lake fault (OLF), Pasayten fault (PF), Phair Creek fault(PCF), Quilchena fault (QF), Ross Lake fault (RLF), Red Shirt fault (RSF), Shuskanfault (SF), Thomas Lake fault (TLF), Tyaughton Creek fault (TyF), West Coastfault (WCF), Yalakom fault (YF).FT Overlap Assembly/  Successor BasinsNorthwest Cascades System / Cascade Metam.^ Core(Deformed Rocks from Adjacent Belts)LITHOPROBESOUTHERNCORDILLERATRANSECTCORRIDORVolcanic Center(Neogene-Recent)the Fraser fault and, equally important, (ii) the establishment of an effective processingstream for future reprocessing of crooked line deep crustal datasets.The first objective stems not only from the complexity of the dip patterns observed onthe result produced by the contract processing, but also from the fact that new geologicalmapping and a recently-acquired better understanding of surface geological relations inthe region together provide an excellent opportunity for relating the seismic section tosurface features.The second objective arises because our work represents the first-ever effort atreprocessing a southern Cordillera reflection dataset at the University of British Columbia,where several other reprocessing projects are either in initial stages of progress (SBC13and SBC15 from Figure 1.1) or have been proposed (SBC14 and SBC17). Deepcrustal datasets differ from their shallower counterparts encountered in the oil industry inseveral important ways. For instance, they are characterized by a lower signal-to-noiseratio (S/N) and the acquisition typically takes place along crooked lines. As a result,while several of the processing techniques successfully employed in the oil industryare readily adapted to the deep crustal environment (e.g. deconvolution, refractionstatics), others require specialized modifications and/or yield disappointing results (e.g.,DMO and 2—D migration). Moreover, the significant offline scatter of source-receivermidpoints necessitates the implementation of non—standard techniques in order to accountfor reflector crossdip (i.e., that component of dip perpendicular to the survey line).In light of the multidisciplinary nature of the Lithoprobe project, the integration ofour interpretation into the existing geophysical/geological framework necessarily figuresamong our objectives. However this third objective is ancillary to the above two in thesense that it represents a preliminary effort. A final synthesis encompassing results fromall facets of the scientific program awaits the reprocessing of other reflection datasets and4the completion of refraction studies.1.2 Tectonic settingSBC18 straddles the boundary between the Intermontane and Coast belts, two ofthe five sub-parallel morphogeological zones into which the entire Canadian Cordillerais divided (Figure 1.1, inset). The formation of these two belts, and more generally,the evolution of the Cordillera as a whole, reflect a protracted history of Mesozoic andCenozoic collision and deformation along the western margin of the North Americancontinent.The concept of a "terrane" is commonly invoked in describing the Cordilleranorogenesis. Yorath (1990) defines a terrane as "a part of the earth's crust whichpreserves geological rocks different from those of neighbouring terranes". Implicitin his definition is that no assumption is made about the location of origin of therocks. While some terranes were formed in proximity to the ancient North Americancontinent ("autochthonous" terranes), others travelled great distances before reaching theirpresent locations ("allochthonous" terranes). The dominant mechanism responsible forthe creation of the Cordillera is that of terrane "accretion". Accretion refers to the processof attachment of the terranes onto the North American continent. The various terranesof the Canadian Cordillera are shown in Figure 1.2.Various models have been proposed that attempt to explain the formation of the Coastbelt. The generally accepted view is that of Monger et al. (1982), who postulate that theCoast belt contains the suture that resulted from the mid-Cretaceous collision between anexotic Insular "superterrane", which is a composite terrane formed by pre–collisionalamalgamation of Wrangellia and the Alexander terrane (Figure 1.2), and the NorthAmerican continent, whose western margin at that time consisted of the previouslyaccreted Intermontane superterrane, itself comprising three terranes—Stikinia, Cache5(5ooAAAAagoCr .r.:.lb01"•V.0.;• vv..y....vv'yvvvvvv••A, v v. vI'vvvvv • •;vvvvv• vvvvv1.vvvvv.vvvv,:..:' v v v v  •^ ,.- :vvvv, 3 vvv,-vv.......:,^ ... .^. ^•...., V IWINIM=MOW UMMMt:■"/ MP". rev•iviiVe l^MAIVA,A v •11.-as !AIM.,vvv2 v v v Immo'. la lialn r AIM.:vvvv IVEM 4 • MI•vvvvv lim■ W 11•11•11:vvvvvv ...ris 1.1 ii•ringlvvVvVVv um s Milyvvvvvvvv MO& IMMvvvvvvvvvvIN..V^UI1111111111::vv vvvvvvv vvV i allvvvvvvv vvv•yvvvvvvv vvvv MI•tvvv vvvvv V vv V 1Mlvvvvvv v vv vv v MOlyvvvvvvvvvvvv NM:vvv vvvvvvv V vv .•vv vvovvv vvvvv^vvvvv aniZitvvvv vv vv ■•tv vvvVv vvvv IMyvvvvvvv vvv MN::.., vvv vvvvvvv A..v v vvvvvvvv i.^mei••:‘, vvvvvvvvv .zv vvvvvvV^a, .sV an .1:VVVVVVVVV aw,^is.vvvvvvvo,..;^NIA A? :VVVVVVVV .M. A...vyvvyvv„:vvvvvvvy um AAr:VVVVVVVV =1,^...A ,,g,,•vvvvvvvv.:.vvvvvvvvv....NcifkkVitvvvvvvvvv gaolvvvvvvvv., vvvvvirVvvvvi.v vvv^'y vvfivvvvvv•-;vvvvvvv, . . .; V., yv VV VV VVx-:::.v.v v v vV.- -_. v v vV:-. 45^•TERRANES AX ALEXANDERBR BRIDGE RIVERCD CADWALLADERCC CACHE CREEKCA CASS IAR*CG CHUGACHCN CHI LL IWACK-NOOKSAC KCR CRESCENTHO HOHKO KOOTENAY*MO MONASHEE*MT M ET HOWOZ OZETTEPR^PACIFIC RIMQN QUESNELSH SHUKSANSM SLIDE MOUNTAINST STIKINIAWR WRANGEL L I AY A YAKUTATY^YUKON-TANANA*CDINN1.1111/MkAAAAAAAi n nn nAAARIM AAAA AAA 0A) •AA A nnAA INnnnnnnnAA A A A•,A A A A A A A AAA A222222INATA /A^AA\ A 500 KM.Figure 1.2. Terrane map of the Canadian Cordillera (adapted from Clowes, 1990). Thevarious terranes are depicted using different shading patterns and are labelled withcircled letters. Asterisks are used to denote terranes which are thought to have formednear the western margin of ancestral North America (autochthonous terranes). All otherterranes are probably exotic (allochthonous terranes), having been accreted to thecontinent at various times in the Mesozoic.Creek, and Quesnellia. The collision followed the subduction-related closure of anintervening ancient ocean basin, vestiges of which are presumably contained in the rocksof the Bridge River and Methow terranes. The suture has since been overprinted bya magmatic arc related to a post-collisional east-dipping subduction zone. Recentlyhowever, van der Heyden (1992) has suggested that the Coast Belt magmatic intrusionsare due to a prolonged period of east-dipping subduction ongoing since the mid Jurassic,at which time a single "megaterrane" consisting of Wrangellia, Alexander and Stikiniawas accreted to ancestral North America along a suture which is today represented byrocks of the Cache Creek and Bridge River terranes.Between latitudes 49° and 51° N, Journeay and Friedman (1993) have divided thesouthern Coast belt into western, central and eastern parts, the easternmost two of whichare crossed by SBC18 (Figure 1.3). The western Coast belt (WCB), which consists ofvoluminous mid-Jurassic to mid-Cretaceous plutons that have intruded mid-Triassic toearly Cretaceous arc sequences, is of low metamorphic grade. Except in the vicinity ofits eastern flank, where it is imbricated along a series of east-dipping thrusts, the WCBis presumed to have acted as a rigid crustal block during two stages of vigorous lateCretaceous shortening that took place along a west-vergent contractional belt, the CoastBelt Thrust System (CBTS) (Figure 1.3, inset). Journeay and Friedman (1993) interpretthis shortening to be a reflection of (i) late phases of the northeastward underplatingof the Insular superterrane, postdating the main collisional event and/or (ii) westwardramping of the central Coast belt (CCB) over the WCB. In the study area, the CBTSextends across strike for approximately 35 km, encompassing both the eastern flank ofthe WCB as well as the western portion of the central Coast belt (CCB), where it ismanifest in a stack of east-dipping thrust sheets which carry highly metamorphosed deeplevels of the eastern Coast belt (ECB) in their hanging walls. The CCB and ECB featuremetamorphosed oceanic rocks of the Bridge River and Methow terranes, as well as island7arc sequences of Cadwallader terrane affinity. Of particular significance to our study isthe fact the basal detachment associated with the later stage of late Cretaceous shorteningis thought to root in the middle to lower crust to the northeast of the CBTS (Journeayand Friedman, 1993), near the western edge of the SBC18 profile (Figure 1.3).In the vicinity of the study area, the Intermontane belt consists primarily of Quesnelterrane (Quesnellia) rocks, specifically Triassic and Jurassic granodiorites of the MountLytton Complex (Figure 1.4). The Mount Lytton pluton, which was probably emplacedat deep crustal levels within a Late Triassic-Early Jurassic Quesnellian crustal arc, wasuplifted in late Early Cretaceous time together with the Late Jurassic-Early CretaceousEagle Plutonic Complex which it abutts to the south (Monger and Journeay, 1992). Theuplift was apparently accommodated by thrusting on the southwest flanking, northeast-dipping Pasayten fault (Grieg, 1992), and was coeval with the extrusion of the SpencesBridge volcanic group (Monger and Journeay, 1992), which lies immediately to thenortheast of the line (Figure 1.4).The SBC 18 profile is effectively divided into eastern and western halves by itsintersection with the Fraser fault (Figure 1.1, notation "FF"), a major dextral strike-slipfault which in combination with its southern extension in Washington state, the StraightCreek Fault, stretches for at least 500 km in a north–south direction, cutting acutely acrossthe north-northwest trending regional grain. The fault, or more properly the associatedfault system (in the vicinity of our study area, the system is represented by the Cantileverfault—see Figure 1.4), was active in mid to late Eocene time (35-47 Ma, Monger andJourneay, 1992). Over the last fifteen years, various estimates of dextral offset across thefault have ranged from 80-190 km (Misch, 1977; Mathews and Rouse, 1984; Kleinspehn,1985; Monger, 1985; Coleman and Parrish, 1991). The currently-accepted figure is 130km (Parrish and Monger, 1992).8Figure 1.3. Geological map of the southeastern Coast belt and adjacentIntermontane belt, adapted from Journeay and Friedman (1993) (followingpage). Inset shows a composite geological cross-section of the CoastBelt Thrust System taken from profiles AA and BBB displayed in the figure(modified from Monger and Journeay, 1992). Abbreviations: Thomas Lakefault (TLF), Fitzsimmons Range fault (FRF), Terrarosa thrust (TT), FireCreek fault (FCF), Ascent Creek fault (ACF), Harrison Lake shear zone(HLSZ), Breakenridge fault (BF), Slollicum River fault (SRF), Central CoastBelt Detachment (CCBD), Castle Towers pluton (CTP), Ascent Creek pluton(ACP), Mt. Manson pluton (MMP), Breakenridge plutonic complex (BPC),western Coast belt (WCB), central Coast belt (CCB), and eastern Coast belt(ECB).917, Mu : Sealer • Chitin Crk S ehtrtTr!! :Hornet Creek G nettsTrC Cadwallader GroupInsular SuperterraneEagle PlutonicComplex*ft ° 1 *//9 1 ,,94"1/,1,  4.\\■•,,p//11$ fr t*i, '0 111, 01, 1 *,..• U m, ‘1*.1/9.% )1/9•tAAaII ,f ".//• ,0A^ 1,""^\\"'//,""^\‘**▪ "Q,‘‘""",,Ilt,t%;•^%1,,,11;;:„%4frz. 1,19 4%/1./1 1,1* °s @AN 9.4 ,„**$Nll t,/,^ ,#Mgd• •^• • •• •^•• • • •• • ••• ♦• • •)4•WCB CCB TgA••..•••fr'^20-,------Coast Plutonic ComplexTR ; Tertiary plidorteLK. :Lair Cretaceoneplutont°DKR :Early-Mid-Cremeeoplurone.1XRu :On&fl. .1^&Cretaceout plitiont35 &•TM^Jurattieand Triatrie alumniTvEastern Coast Belt171 JK. Undiff. Relay Attn. and nameGroupsF7-1 JL Ladner CrampJKm' : enelamorpAesed equimients a/.11.• &pin :Bridge Rirerillotameen Groupeand meiamorpAotedPJDu alirsinettirt• Bridge River Grovp• .f•Y .  . 1 „rs^rsei •• ikv^e_t,kikvv>ez.1 /A Vs;. te.t.r744rAvirs,,437^r..., 1.12>AvA^'4 • `1.4"147t'vls/C U^10=_ "I30A BQIIWestern Coast BeltLEGENDCentral Coast BeltKC : Gamble•Fire Lake Grp351. : Ilarriton Lake GroupMTI Tudialland SchistFigure 1.4. SBC18 profile (nomenclature "88-18") superimposed atop local geologymaps of Monger (1989a, 1989b) (following page). Station numbers are identified in thefigure. Extreme geological complexity of the region provides motivation for the detailedreprocessing of the SBC18 dataset. With reference to Section 1.2, note that in the vicinity ofthe profile, the Intermontane belt consists primarily of Quesnellian rocks (see stations 900-1500 on figure). Note also that the Fraser fault assumes the name of "Cantilever fault" onthese maps.CRETACEOUS AND1OR TEP.TIAPsCUSTER NAY DKR,.10,0cg^DDKA5 DORN 5,,a,s, RPRaranAKNAIS^rnarG0 arP afiremaar, roofs prob.& KeeR50 5.05,frrar 5405,,,K, and possiRaleoroc 0,,G ',Ka0^.5/ meaPseo f.att, CrKfacnouA Roe oafry Patna,' lavaSamar DaKfr, 5,0,5 , 5,105 Apo*, Arprl sAfroanee srforaf aripa ,PATILEP SON'S kocalartrfatmaae, englOr Ultranratr: nara oaf I5.0,01:5 505,5 l, Ka5 -0 a, Dorf^fpoonaLlosr,aadvar e, peAre Ono ha., from., ,K,AnafoohosagY r C. 51161,51,5505NCEIN YCHIS: ”IAJoly ofrenfonn/^ra .,00,5A0Aer,Katao,^ ,,A5D / 5,05 arKoao, aocl carbooaTe-cias,roarafoorahoseo CfatArpoo,CRETACEOUSLATE cqs , AcrAIDE,D AND 0,1= DRETACED,S(alf, PPE!), rOPIAAPON of SPE CEA FRAGG,- GPO,foal2rf Kokaa,CDert-5,0 san5,51,,,..ATE EARLY, EARLY LATE CRETACEOUSPASAYLEN GROUPiv„,,,,„ faro, - %Naar PASA,EN GPOUP arias, Koppboart, 0,5DAN not• • .1 OLT LTrsirEertsOaterlsandskoc, conAganerare argAga, (0) .• • • I ono 5, Ge5fs Aoc Kfa, (c); - Vngc000^faces (Pa) a ,PASAKTEN SOGGY, POOR gafn ssocKlano. 09AR) 05-^Dasere,, ,es oast of .C.RawarKeK AA.,^,s ornhatLy a oar: olooaotaco, orproak, tha, e unpfa part or thoLACKASS KIfftlalTA, GPoKfaSADLY AND MIDDLE CRETACEOUSJACKASS MOIADA N GPO,Sararkrr,n0 0, 5pAre oonOrtaaaP. AL, off, nf 5,51 ,50,a P01,1and Kari rianue Ka, ;0,RASA VIED GROUP11.1 Ga0,D Dropie KKR. ocPP,^4d,(SPA,Z;CPAK PA WON) 554-0) gnerss,EAR, AND SAIDD.E.URASSIDHAPIPSOK, LAKE FOPIAAPC, , everam,a015,pyrsplasar, boa, app.. conalnr,ateADDER OR M,state spAsfroo Off, as ,a0,0Thl,fler LOP Se17,11,11111 INDIVE, CREAK P)PAIATION of [POW G- ROUPaf JPre.ora: maar tr, aKeraloomo AnkantK57114IASSIO AND/OR JURASSIC111.1Grarvrtirxrrc Quart/ mooznool, /SUIT:HILLS? CREEK. PEPNASK,0>10 HORSE CREEK 8A ,PONITHS. DOUGLAS LAKE 570CSgmsodurle ol MOUNT LYTTON COMPLEX)la r„0 gabbro. syen,a. warn, and , oral 00010, rook of 'POPMASK PA PROW', and 5,0505^KOK, alkaArs rorroarons111. (Korfe and Art10.0., OR 440,1N, LL,TCP COblo,AND,55,05.r NAKOL A Gag.,faoarfrofekisamOK^fopo.AK^or AC,000K, CCMPLKA 5050, e(1,4i no !we, PIK f4r0L A OATHS:sERMIAN TO JURASSICPR OISE POKE COVEIRAMI ower^,5,55f rk ErIOVE13 C. ^LX, UT/V),DR. D .,0,5; rpopmaw^cros, :Kpoo Korona fh, OKA, an, 5,05,0rareKJan,1 7J11,0,101t70Transcurrent motion along this fault and several other coeval strike-slip featuresfound throughout the Cordillera may be related to an episode of Eocene extension, andwas possibly a relaxation response to the transpressional nature of accretion of the Insularsuperterrane to the North American continent (Coleman and Parrish, 1991). In an alternateyet related interpretation, the right-lateral motion is attributed to shearing induced by theinteraction between the northeast-bound Kula oceanic plate and the westward-movingcontinental plate (Yorath, 1990).1.3 Thesis outlineIn performing a detailed reprocessing of the SBC18 dataset, we attempted a number ofdifferent procedures. While some of these were successful, others yielded disappointingresults. After considerable testing, we arrived at a final processing stream which embodiesthose more effective processes. We present the sequence, whose details and underlyingtheoretical considerations are described in Chapters 2-7, in Figure 1.5. In this section,we describe the organization of the thesis with reference to this figure.In Chapter 2 we describe the data acquistion and the initial steps undertaken inreprocessing. Deconvolution is addressed within the framework of the deep crustalvibroseis survey.In Chapters 3-5 we present details of our main processing stream together withrelevant theoretical discussion. In Chapter 3 we address the statics computation, whichis essentially a two-step procedure consisting of (i) identification of systematic error inthe first break picks and subsequent error correction, followed by (ii) application of aconventional 2—D refraction statics algorithm. In Chapter 4 we describe the procedure weadopted in performing dip moveout correction (DMO) as well as our velocity analysis.In Chapter 5 we address the crossdip correction. We derive a 3—D reflection traveltimeexpression which allows us to verify the validity of the application of a first order13Istack (pre andpoststack AGCgain)cascaded applicationof crossdip correctionand residual staticsI start with shot gathers II I spherical spreading correction1 (1st break picks; Itrace edits I predictive decon ItCHAPTER 3 II refraction statics V ^ I CMP sort IVvecwl-a-<IC.)ICHAPTER 5 I CROSSDIP CORRECTION 'i I stack (pre and poststack AGC gain) II I data merge to productfinal stacked section I I phase-shift migration IV^1 coherency filtering '.I velocity analysis I.'t I DMO (upper 5.0 s) It^INEAR CANYON ONLYcreation of several CMPbin swaths throughmidpoint scatterFigure 1.5. Flowchart of SBC18 processing stream. Chapter references are indicated.In practice, order of application of several procedures has been interchanged. Notethat a 1.0 s window was used in all AGC scaling.correction proposed by Lamer et al. (1979). We also develop a method for estimatingthe magnitude of this correction.In Chapter 6 we describe the additional processing of the portion of the dataset nearthe Fraser Canyon, and in Chapter 7 we describe the three final stages of processing—datamerging, migration and coherency filtering.14In Chapter 8 we present our revised interpretation which is based on the results ofour reprocessing; in Chapter 9 we provide a summary of the key aspects of our worktogether with a concluding discussion.15Chapter 2ACQUISITION AND INITIAL PROCESSINGIn this chapter, we provide details on the data acquisition and describe the initialprocessing steps. We present a thorough, tutorial-style discussion of the deconvolutionproblem in the context of vibroseis deep crustal processing. We address wavelet phaseconsiderations, present synthetic tests on a mixed-phase wavelet which embodies antic-ipated reverberatory effects, and describe the deconvolution procedure used for SBC18.Finally, we discuss the spatial resolution of the dataset.2.1 Acquisition detailsSonix Exploration Ltd. performed the data acquisition. The asymmetric split spreadrecording geometry is illustrated in Figure 2.1. The acquistion parameters are listed inTable 2.1. The data were recorded in "master—slave" configuration using two DFS-Vrecording units. The master unit recorded channels 121-240, while the slave recordedchannels 1-120. Each receiver group consisted of 12 geophones which simultaneouslymeasured the signal (Fig. 2.1, inset 1). For further redundancy in acquistion, fourvibrator trucks vibrated simultaneously, performing eight separate frequency sweeps at asingle shot station or "vibrator point" (VP). The trucks "moved up" a distance of 7.14 mbetween sweeps (Fig. 2.1, inset 2). The details of the source sweep are given in Table2.1. Cross-correlation with the sweep signal was performed in the field.Geophones were deployed at every station, so that the "group interval" was 50 m.Shooting took place at every second station (i.e., VP interval of 100 m), resulting ina nominal common midpoint (CMP) fold of 60 and a nominal CMP interval of 25 m( the "nominal" CMP fold is the number of coincident source-receiver midpoints thatwould correspond to our VP and group intervals in the case of a straight line survey;16Figure 2.1. Acquisition geometry for SBC18.inset 2direction of line progression:^Ech#1 Ch#250 m+ + + +^++^+ +.4- 5 mi...5 m*sweep 1 ^.1 El40m-Iv- sweep 8inset 1 inset 2= station+ = geophoneLI = vibrator truckCh#120 Ch#121^Chtti^ Ch#80^ Ch#81r^I Z1^1-1^/ I I \ I 3950 m^ 111111 1;t1111--I) Slave channels 1-80inset 1^E 350 m *E- 350 m -(slave recorder truckCh#24050m^1950 m^Slave channels 81-120>^<50m5950 m^Master channels 121-240di/master recorder truckRecording filterRecord length (uncorrelated)Record length (correlated)Sampling intervalEnergy sourceVibrator modelSweep frequencysweep lengthsweep tapergeophone typeout-64 Hz; 72db/oct slope32 s18 s4 ms4 vibratorsL. R. S. 31510-56 Hz.; linear14 s0.5 sMark L 1OaTable 2.1 Acquisition parameters (from Hostetler et al., 1989).an analogous definition exists for the nominal CMP interval). At both ends of the line,the recording geometry was modified to allow a gradual tapering of the CMP fold, aprocedure usually referred to as "roll-on" ("roll-off').Midway along the line, the SBC18 profile crosses the Fraser Canyon. While therugged topography of the canyon walls prevented continuous recording, subsurfacecoverage beneath the canyon was obtained by means of the "undershooting" acquisitionscheme that is illustrated schematically in Figure 2.2.2.2 Processing systemHardware used for the prestack processing consisted of a MicroVAX II minicomputer,a METHEUS 52500 graphics processor and a Sony monitor. Poststack processing(migration and coherency filtering) was performed on a SUN SPARCstation 10. AVersatec 36" electrostatic plotter was used to plot the final sections presented in Chapter7. We used the Inverse Theory and Applications (ITA) INSIGHT software for mostprocessing tasks.18VP ^Ch#1^Ch#72station station442^517(a)Ch#1^Ch#40^Ch#120station^station station562^601 681(b)LjCh#240stationCh#200station641 681 >-Ch#121^ Ch#240Z^station station0 682 8010<0 0Ch#1station562(0>-ZCh#120stationG681Ch#121station682Ch#202^Ch#240station^station763^8010Ch#1 Ch#40 Ch#86 Ch#240Z station station station station0^682^721^767^ 921(d)Figure 2.2. Acquisition near the canyon. (a) gap closes when cable reaches westedge of canyon. Trucks vibrate between stations 517 and 641; (b) undershooting.Master portion of cable moves to the east side of the canyon. Trucks back upand vibrate between stations 601 and 681; (c) undershooting. Cable remainsfixed and trucks move to east side of canyon. Trucks vibrate between stations682 and 763; (d) Trucks back up and vibrate between stations 721 and 767.Gap then reopens and normal roll-along shooting is resumed.Z1923 Initial processing stepsWe obtained the unprocessed, demultiplexed common shot gathers (CSGs) in SEG-Yformat from the Lithoprobe Seismic Processing Facility (LSPF) in Calgary. The LSPFalso provided us with the Sonix Exploration "observer notes" which provide detailedinformation concerning the acquisition geometry, as well as a set of "survey notes" whichcontain the Universal Transverse Mercator Grid coordinates for every station along theline. We converted the data to 1TA internal (binary file) format, and entered the linegeometry information from the observer and survey notes into the trace headers.Next, we applied a spherical spreading correction based on a single regional velocity-time function that we derived from the velocity analysis information available fromWestern's preliminary processing. We performed first break picking for our refractionstatics analysis using the 1TA interactive editor "VAQ2". This editor was also used fordeleting noisy traces and correcting polarity reversals.The next processing step was the creation of CMP "bins". In a crooked line survey,source-receiver midpoints are not colinear. In order to process the dataset using two-dimensional (straight line) techniques, neighbouring midpoints are grouped into binsand each bin is treated as a single CMP in the subsequent processing. Such a procedurerespresents a trade-off between spatial resolution and any S/N enhancement that we mighthope to gain through an increased redundancy of information. Related to this limitationin subsurface resolution is the crossdip problem, which we describe in detail in Chapter 5.We performed the binning using the ITA interactive module "CDPBIN". Thetechnique entails first choosing an effective profile line or "slalom" line which ideally cutsthrough the centre-of-mass of the midpoint scatter, then specifying the (rectangular) bindimensions (Figure 2.3). The bin "width" is measured in the direction of the slalom linewhile the bin "length" runs perpendicular to the line (Figure 2.3, inset). We constructed20a "main" slalom line extending across the entire length of the profile (in Chapter 6,we describe some additional binning schemes that we used in the vicinity of the FraserCanyon). We chose a bin width equal to the nominal CMP interval of 25 m. We chosea large bin length (2000 m) in order to encompass the majority of the midpoints. TheCMP bin map for SBC18 is presented in Figure 2.3.2.4 Data qualityFrom our initial processing, we observed that the data quality varied quite dramat-ically over the line. Near the western end of SBC18 and again just east of the FraserCanyon, the signal-to-noise ratio was relatively high. On the other hand, shot gathers inthe vicinity of station 500 were very noisy; according to the observer notes, this was dueto the proximity of the fast-flowing Nahatlach River. However as a general statement,the data quality was good.A periodic noise pattern was observed on many traces. It was associated with theproximity of receivers to the recording trucks. On average, 10 traces per shot gatherwere affected by this systematic ringing. Analysis of the amplitude spectra revealed thepresence of spurious Fourier components between 40 and 50 Hz. Although a simplezero-phase notch filter succeeded in removing a significant portion of the noise forsome traces, it did not improve the result for others. While this observation mightsuggest a selective application of the filter based on individual trace characteristics, sucha scheme would be prohibitively time-consuming. Moreover, any wavelet alterationbetween filtered and non-filtered traces would adversely affect subsequent processing. Onthe other hand, a universal application of the filter (i.e., applying the filter indiscriminatelyto the entire dataset) would remove useful signal from the uncontaminated traces. Withthese considerations in mind, we decided to simply delete all of the contaminated traces.211kb.":\\• \ \ " \‘'^\ •\ 1,1%,^\: .••Figure 2.3. The CMP binning process. The SBC18 profile (black dots) is displayed in the main figure together with scattered source-receivermidpoints (blue dots). Station numbers are indicated in black. The slalom line (red line) is defined by a series of points (red dots). Insetprovides an expanded view of midpoint scatter near station 300 together with CMP bins. Because each bin acts as a single CMP inthe subsequent processing, the algorithm attempts to tie bin numbers (red) to station numbers (black) to within a scale factor of ten.Additional slalom lines were run through the significant midpoint scatter near the Fraser Canyon.A significant number of traces were contaminated by the direct shear wave arrivaland/or ground roll energy both of which are manifest on the shot gathers as a linearpattern of coherent noise (Figure 2.4). Unfortunately, the typical time dips (slopes inx-t space) associated with these events were sufficiently steep to cause spatial aliasing,a phenomenon we discuss in Section 4.2.2. As a result, a standard f—k dip-filteringprocedure (see, for example, Yilmaz (1987)) could not be employed. Considering thatthe majority of the spurious energy was confined to early times (0— 2 s) together withthe fact that our analysis was based on a crustal scale, we chose a simple approach toremoving the coherent noise, namely the deletion of heavily contaminated portions ofthe dataset.2.5 DeconvolutionAlthough deconvolution was performed after the refraction statics analysis (Chapter3), conceptually it represents a preliminary processing step and so we describe it in thischapter. To appreciate the objective of the popular processing technique let us consider anoise-free, zero-offset (coincident source-receiver) experiment. From the viewpoint of theinterpreter, the ideal output would consist of a "reflectivity spike series", each spike beingproportional to a reflection coefficient at depth. In reality, the output section deviatessignificantly from this ideal. Reverberations, earth attenuation effects, the intrinsic sourcesignature, the nature of the near-surface coupling for both source and receiver, as wellas the response of the recording instrument all conspire to hinder the interpretation ofthe recorded seismogram.As a first order approximation, we may represent each of the above "undesirable"effects by a linear, time-invariant filter and model the output seismogram as the con-volutional product of these filters together with the reflectivity spike series. The act23trace sequential no.20 40 60 80 100 120 140 160 180 200 220 2400.00.40.81.21.62.0tr.. 2.42.83.23.64.04.44.8Figure 2.4. Common shot gather (near station 500) contaminated by groundroll. AGC scaling has been applied.of deconvolution, then, is to remove the various filter effects in order to recover thereflectivity spike series.In its various forms, deconvolution enjoys widespread use by seismic data processors,including those addressing the crustal scale problem. Yet despite its popularity, it remainsone of the least understood and most often "abused" of all processing techniques. For-tunately, the abusers are afforded a degree of impunity, because the method is generallyrobust in character. We admit to a certain amount of exploitation of this robustness, forafter considerable testing, we opted to use a standard predictive deconvolution algorithm.24In this section we describe our synthetic testing as well as the procedure undertaken inperforming the actual deconvolution.2.5.1 Deconvolution theory23.1.1 The convolutional modelWe may write the mathematical form of the convolutional model asx(t).r(t)0a(t)Ok(t)Os c (t)Orc (t)0i(t)0e(t) , (2.1)where the "0" symbol denotes convolution, and r(t), a(t), k(t), scW, rc(t), and i(t) arethe linear, time-invariant filters which attempt to describe the reverberation, attenuation,source signature, coupling between source and near-surface, coupling between receiverand near-surface, and recording instrument response, respectively. x(t) is the recordedseismogram and e(t) is the reflectivity series. Yilmaz (1987) discusses the approximationsmade in forming a convolutional model. At this point in the analysis, we are assuminga zero-offset, noise-free, compressional wave dataset.The recording filter impulse response, i(t), is known, since the recording filterparameters are documented (Table 1.1). Because we know the exact impulse response, inprinciple we could remove the effect of the recording filter deterministically by, say,performing a spectral division. However, for reasons discussed below, we are notinterested in any enhancement in temporal resolution that such an exercise might afford,so conceptually, we will group the recorder response as part of the source signature term.The "new" source signature term is just the convolutional product of k(t) defined aboveand the recorder impulse response i(t).The nature of the coupling between the vibrator baseplate and the earth surfaceis poorly understood at the present time, and as such is the topic of much activeresearch (e.g., Baeten et al., 1988). This effect, though quite significant for a shallow25high-resolution survey, may be viewed as second-order for a deep crustal study andconsequently neglected. Similarly, we ignore the complex coupling between the geophonearray and the earth surface. Under these simplifying approximations, we can rewrite(2.1):x(t).r(t)Oa(t)Olc(t)Oe(t) ,^(2.2)where the "new" k(t) incorporates the effects of both the source signature and therecording instrument response.2.5.1.2 The waveletBy definition, a wavelet is a signal that is both one-sided (i.e., it has a definiteorigin time before which it is identically zero) and stable (i.e., it has finite energy andtherefore must die out as time progresses) (Robinson and Treitel, 1980). There is muchambiguity in the literature surrounding what constitutes "the wavelet" in the context ofdeconvolution. "The wavelet" w(t) in our present discussion is given byw (t) = r (t) 0 a (t) 0 k (t) ,^(2.3)and as such it embodies both earth effects (i.e., reverberation and attenuation) and thesource signature. This is the wavelet that, ideally, we would like to deconvolve from theseismic trace, since from equations (2.2) and (2.3)x (t) = w (t) ®e (t) .^ (2.4)2.5.1.3 Statistical deconvolutionAt this point, it may appear that the deconvolution problem is solved, that we maysimply calculate the wavelet inverse and use this as the operator in a deterministic26deconvolution. Unfortunately, such a procedure is predicated on the assumption of an apriori knowledge of the wavelet form. In practice, it is impossible to acquire knowledgeof the reverberation and attenuation components of the wavelet, at least not withoutperforming extensive field tests at considerable expense.We may design a "statistical" deconvolution operator without knowing the shape ofthe wavelet if we make an assumption about the statistical properties of the reflectivitysequence. Specifically, we might assume that this sequence has a flat or "white" amplitudespectrum, Ae(f), where f is the temporal frequency:A, (f) Ao = constant (2.5)(e.g., Yilmaz (1987)). Under this assumption, the amplitude spectrum of the unknownwavelet is equal to the amplitude spectrum of the seismic trace to within a constant scalefactor (this is easily seen by applying the convolution theorem to equation (2.4)). Statedalternatively, the autocorrelation of the wavelet is equal, again to within a scale factor,to the autocorrelation of the input seismic trace.2.5.1.4 Phase considerationsBy way of the white reflectivity assumption (equation 2.5), we have a means ofestimating the wavelet amplitude spectrum. As for the wavelet phase spectrum, standardstatistical deconvolution algorithms make the assumption of minimum phase. As in thecase of the wavelet defined in Section 2.5.1.2, a minimum-phase signal is well-behavedin that it is causal (i.e., it is identically zero before time zero) and stable. Moreover,minimum phase is preserved under inversion; this bodes well for our present situationsince the wavelet inverse is the ideal deconvolution operator and we desire that thisoperator be well-behaved in the above sense. The question remains, however, as to thevalidity of the minimum phase assumption for our wavelet (equation (2.3)).27Robinson and Treitel (1980) consider a perfectly elastic earth model consisting ofan arbitrary number of horizontal, homogeneous surface reverberating layers overlying adeep reflector. Ignoring the time delay due to the two-way propagation time down to thedeep reflector and assuming that the magnitude of all reflection coefficients is less thanunity, they show that the impulse response at zero-offset or "reverberation spike train" isminimum phase. In the context of our convolutional model (equation (2.2)), this impulseresponse may be identified with the filter r(t). The deep reflector propagation time istaken into account by the timing of the spike arrival in the reflectivity series.We may infer from their analysis that the reverberating spike train encounteredin many physical situations ought to be approximately minimum-phase. Even if thereverberatory effects observed on SBC18 conform reasonably to this simple model, oursituation differs in two important respects: we do not have zero-offset data and theincidence is generally non-vertical. This means that strictly speaking, the periodicity ofthe multiples is not preserved (a lack of periodicity may adversely affect the deconvolutionprocess). To rectify this situation, Yilmaz (1987) suggests performing a predictivedeconvolution in the slant-stack domain (periodicity of multiples is preserved for non-zero offsets in this domain). We do not feel that the reverberatory problem for SBC18is sufficiently severe to warrant such a complex analysis.It may be argued that the impulse response of a homogeneous attenuating (i.e.,inelastic) earth is approximately minimum phase. The justification arises from theconsideration that the energy of the wavelet associated with the impulse tends to beconcentrated near its onset or "front end". Of the entire suite of signals with a givenamplitude spectrum, the one whose energy is maximally concentrated near its front endis that signal having minimum phase (Robinson and Treitel, 1980).Despite its apparent minimum phase character, it is not appropriate to directly28associate this impulse response with the time-invariant filter a(t) in equation (2.2). Theproblem is due to the "non-stationarity" of the attenuated wavelet. Attenuation modifiesthe wavelet as it propagates through the subsurface, broadening it and removing high-frequency content. The true filter describing the attenuating earth is time-variant; yet filtertime-invariance is one of the two fundamental assumptions underlying any convolutionalmodel (the other being linearity). In our analysis, we have attempted to compensate forthe non-stationarity by performing a time-variant deconvolution, designing different data-dependent operators for different time windows, then merging the output results. Withineach window, we assume that the attenuation effect may be adequately represented by aminimum phase filter a(t) in the convolutional model of equation (2.2).We have seen that both reverberation and attenuation effects may be plausiblymodelled using minimum-phase filters. Minimum phase is preserved under convolution.From equation (2.3) then, we see that we would have some reasonable representationof a minimum phase wavelet, if only the source signature k(t) were minimum phase.Unfortunately for the present situation, it is zero-phase. The vibrator trucks input asignal to the ground that is "swept" through a range of frequencies over a time intervalon the order of ten seconds. To increase the temporal resolution of the trace (i.e. todecrease the effective width of the basic source wavelet), the output seismogram is thencross-correlated with the source sweep signal. The source signature is the autocorrelationof the input sweep signal and is referred to as the "Klauder wavelet" (e.g., Yilmaz (1987)).Because it is an autocorrelation, the Klauder wavelet is zero-phase. The Klauder wavelet(modified by the zero-phase recording filter) for SBC18 is shown in Figure 2.5.Gibson and Lamer (1984) describe the phase correction that must be applied toseismic data generated by the Vibroseis source. The operator that performs the correctionis that operator which transforms the Klauder wavelet, k(t), to its minimum phaseequivalent. Denoting the amplitude spectrum of the Klauder wavelet by Ak(f), the29TRACE AMPLITUDE (NORMALIZED)-0.20- 0.18- 0.16- 0.14- 0.12-0.10- 0.08-0.06-0.04CO -0.2eU.1 -0.00rE17:O.040.060.080.100.12O.140.16O.180.20DATA:CPERZ.TEST.DECONWLAUDREC.SYM;1Figure 2.5. The Klauder wavelet for SBC18. This signal has passed through the recordingfilter. Ordinate is trace amplitude normalized to one.minimum phase equivalent of k(t) has an identical amplitude spectrum and a phasespectrum #min(f) given by1 00 lOgeAk (fi )  dr1Omin (f)^f fi (2.6)—00Unfortunately, the Klauder wavelet is a band-limited signal. For SBC18, the onlymeaningful energy content lies between 10 and 56 Hz. Moreover, the high-cut recordingfilter explicitly removes any high frequency noise. The implication relevant to thepresent discussion is that, strictly speaking, there is no minimum-phase equivalent for theKlauder wavelet because the natural logarithm is singular when Ak(f) is equal to zero. Tocircumvent this, a small amount of "white noise" is added to all frequency componentsof the Klauder wavelet in creating the minimum-phase conversion operator.30The theoretically "rigourous" procedure for the deconvolution of our dataset maynow be set forth: we find the (approximate) minimum phase equivalent of the Klauderwavelet using equation (2.6). By taking the ratio of the Fourier transform of the minimumphase signal to that of the original Klauder wavelet (the addition of a small amount ofwhite noise is required in performing this spectral division due again to the band-limitedcharacter of the Klauder wavelet) and inverse transforming, we find the minimum phaseconversion operator m(t). By convolving m(t) with the seismic trace x(t), we see fromequations (2.2) and (2.3) that we obtain a "new" wavelet w'(t):tv i (t) = m (t) k (t) r (t) a (t) .^(2.7)To within the approximations outlined in the discussion above, this new wavelet isminimum phase. Hence, the new seismic trace x'(t) given by(t) = m (t) x (t) ,^ (2.8)is in a suitable form for the application of a standard minimum-phase deconvolution.There is one subtle point that remains to be addressed. The band-limited nature ofthe source signature implies that we cannot expect the output to be a true reflectivity spikeseries having energy in all frequency components. Any energy in the output seismogramat frequencies outside the source pass-band is, by necessity, noise. Hence, we must applya bandpass filter or "interpreter's wavelet" to the deconvolved output. Recalling the band-limited character of the Klauder wavelet, it stands as a natural choice for such a filter.We should not consider the ideal output to be the reflectivity series alone, but rather theconvolutional product of the reflectivity series and the Klauder wavelet. Because of thecommutative and associative properties of the convolution operation, the method we havehere outlined is identical to the phase-correction method of Ristow and Jurczyk (1975),which consists of applying standard "spiking" deconvolution followed by convolutionwith the Klauder wavelet minimum phase equivalent.312.5.1.5 Predictive vs spiking deconvolutionIn Section 2.5.1.4, we stated that the wavelet inverse is the ideal deconvolutionoperator. We referred to the process of convolving the seismic trace with an estimate ofthe wavelet inverse as "spiking" deconvolution, because the operator attempts to convertthe wavelet to a spike. Although this would appear to be the process of choice, in practicenoise amplification at higher frequencies becomes a problem. Even after convolution withan interpreter's wavelet, we may find noise contamination in frequency components ofthe output that are "high", yet still resident within the source passband. We find inthe process of "predictive deconvolution" a means of trading off between the resolutionof the output wavelet and the high-frequency noise. The two parameters a and n, theprediction distance (also called the "prediction gap length") and prediction operator length,respectively, determine the action of the filter. The length of the prediction operator isnot to be confused with the length of the predictive deconvolution operator, althoughthese two quantities are related in a straightforward manner. Robinson and Treitel (1980)show that predictive deconvolution attempts to convert an input wavelet of length a+ninto an output pulse of length a. We will refer to this as the "pulse-shaping" propertyof predictive deconvolution in the discussion that follows.Robinson and Treitel (1980) show that spiking deconvolution is a special case ofpredictive deconvolution with a set equal to unity. Hence, predictive deconvolutionmay be viewed as a generalized approach to deconvolution. It is hardly surprising then,that the minimum phase assumption is required for predictive deconvolution as well.Ulrych and Matsuoka (1991) show that the output of predictive deconvolution applied toa minimum phase wavelet is identical to the input wavelet for times up to the predictiondistance, and is identically zero for times greater than this prediction gap length. In otherwords, for a minimum phase input, predictive deconvolution enjoys perfect success in32its pulse-shaping. If, on the other hand, the wavelet exhibits mixed phase characteristics,the output again preserves the wavelet shape up to the prediction gap, but beyond thistime it may display a ringy "tail", whose nature is dictated by the phase characteristicsof the input wavelet. As we shall see, the spurious effects of the tail may not be toosevere for a suitably chosen prediction distance, given the zero-phase properties of oursource signature.2.5.2 Synthetic testsThe likely source of reverberation or "ringing" on the SBC18 dataset is the near-surface weathering layer, whose low velocity results in sharp acoustic impedance con-strasts at both the free surface and the weathering layer-bedrock interface. In the follow-ing example, we consider the reverberation response associated with a one-dimensional,constant density model consisting of a constant velocity weathering layer overlying abedrock refractor. We choose a weathering layer thickness of 100 m, a weathering layervelocity of 2500 m/s, and a refractor velocity of 5600 m/s. All these estimates are basedon the refraction statics analysis performed in the following chapter. Because we want toidentify this response with the filter r(t) that appears in equations (2.2) and (2.3), we mustaccount for the totality of the reverberations due to an initial downgoing source ray, aswell as all ringing associated with a reflected upward travelling ray (the reflection beingassociated with an interface at depth) that impinges on the reverberating layer from be-low. The calculation of this "ringy" spike train is based on equation (12-18) of Robinsonand Treitel (1980), who show that it is minimum phase. We display it in Figure 2.6a.In Figure 2.6b, we have convolved the ringy spike train with the Klauder waveletshown in Figure 2.5. For display purposes, we have time-shifted the output waveletby +410 ms so that in effect, the output represents the result of a zero-offset, noise-freeVibroseis experiment conducted over a perfectly elastic, constant density one-dimensional330.00.10.20.30.40.50.60.70.80.9^0.0^0.1-0.2-0.30.40.5l^ir^0.6 ^0.70.80.9(b)0.00.10.20.30.40.50.60.70.80.9 (d)0.00.10.20.30.40.5 ^0.6 ^0.7 ^0.8 ^0.9 ^(a)(c)Figure 2.6. Comparsion of predictive deconvolution and spiking deconvolution followedby phase correction: (a) the ringy spike train; (b) the convolutional product of the ringyspike train and the Klauder wavelet (output has been time-shifted downward by+410 ms for display purposes); (c) predictive deconvolution (a=33 ms, n=400 ms)applied to the ringy wavelet in (b); (d) spiking deconvolution of the ringy wavelet (b)followed by convolution with the minimum phase equivalent of the Klauder wavelet.Abscissa is trace amplitude normalized to one and ordinate is two-way traveltime (s).earth that consists of a single deep reflector (two-way traveltime 500 ms) embeddedbeneath a reverberating constant velocity weathering layer.Figure 2.6c shows a predictive deconvolution applied "blindly" (i.e., without con-sideration of the wavelet phase) to the data trace in Figure 2.6b. Acknowledging thecharacteristics of the ideal output (i.e., a single Klauder wavelet centred on t=500 ms),and further recalling the pulse-shaping properties of predictive deconvolution describedabove, it makes no sense to choose a prediction distance a that is shorter than the ef-fective length of the Klauder wavelet. Following the suggestion of Gibson and Lamer(1984), we have used a prediction distance of 33 ms, this being the effective width ofthe central peak of the Klauder wavelet (Figure 2.5). Much of the ringiness has beenremoved. The spurious "tail" due to the mixed phase character of the wavelet is actuallyfairly innocuous, although this result is arguably less desirable from an interpretationviewpoint than the ideal output.Figure 2.6d is the output of a deconvolution using the phase-correction methoddescribed in Section 2.5.1.4. Note that minimal improvement, if any, is afforded byaccounting for the wavelet phase. This observation spurred us to apply and compare thetwo methods on a test portion of SBC18. Again, very little benefit was gained throughapplication of the phase-correction procedure. Ulrych and Matsuoka (1991) show thatthe two methods (i.e., predictive deconvolution and the phase-correction method) aremathematically identical in the limit of infinite prediction distance. We conclude that aprediction distance judiciously chosen so as to bypass the effective width of the Klauderwavelet is sufficiently large that predictive deconvolution has a similar action to the morerigorous method that attends to the wavelet phase.The results of this synthetic experiment suggest that a simple predictive deconvolutionwithout minimum phase conversion suffices to remove the reverberatory effects of the35weathering layer from the SBC18 dataset. Having hereby waived the requirement of aminimum phase wavelet, we remain optimistic about the success of the deconvolutionin removing both the ringiness due to the near-surface, as well as attenuation effects, tothe degree that the other assumptions underlying the convolutional model (i.e., randomreflectivity sequence, zero-offset data, the absence of noise, no complex source and/orreceiver coupling with the near-surface) are not too severely violated.2.5.3 Deconvolution in practiceWe used the ITA prestack module GAP2 to perform a time-variant predictive de-convolution in the common shot domain. The module calculates the autocorrelation ofthe input traces in the shot gather and uses this information to estimate the wavelet andthereby design the predictive deconvolution or "prediction error" operator. We recallfrom Section 2.5.1.3 that the autocorrelation of the wavelet is identical to the autocorre-lation of the input seismic trace under the white reflectivity assumption. Naturally then,an analysis of the autocorrelation of the input CSGs serves as a useful tool for estimat-ing the characteristics of the input wavelet, and ultimately, for choosing the predictionoperator length and prediction distance. Figure 2.7 is an "autocorrelogram" of CSG 773,that is, a plot of the autocorrelation of the traces of the input shot gather. The autocorre-lation was computed over a time window from 9.0-12.0 seconds. The first isolated burstof energy that is common to all the traces should represent the autocorrelation of thewavelet (Yilmaz, 1987); hence, the length of the wavelet may be estimated by the lengthof the first transient zone on the autocorrelogram. We estimated the wavelet length hereto be 160 ms.In Section 2.5.2, we explained our rationale in choosing a prediction gap of 33ms, but we have yet to choose the prediction operator length n. The pulse-shapingproperty of predictive deconvolution is such that an input wavelet of length a+n is36O.000.040.080.120.160.200.240.280.320.368.40O.44LlJ 0.482 0.520.560.600.640.688.720.768.800.840.880.920.961.00DATAaPERZ.CROSSKSG.COR;2Figure 2.7. Autoconelogram for CSG 773. Inferred wavelet width is indicated bythe arrow in the upper right hand corner of the figure.shortened to an output pulse of length a. Thus, the prediction operator length shouldbe chosen so that a+n is equal to the estimated length of the wavelet. Yilmaz (1987)describes the degradation of the output result when the prediction operator length farexceeds the wavelet length. Our present analysis suggests a prediction operator lengthof 160 — 33 120 ms .The autocorrelogram analysis was performed on (roughly) every 40th CSG along theline. To account for wavelet non-stationarity, we partitioned the input CSGs into 4 timewindows, computed separate autocorrelograms for each, and chose different predictiondistances and prediction operator lengths, based on the individual autocorrelogram analy-ses. The deconvolution was performed separately over each window in the sense thatthe algorithm designed and applied a separate prediction error operator for each, basedon our selection of input parameters a and n, then merged the results together on output.The top window extended from just below the first break arrival (we excluded the first37break energy from the analysis) down to 3.5 seconds. The second window extendedfrom 3.5-7.0 s, the third from 7.0-10.0 s, the fourth from 10.0-13.0 s, and the fifthfrom 13.0-16.0 s. At certain points along the line, it was possible to see a slight trendtoward lower frequency content and a more "dispersed" appearance in the autocorrelo-gram character as the time window increased with depth. This, of course, is a testamentto the wavelet non-stationarity. However as a general statement, the variation was notparticularly significant.Figure 2.8 displays the first 4 seconds of CSG 776 before deconvolution. Figure 2.9adisplays the results after a predictive deconvolution based on our parameter selection.Figure 2.9b displays the result after a time-variant deconvolution using a predictionoperator length of 180 ms and a prediction gap length of 24 ms (these parameters wereselected by Western in the preliminary processing). Clearly both deconvolution runs are"successful", since they remove a great deal of ringiness. Comparing Figures 2.9a and2.9b, it is also evident that there is not much difference between the two deconvolveddatasets. The Western result has a slightly higher frequency content. This may be directlyattributed to the discrepancy in the choice of prediction lags (24 ms vs 33 ms). However,it is unclear from this example whether one result is "better" than the other.As a general statement, our final stacked section reveals enhanced coherency of eventsat later times compared with its Western counterpart. While some of the improvement islikely due to our statics application and crossdip correction, we believe that deconvolutionhas also figured significantly in the success. Recalling our discussion in Section 2.5.1.5,we expect a narrower prediction gap to boost high frequency noise. As well, we areunsure if the 24 ms gap is sufficiently large to avoid problems with wavelet phase. Inshort, we are content to trade off a small degree of temporal resolution in the interestof a slight enhancement of the S/N.38TRACE SEQUENTIAL NUMBER^240Figure 2.8. Common shot gather (CSG 773) before deconvolution. A spherical spreadingcorrection and a 1000 ms AGC gain have been applied.2.6 Spatial resolutionBeyond making the qualitative observation that deconvolution has succeeded inremoving reverberation effects, thereby compressing the basic wavelet (equation 2.3)(or alternatively stated, broadening the wavelet spectrum), we may address the issue ofvertical resolution in a quantitative manner by considering the dominant wavelength ofthe seismic waves. The effective vertical resolution is given by (Yilmaz, 1987) 4 = it); ,where Ae is the effective wavelength which may be computed from the velocity v andthe dominant frequency fe. Taking v = 6000 m/s and f; = 30 Hz, we estimate a vertical390.00.20.40.60.81.01.21.41.61.82.02.22.42.62.83.03.23.43.63.8(a)0.00.20.40.60.81.01.21.41.61.82.02.22.42.62.83.03.23.43.63.8(0)trace sequential number20 40 60 80 100 120 140 160 180 200 220 240 20 40 60 80 100 120 140 160 180 200 220 240Figure 2.9. Comparison of predictive deconvolution runs applied to CSG 773: (a) our parameter selection;(b) Western's parameter selection. In both cases a spherical spreading correction and a 1000 ms AGCgain have been applied.resolution of 50 m. In other words, we do not expect to be able to distinguish tworeflectors which are separated by a depth interval of less than 50 m.The lateral resolution may be quantified in terms of the Fresnel zone radius r(t)1/2which is given by r (i)^(i) (17)^(Yilmaz, 1987). Synthetic tests have indicatedthat a lateral dimension of r(t)/4 represents the threshold for event detection (Guy Cross,personal communication, 1993). Thus, at 2 s two-way traveltime, a corresponding Fresnelradius of 750 m implies that our experiment is capable of detecting a feature having alateral extent of 200 m. At 10 s, the minimum detectable lateral dimension increasesto roughly 500 m. Interpretation of the final stacked sections must be governed bythe recognition that our processing efforts provide a subsurface representation which isdistorted by significant lateral blurring.41Chapter 3STATIC CORRECTIONSThe "statics" problem has received much attention over the last twenty years andtoday remains a primary focus of seismic processing research. Static corrections areapplied to compensate for traveltime anomalies introduced by variations in near-surfacestructure. As such, they comprise the conventional elevation adjustments as well ascorrections for heterogeneity in the shallow, unconsolidated "weathering" layer. Staticeffects whose spatial variation is on the order of several cablelengths ("long wavelengthstatics") can lead to the erroneous positioning of deep reflectors on the stacked section. Onthe other hand, near-surface traveltime anomalies which vary significantly on the orderof a single cablelength ("short wavelength statics") can seriously impair stack qualitysince they introduce differential time shifts among traces in a single CMP gather (Farrelland Euwema, 1984).We adopted a two-step procedure for our refraction-based statics computation, firstidentifying and correcting systematic errors in our picked first break traveltimes, thenproceeding with the application of a 2—D statics algorithm.3.1 The shortcomings of the residual statics methodWe performed a preliminary assessment of the severity of the statics problem byconstructing a stack that was essentially identical to the Western section, except for theapplication of statics. Whereas Western computed statics by means of a surface-consistentresidual statics algorithm, we corrected only for elevation effects. The significance ofnear-surface heterogeneity was clearly illustrated by degradation in the quality of thispreliminary stack.42Despite improvements gained through Western's application of residual statics, it isimportant to note the method has shortcomings. Residual statics solutions are unableto reliably estimate the long wavelength component of the statics solution (Wiggins etal, 1976). Moreover, Western's in-house residual statics algorithm "MISER" requirestrace-to-trace static deviations as input. These are computed by a separate algorithmwhich measures relative time shifts across a reflection horizon from cross-correlations.In the deep crustal environment, the lack of a clear, continuous horizon can impairthe performance of correlation-based picking routines. For instance, they may sufferfrom "cycle-skipping" problems due to low S/N. A cycle-skip occurs when the peakcorresponding to the actual horizon is obscured by relatively high amplitude noise and"missed" in the picking analysis. Moreover, standard residual algorithms require amodification for crooked line geometries to account for the effects of reflector crossdip(Larner et al, 1979). Crossdip is the component of reflector dip perpendicular to theseismic line. Crossdip effects are discussed in detail in Chapter 5. This imposes anadditional degree of solution non-uniqueness. The "MISER" routine did not correct forcrossdip effects (James Hostetler, personal communication, 1992).3.2 Refraction staticsIn principle, an analysis of refraction traveltimes can provide a model-based staticssolution that is complete in the sense that all orders of wavelength are correctly computed.Moreover, the "refraction statics" method is robust in the presence of noise, since forVibroseis data, first breaks are easy to pick on all but the noisiest shot gathers. This isbecause the onset of first break energy is effectively located at the dominant peak of thefirst break event that appears on the gather (a consequence of the zero-phase characterof the Klauder wavelet) and therefore usually affords unambiguous detection.43The practical reality is that restrictive assumptions made about the near-surface inthe automated implementation of the refraction statics analysis as well as a sparse spatialdistribution of shots and receivers may adversely affect the success of the final staticscorrection (Hampson and Russell, 1990). However, the ITA module "REFSTAT2" isa relatively sophisticated algorithm, and the multifold acquisition geometry of SBC18ensures a reasonable sampling of the near-surface.3.2.1 The REFSTAT2 modelREFSTAT2 assumes a two-dimensional model which consists of a constant-velocityweathering layer (velocity IC), of variable thickness h(x) and variable surface topographye(x), overlying a bedrock refractor. V(x), the velocity at the top of the bedrock, isconstrained to be slowly varying. The variable x here denotes position along the seismicline. The algorithm models the first breaks as head waves which propagate along theinterface between the weathering layer and bedrock at the bedrock velocity (Figure 3.1).It should be noted that the algorithm can honour a multi-layer model, but that the characterof the first break picks along the entire line suggested that there was little, if any, firstbreak energy associated with deeper layers.Because this near-surface model does not honour any abrupt geological changes suchas those associated with the Fraser Fault, the input dataset was divided into two discretesegments before being passed into the REFSTAT2 algorithm. The statics were determinedseparately for each segment. The first segment contained all first break picks for shotsand receivers on the west side of the canyon, and the second contained all picks for shotsand receivers on the east side of the canyon. No picks associated with the undershootportion of the line (i.e., shot and receiver on opposite sides of the canyon) were used inthe statics computation, although they were considered in the systematic error analysisdescribed in Section 3.4.44bedrock velocity V(X)1^weathering layer^ I11^velocRy^weathering layer1^thickness h(x)Figure 3.1. The REFSTAT2 model.3.2.2 The REFSTAT2 algorithmWe embarked on a thorough investigation of the REFSTAT2 algorithm for two mainreasons. First, the procedure we have adopted for identifying systematic errors in the firstbreak picks (Section 3.4) requires an understanding of the algorithm. Second, we notedthat the ITA documentation for this popular package is cryptic and includes significanterrors of statement. As a result of the latter point, we presented our findings to theLithoprobe processing community (Perz and Wang, 1992).The first step in the statics computation is the calculation of the refractor velocity V(x).REFSTAT2 uses the "abc" method (Coppens, 1985). The calculation of the velocity at thekth station (position xk) involves forming a linear combination of three first break traveltimes that correspond to certain shot-receiver pairs in the vicinity of xk. Several differentfirst break "triplets" are considered in the analysis, thereby providing independent velocityestimates. These are then averaged and smoothed to yield a slowly varying final result,V(xk).45It is appropriate at this point to introduce the concept of a "delay time". The shotdelay time at station j, VI, is defined as the raypath time between the source and therefractor minus the travel time measured along the normal projection of this raypathonto the refractor (for example see Barry, 1967). A corresponding definition exists forthe receiver delay time, trkd. These definitions assume that the interface between theweathering layer and bedrock is locally planar. With reference to the raypath lengthsgiven in Figure 3.1 these delay times are given byd ac bets (3.1)—VwdfV (xj)ofandd (3.2)VwthatdSi^=V (Xk)ri ll'rkBy reciprocity, we have the condition(3.3)recalling that there is no uphole time associated with the Vibroseis source. Note thatthe delay times are "surface-consistent" in the sense that the same station delay timeis attributed to any first break arrival associated with a particular site, independent ofwhether the site contained a shot or receiver, and furthermore, independent of the othersite (shot or receiver) to which the first break is coupled.From the above discussion, 7:ik, the first break traveltime observed at receiver k dueto shot j may be approximated by the sum of its associated shot and receiver delay times,plus a term which accounts for the propagation time along the refractor:^Tjk = p * Xjktajd trkd ,^ (3.4)where Xjk is the source-receiver offset, and p is the reciprocal of the spatially-averagedrefractor velocity given byxkP = f ( 1 ^xk — xi) J v (x ) dxr i.^(3.5)X••46Assuming that a sufficiently large number of first break picks is properly distributedover the shot and receiver spaces, equations (3.3) and (3.4) represent an overdeterminedfull-rank system. The algorithm uses the method of least-squares to solve for the delaytimes.If we assume that the shots are located at the surface and the weathering layer-bedrockinterface is horizontal, it is easy to show that the delay time at the kth station is relatedto the local weathering layer thickness h(xk) and bedrock velocity V(xk) by2h (X41 ( V(x"k) )tskd^trkd •VioOnce calculated, the delay times are separated into high and low frequency spatialcomponents by means of a nine-point median filtering operation followed by three-pointsmoothing. REFSTAT2 then simply inverts (3.6) using the low-frequency componentof the delay time to obtain the layer thicknesses at all stations. Note that the filteringoperation effectively imposes a smoothness constraint on the layer thickness estimates.The final step in the process is the actual application of the statics correction.REFSTAT2 explicitly distinguishes between the high and low frequency statics. sibthe low frequency static component at station k, is given bySlkh (xk)^h (X k)77Erepl^Vw(3.7)where Vrep1 is the user-specified replacement velocity.As we stated previously, the model described in Figure 3.1 is restricted by smoothnessconstraints, both in V(x) and in h(x). While it is reasonable to expect the bedrock velocityto be a slowly varying quantity, the weathering layer thickness can change significantly(3.6)47over the order of only a few group intervals (Hampson and Russell, 1990). Thus, there isa basic error in the model specification. Nonetheless, the short wavelength information iscontained in the high frequency component of the delay time, and it is this latter quantitythat is considered to be the high frequency component of the refraction statics solution.The total static at a given station is simply the sum of its long and short wavelengthconstituents.3.3 Systematic errorsIn practice, the first break picks suffer from the usual random observational errors.More significantly, they may be tainted by a component of systematic error. Giventhe error in the model specification, as well as the presence of both systematic andrandom errors in the first break traveltime picks, the least squares solution of equation(3.4) with constraints (3.3) is properly considered an estimate of the delay times (thevalidity of the very concept of the delay time becomes questionable for a true 3—D staticsproblem). Nevertheless, we shall see that this estimate may be used to identify andremove the systematic errors associated with the first break picks. Using the delay timescalculated through a preliminary pass of REFSTAT2, we may model the systematic errorby performing a time term decomposition of the error-contaminated first break picks,Tike :.7 =p*X+t.7^.7•k•d -1- tk d^eiksys^ (3.8)where we have emphasized the surface-consistent property of the shot and receiver delaytimes by dropping the shot and receiver subscripts:tsjd^trjd EE tid^(3.9)trA:1 == isA(ri48In equation (3.8), ejksYs is the systematic error whose component parts are identifiedin Section 3.3.4. Seik is presumed to be a small random error that embodies any residualmisfit due to the imperfect model specification and/or random first break measurementerror. Note that even the traveltime decomposition with error terms, equation (3.8), is anapproximation. It is quite possible in some instances that the systematic error actuallydiffuses into the delay time estimates themselves in the least squares fit. Nevertheless,we shall see that equation (3.8) can be successfully used as the basis for a systematicerror analysis.3.3.1 The surface stacking chart as a diagnostic tool inthe analysis of systematic errorMilkereit (1989) recommends the use of surface stacking charts (SSC) as a means ofquality control and general information display. The SSC is a contour plot in shot-receiverspace of trace-specific information (e.g., trace edits, first break picks). The relationshipbetween shot, receiver, midpoint and offset axes (assuming a straight line geometry) onthe SSC is illustrated in Figure 3.2. One of his examples is a SSC display of reducedfirst break traveltime, Tjk, defined bye X jkTjk^.k — V red •(3.10)Here Vred is a "reducing velocity" which is a constant value that is representative of theregional bedrock refractor velocity. We expect the reduced traveltime to be a rapidlyvarying quantity in shot-receiver space, because from (3.8) and (3.10), Tjk is seen tocontain short-wavelength information about the near-surface in the form of the delaytimes, as well as possible systematic error (neglecting the small random error).49,kshot Indexk=recelver Indext.4e observable Oik—♦^k receiver station■o4•‘e‘\Figure 3.2. Relationship between the shot, receiver, offset and midpoint axeson a surface stacking chart (SSC).3.3.2 The residual traveltimeThe reduced first break plot described in the previous section is useful for highlightingchanges in the near-surface and thereby assessing the severity of the statics problemeverywhere along the line, but it tends to obscure any systematic errors, these being hardto distinguish from the high (spatial) frequency background. Following a suggestion byWeizhong Wang (personal communication, 1992), we have plotted the residual times inSSC format. We define the residual time, Tikres, by^T res =T e^'L—t°—td •jk^jkredX^kSubstituting equation (3.8) into this last expression gives(3.11)Tir = kik * (1)— Vred 1) e • eye + be •jk^jk • (3.12)I50From (3.12), in the absence of any systematic errors, we expect the residual plotto display a smoothly varying character on a regional scale as it reflects (presumably)gradual lateral changes in the bedrock slowness parameter p, and gradual changes insource-receiver offset. We expect symmetry about the midpoint axis because of thereciprocal property of the residual time (Tikres=rkires•.) Superimposed atop the regionaltrend, we expect a small amount of random noise. For a judicious choice of reducingvelocity, we anticipate numerically small values for Tikres. By design, any systematicerror will appear on the plot in the form of an easily recognizable pattern.3.3.3 The reciprocal difference timeIn addition to the residual plots, SSC plots of "reciprocal difference time" werecreated, again following a suggestion by Weizhong Wang (personal communication,1992). The reciprocal difference time, 4, is defined byAik a- Tjk — Tide . (3.13)By substituting equation (3.8) into this last expression, we may express the reciprocaldifference time in terms of the error terms:Ajk = (eirs — ekis") (Sejk — bekj)^(3.14)The residual plots, which we used as the primary tool in the error analysis, wereconsidered in conjunction with the reciprocal difference SSCs.3.3.4 Sources of systematic errorIn practice, several sources of systematic error may produce identifiable patterns onthe residual plot. A "shot mispositioning" error arises when the vibrator trucks do notshoot exactly on the station. For instance, this may occur if the drivers are unable tolocate the survey marker at a particular station because it is obscured by the roadside51vegetation, and as a result, drive a few metres beyond the actual shot station. Thenforward receivers record a first break that is systematically "early" by some fixed amountthat corresponds to the portion of "missing" raypath between the actual and expectedshot location, and similarly, reverse receivers detect a first break that is systematically"late". The anomalous first break pattern will appear on the residual plot along a locusof constant shot, and is readily detected by the human eye.When a receiver site suffers from a severe local statics problem, or when a receivergroup is affected by a polarity reversal, the corresponding first break appears time-shiftedon a shot gather compared to neighbouring first breaks. First break picks used in therefraction statics analysis were made on shot gathers using the automatic picker of theITA interactive editor "VAQ2". The cross-correlation based picker "tunes" the user'sinitial crude estimate of the first breaks to the local dominant peaks along the first breakevent. Generally, the picker does a good job; however, it often cycle-skips over thesetime-shifted first breaks. Although VAQ2 provides a visual display of the tuned picks,the plotting scale is such that single cycle-skips often go undetected. This "tuning error"is manifest on the residual plot as an anomaly along a locus of constant receiver. Notethat the fact that the statics are particularly problematic at a specific site underscores theimportance of an accurate first break traveltime measurement.Another systematic error results when the side lobes of the Klauder wavelet renderthe detection of the dominant first break peak ambiguous. A side lobe may be erroneouslyidentified as a first break peak. Typically, this "side lobe error" appears on the residualplot as an anomaly along a locus of constant shot, because the picking is performed onshot gathers.A "recorder error" results when there is a zero-time discrepancy between the masterand slave recorders. Because the slave recorder records the signal from the first 12052channels and the master records channels 121-240 (Figure 2.1), this error appears asa bulk time shift along the constant channel locus corresponding to channel 121. Thistype of error plagued the data from the Lithoprobe Kapuskasing Structural Zone (KSZ)transect (Weizhong Wang, personal communication, 1993), but as we shall see, was nota problem for SBC18.Finally, "geometry errors" result when the geometry information is incorrectly enteredinto the trace headers. Because of the regular plotting patterns associated with all threemodes of shooting (roll-on, roll-along, and roll-off ) on the SSC, such errors are readilydetected.3.3.5 The residual and reciprocal difference plotting algorithmsThe delay times were calculated by REFSTAT2 on a preliminary run using theerror-contaminated picks. We wrote a FORTRAN program to calculate the residual andreciprocal difference values along the line using equations (3.11) and (3.13). A value of5600 m/s, representative of the average bedrock velocity observed throughout the region,was chosen for the replacement velocity used in calculating the residual traveltimes.Because the shot interval for SBC18 is twice the receiver interval, it was necessary toincorporate a data interpolation scheme into our plotting algorithm in order to "fill in" thegaps in data coverage on the SSCs. In general, shooting took place on the odd statiionnumbers, but there were many exceptions to this due to culverts, rough spots along theroad, bridges, observer error and slide areas.The first break traveltime corresponding to a "missing" shot at a given source-receiveroffset was estimated by forming a weighted average of two first break traveltimes, namelythe one due to the nearest shot in the forward direction measured at the receiver of thesame (nominal) offset and its counterpart in the reverse shot direction. Suppose that thestation at position x1 was not a shotpoint, and that the nearest shotpoints in the forward53and reverse directions were at sites xp.ifor and^respectively, where ifor and irev arepositive integers. We estimated Tbnest, the first break arrival time corresponding to themissing shot and the mth receiver, byest —irev*^m+ifor + if or * Ti—irev m—irevi f or + irevEquation (3.15) gives the general method of interpolation; however geometricalcomplications associated with the roll-on and roll-off portions of the line necessitatedthe use of a slightly different scheme for estimating traveltimes near the ends of thespread. Also, we modified the interpolating process in the vicinity of the Fraser Canyon.Near the canyon edge the use of (3.15) would yield erroneous estimates.Once calculated by the algorithm, the residual and reciprocal difference times werecontoured and colour-plotted.From equation (3.13), note thatAjk = —Akj •^ (3.16)Because of this symmetry, all reciprocal difference information can be plotted on one sideor other of the midpoint axis i = j (Figure 3.3). To avoid redundancy in our informationdisplay, we plotted Au for i>j and the arithmetic mean of Tures and Tiles for kj (recallthat residual times are reciprocal in the absence of any systematic error), hoping that thislatter quantity would provide a useful reference or "tie-in" with the accompanying residualplots. Under this plotting convention, any type of systematic error that is specific to asingle shot or receiver (such as those described in Section 3.3.4 below) is manifest on thereciprocal difference plot as an anomaly that follows an inverted "L" shape (Figure 3.3).3.3.6 Result presentation and discussionThe very small master-slave recorder discrepancy revealed in Figure 3.4a is the onlyvisible recorder error observed over the entire line. The insignificant time shift between(3.15)54Figure 3.3. The plotting convention for the reciprocal difference plots. The reciprocaldifference traveltimes are plotted above the midpoint (i = j) axis, and the average of the tworesidual times Tdesand Tkires are plotted below. Systematic errors that are specific to asingle shot or receiver plot as an inverted "L", as shown in the figure.channels 120 and 121 is indicated on the figure. One of our initial concerns was thata recorder error might have occurred for the undershoot, when the master and slaverecorder trucks were located on opposite sides of the canyon. Such an error wouldnot be discernable on the residual plot because the geological discontinuity across thecanyon coincides with the gap between channels 120 and 121 and would obscure anytime shift. However, from the reciprocal difference plot (Figure 3.4b), we infer that therewas negligible recorder error, since such an error would result in non-zero reciprocaldifference times in the portion of shot-receiver space delineated by dashed box B inthe figure. The zero-time discrepancy between the master and slave recorders couldconceivably affect a significant proportion of the total number of traces along the line.The SSC plots, in revealing that such an error was negligible on SBC18, provided areassurance of the excellence in data acquisition.55Figure 3.4a. Residual traveltime plot for VPs 27-199 (following page). A smallrecorder error is highlighted by the dashed box. To see, take a line of sightalong the dashed arrow. The solid arrows indicate the transition between themaster and slave recorders. The boldface dashed line indicates the transitionbetween roll-on and roll-along shooting configurations. A polarity reversal atreceiver site 248 shows up on this figure as a linear (vertical) anomaly. Theinset displays a portion of the shot-receiver space near station 248 aftercorrection of the polarity reversal. Note that the inset displays additionalinfilling of colour near the right edge of the plot compared with the uncorrectedresult, reflecting the fact that during the correction process, additional pickswere made using the interactive editor (white areas within the shot-receiver spaceindicate an absence of first break picks).Figure 3.4b. Reciprocal difference time plot for VPs near the Fraser Canyon(following page). The plotting convention is illustrated in Figure 3.3. The shot-receiver space is divided into three separate regions, A, B and C, each of whichis associated with a different acquisition geometry. In particular region B, whichcorresponds to the undershoot, displays near-zero reciprocal difference times,suggesting that there was negligible recorder error when the master and slaverecorders were located on opposite sides of the canyon.c 1500•1 00017.3Cr)50806040200204060-80(a) 502b0600^650^700^750receiver station(b)800receiver stationNO0INSET^ °X = shot0 = receiverAN^IO5 7A polarity reversal is also indicated in Figure 3.4a. Correction was performed usingthe ITA interactive editor "VAQ2" (all trace amplitudes were multiplied by a factor of—1). The corrected result is displayed in the figure inset.A tuning error associated with receiver site 587 is indicated in Figures 3.5a (eventA) and 3.5b (dashed boxes). From this latter figure, we note the anomaly is clearlycharacterized by the inverted "L" signature illustrated schematically in Figure 3.3. Onelimb of the "L" is systematically "high" whereas the other is systematically "low". Acareful inspection of the first break picks at this site revealed a severe local staticsproblem that had caused the automatic picker to cycle-skip over the correct first breaktraveltime. From the residual plots (Figures 3.5a and/or 3.5c), we infer that here, thestatics are particularly severe. This is evident from the relatively rapid variation inresidual traveltime observed throughout the shot-receiver space, even in areas that donot suffer from any systematic error. We recall from Section 3.3.2 that in the absenceof systematic errors, the residual traveltime is generally a smoothly varying quantity.Rapid residual traveltime variation indicates (i) highly variable bedrock velocities or (ii)poorly-estimated delay-times. Either possibility points to an extremely heterogeneousnear-surface. The error, which plagued several receiver sites along this portion of theline, was corrected by careful manual repicking. The corrected picks for station 587 areshown in Figures 3.5c and 3.5d.A representative example of a shot mispositioning error is shown on the residual plotin Figure 3.5a (event B). Note that the residual traveltimes associated with the "reverse"receivers (receiver indices less than shot index) are systematically "high" compared to thebackground, while the forward residual traveltimes are systematically "low". The error isalso shown on the corresponding reciprocal difference plot in Figure 3.5b (solid boxes).As in the case of the recorder error, this type of error was not particularly problematicfor SBC18. In fact the portion of the line displayed in Figure 3.5 (near the western edge58Figure 3.5. Residual traveltime and reciprocal difference time plots for VPs 400-641 located near the western edge of the Fraser Canyon (following page).The colour time scale for all four plots is shown in Figure 3.5b. Results aredisplayed both before and after correction of systematic errors. (a) Residualtraveltime plot before correction. Event A is a tuning error. Event B is a shot mis-positioning error. (b) Reciprocal difference time plot before correction. Here, thetuning error (event A in (a)) is indicated by the dashed boxes. The solid boxeshighlight the shot mispositioning error (event B in (a)). (c) Residual traveltimeplot after correction. Compare events A and B in (a) with the correspondingregions in this figure. The stippled pattern assocated with the correction of thetuning error at receiver site 587 is an interpolating artifact. The solid box nearthe top of the figure indicates the zoom area shown in expanded view in Figure3.6. (d) Reciprocal difference time plot after correction. Compare the boxedregions in (b) with the corresponding regions in this figure.receiver station350^400^450^500^550receiver station450^500^550650600 350 650400 GOO600^650^350^400^450^500^550receiver station600350^400^450^500^550receiver station650600450400450400550 °-0)500 5600Ci)550Cr)0)500 5of the Fraser Canyon) is the only section which suffers from such errors. Because of therapid near-surface variation, a departure from the surveyed shot site on the order of onlya few metres could induce an appreciable change in first break arrival time.Positive identification of this type of error was difficult because of the near-surfaceheterogeneity. In all, five systematic anomalies were attributed to shot mispositioningsand were subsequently corrected. Only the first break traveltimes were corrected. Shotmispositioning corrections to reflection arrival times are negligibly small for all but theshallowest horizons. We adjusted the first breaks for VPs 513 and 511 by adding 10 ms tothose traveltimes measured at forward receivers and subtracting 7 ms from those measuredat reverse receivers (the forward and reverse corrections need not necessarily have thesame magnitude in the case of an extremely heterogeneous subsurface). For VPs 547,549 and 569, 9 ms was added to forward receiver traveltimes and 8 ms was subtractedfrom the reverse receiver traveltimes. The amount of correction was determined visually,by simply inspecting and comparing the residual and reciprocal difference plots beforeand after adjustment (the correct adjustment ideally restores the anomalous region to thebackground colours). The corrected picks are displayed in Figures 3.5c and 3.5d.Note that the correction of both shot mispositioning errors and tuning errors due tosevere local static anomalies led to interpolation artifacts on the final plots. Figure 3.6is a zoom of the boxed portion (solid box) of the corrected residual plot of Figure 3.5c.The expanded view shows clearly that the points in shot-receiver space corresponding toreal VPs are properly corrected. The stippled pattern presumably arises because equation(3.15) does not serve as a good interpolator in the case of severe local static anomalies.A side lobe picking error is highlighted in the residual plot of Figure 3.7a (dashedboxes). Very strong first arrivals were recorded here, resulting in high amplitude Klauderwavelet side lobes. This type of error occurred at several locations along the line. In61 - 80- 60- 40- 20- 0- -20- -40- -60- -803CV570^580^590^600receiver stationFigure 3.6. Expanded view of solid box appearing in Fig. 3.5c. It is clear from this figure that thestippled pattern associated with receiver site 587 is an interpolating artifact.each case, a careful manual repicking of the first break traveltimes rectified the situation(e.g., Figure 3.7b).Figure 3.8a (residual plot) displays the sole geometry error that occurred on SBC18(dashed box). The error was due to a data entry error we committed while transcribingthe Sonix Exploration observer notes to ITA format. The corrected result is shown inFigure 3.8b.3.4 Elevation correctionOnce the systematic errors were identified and removed through the use of the SSCs,the corrected dataset was divided into two segments in the manner described in Section3.2.1. The segments were input to the REFSTAT2 algorithm on two independent runs,and a final solution for the statics for all the stations on SBC18 was obtained. Anexamination of equation (3.7), the expression for the low frequency static component,reveals that REFSTAT2 does not refer the corrections to a specific datum plane. To seethis consult Figure 3.9. In the figure z(x) is defined as the distance between the surfaceand the datum plane; thus at station kz (xk) e(xk) — d , (3.17)where d is the datum plane elevation.We seek to "replace" the near-surface structure by a medium of uniform velocity,17,,p1, and constant surface topography, d. A straightforward analysis based on exami-nation of Figure 3.9 reveals that the statics correction Sk (elevation and low-frequencyrefraction statics) is calculated according toSk — ((h (xk)v—e: (x0) h k))But the conventional elevation static at the kth station, ak, is given byz (xk)ak = Trrepl^•(3.18)(3.19)63Figure 3.7. Residual plot for VPs 721-800 (following page; top). Ordinate is shotindex and abscissa is receiver index. (a) Before correction. Side lobe pickingerrors are indicated by the dashed boxes. (b) After correction.Figure 3.8. Residual plot for VPs 1000-1050 (following page; bottom). Ordinateis shot index and abscissa is receiver index. (a) Before correction. Note thegeometry error (dashed box). (b) After correction.6It100An6040^800200700Figure 33 800- - L140120 750 -900 950/00^750^800^850(b)750 --20(b)Figure 3.8806040200-2040-60-80BOO) 850(a750 950900GSdatum planeAelevation %.4station k ;position xkdistance between surface anddatum plane z(x)surface a iv%elevation Ws,SIM^•■■weathering layervelocitYweathering layerthickness h(c)Figure 3.9. Relationship between the datum plane and the refraction statics model.From equations (3.18) and (3.19), together with (3.7) (which describes the low frequencystatics computation), it is clear that the complete statics solution requires an explicitelevation correction. We performed the correction by means of the ITA module "DATM"(again, using a replacement velocity of 5600 m/s).3.5 Data results after statics application—stacked sectionsIn order to assess the overall merit of the application of refraction statics, we designeda "brute stack" processing stream, which aside from its statics treatment was essentiallyidentical to the one used by Western in the preliminary processing: geometric spreadingcorrection, predictive deconvolution, refraction statics, CMP sorting, NMO correctionusing the same stacking velocity file, prestack and poststack trace balancing. From ourdiscussion on deconvolution (Section 2.5), we recall one other processing difference,namely the discrepancy between prediction gap parameters, 24 ms (Western) versus 33ms (our reprocessing). This accounts for the slightly higher frequency content of theWestern sections here and in the data comparisons in subsequent chapters. We havedisplayed a portion of Western's stacked section taken from near the western edge of the66profile in Figure 3.10a and present our corresponding brute stack in Figure 3.10b. Withregard to this latter figure, we note that CMP station numbers have been multiplied by afactor of ten (ITA axis-labelling convention). This plotting convention is adopted in allsubsequent figures which display our stacked sections. Enhanced continuity of reflectorsis apparent in several regions of Figure 3.10b, particularly between 9.6-10.0 s.The only truly disappointing result occurs in the vicinity of the western edge of thecanyon, between midpoints 450 and 550. Here, the Western stacked section revealedvirtually no signal. Visual inspection of the shot gathers showed that the S/N ratio wasvery low in this area (Section 2.4); thus, we expect that the residual statics algorithmused in the contract processing suffered from cycle-skipping problems. Although thefirst break picks were noisy, they were nonetheless discernible, so we had hoped thatapplication of refraction statics would help to eliminate the severe statics problem in thisregion (we recall that the residual plots in Figure 3.5 suggest rapid near-surface variation).Unfortunately, the application of refraction statics was unable to draw out any signal. Weattribute the absence of observed reflectivity to the severe noise problem in the area, andnot necessarily to the subsurface geology.67E^CMP bin no. (x1 0)280^800 900 1000 1100^1300 1400 1500 1600 1700 1800E Trace sequential number120^160^200^2408.48.89.29.613 6.4a)6.8CD7.2)'• 7.66",8.0F-(a) (b)5.25.66.05.25.66.06.46.87.27.68.08.48.89.29.610.DATA:EPERZ.CROSS7BRUTE.STK;210.DATA:EPERZ.CROSSNESTERN.STK;2Figure 3.10. Comparison of stacked sections after application of statics. Processing streams for the two sections areessentially identical except for statics (see text for details). (a) Western stacked section. (b) Our reprocessedbrute stack.Chapter 4DIP MOVEOUT CORRECTION ANDVELOCITY ANALYSISCompensation for the effect of source-receiver offset on observed reflection travel-times is conventionally achieved through application of the "normal moveout" (NMO)correction. However in the case of a dipping interface, NMO correction does not restorethe associated reflection hyperbola to zero-offset time; rather it overcorrects, resulting in"too early" a reflection time. Dip moveout correction (DMO) removes the effect of re-flector dip from non-zero-offset arrivals, thereby improving the stack quality for steeplydipping events.In this chapter, we describe the theory which underlies the DMO algorithm andthe practical considerations which arise when the method is applied to the crooked lineproblem. Because of its intimate relation to DMO, we also describe our velocity analysis.4.1 DMO theoryThe traveltime expression for a single, horizontal, uniform layer over a halfspace isthe familiar normal moveout (NMO) equation4h2t2 = t2° V2where to is the two-way traveltime measured at zero offset, V is the layer velocity, and his the half-offset. If we now allow this layer to dip, say at an angle 0 from the horizontal,(Fig. 4.1) then the corresponding traveltime equation is given bytt^ 2 ^^— t^4h2 costV2(4.2)(Dix, 1955).(4.1)69•—h = half-offset—b.1S^y= source-receiverid In rFigure 4.1. The earth model assumed in deriving dip moveout equation (4.2).From equation (4.2) we see the problem associated with performing a standardcorrection to normal moveout time, tn, given by4h22^2tn = t —V2^(4.3)'since to < to . The overcorrection due to application of NMO obviously misaligns eventswithin a CMP gather, thereby impairing stack quality.An optimum stack would be obtained if the NMO correction were performed usinga "stacking" velocity c÷.  This observation suggests that we directly incorporate themoveout correction implied by equation (4.2) into the velocity analysis; in other words,we might expressly choose "too high" a velocity in the interest of optimizing thestack quality. There are several reasons why such a procedure is undesirable froma processing viewpoint. For instance, we require knowledge of the true subsurfacevelocity structure to perform a wave-equation migration (and the associated time-to-depth conversion). Moreover, one objective in seismic reflection processing, thoughancillary to the delineation of geological features on a stacked section, is the acquistionof information about the P-wave velocity structure. Additionally, there is an ambiguity70concerning the choice of stacking velocity in the case of multiple dipping reflectors. Inother words, which value of 9 do we choose if there are several events, each associatedwith a different interface and therefore a different dip, that intersect (or at least are inproximity to one another) at a certain time t and half-offset h on the input CMP gather?Operating in the common-offset domain (Fig. 4.2), Hale (1984) devised a schemeto remove the effect of reflector dip without prior knowledge of the dip angle by Fouriertransforming the input NMO-corrected dataset. Although computationally expensive, themethod now known simply as "DMO" is capable of performing a simultaneous correctionfor all dips. This correction, most significant for early times at large offsets and steepdips, restores the input common-offset sections to zero-offset sections. In an alternateinterpretation of the action of DMO, Deregowski (1982) shows that the method effectivelyeliminates "reflector point dispersal" on a CMP gather by "migrating" energy associatedwith a particular reflection point on a common offset section updip to the midpoint thatis associated with normal incidence to that reflection point (Fig. 4.3). For this reason,DMO is also referred to as "prestack partial migration". Although the method assumesa constant velocity, empirical studies suggest that DMO works well on real data.4.2 DMO—practical considerations4.2.1 The time-variant DMO impulse response: synthetic testsITA has implemented the algorithm of Liner and Bleistein (1988), who use a loga-rithmic stretch of the time axis to perform a computationally efficient DMO correction,in the poststack module "DMO2F'. In our first synthetic test, we seek to recover the"DMO ellipse", which is properly viewed as the DMO time-variant impulse response.Such a test serves to "calibrate" the DMO2F algorithm and verifies that we are correctlyinterpreting the input parameters.71= midpointt = time= common midpoint gatherFigure 4.2. The dataset occupies a volume in midpoint-offset-time space. There is no loss ingenerality in using the half-offset, instead of the offset, to describe the data space. For easeof display, only positive offsets are indicated in the figure. Under this data representation,both common midpoint and common offset gathers map to planes.Figure 4.3. The elimination of reflector point dispersal by application of DMO. The energyassociated with the reflection point P is initially "incorrectly" associated with the actualsource-receiver midpoint n. After DMO correction, the energy reappears in the common offsetsection at the trace associated with the "correct" midpoint yf, at time t=2D.N.Deregowski and Rocca (1981) show that a single impulse occurring on a common-offset section at a point (tp, yp) may be associated with an elliptical reflector embedded72in a homogeneous earth whose shape is given by(Y — Yp)2^(2!) 21 ,^ (4.4)(2?)^(t?, _ trowhere y is the midpoint position, h is the half offset, v is the velocity and z is the depthmeasured at y=yp .Figure 4.4a is the input common offset section (half offset h=1200 m, midpointspacing Ay=25 m). This section was produced by convolving a Klauder wavelet withfive impulses on trace 70, these being equally spaced at 0.5 sec intervals and spanning atime window from 1.4-3.4 s. Figure 4.4b shows the same section after NMO correctionusing a velocity of 2000 m/s (i.e., the assumed medium velocity). This NMO-correctedsection was input to the INSIGHT algorithm DMO2F. Figure 4.4c shows the DMO-corrected result. The coherent features on this figure are not the elliptical reflectors, butrather their corresponding zero-offset events, which still require migration. Figure 4.4ddisplays the migrated result. A simple conversion from two-way migrated time, t„, todepth (t,n=2z/v) allows a verification of the lengths of the semi-major and semi-minoraxes, a and b, respectively, for the first pulse at 1.4 s on Figure 4.4a. According toequation (4.4),a = v2tp2 = V(20002)4 (1.42)4^= 1400 m = 56 traces^(4.5)and, 4h2^12002b^P — — 111.42 — (—20002) = 0.721 s^(4.6)V2 The lengths are in agreement with Figure 4.4d.4.2.2 Spatial aliasing considerationsThe "energy smearing" action of DMO, which moves energy from a single midpointto neighbouring ones on a common offset gather, is clearly illustrated by the impulse738.0ea0.40.68.01.00 1.2E "23 1.6CD 1.9(1)Iii 2.02.62.03.03.23.49.63.06I2.22.4COCO0.20.48.6CO1.01.41.61.62 12.42.62.89.03.23.43.63.0(a)28^60^00^1^1^14811^lull, 111111 .!Lllllll II^ill^111,. 1111^II1111111,111.1.:: :^ill lku111IIyIllgllblll^I ; 1[111^11 1 111111 II m$ 1 111 11.1111' 1 1 1^IIII III !i1111Impgq,19 Ildhdl1 1 1 1111111;11111111111111 M,,11111 1 1111 1111111 1 11$;" „,„ , Imo: ill 0101 11111111 1 1 1I I, III 1111 111 1 11, 1111^11 111411111'4 WIrliit.1111111111,11111tmilimin1111 1111 11 1 11111111111111))n ,1111 Iii IIIII11111,1,,i,',„,1111111''111,,„11,1111^HilimilHum imilimmillili 111 ,1 1 ,1 111 , illitiliiloihrsio 1111 111111 I III III1. 1.1 1 1 1, 1J11 1.11 11.111 ^,„^1,11 1,11.1 1.11 11.11 1. 1.1 1. 1, 1. 1.E11 1,11^1. 1 1^„, ^„„1ft^1 11 11  111 1 1 H^11111 liilli1111111111111111111111111 111111111 111111111111,1111111111111111111111111111111,11111111:11:"'1111:111111:11111 1)1111'111^1111 1111 II I^III 11 11„„11„11 1 1 1 1111 HIV NI 1DATCHIPERZ.910.DEMO1COFF.D11031(c)8.28.4O.68.81.01.21.41.6i.e2.82.22.42.62.83.83.23.43.63.0trace sequential numberze^40^60^80^100^1201111111111111 1 1 1 1 1111^III I 11 11 1ii"1IIII I III^1111'11 1 1 11 1"1^1 1 11^111111111111 1 1^111111'111 1 1111111 11 111111 1^11 11111 1^Ill 1^1,1 ill^111 1 11 11 1 1 111 ^III 1111 1111 111111 11 1 1 1111111 11 11  1 ,11 1 „11 1 1,^1111 1^ 1  1 111 1 11^1 1^1 1 11^I 1 « 1 1 1 1 111 1 1 1 11  1 , 1^1 1 1  1 1  1 , I1 11 11111 11,11^ II^II^ III 111111'^II 1, 1 1 1,^11, 1 II I I^I]^1 1 1^1111 111 11111 ^III^1 1 1 1111 111111 111111 111111 11^11.1111 II II 111111^II^III^1 1^11 1^1111 11111 A I 11111 I ^1 11111 1^1111 1 11111 11111 1 1 1 1 1 1 1^1111111^1 1  1 1 1^1 1  1 111111 1 1^1 1  111. 1 1 1  1 1^1 11^1 1 1. 1^1 1 1 1^1 1^1  11 1 11 111 1 11 1  II1 111111111 11111^11 1 1^11^IIIIII^1^III III 1111^II I I II I^III 11 111111 1 ^1 1 11111 1 1 11 1111 II1 1 1111^11111 1 1^11 1 111^III II 1 1^II 1^111 1 11 1 111 III 1^III^11111 III III II I I 1 1 1.1^1 1111111 I 111 1 I^1 1^1 1 111^11 11 "^"1 11^1 1I^1"111 1 1^11^11 " 1 1 1 1 1 11^1 " II " 11 1  11111 111 III 1 1^1 1111^I IIIIIIllil^llI1^111I11iIII11I1^11 II 1111111 I I I 111111 1 I 1 11111111111111111111111 ^111111^1111111^11111111^11 111 11111 II 1 11111 1111111111 1 11111 1 1111 III1111111111111 1 11 11 1111h^11111 ill III :111111^1111 11 1'11111 1 1111 1 1'1111 1 III 11 1111111 III 11111 1 1111111 1111 IIIIII 11111111^IIII 11111 I 1111111'11^III^1111111II111; 1111;1IIII III 1111 III 1111 11111 1^1 111 1 1111^III,!!!! 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'i .)i)iiiiiiii li'bifY.-9i i-"''Y) ut 1J ' )11 Iirock,314 :IINIIII I Ii'l,'IiiiIIII 111, 1,, 1'41,111,111 1 1i^tf , 141 1 ;11 1, 111 1 111 1 '^9 ' 1 11' 1 1 1 11 011;01111'h'; ',9111II1 111 1 11'111 1 1 ! 1,1',11^1 ' I I I^0 11^1 i',1J1J'i 11.0 .it 1 1^li i^11^1111 1 11:111111 1, 1 11 11111:1i1011:41i;1111,1t,,,,INII 11 „ 0.,41 1 0;t111 11 1 :11111i:4;40M ii111 11 1 1 1^PA 'l 1111'1 1,11 1M11 ,11(d)Figure 4.4. DMO impulse response testing: (a) the input common offset section;(b) the NMO-corrected section (v=2000 m/s); (c) the DMO-corrected section; (d)result of migrating (c). Note that the "smiles" appearing at later times on (d) aremigration artifacts associated with edge effects.responses in Figure 4.4c. We anticipate such "smearing" because from the migration-likeaction of DMO. Intuitively we might expect that DMO can act as an "interpolator" inthe following sense: if the traces of an input common offset gather were interspersedwith zero traces, then DMO would restore continuity of reflectors by shifting energyinto the dead traces. This "interpolating property" is highly desirable from a practicalviewpoint (Ronen and Liner, 1987; Bolondi et al., 1982; Deregowski, 1986). Since itpermits, in effect, a finer sampling of midpoint space on the stacked section, beyond theobvious consideration of improving the final result from an interpretative viewpoint, DMOacts as a safeguard against the phenomenon of spatial aliasing during the application ofsubsequent processes (such as migration) which involve a 2—D Fourier transform fromx-t (space-time) to f-k (frequency-wavenumber) coordinates.The DMO process itself, being predicated on the well-known fact that all linear eventsin x-t space having a particular slope map to the same radial line in the f-k domain, may besusceptible to aliasing problems. Fortunately, we need not exploit the anti-aliasing featureof DMO in our present analysis. For a constant velocity medium, it is easy to show thatthe maximum slope of a reflection event on a constant-offset section is given bydt) 2(4.7)dx maxThis result, which corresponds to a 90° dipping interface, is offset-independent. TakingV = 5000 m/s as a lower bound on the velocity for SBC18, we may use equation (4.7) tocalculate an upper bound on the time dip that we expect to see on the SBC18 constantoffset sections:The frequency associated with the onset of aliasing, f,,, is related to the spatial samplinginterval Ax byfmax = 1 1( dt r2Ax lAdx max(dt= 4 x 10-4 s/m .^(4.8)dx) max(4.9)75The spatial sampling interval on a common-offset section is simply the midpoint interval,which in our case is 25 m. Hence, from equations (4.8) and (4.9), we find that thethreshold aliasing frequency for SBC18 is 50 Hz. Given the characteristics of the sourcesweep (frequency range 10-56 Hz), it is unlikely that DMO-induced aliasing effects aresignificant for SBC18.Despite having been spared the problem of spatial aliasing for our present processingtask, we decided to test firsthand the anti-aliasing characteristics of DMO. Ronen (1985)describes the theoretically rigorous procedure for the exploitation of the DMO anti-aliasing property. Here, we content ourselves with a less-sophisticated approach. Weconsider a synthetic model consisting of two steeply dipping reflectors. The correspondingzero-offset section is shown in Figure 4.5a. Next, we construct a synthetic common-offset section (h = 1200 m ). Note that the resulting time dip on this section (Fig. 4.5b)is well beyond (Mmax' given the frequency content of the Klauder wavelet used inproducing the synthetic. Figure 4.5c shows the result of applying DMO to the NMO-corrected version of the section (NMO was performed using the same velocity that wasused in constructing the synthetic earth model). Spatial aliasing has caused a drasticmispositioning of the reflection event (e.g. white box in Figure 4.5c); this is evidentfrom a comparison between the linear coherent energy within the white box and thecorresponding event on the zero-offset section (Figure 4.5a), which represents the DMOideal output. Next, we interspersed the traces in Figure 4.5a with zero traces, therebydoubling the size of the input gather. Figure 4.5d shows the result after DMO. Wenote that the "smily" artifacts present in Figures 4.5c and 4.5d are a manifestation of thesuperposition of the various DMO impulse responses (we performed similar synthetic testsfor much shallower (unaliased) dips, and noted in such cases that the smiles interfereddestructively everywhere, except along the reflection events).76It should be emphasized that our method is grounded only in intuition, and thatwe have chosen for simplicity the crudest of interpolation schemes. Infilling using theaverage of adjacent traces on a common offset gather would undoubtedly improve theresults. We feel that the results of our simple test are worth mentioning. They bring tolight a characteristic of DMO which is not universally recognized by the crustal seismicprocessing community but which, at least to a first-order approximation, may be readilyexploited.4.2.3 The partial stackDMO correction is based on a two-dimensional theory. Although we hope to gainsome improvement in the imaging of dipping reflectors through its application, we cannotdirectly port the method over to our three-dimensional situation. A complication arisesbecause of the irregular offset distribution associated with a crooked line geometry. Withreference to Figure 4.2, we do not expect more than one or two traces to map to a givencommon offset plane, and further, we expect that a very large number of such planeswould be required to describe the entire collection of traces over the line. This is highlyundesirable from a practical viewpoint, since the DMO algorithm operates separately oneach common offset gather.We need to group the traces according to some measure of nominal offset. Theprocedure we follow is analogous to the approach we adopted in performing the CMPbinning. "Common offset binning" effectively decreases the number of common offsetplanes and increases the fold (i.e., the number of traces) within each common offsetgather. Operating in the CMP domain, the procedure groups the traces into regularly-spaced offset bins (Figure 4.6). The bin assignment is based on the true source-receiveroffset. In the case that several traces occupy the same bin, the arithmetic mean of the traceamplitudes is calculated and assigned to that bin. Since this averaging process involves77Figure 4.5. Testing DMO antialiasing properties: (a) zero-offset section for asynthetic earth model consisting of two steeply dipping reflectors; (b) constantoffset section (half-offset=1200 m); (c) application of DMO without prior insertionof dead (zero) traces; (d) same as (c) except that dead traces were insertedprior to applying DMO. Note the mispositioning of the reflector in (c) (white box)due to spatial aliasing. By contrast, the same reflector in (d) (white box) has beenrestored to the correct zero-offset location in (x-t) space (compare (c) and (d) withthe DMO ideal in (a)).two-way traveltime (s)V CO 61 CD 4) ta NN NNN.r r . r OS MOM•^•^•^•^•^•^•^•^•^•^•^•^•^•^•^•^•^•^•^•3) CD CD A N 0) CO 0, A N CD CD 0, A N t9 CD ch 16 ID CDN33MAI^NNNNN ^D 6 6 a 6 ;ID OD^N N 6 N a N 6 6 6 'a 6^it, 1.0 14 CD6 6 1. N N 0 6 1. 6 6 6 6 A 6 6 6 6 1. 6 6a summation or "stack" in the CMP domain, the common offset binning procedure isreferred to as the "partial stack".The partial stack has been implemented by ITA through the pre-stack module "PSTK".In the case that no traces occupy a particular bin, PSTK introduces a single zero (dead)trace. Although we do not expect the DMO process, given its energy smearing property,to be significantly affected by this artificial "seeding" of dead traces, we can improvethe partial stack by infilling the empty bin with a trace formed by taking the mean ofthe two traces that occupy the surrounding (adjacent) bins, then discarding the seededtrace after applying DMO.A second improvement to the ITA algorithm may be realized by recognizing that theDMO correction does not depend on the polarity of the offset, rather only on its absolutevalue (see equation (4.2)). Moreover, two traces in a single CMP gather having the sameabsolute value of offset but opposite polarity ought to be identical by reciprocity. Whilethe PSTK module maintains offset polarity, the above considerations imply that we maybin the traces according to absolute value of offset. This has the effect of reducing thenumber of common-offset gathers input to the DMO algorithm, and therefore minimizingthe run time. As well, the increase in the number of traces that contribute to the partialstack performed within each bin may help increase the signal-to-noise ratio along noisyportions of the line.Weizhong Wang (personal communication, 1992) has modified the PSTK algorithm,incorporating these two improvements. We used his FORTRAN subroutine in designingour partial stacking algorithm, which we have illustrated schematically in Figure 4.6.4.2.4 DMO and velocity analysisWe have seen that the complete compensation for reflection event moveout on aCMP gather may be achieved via two cascaded processes: NMO correction followed by80zoom box h = half-offset• y = midpointzo m boxbin width (b)trace G = mean (trace C, trace D, trace E)trace H = mean (trace G, trace I)trace I = mean (trace A, trace B, trace F)(c) tFigure 4.6. The partial stacking procedure: (a) the zoom box is defined on a commonmidpoint plane; (b) expanded view of zoom box together with definition of the offset bin;(c) result of applying partial stack to (b). Traces D, E (which lie in the same bin in (b))and C (which, on the basis of absolute value of offset, also lies in this bin) arestacked together to form trace G. Although no traces in (b) lie within the bincorresponding to trace H, this trace is formed by taking the mean of its non-zeroneighbour traces in (c).DMO. The NMO correction requires a priori knowledge of the P-wave velocity field;however, such information is generally unavailable to the processor. The process ofvelocity estimation or "velocity analysis" entails performing the full moveout correction(NMO + DMO) for a number of different trial velocity profiles ("profile" here refers toa set of time-velocity pairs) and choosing an optimum one based on a certain coherencycriterion. This velocity analysis procedure, summarized in flow chart format in Figure4.7a, is prohibitively expensive from a computational viewpoint since DMO run-timesare typically an order of magnitude larger than their NMO counterparts. We would preferto interchange the order of the DMO and the NMO processes as they appear in Figure4.7a, apply the DMO correction once, and iterate through only the NMO correction inperforming the analysis. Hale (1984) shows that NMO and DMO do not commute,but that there exists a reasonable approximation to the theoretically accurate process ofNMO followed by DMO, namely an approximate NMO correction, followed by DMOand a subsequent residual NMO correction. Conceptually, residual NMO is equivalentto removing the approximate NMO, then performing the true NMO correction. Thissuggests a practical scheme for velocity analysis (Figure 4.7b).Of the many coherency measures proposed over the last twenty years for velocityanalysis, the "semblance" criterion (Neidell and Taner, 1971) is the most commonlyused by the exploration industry. Basically, the method involves fitting a set of normalmoveout hyperbolae to an input CMP gather. Unfortunately, it is unsuitable for use onSBC18, and may have limited application in deep crustal reflection processing in general.There are several reasons for this. The signal-to-noise ratio is typically very low in thedeep crustal regime, so the method encounters difficulties in event detection. Also, thevelocities are sufficiently high that very little moveout is observed over the spreadlengthstypical of most deep crustal experiments and there is an ambiguity in velocity resolution.In other words, all the deep events appear "flat" over the range of observation. Yet82 approximateNMOpick a trialstacking velprofileNMO11111■■•••■DMODMOpick a trialstaddng velprofileaPPlYcoherencycriterion NMO aapplycoherencycriterion  choose finalstacking velprofile (b)choose finalstacking velprofile(a)Figure 4.7. Velocity analysis flow charts. (a) theoretically rigourous but computationally expensiveprocedure; (b) computationally efficient scheme that approximates the procedure in (a).another problem is the fact that deep reflectors typically lack substantial continuity, andas such, may not be detected by all the source-receiver pairs within a CMP gather.Given the limitations of semblance, we have chosen to estimate velocities by meansof the "constant velocity stack" (CVS). This method entails the simultaneous analysis ofa series of test stack panels. Each panel is created by first performing the residual NMOcorrection using a constant trial velocity (Figure 4.7b), then stacking (see, for example,Yilmaz, 1987). The panels are displayed side-by-side on the graphics monitor, and thevelocities chosen simply on the basis of the optimum stack. By performing the CVSanalysis at regularly spaced intervals along the line, we can account for lateral velocityvariations.Having obtained a set of stacking velocity profiles along the line, the question remainsas to their physical interpretation. When the spreadlength is small compared to the depth,the reflection event moveout for a horizontally-layered one-dimensional earth is governed83by the rms velocity, V,„„„ given byV,.2„„ (t) = I v2 (u) du^ (4.10)0(e.g., Yilmaz, 1987). Of course the situation with real data is much more complicatedthan the simple model used in their analysis, but to a first order approximation, we canconsider our set of stacking velocity profiles to be a measure of the RMS velocity fieldalong the line.4.3 The DMO/velocity analysis processing streamThe theoretical and practical considerations discussed in this chapter were incorpo-rated into our DMO/velocity analysis processing stream (Figure 4.7b). The input datasetconsisted of static-corrected CMP gathers. We constructed a single velocity-time profilerepresentative of the regional velocity field, based on velocity information acquired fromthe preliminary processing. An approximate NMO-correction was then performed for theentire line using the ITA pre-stack module "NMO2". This module was used to performall NMO corrections in the subsequent processing, as well. It should be noted that thealgorithm automatically mutes portions of the dataset that are NMO-stretched beyonda default threshold value (for a description of the phenomenon of NMO-stretching, seeYilmaz, 1987).Next, we performed the partial stack. We selected an offset bin width (Figure 4.6b)of 200 m (the nominal offset increment observed in a CMP gather) and performed thepartial stack over an offset range of —8000 m to +8000 m (this offset range was modifiedappropriately for the roll-on and roll-off sections of the line).Next, we applied DMO using the ITA poststack module DMO2F. The algorithmsorts the partially-stacked CMP gathers to the common offset domain before proceedingwith the DMO correction. Since it allows the specification of a minimum velocity, V„ ii„,84the algorithm effectively acts as a dip filter, excluding all dips greater than 2/ 14nin (seeequation (4.7)) from the analysis. Hence, we hope to benefit from the removal of any(unaliased) coherent noise whose common offset signature is of a steeply-dipping linearnature. Because of the large computational expense and the fact that the DMO correctionis not significant at later times, only the first five seconds of data were input to theroutine. The DMO correction was performed piecewise, since the algorithm could notprocess more than (approximately) 250 CMP gathers simultaneously. To avoid any edgeeffects that might be produced by the DMO algorithm, we allowed an overlap of 25 CMPsin constructing these input data segments. Even operating on a single truncated dataset(i.e., 250 CMP gathers, 0-5 sec), the algorithm required roughly 8 hours of run-time.The approximate NMO correction was then removed by use of the prestack module"RNMO", and the CVS velocity analysis performed. Each test stack panel consisted of50 midpoints. The analysis was repeated at 1.5 km intervals along the line to account forlateral velocity variation. The results obtained from noisy sections of the line, particularlybetween midpoints 4400 and 5800, were considered unreliable and were not used inconstructing the final stacking velocity model. We noted that the DMO process actuallydegraded the stack quality along particularly crooked sections of the line. In these regions,velocities were estimated using only NMO correction. Below about 5 seconds, we notedthat the quality of stack was insensitive to the choice of stacking velocity. A similarobservation was made in the preliminary processing (Hostetler, (1989)). As a result, wedid not perform a detailed velocity analysis on the deeper portion of the dataset; rather,we used the stacking velocity information available from the preliminary processing.4.4 Data results—stacked sections after DMOGenerally speaking, application of DMO yielded modest improvement. An exampleof a significantly enhanced dipping feature near the western edge of the line is displayed85in the stacked section of Figure 4.8b. For purposes of comparison, we show thecorresponding portion of Western's final stack in Figure 4.8a. The improvement in theimaging of the east-dipping reflector is attributable to the DMO processing, and not torefraction statics, since the feature was barely visible on the brute stack (the brute stackprocessing flow is described in Section 3.5).On the east side of the Fraser Canyon, DMO has apparently succeeded in providingan image of the Pasayten fault, a northeast-dipping thrust fault of regional scale. From atectonic viewpoint, this represents one of the major accomplishments of the reprocessing(Chapter 8).86CMP bin no. (x10) W— E270^550^850^1000^15750.40.81.21.62.02.42.83.23.64.04.44.80.00.40.817C1.2(1) 1.62.02.4cts>"2.8O 3.2Op 3.64.04.44.8Trace sequential no. W20 40 60 80 100 120 140 160 180 200 220 240DATA:PERZ.CROSSNESTERN.STK;2DATA:EPERZ.DM0]270_1575.STK;3(a)^ (b)Figure 4.8. Comparison of Western stacked section and our section after application of DMO. (a) Western final stackedsection near west edge of line. (b) Our result after application of DMO (otherwise same processing sequence as brute stack).Note the enhanced continuity of dipping events (white boxes, (a) and (b)) in our result.Chapter 5CROSSDIP CORRECTION5.1 IntroductionUp to this point, our analysis has been based on the assumption of a straight lineacquisition geometry. Central to this "pseudo-two-dimensional" treatment is the conceptof the CMP bin. Obviously the many-to-one mapping, through which several scatteredmidpoints are assigned to the same effective midpoint for the purposes of subsequentprocessing, will impair the quality of the output stack compared to its true 2—D counterpart(i.e., the stack we would have obtained had the line been straight). Two questions requireaddressing: first, how might we compensate for the error introduced by the CMP binningapproach; and second, having performed such a correction, is it possible to exploitthe line crookedness to provide three-dimensional information about the subsurface?Before seeking the answers, we must understand the principal error source, the reflector"crossdip". Crossdip refers to the component of dip that is perpendicular to the slalomline.In the first part of the chapter, we present the crossdip correction in the context of thegeneral 3—D traveltime expression that we derived for a crooked-line survey conductedover a single constant-velocity dipping layer overlying a halfspace. Then, we present amethod that we have developed for estimating the size of the correction. Finally, wedescribe the incorporation of the crossdip correction into our processing stream.5.2 The 3—D CMP bin traveltime equation for a uniformdipping layer over a halfspaceIn order to quantify the midpoint scatter in a direction perpendicular to the slalomline, we define the the "transverse offset" Y (Figure 5.1). In the case of a constant velocity88dip direction(pure crossdip)bin centrex(profile direction)midpoint^I I Y = transverse offsety (direction of midpoint scatter)(a)^ (b)Figure 5.1. The crossdip correction. (a) Plan view of a CMP bin. Midpoints lying within the bin arescattered in the y-direction; the scatter is quantified by the "transverse offset" Y; (b) Cross-sectionalview. A simple geometric argument gives rise to the crossdip correction (equation (5.1)).medium, Lamer et al (1979) calculate the correction for a single reflector exhibiting purecrossdip (i.e., no inline dip). They assume that processing to the stage of NMO-correctedCMP gathers reduces all traveltimes to those which would have been measured in a truezero-offset experiment (source and receiver coincidentally located at the midpoint). Thencompared to its counterpart measured at the bin centre tc (subscript "c" is a mneumonicfor "bin centre"), the zero-offset reflection time t associated with a scattered midpoint isdelayed by an amount AT given byAT — 2 sin C YV(5.1)where C is the angle of crossdip and V is the velocity (Figure 5.1).Generalizing their argument to a multi-layer model (uniform layers, arbitrary cross-dips, no inline dip), they show that the appropriate delay may be obtained from equation(5.1) by replacing V with the velocity of the uppermost layer, and C with the angle ofemergence of the normal incidence ray (measured from the vertical). In either case, the89implication is that the traveltime perturbation due to crossdip is linear in Y:t=tc-FpY^ (5.2)for some "crossdip parameter" p.Equation (5.2) suggests that the crossdip correction might be performed by stackingNMO/DMO-corrected CMP gathers along linear trajectories in (Y-t) space. Such aprocedure is readily implemented using the existing ITA software (Wang, 1990). The ITAmodule "SLNR" performs the conventional "slant stack" filtering (e.g., Yilmaz (1987))by summing input gathers along linear paths r in (X-t) space given byr = to aX , (5.3)and placing the output result at time to . Here, X denotes source-receiver offset, to is thetwo-way traveltime measured at zero source-receiver offset and a is some specified slope.From equation (5.2), we wish to perform the analogous summation in (Y-t) space. Thismay be accomplished simply by first writing the transverse offset into the ITA trace headerword that conventionally contains source-receiver offset information, then running SLNR.Because of its ease of implementation, a crossdip correction based on (5.2) isattractive from a practical viewpoint. Unfortunately, the simple geometric argumentused in deriving equations (5.1) and (5.2) does not account for the presence of an inlinecomponent of reflector dip; further, it ignores any variation in source-receiver azimuthfor a set of midpoints lying within a particular bin. Along many portions of SBC18, weanticipate dip components in both the inline and crossline directions. Furthermore, thecrookedness of the line results in a wide range of source-receiver azimuths.In order to assess the validity of applying the proposed simple crossdip correction,we consider a three-dimensional model consisting of a single dipping reflector embeddedin a medium of constant velocity V. Despite the obvious oversimplification of the model,90we hope that the insight gained from the present analysis will carry over to the real worldsituation. In Appendix A, we derive the reflection traveltime equation for a crooked-lineCMP gather. Here we present the result with reference to Figure 5.2. For compactnessof notation, we define.\/1 + tan2 I + tan2 C ,^ (5.4)anda- tan /cos p + tan C sin p ,^(5.5)where I and C are the angles of inline dip and crossdip, respectively, and p is the source-receiver azimuth. Next, we define the "crossdip slowness" p:2 tan C^P = V^7Then the reflection traveltime t associated with an arbitrary midpoint is given by8 )2^t 12 = (tc + pY)2 + B2 (1 — (—^ (5.7)V2^7where B is the source-receiver offset and tc is the zero-offset two-way traveltime measuredat the bin centre (Appendix A).An identical expression (i.e., equation (5.7)) was derived independently by WeizhongWang (personal communication, 1993), who is using it to develop a DMO procedure moresuitable for crooked line processing than the conventional 2—D algorithm.Note that in the limit of zero crossdip, for a source-receiver azimuth along profile,equation (5.7) reduces to the standard dip-moveout equation (cf. equation 4.2)2tit^t2^B ^2+ v2 (COS^, (5.8)a result which is independent of the transverse offset. In the limit of zero inline dip(source-receiver azimuth again along profile), we have2ti2 = (t, + pY)2 +V2^ (5.9)(5.6)91shot 1direction of midpoint scatter)o = midpointB = source-receiver offset!p source-receiver azimuth(a)Fig. 5.2: The model assumed in deriving equation (5.7). (a) Plan view. The slalom line is coincident with the x-axis and the CMPbin centre is located at the origin. (b) Three-dimensional view of the earth model. The uniform dipping layer over a halfspace is definedin terms of its perpendicular distance from the origin, d, the layer velocity, v, and the angles of inline dip, I, and crossdip, C, defined in the figure.normal incidence raypath, two-waytraveltime to = 2dN(b)where p simplifies toPcross—2 sin CV(5.10)Considering equation (5.9), we see that the application of standard NMO has the effectof reducing the reflection traveltime t to the "incorrect" zero-offset two-way traveltimeto' given byto = (tc PcrossY) • (5.11)The residual error in zero-offset traveltime is in agreement with the result of Lamer etal (1979) (equation (5.1)).Returning to the general 3—D situation (equation (5.7)), we note that all dependence onthe source-receiver azimuth is confined to the second term in the equation, the "moveout"term. For a typical CMP bin along SBC18, we might assume that —15° p 15° definesa "reasonable" domain for the source-receiver azimuth. If the crossdip and inline dipangles both vary between 0° and 45°, the "moveout perturbation" term (0 2 rangesbetween 0 and 0.54 (instead of extremizing (5.7) analytically, we arrived at this resultiteratively by writing a simple FORTRAN program). Therefore 3—D effects on traveltimemoveout may be described in terms of an increased "effective" moveout velocity Ve (forour region of interest then, V 5 Ve 5 1.5V). In Section 4.3 we noted that the actual P-wavevelocities of the mid to lower crust were sufficiently high that moveout effects were notsignificant for later events (beyond approximately 5 sec). We see here that the three-dimensionality serves to further reduce the amount of traveltime moveout; hence, we donot expect the crossdip effects to seriously hinder our efforts to reduce traveltimes to theirzero-offset counterparts, except possibly at early times. The significant implication is thatthe crossdip effect is essentially manifest as a residual error in the zero-o f set traveltime.A noteworthy corollary to this observation is that the crossdip correction, in contrast to93the NMO and DMO processes, may be significant for late times. On the basis of theseobservations, we feel that we are justified in correcting crossdip effects, at least to firstorder, by application of the slant stack.Having ascertained that a first-order crossdip correction may be obtained through useof the slant stack, we now address the second of the two queries presented in the chapterintroduction, namely the issue of whether or not knowledge of the crossdip parameter pmay be used to provide information about the true 3—D structure. As a general statement,quantitative estimates of true (3—D) reflector dip angle would be unreliable. It is onlyunder very restrictive circumstances that the simple 3—D model (Figure 5.2) adequatelyrepresents the real earth situation, and even then, severe crossdip can adversely affect thesuccess of the calculation. In Appendix B we show that for a range of modest crossdipangles, the inline dip component may be directly measured from the seismic section. Insuch a case an estimate of true dip, which requires knowledge of both orthogonal dipcomponents (crossdip and inline dip), may be obtained. In this appendix, we perform asample calculation for one of the shallow reflectors associated with the Pasayten fault,10 km to the east of the Fraser Canyon.5.2.1 Applying DMO before crossdip correction: synthetic testsIn order to test the validity of cascading DMO and the slant stack crossdip correction(equation (5.2)), we wrote some FORTRAN code to generate 100 synthetic crooked-lineCMP gathers based on equation (5.7). We chose the midpoint spacing, the number oftraces per gather (i.e., the CMP fold), and the source-receiver offset increment within asingle gather based on the corresponding SBC18 nominal values. To simulate midpointscatter, we synthesized transverse offset values using a random number generator (zeromean, standard deviation = 200 m). We generated a similar set of random numbers tosimulate a spread in the source-receiver azimuth (zero mean, standard deviation = 15°).94We created a reflecting interface by specifying a normal distance to the first midpointbin centre of 5000 m. We set both dip components equal to 30° and assumed a velocityof 5000 m/s.In our first test, we performed a crossdip correction without application of DMOby slant stacking NMO-corrected gathers (NMO correction was performed using thetrue medium velocity). A satisfactory result was obtained using p = 2 x 10-4 , whichcorresponds to a crossdip of 30° using the simple relation given in equation (5.1). Hopingthat DMO would improve the result, we performed NMO followed by DMO before slantstacking. However, the application of DMO had a deleterious effect on the stack quality;presumably this was because of a violation of the 2—D assumptions which underlie themethod. On the other hand, after running tests using different earth model parameters,we found that applying DMO actually improved results when the inline dip was muchgreater than the crossdip.Therefore, the question of whether or not to include DMO in the crossdip correctionstream appears to depend on the severity of the crossdip. Of additional interest is thefact that the dip measured on the synthetic stacked sections after crossdip correctioncorresponded approximately to the inline component of dip, an observation rooted inintuition, and moreover one which is in harmony with the investigation carried out inAppendix B.5.3 Crossdip parameter estimationThe "constant slowness stack" (CSS) provides a straightforward approach for esti-mating the optimum value of crossdip slowness p. Operating in complete analogy to theconstant velocity stack (CVS) described in the previous chapter, the procedure is sim-ply implemented using the SLNR module, and has been used in previous crustal scalecrooked line processing studies (Wang, 1992; Kim et al., 1992). As in the CVS case,95the optimum parameter choice is often ambiguous. In this section, we describe a methodwe have developed for determining p that operates on NMO-corrected CMP gathers. Itis based on the work of Key and Smithson (1990), who have devised a new methodfor velocity analysis which is based on the eigenstructure of the data covariance matrix.Compared to the traditional method of semblance, their procedure offers enhanced res-olution of events closely spaced in time and velocity. Moreover, it offers robustness inthe presence of both low S/N environments and static shifts.We begin by considering a coincident source-receiver pair at the bin centre (zerotransverse offset). We assume that a crossdipping reflector gives rise to a signal centredat time t, on the associated zero transverse offset trace (we assume here the existenceof a wavelet of finite duration). We postulate that the reflection signal on the ith traceis delayed by an amount= PYi (5.12)compared to the corresponding signal measured at the bin centre. Here, the transverseoffset Yi has been subscripted to emphasize that it is a trace-specific quantity.We consider a narrow time window comprising N time samples, whose duration ison the order of the Klauder wavelet, centred on the linear trajectory or "search path"ti defined byti = t, . (5.13)By following or "tracking" the signal along the trajectory (equation (5.13)), we maydecompose each data trace ri(t) into its signal and noise components, s(t) and ni(t) overthe time window of interest:ri (t) = s (t)^ni (t) .^ (5.14)96We have omitted the subscript in writing the signal term to emphasize that we areassuming that the signal component is common to all traces in the gather.The procedure entails combing over a range of values for both tc and p, and findingthe search path that best tracks the signal according to some coherency criterion. Hence,we are engaged simultaneously in a task of crossdipping event detection (finding tc) aswell as crossdip slowness resolution (finding p). Of course over the entire length ofthe data trace, we anticipate the presence of many crossdipping interfaces. The crucialassumption is that at any fixed value of zero transverse offset time te , there exists onlyone signal associated with a unique crossdip slowness. In other words, we assume thatthere are no intersecting crossdips for a given value of tc. This assumption may beviolated in complex geological environments.We associate each trace with a different random variable and regard the traceamplitudes as realizations of these random variables which we group into a 1 x Mvector r = (ri, . . . , rM). Here the re's denote the random variables for each trace and Mis the total number of traces in the CMP gather. Proceeding in an analogous manner forthe signal and noise components, we write s = (s, . . . , s) and n = (ni, . . . , nM) wherer=s+n . (5.15)In practice, Key and Smithson (1990) suggest stacking several adjacent traces along thetrajectory given by (5.13) in order to reduce run-time and to increase the S/N, therebyreducing the row dimension of r, s and n from M toThe "covariance of ri and ri", Rid, is defined byRig = E [( ri — E hi) (ri — E [rip] , (5.16)where EN denotes the expectation operator. The hi x M I data covariance matrix R maybe formed by taking expectations of the outer product of r and rT. If we assume that9712 —^ V A•— Aff — 1 z—d si=2(5.19)both signal and noise are zero mean with variances as2and ant respectively, that there isno correlation between signal and noise, and further that the noise is uncorrelated fromtrace to trace, then from equation (5.15) we haveR = E {rTr} = 4( + onI , (5.17)where I is the identity matrix and ( is the matrix whose elements are identically equalto one. The largest (major) eigenvalue of R, Ai, is equal to Nrcrs2 +v.2 (there appearsto be an error in the paper of Key and Smithson (1990) with regard to the size ofthis eigenvalue), and the smallest (minor) eigenvalue is an2 , of multiplicity Ai-/ (i.e.,A2 . . . Am, are equal to an2).Of course in our statistical formulation there is no way of knowing the values of thetrue covariance elements, but we may estimate them nonetheless according to1=  Vr.n r?'N n=1(5.18)where [*] denotes an estimate, N is the number of time samples per trace within thewindow of analysis, and re is the nth sample within the window of the kth trace.We may estimate the noise variance by taking the average of the minor eigenvaluesof R, our numerical estimate of the covariance matrix:We may then estimate the signal variance byM' = A 1 — Qn .^ (5.20)If there is a strong signal present along the trajectory defined by fixed values oft, and p, then we expect a relatively large value for the signal variance. The question98remains of how we might exploit the eigenstructure of the data covariance matrix toyield an optimal signal-noise discriminant appropriate for use as a coherency measure.A measure of the signal-to-noise ratio s/n is provided by forming the ratio of the signaland noise variances:sln = Qn^ (5.21)Key and Smithson (1990) define the "covariance measure" Cc to be the product of thesignal-to-noise estimate sin and a weighting function We defined by(Wc= N In (5.22)Then from equations (5.20)—(5.22), we have(Cc = NAV Inm,E ith^) )Li )^7a..-i i:i=2 Ai'—Til_—_i E XiCM'H Aii=1M'(5.23)We have written a program which computes C c according to (5.23) for a range of trialvalues of p and tc. Because of the large dynamic range associated with the covariancemeasure, we have followed the suggestion of Key and Smithson (1990), and have appliedan AGC gain to the input CMP gathers. We used the subroutines "TQLI" and "TRED2"of Press et al. (1986) to compute the eigenvalues of our estimated data covariance matrix.Best results were obtained using a time window comprising 35 time samples. In orderthat such a window encompass only the Klauder wavelet, we resampled the input CMPgathers using a sampling interval of 0.008 s. We used an increment of 0.03 s in searchingtc , and a slowness search increment of 1 x 10 -5 s/m. For 60—fold data, we found that a99partial stack obtained by summing 6 neighbouring traces provided acceptably short runtimes (-8 minutes per gather for 0.8 5 t, 5 4.5 s and —1.3 x 10-4 < p < 1.3 x 10-4 s/m).Because we were using an estimate of the covariance matrix, the smallest eigenvalueswere often very close to zero. We found it necessary to add a small positive term(0.01 was typically used) to the denominator of the argument of the natural logarithmin equation (5.22) to ensure stability in the computation. We used the ITA interactivevelocity analysis module "VANMO" to produce colour contour plots of Cc in p—ta space.5.3.1 Algorithm testingWe tested the "covariance algorithm" extensively on synthetic CMP gathers contain-ing crossdipping events which we created using the algorithm described in Section 5.2.1.We varied both the signal-to-noise ratio and the amount of inline dip.We present the result of one such test in Figure 5.3, where we have generated twosignals, each associated with a single crossdipping interface, and superpostioned them ona single CMP gather. The first corresponds to p = —4 x 10 -4 s/m, tc = 1.6 s, and thesecond to p = +4 x 10-4 s/m, tc = 3.2 s (no inline dip). We added random noise to theCMP gather and sorted to transverse offset before proceeding with the covariance analysis.Unfortunately, the VANMO software does not display the colour scale alongside the plot,although we know from the documentation that it is a logarithmic one. It is evident fromthe figure that the algorithm has detected the two signals and correctly resolved thecrossdip slownesses. Nevertheless, the peak associated with the later event, whose signalstrength is substantially weaker than its earlier counterpart (even after AGC), is barelyvisible. Aside from illustrating the success with which the algorithm is able to detectsignal in a noisy environment, this example serves to illustrate a problem associated withthe display of the covariance measure because of its large dynamic range. Of course it ispossible to apply a gain function, such as AGC, to the display itself, although there may be100great subjectivity associated with such a process. The display problem notwithstanding,the algorithm generally yielded encouraging results in the synthetic environment.Unfortunately, the covariance algorithm produced disappointing results when weapplied to it to real data. The undershoot processing sequence described in Chapter6 entailed binning along a series of slalom lines that cut through the midpoint scatterin the vicinity of the Fraser Canyon. From the several short profiles we created in theE-W direction, we were aware of the presence of a dipping reflector at approximately3.6 s. Results of the constant slowness stack tests that we performed on the E-W profilessuggested that there was no significant crossdip component. However, as part of theanalysis, a slalom line was constructed along the direction of regional strike, essentiallythe N-S direction (the CMP bin map is presented in Figure 6.7), and we expect that theinline dip observed on the E-W sections at 3.6 s gives rise to a crossdip on the N-Sline. The associated crossdip slowness is equal to the (readily measurable) time dip onthe E-W stacked sections, namely —1.3 x 10 -4 s/m (examine Figures 7.6b-d near 3.6s). We performed a constant slowness stack analysis on the N-S line, and determinedthat slant stacking using p = —1.0 x 10-4 s/m provided optimum reflector continuity at3.6 s (compare Figures 5.4a and 5.4b). Hence, there is general agreement between theoptimum crossdip correction and the observed time dip on the E-W profiles.Figures 5.5 and 5.6 show the result of applying the covariance algorithm to twoCMP gathers along the N-S line, where we tested slowness values on the interval—1.6 x 10 -4 < p < 1.6 x 10-4 s/m. The gather displayed in the first of these figurescorresponds to trace 101 in the stacked sections of Figure 5.4, while the gather shownin the second figure corresponds to trace 45. Note that the algorithm appears to have"correctly" resolved the crossdipping feature in the first of these figures, but not in thesecond. Yet from Figure 5.4 we know that the crossdip correction is significant in thevicinity of both the midpoints in question. We feel the poor results are due to an error101transverse offset (m)^-0.0005^ 0.0005-200^ 200^crossdip slowness (s/m)^v. 0input CMP gather^ covariance plot(sorted to transverseoffset)Fig. 5.3,, Covariance analysis for a synthetic CMP gather. Two synthetic crossdipping eventsare embedded in the noise, one at t c =1 .6 s, p=-0.0004 s/m (event A), the other at t, =3.2s, p=+0.0004 s/m (event B). The algorithm has succeeded in correctly resolving bothevents in p-t c space, although the peak corresponding to event B is barely visible on the plot.AGC scaling of the righthand panel would help better highlight this later peak.toa.(q)^(e)8 • P0'b9'62'68'2b • 20'29'T2'T8'0• 00.0 02T^OT^08^09^OP^02(9's •pu)sisAleuE eouupencoui pesn lupdpse(s's .61d)soisuu eauupencoU! pesn lu!odp!w02^00^08^•'^OP^02(e)^(o)^(a)3•-Mou leRuenbas.peoueque Agueolpu6p ueeq sey s 9•6Jeeu Aruiwoo .101381108 *LIJ/S 1.900*9 Jo sseumois clIpssolo e 6wsn uogoenoo Opsson lop uopes ewes (q) •s 9.EmeuMine pessnoolep (An eloN •(Alengoedsei 'p-q 9 L se.m6w 0l Bu(puodsenoo) seu!I Aft-3 !o smod uopoesiewi emo!pui wag jodol le (a) pue (0) 1g) smonv •pencide ueeq seu uogoauoo Opssalo oN^woleis s-N woad uopes peNouis (e) les Eunqdin model specification. The left panels in Figures 5.5 and 5.6 show the CMP gathersafter sorting to transverse offset. Note that there is no obvious linear dipping signatureassociated with the the energy near 3.6 sec. In fact, over the entire line, very fewcrossdipping events displayed continuity on a length scale representative of the rangeof transverse offsets typically observed within a single CMP gather. Nevertheless, thecrossdip correction obviously enhances the image of the reflector in a "bulk" sense, ascan be seen from a comparison of Figures 5.4a and 5.4b.We performed the covariance analysis on many CMP gathers along the main SBC18profile and found, without exception, that the constant slowness stack gave a more reliableestimate of crossdip slowness. In spite of the promise it displayed in the syntheticenvironment, the covariance algorithm was deemed unsuitable for inclusion in the SBC18processing stream.5.4 The crossdip correction processing streamThe first step in the crossdip correction process is the calculation of the transverseoffset. We wrote a program to compute the transverse offset for a series of input CMPgathers. In designing the algorithm we considered the SBC18 line to be composed of twodiscrete segments separated by the Fraser Canyon, a western half essentially oriented inthe E-W direction, and a (nominally) eastern half principally oriented in the N-S direction(Figure 1.1). We applied the program separately to these two portions, choosing southand east as the direction of positive transverse offset in the analysis of the (nominally)western and eastern segments, respectively.After computing the transverse offset, we performed the CSS analysis in piecewisefashion, operating on 180 NMO-corrected input CMP gathers at a time. We used acrossdip slowness window defined by —1.3 x 10 -4 < p < +1.3 x 10-4 s/m and aslowness increment of Ap = 1.0 x 10-5 s/m in running the ITA prestack module "SLNR".104trace sequential number^crossdip slowness (s/rn)10^20^30 -0.00016^+0.00016covariance plot^covariance measure(normalized to one)Fig. 5 ,5, Covariance analysis applied to a CMP gather extracted from the N-8slalom line near the Fraser Canyon. The algorithm appears to have correctlyidentified the crossdipping event at 3 6 sec.Input CMP gather9::>" 2.46 2.80.00.4-0.81.2-6, 1.62 2.01— 3.23.64.04.44.8-covariance plotInput CMP gathercovariance measure(normalized to one)crossdip slowness (s/mltrace sequential number10^20 -0.00016^+0.00016Fig. 5.6, Covariance analysis applied to a CMP gather extracted from the N-Sslalom line near the Fraser Canyon. The algorithm does not detect anycrossdipping event near 3.6 sec. Compare with Fig. 5.5,Assuming a homogeneous medium of constant velocity 6000 m/s and no inline dip, thisslowness window maps to a range of crossdips —23° < C < 23° (see equation (5.1)).Each output CSS file consisted of 27 stacked panels (one panel per slowness), witheach panel containing 180 traces. Unfortunately, we were unable to pick the slownessesinteractively using the graphics monitor due to limitations in the ITA plotting software,so we produced hardcopies of the panel tests using the 36" plotter. From these papersections, we determined the set of slowness-time profiles that gave rise to the optimumstack.5.5 Data results—stacked sections after crossdip correctionThe crossdip correction significantly enhanced continuity of reflections in many areasof SBC18. In general, the correction was not very important beyond approximately 8s, a statement attesting to the essential flatness of the lower crustal fabric. Figure 5.7adisplays a portion of the brute stacked section near the western edge of the line. Figure5.7b shows the same section after application of crossdip correction (otherwise sameprocessing sequence). For the event at 2.0 s, the improvement in both reflector strengthand continuity is quite impressive (here, a crossdip slowness of 8 x 10 -5 s/m was usedin performing the correction). As well, subtle improvements may be noted elsewherein the figure.107two-way traveltime (s)ry -4 N 4-▪ ) 0 cn k 0 w 6:1 1.1) -40) O0) O N CDo zIN3 O O 4s•AJ 0 CD CA CD O O OST).O-D•CO^A^CD^V.^N^CO^Jz,NN 03^N„TWINIM _ AIRWIPIIIMFITIMMEMENIMPIIIPOP7i'V531ti8 0 /4 %• )Z g 53CDo^01.-•- 2.) •= CD -0 (15. P--oOCTCD^0CL cn N o3 3 E3SD CD (/) CnCD gp CLN^S1)0S:U 0 o8 a30 a) 0.aro o0 R• - o ojco Oco •-•- ocn ca,o03 '4-o 22,^7-cp 6--=71 ""hX 0Q. 3(i)-1 CTCD (D CDCO CD sp5'co -o= -o 5/2.(1-^.- CDfl'OSD CL C CDcnre,CO CDia) 00 wO COco cn 0-0 •Z(7) 0 ocr) (I)COO)0) ca.0 C:) 0•0OCDCD 0O.-41CO 0 OChapter 6PROCESSING NEAR THE FRASER CANYON6.1 IntroductionIn Chapter 1, we stated that a more detailed subsurface characterization in the vicinityof the Fraser fault figured among our primary research objectives. Results of the contractprocessing revealed apparent mid-crustal continuity of reflectors across the fault zone,implying that the fault does not penetrate the middle crust. In an effort to clarify questionsconcerning both fault geometry and depth extent, we performed additional processing ofthat portion of the dataset acquired near the Fraser Canyon, exploiting the large degreeof midpoint scatter to yield three-dimensional subsurface information. Predictably, DMOtests yielded disappointing results and no dip moveout correction was applied. Processingefforts were complicated by the incomplete removal of static shifts in the main processingstream (Chapter 3), crossdip effects, and rapid spatial variation of subsurface structurewhich rendered the character of the output stack very sensitive to the choice of binninggeometry.6.2 CMP binningIn order to perform a "pseudo 3—D" subsurface characterization near the Fraser fault,we considered several different binning geometries which cut through the midpoint scatter.During the course of the preliminary processing, Western experimented with severaldifferent bin lengths along this part of the line; it was concluded that exceedingly largebins (-5 km) did not produce satisfactory results (John Varsek, personal communication,1992). We tested bin lengths ranging from 700-2000 m before choosing the binningschemes or "swaths" presented in Figures 6.1-6.7. Unfortunately, ITA does not providean algorithm for plotting the CMP bin maps; consequently, "screendumps" were used109in the following result presentation (midpoints, indicated in red, have been multipliedcompared with the displayed station numbers (black)). Details of the plotting conventionare provided in Figure 6.1. Although we have provided approximate distance scales foreach of these figures, it should be noted that the aspect ratios are not precisely 1:1.6.3 Static and crossdip effectsIn Chapter 3 we noted that the weathering layer heterogeneity appeared to beparticularly severe near the western edge of the Fraser Canyon. On our brute stack,reflection horizons in this area lacked the coherency apparent on the section producedby the preliminary (contract) processing, where the statics calculation was performedsimultaneously on the entire line, rather than on the two separate segments correspondingto either side of the canyon. Incidentally, our initial concern that the Western staticsanalysis might have induced false continuity of reflectors across the fault zone (where weanticpate the possibility of abrupt geological discontinuity) was allayed when we learnedthat the parameters chosen for the computation caused very little structural smoothing(Peter Cary and Roger Hawthorne, personal communication, 1993).In Section 3.2.1 we stated that we split the dataset into two segments—one on eitherside of the Fraser River—before proceeding with the refraction statics analysis. Therefore,we anticipate a deterioration in the quality of the statics solution near the canyon due toedge effects. We noted that the near-surface model broke down over the final kilometerleading up to the western edge of the canyon, where the REFSTAT2 algorithm assumeda constant velocity bedrock model (V =5643 m/s). In addition, it is quite possible thatthe spatial sampling in this area was too coarse to permit an accurate analysis of rapidlyvarying near-surface structure (recall that roll-on and roll-off acquisition schemes wereused near the canyon (Figure 2.2)). Reliable estimation of the high-frequency static1105534185.7 2 km0.0217 bin 05591988.9"4 station number55n (without multiplier) -4--,A ' CMP bin number --4.. 78855 (with multiplier of 10)^0Znorthenst748736608Fid.6.1. Main slalom line across Fraser Canyon. Some bin locations in thefigure are obscured by the source-receiver midpoints (dark blue).Fig.6.2. Slalom line (west side of Fraser Canyon).bin fold bin 60000.0) .0.0&I!)13,018.00.00.0northeast60310245580018.0MI3533699.3608679.72 kmOngMECMINMrfacchiubsti rfacti plot605426 .95541871.661.0737.1)—LinorthE-21>eastbind au rfacele tabsu data plot746Fig.6.3. Slalom line (east side of Fraser Canyon).010302.8005420.9fletbin 0 ^o050.055305211.5^_1:rnortheast5534023.5norfacesiubanu rift.. plotEXIT' 1BI1MSIDEbut 600042.8•16 7Fig. 6.4. Southern slalom line (undershoot).141 bin bin 6200.0menuEXITdoteetnkilltoutelserotpontIbexfoldbinsernfullzoom5533993.92 km010330.2700905400.33539779.9frnorthemit<- 1.urfuceteubsurfacc plotFig. 6.5: Central slalom line (undershoot).bin 0 bin fold0 .0605426.95540120,42 kmnonorfhvast74055342E19.0610403.0snrincehntbaurfnce plot■ln•bin 33579.262.347.531.75e:irt15.R0.01.0Fig.6.6 Northern slalom line (undershoot).33 ban 0 bin 313bin fold0.057.546.034..523.0[1.50):t ,.• •605193.1155401013.12 km_1‘northtneat7374805534234./6E04010surfacetrubsurfano plotatn#‘,;Fig.6.7. Slalom line in NW-SE direction (undershoot).component is contingent on an adequate distribution of sources and receivers whoserefractor raypaths contribute to the analysis.The fact that the statics computation was based on a two-dimensional earth modelrepresents an additional shortcoming. In September, 1992, shortly after we completedour refraction statics analysis, Hampson-Russell Software Services Ltd. donated theirthree-dimensional refraction statics software "GLI3D" to the UBC Department of Geo-physics and Astronomy. Their iterative statics computation comprises two basic steps:first forward modelling by ray-tracing head waves through the "current" 3—D earth modelestimate (an initial model is specified by the user), then refining the solution by consid-ering the discrepancy between the modelled first break times and the observed picks.The latter objective is achieved through the method of Generalized Linear Inversion (see,for example, Hampson and Russell, 1984). Although the algorithm inverts for a dis-crete set of model parameters defined on a 2—D grid, for the purposes of ray-tracing, thenear-surface model is represented by a series of continuous functions E(x,y), Ddx,y) andVi(x,y), representing the surface elevation, the elevation at the base of the ith layer, andthe velocity within the ith layer, respectively. After each iteration of the inversion, thesefunctions are updated according to the following procedure: First the x-y space is dividedinto a series of rectangular "patches". Then within each patch, a bi-cubic polynomialis calculated which best fits the subset of model parameters lying inside the patch in aleast-squares sense. Across the patch boundaries, these functions are constrained to becontinuous with continuous first derivatives.Because of the smoothing inherent to the bi-cubic spline, the earth model is forcedto exhibit relatively low-frequency spatial variation. This gives rise to a short wave-length discrepancy between the predicted first break traveltimes computed from the final(smooth) model and the actual picks. The remaining high frequency static component118is estimated by a surface-consistent decomposition of this discrepancy (it is simply ap-portioned into a shot and receiver component), so that the final static solution embodiesall orders of spatial variation. We specified a near surface model consisting of a singleweathering layer overlying a bedrock refractor and tested the algorithm on the profileassociated with the slalom line of Figure 6.2. The result is presented in Figure 6.9,while the corresponding result based on our 2—D refraction statics analysis (brute stack)is shown in Figure 6.8. Application of 3—D refraction statics appears to have slightlyenhanced reflector continuity; however we do not feel that the degree of improvementwas sufficient to warrant a complete 3—D analysis in the vicinity of the canyon. On theother hand, inclusion of the 3—D algorithm into the general processing stream wouldlikely have improved results along particularly crooked sections of the profile, althoughtime did not permit the undertaking of such a task.6.3.1 Cascading crossdip and residual statics correctionsIf indeed the refraction-based analysis failed to completely correct for the shortwavelength static component, then we would hope that a subsequent application ofsurface-consistent residual statics would remove any remaining time shifts associated withnear-surface variation. In Section 3.1, we stated that crossdip effects may detract fromthe reliability of the residual statics solution. Conversely, the presence of static traveltimeanomalies may hinder estimation of the optimum crossdip slowness. Nevertheless, wefollow the procedure proposed by Kim et al. (1993) and cascade the two processes,correcting first for crossdip, then applying residual statics.We estimated the surface-consistent residual statics using the method of Ronenand Claerbout (1985). Rather than performing a time-term decomposition of reflectiontraveltimes in the manner of the Western proprietary algorithm MISER, their methodentails choosing the set of shot and receiver statics that maximizes the stack power. Like119CMP bin no. (x10) VV--► E^ground roll5900 6000^63006400 6500 6600 6700 6800DATA:CPERZ.CROSSNEST4.STK;1Figure 6.8. Brute stack corresponding to CMP bin map in Fig. 6.2.Brute stack processing stream is described in Section 3.5.1A C▪ OAAAN• • co Atwo-way traveltime (s)0.3^N^N^N^o-aN^co ^A^isaER 0 0 t m 0 0 0 cn 0cs) o) 7bp 32Cc3" at.O)OzoO(I)(3,T-;(13 133 20. 0.O5cn 8s:). g c;13)Og QCD _ co(7)* oCD to 03• 71 C7CD 0)cn "1:3Ca 5-co 7(4(a) (1)3 9)•NO 71 a)C CDDthe MISER algorithm, it is unable to reliably estimate the long-wavelength componentof the static anomaly but is successfully used in the oil industry for the computationof high-frequency statics. Theoretically speaking, the fact that we are applying bothrefraction and residual statics represents an improvement to the processing flow of Kimet al. (1993), because our analysis accounts for the presence of both long and shortwavelength statics.We performed the residual statics analysis on the crossdip-corrected profile corre-sponding to the swath displayed in Figure 6.2. After considerable testing, we chose tomaximize the stack power for all midpoints on the west side of the canyon over a verylarge time window (2-11 s). The resulting residual statics solution was applied to allprofiles described in this chapter with the exception of the one located on the easternside of the canyon (Fig. 6.3), the latter profile not being associated with any shots orreceivers located on the western side of the canyon.6.4 Summary of processing stream and data resultsThe undershoot processing flow is summarized in Figure 6.10. The creation ofmultiple swaths through the midpoint scatter associated with the undershoot succeededin providing a more detailed characterization of the fault zone (the associated resultinterpretation is presented in Chapter 8). Cascaded application of crossdip correction andresidual statics resulted in a modest improvement in the appearance of the final stackedsections compared with the brute stacks. Figure 6.11 is the final stacked section forthe swath illustrated in Figure 6.2. Comparison of this figure with the correspondingbrute stack (Figure 6.8) reveals, in particular, an enhancement of the continuity of theeast-dipping event at approximately 3.4 s.As a means of calibrating our work against the preliminary processing, in Figure 6.12we present a composite stacked section which we created by merging the final stacks122start with static-corrected,deconvolved shot gathersVchoose slalom line andsort to CMP domainVCVS velocity analysis(no DMO)V 3-D refraction statics testsNMO I brute stack  el.VCSS crossdip analysisVcrossdip correctionVresidual statics(shots and receivers onwest side of canyon only)Vfinal stacked sectionFigure 6.10. Processing sequence used in the vicinity of the Fraser Canyon.for the swaths presented in Figures 6.2 and 6.4. The resulting binning geometry closelyapproximates that used in the preliminary processing. Comparison of our composite stack(Figure 6.12) and the corresponding Western result (Figure 6.13) indicates that essentialfeatures of the reflectivity are present in both sections. Note in particular the strongreflectivity at 5.0 s which appears to be continuous across the fault zone (the reflectiveband also extends onto the section corresponding to the eastern edge of the canyon, whichis not displayed in these two figures), providing a basis for the interpretation of a shallowdepth extent for the Fraser fault.Although the plot scaling has arguably biased the displays in the favour of our result(Figure 6.12), we feel that these two sections are of comparable quality from the viewpointof reflector continuity, this in spite of our more elaborate processing sequence. Ronenand Claerbout (1985) state that their residual statics method (i.e., the statics algorithm123two-way traveltime (s)IV^IN). ^.^. ^.^.D m N 0 C.0 Or) D• -n r- 1_1 rrl CA -11 TI •• •coa a; =11CnCO-0 a c-0 c (7,3EO)x. co3 si)CD ^m CDCD wcr 11)CD CD = (1) u)-0 2 _.P- g mCD — (APct) a).•9°7:3 CD •g< CDCD 133 CD 55.a) 51=•• (/)CD aa -50 00oo(t. 0 5•c q."-.a.3.23.64.04.46.87.27.68.0west side of canyon (Figure 6.2)^10-undershoot--southern swath(Figure 6.4)CMP bin no. (x10)^E5900 6000^6308400 6500 6600 6700 6800 100Figure 6.12. Composite stacked section created by merging the final stackedsections for the swaths displayed in Figures 6.2 and 6.4. This binning geometryis essentially identical to the one used in the preliminary processing. Comparewith Fig. 6.13.as8.0undershoot-41^ lo-west side of canyon3.23.64.04.46 kmtrace sequential no.^W^E1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220Figure 6.13. Western stacked section near the Fraser Canyon. Comparewith Fig. 6.12.a6we used in reprocessing the data near the Fraser Canyon) is more robust in the presenceof noise than the standard "time-term decomposition" algorithm based on the work ofWiggins et al. (1976) (i.e., the algorithm used in the contract processing); however,experience has shown that the latter method often produces "better" results on noisy data(Peter Cary, personal communication, 1993). We were unable to perform comparativetesting of the two methods because the ITA software does not support a version of thetime-term algorithm. Nevertheless, its inclusion in the Western processing stream hasapparently yielded a satisfactory result in this region, in spite of the fact that the methoddoes not account for reflector crossdip.127Chapter 7 FINAL PROCESSING ANDRESULT PRESENTATIONIn this short chapter, we describe the three final stages of processing—data merging,coherency filtering and migration—and present the output sections.7.1 Data mergingIn Chapter 4, we noted that the application of DMO degraded the stack quality inmany areas along the line, while improving it in others. To create the final SBC18stacked section, we included the DMO version of the stack only for those regions alongthe line where it appeared superior to its "non-DMO" counterpart (stations 60-120 and950-1300). We merged the DMO and non-DMO stacks using the ITA poststack modules"MERGE TRACE" and "MERGETIME". We first performed the time merge, joiningthe upper 5.0 s of the DMO stack with the lower 11 s of the corresponding non-DMOstack. We specified an overlap window between 4.5 and 5.0 sec, in which the two datasetswere blended using a linear weighted taper. Next, we performed the spatial or "trace"merge to join adjacent portions of the DMO and non-DMO stacks. Here, we used thefull 16 s of input data and specified a trace overlap zone of 20 traces over which thelinear weighted taper was applied. All final sections displayed in this chapter have beenmerged in this manner, with the exception of those associated with the special processingnear the Fraser Canyon described in the previous chapter.7.2 Coherency filteringThe low S/N associated with deep crustal profiles presents a problem from the view-point of result presentation. The compressed spatial scale at which the sections aredisplayed often exceeds the resolution capability of the human eye, rendering event de-tection difficult, if not impossible. Automated coherency filtering provides an objective128means of isolating coherent, linear signal from a background noise field, thereby im-proving the display.We used the coherency filtering algorithm of Lane (1991). For a given input point(xo, to), the algorithm computes semblances over a lateral trace window for a range ofapparent slownesses (i.e., time dips). A coherency measure equal to the semblance valueraised to a user-specified exponent is then computed for each time dip, and the traceamplitude at the point is smoothed by averaging the amplitudes over the trace windowalong the direction of maximum coherency. Finally, multiplication of this smoothed resultby the maximum value of the coherency measure yields the output trace amplitude at(xo, to). Additional noise rejection is accomplished by the introduction of a plotting bias.A constant negative value, specified as a percentage of the average absolute amplitudecomputed over the entire dataset, is added to all trace amplitudes. When the coherency-filtered dataset is plotted using the variable area display only (i.e., no wiggle trace), onlyvery large positive values contribute to the plot.Because linear events significantly shorter than the window length are attenuated,we specified a lateral window equal to the shortest length of coherent, linear energyobservable on our final zero-offset stacked section (11 traces). We computed semblancesfor 11 time dips between ± 0.34 s/m , these bounds corresponding to the maximum timedips observable on the final zero-offset section. Based on a visual inspection of theoutput of several algorithm test runs, we chose a semblance exponent of 1.0 (i.e., thecoherency measure was set equal to the semblance) and a plotting bias of —150%. Larger(magnitudes of) plotting biases tended to obscure weaker coherent events, and smallervalues introduced undesirable levels of background noise.7.3 MigrationMigration seeks to restore dipping reflection events to their true subsurface loca-129tions—by shortening and steepening them, as well as by moving them in the updipdirection—and to collapse diffraction hyperbolae. In spite of its largely successful andwidespread use in the petroleum exploration industry, wave-equation migration oftenyields "disappointingly poor results" (Warner, 1987) when applied to crustal datasets.Deep reflection horizons often appear to migrate "best", in a subjective sense, at veloci-ties which are up to 50% lower than the interval velocities derived from an analysis ofthe stacking velocity profiles. Warner (1987) has postulated that the problem is relatedto spurious gaps in reflector continuity on the input stacked section caused by ampli-tude distortion and attenuation in the near surface. Under his hypothesis, the apparenttruncation of a reflection horizon is not accompanied by a diffraction hyperbola, andconsequently the migration algorithm must invent a synclinal reflection to cancel out the"missing" hyperbola, resulting in a "smiley" migrated section. The lateral extent of thesmiles increases with increasing migration velocity and two-way traveltime, so that theproblem is essentially manifest in the deeper portion of the section. In addition, sev-eral more "conventional" problems known to adversely affect the migration process canparticularly beset deep crustal profiles, namely a low S/N, the incomplete removal ofcrossdip effects, and a poorly-determined velocity structure.In short, our final stacked section is not ideally suited for migration. Nevertheless,we have proceeded with the application of a phase-shift migration in the hope of gainingsome information concerning the approximate positioning of reflectors. We used the ITApoststack routine "PSMIG_FAST", specifying full (i.e., maximum) aperture width. Theamount of aperture refers to the effective width, in traces, of the diffraction hyperbolaalong which summation occurs (the migration process entails summing energy alonga hyperbolic trajectory and placing the output result at the hyperbola apex). Afterconsiderable testing, we chose to perform the migration on the coherency-filtered versionof the zero-offset section (no plotting bias was applied). The S/N enhancement provided130by the filtering appeared to improve the result. The zero-offset section was broken intotwo segments, one on either side of the Fraser Canyon, before migration. In order toallow reflectors near the edges of the section to migrate freely, we appended one thousandzero traces to either end of each of the two input segments.We used a single regional velocity function which we derived by considering thespatial average of our stacking velocity profiles. Although ITA supports a phase-shiftmigration algorithm that honours lateral velocity variations, we chose not to use it becauseof the limitation imposed on the number of input traces (such a limitation effectivelyrestricts the aperture width). Because migration algorithms are extremely sensitive toerrors in the velocity structure, several portions of the migrated result display "smiles"characteristic of overmigration (because many of the smiles appear at early times, theymay be positively related to overmigration, and not to the problem associated withapparent reflection truncation which we have described above).Again we emphasize that our present objective is an approximate restoration ofsubsurface reflector geometry. Chun and Jacewitz (1981) present formulae that describethe repositioning of a dipping reflector on a migrated section for a constant velocitymedium. In order to assess the validity of applying the phase-shift migration algorithm,we selected several reflectors that were positively identifiable on both the final stacked(zero-offset) section and its migrated counterpart. We compared the analytical mappingbased on their formulae (assuming a "reasonable" constant velocity) to the output ofthe wave-equation algorithm. In each case, the amount of reflector repositioning wascomparable, suggesting that we are justified in assuming that application of the algorithmprovides a crude sense of reflector repositioning.7.4 Result presentationThe set of stacking velocity profiles (both RMS and interval velocities) and the station131elevations are shown in Figure 7.1 together with the upper 3.0 s of the final SBC18 zero-offset stacked section. The horizontal-to-vertical aspect ratio is 2:1 assuming a constantvelocity medium of 6000 m/s. In other words, events appear "stretched" in the horizontaldirection (this aspect ratio was chosen in order to reduce clutter in the display of velocityinformation). CMP station numbers have been multiplied by a factor of ten in this andin all subsequent figures in the chapter. Note that the "main" slalom line created in theundershoot processing (Figure 6.1) was used to join the eastern and western halves ofSBC18 across the canyon in producing the final zero-offset stacked section. This sectionis displayed in its entirety in Figure 7.2. In order to facilitate visual inspection of thisresult, we have again chosen a 2:1 aspect ratio. The optimal display properties associatedwith the coherency-filtered version of this section (Figure 7.3) permitted the use of a 1:1plotting ratio. Traces in this figure are plotted using the "variable area only" format (i.e.,without wiggle traces). Note the considerable signal enhancement compared with the"standard" display in Figure 7.2.In Section 7.3, we stated that the zero-offset section (Figure 7.3) was split into twosegments, one on either side of the Fraser Canyon, before migration. The two migratedresults are displayed side-by-side in Figure 7.4 (1:1 aspect ratio). In Section 7.3, we alsonoted that these sections appeared overmigrated based on the presence of "smily" artifactsat all traveltimes. For purposes of comparison, we migrated that segment lying on thewest side of the canyon using a velocity profile equal to 85% of the "true" velocity profilethat was used in the migration corresponding to Figure 7.4 (migration using a "reduced"velocity field is commonly performed in the oil industry). We present the result in Figure7.5 (1:1 aspect ratio). This section reveals a somewhat less smily character at early timesthan its counterpart displayed in Figure 7.4. On the other hand, both sections appearto be heavily contaminated by smiles at later times, presumably because of the problemrelated to the spurious gaps in reflector continuity (Section 7.3).132The final stacked sections associated with the various slalom lines created near theFraser Canyon are displayed in Figures 7.6a—g (2:1 aspect ratio). The coherency-filteredversions are plotted at the same aspect ratio in Figures 7.7a-g.133Figure 7.1. Station elevation and stacking velocity information for SBC18 togetherwith upper 3.0 s of final zero-offset stacked section (following page). Both RMS andDix interval (Dix, 1955) velocities are tabulated. CMP bin numbers have beenmultiplied by ten in this display and in all subsequent figures in this chapter. Gap incoverage near the Fraser Canyon is represented schematically by the insertion ofzero traces near CMP station 6400, and again near station 6850. Top panel showsthe western half of the line, including the undershoot. Note that the "main" slalom linecreated in the undershoot processing (bin map in Figure 6.1) was used to join theeastern and western halves of SBC18 across the canyon. Bottom panel shows theportion of the line east of the Fraser Canyon. Horizontal-to-vertical aspect ratio is2:1 assuming a constant velocity of 6000 m/s.ELEVATION (M)- 1300.0700.0100.0ELEVATION (M)1700.0^700.0100.0 ^COP^77 COP^8275 COP^8830 COP^9570 COP^10115 COP^10650 COP^11170 P 1720 COP^12300 COP^12575 COP^13060 COP^13575 COP^14360tin -R115 viNT 1171E v-Rns v-^N7 1 v-Rnis v-^Nt TIME v-13115 v- INT r 1 Ill 2^Rns IN! Tine v RnS v^INT 1 1 rIf V^RMS IN! 1 1 nE V-RMS -INT TIME v-fins - I NT Inc V -RnS V- INT TIME v-RMS V- IN! t Inc v v -^NT t !ME V-RtIS V- INT841 810 010 031 4700 4700 890 5140 5140 BOO 5600 600 B62 5400 5400 831 5200 5200 867 5000 5000 906 5200 5200 1038 5500 5506 960 5500 5500 10435300 5300 1069 5300 5300 898 5000 500010951779251049205360602826888704144319712547503053685.0544661716276195125213257525054705910534261637216170927954045.0059006700617259767817117825263.5550056006000576456869441132T91426615300560058005567007620414587127273354005608620059386013795465021.0865400580063885684703467961671262409657006100630060146744664•12141671210656005700600059635958703320183345409570063006600609971167549265035680345900630066006273733485531645236538406000620060087017663476613140 6740 740 31320910 7170 4638 6350 7288 4982 6500 913 460 6300 7,3 414 6100 6651 4008 6700 7663 4700 6788 B091 4708 6780 6091 3309 6100 62717084471367908187613604034 070 6387 670 6300 7.0 481 7100 0891 4700 6708 9473.012400 1340013000 1320012800126008000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111r r111111111111111111111111111111111001131111110111111111111111111111111111111111111111111111 111.1111111111,11 --2.02.5ant' •^•^wttar vitt- 34:44,21F:'34 II41111111114 i^tr.:1,442:hgatgti,515. *-0.vetc 41.^;t4Mop IIIPP!0.00.51.01. 52 . 02 . 53 . 0/35ELEVATION (M)^ ELEVATION (M)300.01300.0=700.0 -----=^ -----700.0,----1 100 0100.0COP^425 COP^1005 COP^1465 COP^2065 COP^2735 COP^3300 COP^3785W^ >ECOP^5935.71ME V-RMS V- INT TIME V-RMS V-INT TIME 6-any V- INT TIME V-RMS V- INT TIME V-RMS V - INI 1171E v^HMS v- INT TIM v^any V^INT TIME V-NMS V- INT836146834024102516753135900604751675006309671684618212495373945275167502760476120619351676345.6562646526800113716082070287339935167531356006047619364135167.5.46071016554694676317592982477053135607612064135313502267907041660172220573677553356076047619355335652666266747843t 53■6825607604767.5607618673117011178M O4143575358276390670757535934687371036390026141716652474326347765642573359176000610066585642.58687161917704I I I IIICMP BIN NO^800^1000^1400^1600^1800^2000 2800I3200^3400^3800^4000^4200^■ 00^4600^5000^5400^5600^5800^6000^6200^6600^6800 0.00.0 III 1100111111100111100 0010101 1 III 1 11111 111 fill Ell I HIM 0 101101011011001 1110000011100 1 in HIEN1100 1 1 100 1 1 1111 1111111111111111 1 00001101011 11 1 1 0 . 5, .0>.i• 5 ,_,31-412 . 0(__.f)-2.53.00 51.01.52.02 . 53.0. 4zIra0 t...14:,1,F;1^ttli'117'1 i 3.irfit:442141. 434.4, 1'ItAtin5s,firit•V•Ir14.424.1...:^S...A.^- ..vi- if-^ -or:4 srII lloptimffirilivilatti„vim..slmzq'At ' Viligi. 10,-itttili.i-my.^44l?';,S' ^g.34.44::(0."MO Vir•:liS! nigi*.i."4 •,‘..- ,Rr.0;.114trgal•.II,igi kw.'c-4-.....?r,..1,,LXX)WA!'-fre'^';'*.rrso'lit.iq•+Z4 it,t;e1.43.ei III',?;.0.:,1,...v.:i''^.cfri•li, kr61,4114rit'll;;L3...■.'^•..,,,,la:1:46',74V..1,WO-s.c. 1,•fkiira^Nit,.trr17111111111111:'PM.21'_A,LP Z.,,I'$.il.'..wia -ii.3,40.4.3gr,I, b-t=^ f„ 4 -,.T4. 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N, $X^.^41. lek- it^444.14:4.YE ^fr. vi 4. AV IA .4.1"A" f^.1 ^t03/^1/4 14T -^1^4, ,t ,.... .2 1 ry i . ,^._,... -^lz^1,144; ,-Alkh.^"  S ^ce L §iigtsitti2 ,u)114-:-At ,^431.,1-144^44.97,4411.'--^141;ii.NaltrgiiiiiA111.1.2,..4,31i3AMItil11 11M i.44144.14.44-4NI -r•.^-41/21i0ii.5,1w-4,'•At--tg414 .11111143.-1111 lio11111111111„1111e p,o tiiiittgl."..%,^i, .^. f ( 5 1^1<re I. ....i'diec,^ws^ .= ..;.  .1 ^.V11.1 ..- g .4^-1111 ,,,..4..osts'11/14P t4. Zi-•-•-c:0111IIFigure 7.2. SBC18 final zero-offset stacked section (following page). CMP bin foldis plotted as a function of bin number at the top of the figure. Aspect ratio is 2:1assuming a constant velocity of 6000 m/s.13 (0O=—aIncf,Figure 7.3. Coherency-filtered version of SBC18 final zero-offset stacked section(following page). CMP bin fold is displayed at top of figure. Aspect ratio is 1:1 (nohorizontal stretching) assuming a constant velocity of 6000 m/s.13 ?Figure 7.4. SBC18 migrated section (following page). Coherency filteringhas been applied both before and after migration. The final zero-offset stackedsection (Figure 7.3) was broken into two segments before migration--one oneither side of the Fraser Canyon--and one thousand zero traces were appended toeither end of each segment. In an effort to display the two segmentsside-by-side in this figure, we have omitted presentation of those portions of the datasetcorresponding to the zero trace padding on both the east side of the western segmentand on the west side of the eastern segment. Both of the omitted portionsdisplayed little signal, with the exception of a strong west-dipping event located eastof the canyon at 11.0 s. We have schematically indicated the presence ofthis reflector in the figure (boldface dashed box). No undershoot data were usedin performing the migration; the resulting gap in the migrated dataset is indicatedschematically in the figure by an appropriately scaled blank region in the vicinityof the canyon. Aspect ratio is 1:1 assuming a constant velocity of 6000 m/s./40JSFigure 7.5. Result of migration using a "reduced" velocity profile (following page).Coherency filtering was applied both before and after migration. The velocityfunction was obtained by scaling the velocity profile used to produce thefinal migrated section (Fig. 7.4) by a factor of 0.85. Migration was performed onthat portion of the dataset lying to the west of the Fraser Canyon. One thousandzero traces were appended to either edge of the dataset. Compared with Fig. 7.4,this result reveals a somewhat less "smily" character at early times, althoughmany events are likely undermigrated. Aspect ratio is 1:1 assuming a constant velocityof 6000 m/s.Figure 7.6. Final stacked sections produced by Fraser Canyon processingstream described in Chapter 6 (following page). Each of the seven sectionscorresponds to a different slalom line. Inset at the bottom of each section provides aschematic map view of the associated slalom line. CMP bin numbers are referencedto bin maps displayed in Chapter 6. CMP bin fold is displayed at top of each section.Aspect ratio is 2:1 assuming a constant velocity of 6000 m/s. Section (a) correspondsto bin map in Figure 6.2, (b) to Fig. 6.4, (c) to Fig. 6.5, (d) to Fig. 6.1 (i.e., the "main"canyon traverse which is also displayed in the final zero-offset stacked section of Figs.7.1-7.3), (e) to Fig. 6.6, (f) to Fig. 6.7, and (g) to Fig. 6.3.10.011.012.013.014.015.016.00 . 01 . 02.03.04.05.06.07.06.09.010. 0.012.013.014.015.016.01 . 02.03.04.05.06.07.06.09.010.011.012.013.014.015.016.0OIn0 . 05.06.07.08.09 .010.011.011.013.014.015.016.01 . 02.03.04.0SrO3Figure 7.7. Final stacked sections near the Fraser Canyon after coherency filtering(following page). Details of the correspondence between sections and bin mapsare provided in caption of Fig. 7.6. CMP bin fold is displayed at the top of eachsection. Aspect ratio is 2:1 assuming a' constant velocity of 6000 m/s./6645W E' • -'^•,(d) ^„A CCP18.00.01.02.03.04.05.06.07.08.08.010.011.012.013.014.015.016.01.02.03.04.05.06.07.08 .10.011.012.013.014.015.016.06055^155^305^455NW- SE15.01 16.00.02.0• •^.1^• ■• • , •• • A3.04 .05. 06.07.0CCm(1)10.011.012.013.014.01.0Chapter 8 INTERPRETATION8.1 IntroductionVarsek et al. (1993) have provided a geological interpretation of the results ofthe SBC18 preliminary processing (Figure 8.1). Key features of this interpretation areaddressed in the body of this chapter. They include: (i) possible mid-crustal terminationof the Fraser fault based on the apparent continuity of reflectors across the fault zone(trajectory "FFA" on figure); (ii) mid-crustal flattening of the Pasayten fault (symbol"PF'); (iii) correlation of the east-dipping homocline located at the western edge of theprofile ("Insular ramp") with exposed east-dipping thrust faults of the Coast belt; and(iv) the existence of a west-side-down Moho step east of the canyon ("east flank crustalroot"). An alternate interpretation of the western portion of the contract-processed resultis given by Monger and Journeay (1992) (Figure 8.2a). In this chapter, we present arevised interpretation which we have based on the results of our reprocessing.8.2 Surface geologyIn Figure 8.3, we have reproduced the local geology map of Figure 1.4. From westto east the profile crosses: (i) the Late Cretaceous Scuzzy Pluton, a post-accretionarymagmatic arc; (ii) the polymetamorphic and plutonic rocks of the Settler Schist, boundedon the east by the steeply northeast-dipping Kwoiek fault which delineates the boundarybetween the Central and Eastern Coast belts; (iii) Middle and Early Jurassic fine-grainedclastics of the Ladner group (of Methow terrane affinity); (iv) Permian to Jurassic oceanicrocks of the Bridge River terrane; (v) the Fraser fault; (vi) a thin slice of wrench-faultedMethow terrane consisting of Early and Middle Cretaceous fine to coarse clastics of theJackass Mountain Group and Early and Middle Jurassic volcanic-rich fine clastics of the148CENTRAL COAST I EASTERN COASTBELT^BELTFFKFstation 270INTERMONTANE BELTFF = Fraser faultFFA, FFB, FFC - possible trajectories for Fraser faultKF = Kwoiek Creek faultMRF = Mission Ridge faultPF = Pasayten faultRMBD = Rocky Mountain basal detachmentYF = Yalakom faultelo^= dextral strike-slip1). = thrust fault, displacement arrow-side-upW E I NW12Figure 8.1. SBC18 initial interpretation superimposed atop migrated and coherency-filtered section produced by the preliminary processing(adapted from Varsek et al., 1993). Interpretation is based partially on relationship between SBC18 and other Lithoprobe reflection lines inthe southeastern Cordillera. Key features of this interpretation are addressed in the text. Aspect ratio is 1:1 assuming a constant velocity of6000 m/s.Western Coast Belt Eastern Coast Belt1:1 aspect ratio40 576,7:::! GEOLOGICAL CROSS-SECTION4SBC18 vc-.- 14:rr :14:‘42-47(4-7716'-11-(b)Figure 8.2. (a) Geological cross-section and interpretation of portion of SBC18profile west of Fraser Canyon (from Monger and Journeay, 1992). Migrated andcoherency-filtered stacked section was produced by the preliminary processing.Geological cross-section is based on surface mapping east of the profile. (b)Revised cartoon drawn by Murray Journeay (personal communication, 1993),identifying reflectors CB1 and CB2 (Figs. 8.4 and 8.5) with deep roots of theCoast Belt Thrust System ("CBTS" in figure).150Dewndey Creek Formation; (vi) the Pasayten fault; and (vii) Triassic and/or Jurassicgranodiorite of the Mount Lytton Complex (of Quesnel terrane affinity).Varsek et al. (1993) have indicated that the line crosses the intersection of thenorthwest-trending Yalakom fault and the north-trending Fraser fault (Figure 8.1, symbols"YF' and "FF"). However, Coleman and Parrish (1991) claim that the present-daysouthern extent of the Yalakom fault lies approximately 65 km to the north of our line(beyond the northern edge of the map in Figure 8.3), where it is truncated by the Fraserfault; thus, we infer that SBC18 crosses only the Fraser fault at the canyon.83 Result interpretationThe shortcomings associated with crustal-scale migration (Chapter 7) preclude areliable interpretation based solely on the migrated results, in spite of the fact thatthese sections have restored, albeit crudely, the "correct" reflector geometry. Thus, weperformed our interpretation, of which a schematic representation is displayed in Figure8.4, by concurrent analysis of both the zero-offset and migrated datasets, positivelyidentifying coherent events on the former type of section, and gaining a sense of theassociated subsurface geometrical relationships from the latter. For ease of reference, wehave reproduced the coherency-filtered zero-offset stacked section (Figure 7.3) in Figure8.5. Events are indicated on both the migrated and unmigrated sections (Figures 8.4 and8.5). The following discussion of our interpretation proceeds, in a general sense, fromwest to east.The upper crust near the west end of SBC18 is characterized by fairly strong west-dipping reflectivity between 1.0-4.0 s (Figures 8.4 and 8.5, CMP stations 27-300—notethat CMP stations are multiplied by ten in these figures). This observation implies thatthe overlying (presumably homogeneous) Scuzzy Pluton is a shallow feature (< 3 km).Such a suggestion is corroborated by inspection of the regional Bouguer gravity map151Figure 8.3. SBC18 profile superimposed atop local geology map of Monger (1989),reproduced from Fig. 1.4 (following page). Action of migration of events A and Bdefined in Fig. 8.4 is indicated on the figure (symbols A and B, respectively). Studyarea of Grieg (1992) and the immediate area surrounding the SBC18 traverse of thePasayten fault are also displayed (boxes 1 and 2, respectively).122.00' 46' CRETACEOUS ANC/OR TERTIARYCUSTER GNEIS& pepnaUM guirere gas., seta, sandt andAUNUSicNS rnOrnr^and uNnuTlah IC roes, prolatery deuced Ina..ran rower Masc.. and ...b. P5.070,C. and 01Procarnarran rocka,sad ruseuravphosed ur Leta Cretaceous and se., Tad.ry burnr= Garraubkorr. 0et0050 1,W(0 and siartranee schisr Al pert.SETTLER SCHIST" loc. aenc.0.1o. On. Orem. tack andstrcears schht. adn0 M Fraser Rm. oxhide.' gmenscuurg/edoandslone aNde and h..en loanalian, matemnrohnsen in Crate...aIM SLOLLICUN SCHIST: main', papenschur.smae, mat" re euernpuosu,vote/puce phyMe. maw/ voksn,P- and Peet... Nudes" panglernewue,mebnewphosed in Clamor..CRETACEOUSLATE CRETACEOUS111.^(94 oun,U "Taman.. Nahl rscuzzy PLUTON .,',ODLE AND LATE CRETACEOUSRMS. CREEK FORMATAON ol SPENCER SPOOR GROUP'male voter...Chert.prein sandsrane and emplorneralaAIL I: A r ,L + , EARL '''' LA It. CRETACEOUSPASAYTEN GROUP,..77--1.... (a) undifferenfrated sandstone. corOarneuRa. muSA'a. (01 "WINO,'I. .1(N,p. 4 mon • Pad or RASA ,TEN GROUP. ark. co.lornarare, aver55 andi • .^• • I mg., red.. end rut r. 'Wgrna. R.Ve Iarr.s' IN 05PARAYTEN GROUP civolvairr sands... argOn. as Yapped,Pew. Sas anst t, Mayan. Pa.( do is probably a fing7 , 17,8A,lacrs era... a' 'ha Awe, part al rho JACKASS MOUNTAIN GROUPEARLY AND MIDDLE CRETACEOUSJACKASS MOUNTER/GROUP^i Sarum., ..arte, cong..... Nes west at Cfruwanton Far., reen.4 KJ „ip, and nonurearna; 1.301 parr 0 pot.* a Mors ...lent of- -.a- • i PASS VEEN GROUP1111 0uarlz dome (qc6, dmr. (c6, grarrod.. (55) moor irrtrems. rockCSPUZZUM PLUTON), Tonal operas, phasesEARLY AND MIDDLE JURASSICIIIM MAPRISON LAKE FORMATAON oferrnia.re, loudly W., Pews endproctor., local ardlera, conubmenueLADNER GROCE= A.M., Male, OM., Ile as mopped, ...es .10, no,unrs dDave' Almse sanclmone sod cong..... arraa.. ccmoMTUR WO-Thundar Lake seauenoeM OEWONE1 CREEK FORMAT/0N d LADNER GROUP. sandstonemod.; local mak In ..media. vo.anicsTRIASSIC AND,Oli .10RASSIC11.1 Grarn,alente gm. reamer. (GUCCI.). CREEK, PENNASKWK 0 NORSE CREEK BA THOL(THS. DOUGLAS LAKE STOCKrerrodnrete ol MOUNT LYTTON COMPLEX,. . Donee gale., verr....arato and vial 05001000 Po ef IRONT•id .g", . " 1 MASK RAD-0117H and saa.f,Pro.NY ..., maIII", . hEr.ra'an,= Ow. and araniabckle N NOUN!' LYTTON COMPLEX, srna0 <110617COnnerons rn NICOt A GROUPLa eyed rarmu....pat. rod:, amonraokle and 050050 d MOON'LITTON COMPLEX, SiNIN racks an west side d NICOLA Barka,PERMIAN 10 JURASSICRROGE RIVER COMP, Exar.rarte, llama prIk. basalt. Krug carbon., go&serum." Waco,. ...red verfni.kno1111 Low& gInensc/.1 llscoe5 /WI d BRIDGE RIVER COMPLEX, pheft.50002009 phytd. 50501011/. PhInfi* SOPS?*per greenschist-110.1 em0doo5o pact al PROSE PIPER COMPELseined, 50041. actioultre pd." ma, hi...garnet Weer. comma*cohlsinktp concortfanI end ...CAM Ewen la. dykes and sak1.1. Mama. rock local gr.b.1 5 3Figure 8.4. SBC18 revised interpretation based on the results of our reprocessing(following page). Interpretation is superimposed atop the coherency-filtered,migrated section displayed in Fig. 7.4. Geological units, fault surface traces, andterrane linkages are indicated on the figure. Solid hand-drawn lines indicate aspectsof our interpretation which are strongly supported by the data. Weaker inferencesare indicated by dashed hand-drawn lines. Events are identified on both the migratedsection appearing in this figure and the zero-offset section displayed in Fig. 8.5.Aspect ratio is 1:1 assuming a constant velocity of 6000 m/s. CMP station numbersare multiplied by ten in this display.5Figure 8.5. Final zero-offset stacked section after coherency filtering, reproducedfrom Figure 7.3 (following page). Geological units, fault surface traces, and terranelinkages are indicated on the figure (legend is provided in Fig. 8.4). Events areidentified on both the zero-offset section appearing in this figure and the migratedresult shown in Fig. 8.4. Aspect ratio is 1:1 assuming a constant velocity of6000 m/s.(Riddihough and Seeman, 1982), which does not indicate a substantial anomaly in thevicinity of the pluton. On the other hand, these maps reveal a pronounced gravity lowover the Guichon Batholith (--30 mgal) 25 km to the west, a pluton which Ager et al.(1973) estimate to be of considerable depth extent (> 12 km) based on the results of adetailed gravity survey which they conducted across its surface projection.At later times, the zero-offset section reveals a thick sequence of east-dippingreflectors between 6.5-10.5 s (Figure 8.5, events CB 1 and CB2). A similar patternof reflectivity is observed on SBC13, corresponding roughly to the same position alongstrike (Varsek et al., 1993, see Figure 1.1 for line location). These events migrate well tothe west of the western edge of the profile (Figure 8.4, events CB 1 and CB2). Varsek et al.(1993) suggested that these ramping homoclines represent deep levels of the Coast BeltThrust System (CBTS). In a general sense we concur with this interpretation; however,we disagree with their speculation that this ramp contains Insular superterrane material.Refraction studies by O'Leary (1992) and Zelt et al., (1992) suggest that few pocketsof Insular crust have penetrated eastward beyond the Harrison Lake fault, which liesapproximately 50 km west of the western edge of the profile. In collaboration with M.Journeay (personal communication, 1993), we have modified the cartoon of the CBTS(Figure 8.2a) based on the reprocessed sections. A revised drawing is shown in Figure8.2b.A prominent subhorizontal band of reflectors at 6.0-7.0 s may be traced from thewestern edge of the line eastward to station 400 on the zero-offset section (Figure 8.5,event B1). The lack of signal between stations 450 and 550 on this section is attributableto a low S/N and does not necessarily reflect a lack of structure at depth; consequently,it is possible that these reflectors extend into this noisy region. A similar pattern ofreflectivity is arguably present on the eastern half of the section (Figure 8.5, event158B2). Based on our current knowledge of the regional geology and structural setting,it is difficult to place these features within the local tectonic framework, although wecannot rule out the possibility of a structural origin for this event(s). Possibly, thebanded reflectivity may be related to zones of layered porosity located between the 450°C-730 °C isotherms, which in our study area occur at approximate depths of 13 kmand 20 km, respectively (corresponding to respective two-way traveltimes of 4.0 s and7.0 s) (Lewis et al., 1992). It is interesting to note that rather than being confined to azone between the two isotherms, SBC18 reflectivity is prominent throughout the section.Several Lithoprobe reflection profiles located in the southeastern Cordillera reveal strongreflectivity only within the band bounded by the two isotherms (Lewis et al., 1992).Beneath stations 250-370, a sequence of west-dipping reflectors is visible on thezero-offset section at very late times (Figure 8.5, event A at 12.0-14.0 s). Migrationmoves this package approximately 30 km to the east-northeast, to the opposite side ofthe Fraser fault beneath the eastern portion of the Mount Lytton granodiorite, just abovethe (inferred) trace of the Moho. The considerable lateral displacement of the event (s)under the action of migration presents difficulties in presentation, although in Figure 8.4we have schematically sketched it below station 1000 at - 11 s (event A) (see Figure7.4 caption for details). Because in reality these deep crustal reflectors are located wellto the southeast of the line, we show the restored reflector geometry in map view onthe regional geology map (Figure 8.3, event A). East of the Fraser fault, another west-dipping fabric is visible at 12.5-11.5 s beneath stations 1100-1240 (Figure 8.5, event B).This package migrates 15 km to the northeast, to a position beneath the Spences Bridgevolcanic group, where it also appears as a deep crustal feature flattening into the Moho(event B, Figures 8.3 and 8.4). A similar pattern of reflectivity is observed on SBC12,SBC13, and SBC17 (profile locations shown in Figure 1.1).159Samarium—neodynium (Sm-Nd) (Lambert and Chamberlain, 1990) and initial stron-tium ratio (87Sr/86Sr) (Armstrong and Ghosh, 1990) isotopic studies indicate that thewestern edge of the North American craton is presently located 75 km west of theOkanagan Valley, a finding which led Varsek et al. (1993) to postulate that west-dippingfabric present at lower levels of SBC18 represents faults which accommodated synoro-genic tectonic overlap of the Intermontane superterrane onto the craton. We acknowledgethe possibility that the west-dipping ramps A and B represent deep levels of this tectonicoverlap, although in contrast to the Varsek et al. (1993) interpretation (Figure 8.1, no-tation "RMBD"), we do not feel that the character of the lower crust directly beneathSBC18 justifies the westward extension of the overlap zone beyond the Fraser fault.Approximately 70 km to the northwest of the survey, reconnaissance surface mappingof the Kwoiek fault by Journeay (1990) revealed steeply northeast-dipping (50-80°) faultstrands. Unfortunately, this feature intersects SBC18 along a noisy portion of the line(Figure 8.5, station 450), which probably accounts for the fact that we were unableto image related structure at depth. A (nominally) east-dipping reflector located at 3.5 sbeneath stations 530-630 (Figures 8.4 and 8.5, event C) apparently truncates a (nominally)west-dipping event and, very speculatively, might represent deep levels of the fault.Varsek et al. (1993) provided three possible interpretations for the subsurfacetrajectory of the Fraser fault (Figure 8.1). In particular, Trajectory FFA is based on(i) apparent mid-crustal continuity of reflectors across the fault zone (undershoot region)at 5.0 s and (ii) the premise that such reflections predate motion along the fault. Thisinterpretation implies that the major geological discontinuity has a relatively shallowdepth extent. However, quantitative modelling and inversion of magnetotelluric dataacquired along a profile nearly coincident with SBC18 suggest that the fault penetratesthe entire crust and has a sub-vertical geometry (Jones et al., 1991).160Our detailed analysis of the undershoot region (Figure 7.7) reveals that the strongsub-horizontal reflectivity at 5.0 s is essentially confined to the southern portion of themidpoint scatter, which, significantly, is approximately coincident with the location ofthe CMP bin swath that was used in the preliminary processing. Prominent, continuousreflectors at 5.0 s are apparent in the section corresponding to our southern swath (Figure7.7b). However, they appear to die out or "diffuse" to the north, as evidenced byinspection of the sections corresponding to the central, main and northern swaths (Figures7.7c-e, respectively) as well as the northwest-southeast swath (Figure 7.70. Whereasboth the "main" (Figure 8.5, event D— bin map in Figure 6.1) and "western approach"(Figure 7.7a) profiles reveal strong reflectivity at 5.0 s near the western edge of thecanyon, implying a relatively large spatial extent for the associated subhorizontal fabric,the undershoot region is apparently characterized by a very localized pocket of enhancedreflectivity. This suggests that there is no single, well-defined package of reflectorsextending across the fault zone, and that apparent mid-crustal continuity across the faultderives from the fortuitous alignment of structurally unrelated reflectors.Moreover, Figures 8.5, 7.7c, 7.7d and 7.7e reveal the presence of stronger reflectivityon the east side of the canyon. This juxtaposition of different structural styles appears toextend to great depth (beyond 10.0 s), and implies that (i) the fault roots in, or possiblypenetrates, the deep crust and (ii) it has a sub-vertical geometry. Such an interpretation iscompatible with the results of the magnetotelluric study of Jones et al. (1991). Finally, itis worth noting that our reprocessed results, which suggest that the Moho is flat across theentire profile (an observation we discuss later in this section), do not favour TrajectoryFFC (Figure 8.1) which is based on west-side-down Moho displacement.East of the Fraser canyon, the line cuts obliquely across the surface trace of thepolyphase Pasayten fault (Figure 8.6c), which is properly viewed as a fault system rather161than a single feature. Based on mapping and geochronometric studies conducted in thenearby Eagle Plutonic Complex (Figure 8.3, box 1), Grieg (1992) has identified at leasttwo discrete episodes of transpressional faulting along this complex structure. A mid-Eocene stage of brittle east-side-up thrusting apparently succeeded a mid—Cretaceousperiod of ductile sinistral, east-side-up reverse displacement. The presence of northeast-dipping foliation planes near the surface expression of the fault (Figure 8.3, box 1) ledhim to suggest a similar dip orientation for the fault itself. Several foliation planes ofcomparable orientation are exposed in the vicinity of the SBC18 traverse of the fault(Figure 8.3, box 2) which, on the basis of his argument, imply that the fault dips to thenortheast in our study area.Our reprocessing has significantly enhanced the subsurface image near the Pasaytenfault. However, the obliqueness of the profile to regional strike has complicated theinterpretation. Dipping events P1 and P2 (Figures 8.4 and 8.5, expanded view in Figures8.6a and 8.6b), which were not visible on the section produced by the contract processing,are of particular interest. They appear to cut off a southwest dipping feature at 2.0 s(Figures 8.6a and b, event R) whose strong reflectivity may be related to intercalation offine-grained clastics and volcanic rocks of the Methow basin. Event P2 was not visibleprior to the application of a significant crossdip correction. By considering the size of thiscorrection and by assuming that the zero-offset section has effectively imaged the inlinecomponent of the dip, we estimated a true dip 4. of 41° and a dip azimuth of [E30°1•1](true dip and dip azimuth are defined in Figure A.1). We describe the calculation inAppendix B. Uncertainties have not been formally calculated, although we feel that theassignment of a 20% fractional uncertainty to our estimates of both dip and dip azimuthwould adequately acccount for measurement errors and error in model specification (thecalculation is based on a simple constant velocity model). We estimated the true dip forevent P1 to be 45°, [N40°E].162aszzU)to0500COa., '^r '''''' ''^1) \ ),,,;.../^ft9 -t J•1).1 \i•4;',.,,i^.1^,^vt •1 ,)^• ^l`t4 i,Artief:i' ,Yr^ ,/,..,1 .1 ^,t(6.^/^i. 1 iv'\'' )(4-''0.^r'./,.. i ,i vi') c•,,,;(•^./..\1':',ra.^V1'!„t{.^'/Olt:two-way traveltime (s)OCO8Lc) el^j i ‘i^:.11‘1A( ^, ;t1\q^).\l.^; ■> .1/ , ^t'l^1^1,, 1)1,^/, /L ^• t.;y73vii ("/(' '- J.NYY ';:i'f,17,. ..ii\V“.. ,^,^....rt. •, y :',.' ‘, i iii,C 1 '‘ . .1,/, 1(1,. / '1. , i ,:/,^l 'f.,..C://'( :,i 1,^1^6 ^1/( I .^,.^..-.:4^; , ^1 ( ,^\^'( ' f ,4^),^. t .,.. ••c -0 as a., c/a u)a)^a)(LS T's^Fp cau)I'd^g5)Octx^'--oC)15-5^w0—^-c•^Q)^E .>, •— —^0)—.20.)E zicr)2 as &" a) 0^E`6'0. - a)ola)D(C O^as -co^(3:5(7-5^0E,Ew^;22'5O E Q)Ci O.- 6 01:5• E z-0 U^4—-0 2^w^cifi pc^rri —(15 —0 — L.:^•—■ 0Off. a) o^=Fr, -ow^13..)LI^u)^0 (-)a5 0cc; (7) .-V2^c) itss seO ® 8 U52) rrR a)^o cLL^N (1:5^U)R3-6-^I /111^- ,/,, ..c. ‘. ii (A 'LL co V^;.'co _ca.^1r^a.^iii^(^frIN: 'AV , 'I^,,1^i: k ..c^11`•> ki,/,r^'`Ii`j'fiii'4,t,N\1<‘0'1,\\ u y• ., ill,^,I i^,)11,'^fi'l I I ',Y :^il', i //' ! k t , / :.,^, f ;[ ir I..)3/:/I/s( /; Al r/i i V\ \^/ ., 0/ )^►/ Piii r 9,- IV',,pm ^)^i :(^,,' 1 1 (^6? ' 14 r/4‘. ,,,,'■^'\,,,1.11Both dips are comparable with the orientation of nearby foliation planes, suggestingthat events P1 and P2 represent imbricate thrust faults associated with a northeast-dippingPasayten fault system. Further to the south in Washington state, Potter and Prussen (1987)interpreted the fault to be east-dipping, based on the presence of east-dipping reflectorson COCORP profile W7 (see Figure 1.1 for line location). Based on the observationthat reflectors P1 and P2 are listric into the upper crust at 2.0 s (Figures 8.6a and 8.6b),we infer a shallower depth extent for the fault system than that which was originallyproposed by Varsek et al. (1993) (cf. Figures 8.1 and 8.4).Restoration of 130 km of dextral motion along the Fraser fault places the easternhalf of SBC18 opposite the northwest trending Yalakom fault (Figure 8.4, symbol "YF"),which itself has accommodated more than 100 km of right lateral offset (Kleinspehn,1985 in Coleman and Parrish, 1992). Approximately 80 km to the northeast of our line,Coleman and Parrish (1992) identified this feature as a northeast-dipping dextral reverse-slip fault; thirty kilometres northwest of their study area, the fault is nearly vertical(Schiarizza et al., 1990, in Coleman and Parrish, 1992). Varsek et al. (1993) recognizedthe possibility of the existence of deep levels of this fault beneath the eastern portion ofSBC18. It is our opinion that such structure is not visible on either version of the SBC18section (i.e., our reprocessed section and/or the contract-processed result on which Varseket al. (1993) based their interpretation). As another point of variance, a reconstructionbased on 130 km of Fraser fault displacement places the northeast—dipping Mission Ridgefault well to the south of the eastern half of SBC18, thereby invalidating the proposal ofVarsek et al. (1993), which was based on restoration using an older estimate of dextraloffset (85 km), that the line crosses the deep root of this extensional feature (Figure8.1, "MRF").By definition, the reflection Moho is the deepest laterally extensive, coherent package164of high-amplitude reflectivity appearing on a reflection section (Klemperer et al., 1986).The precise nature of its relationship to the crust-mantle boundary as well as to therefraction Moho, which is defined in terms of a P-wave velocity increase (Steinhart,1967), is not fully understood (Jarchow and Thompson, 1989). On SBC18 we identifythe reflection Moho as a broad band of reflectivity with a traveltime thickness of -0.4s (-2.5 km), centred at approximately 11.2 s (Figure 8.4, event M). It is essentially flatacross the entire line. At the extreme eastern end of the profile, a sequence of strongreflectors centred at 11.0 s (Figure 8.4, event MM) may provide evidence for a Mohotime step of -0.2 s (-0.6 km, west-side-down ramp), although such a small jump is likelyinsignificant given the tenuous nature of reflection Moho identification.On the other hand, Varsek et al. (1993) indicate a significant west-side-down Mohostep (approx. 0.7 s) at this location (Figure 8.1, notation "MOHO").Their interpretation is apparently based on the observation that the zone of strongreflectivity corresponding to event MM (Figure 8.4) is time-shifted by roughly —0.3 s (i.e.,it appears earlier) on the Western final stacked section. Interestingly, near the easternend of the line, all events positively identifiable on both sections (i.e., our reprocessedresult and the contract-processed section) demonstrate the same time shift independentof arrival time, whereas elsewhere along the profile, there is no such discrepancy. Thispoints necessarily to a variance between the two statics computations (in both cases, adatum plane of 1000 m was used for the elevation correction). We are unable to providea definitive answer as to which result is "correct", although it is worth recalling thefact that the residual statics algorithm employed in the preliminary processing is unableto resolve long wavelength static components, whereas a refraction-based treatment cantheoretically remove all spatial orders of static variation.Zelt et al. (1993) performed traveltime inversion and amplitude forward modelling of165refraction data acquired along Southern Cordillera Refraction Experiment Line 3, 100 kmto the south of SBC18 (Figure 1.1). Their velocity model reveals a very slight shallowingof the (refraction) Moho proceeding eastward from the Coast Belt into the Intermontanebelt (from 37 to 34 km depth). However, because these depth estimates are associatedwith an uncertainty of ± 1.5-2.0 km, they do not necessarily imply the existence of awest-side-up Moho ramp (Barry Zelt, personal communication, 1993), and as such, areunable to resolve the discrepancy observed between the two reflection sections.Nevertheless, the results of the preliminary processing of reflection lines SBC13 andSBC17 indicate the presence of significant east-side-down Moho displacement beneaththe western flank of the ECB (Varsek et al., 1993). This may provide an argument forthe existence of west-side-down Moho displacement near the eastern flank of the ECB,since the combination of these two displacements amounts to the existence of a crustalroot beneath the mountains of the ECB, which are higher than those of the flankingregions. Varsek et al. (1993) identify the west-side-down Moho ramp on SBC18 withthe eastern flank of such a crustal root (Figure 8.1), and make a similar interpretation onSBC12 although in the case of the latter profile, we do not feel that the data necessarilysuggest a Moho step.Moreover, our interpretation of an essentially flat Moho across the entire profileis possibly at variance with the proposal of Varsek et al. (1993) that the crust thinseastward of the Coast-Intermontane belt boundary. They postulated that the shallowingof the Moho below SBC18 (i.e., the east flank of the crustal root) is spatially correlatedwith the mid-crustal flattening of two normal faults of opposite dip, the east-dippingMission Ridge fault (Figure 8.1, "MRF") and the west-dipping Coldwater fault whosesurface trace lies approximately 90 km to the east of the profile, which essentially flank theintervening region of (presumed) Eocene crustal extension. Under this scenario, these two166extensional faults accommodated down-dropping of the upper crust, and consequently,crustal thinning.The fact that variance between the two Moho interpretations is attributable to adiscrepancy in the statics computations underscores the tenuous nature of deep crustalreflection interpretation. Although our model does not explicitly support the proposal ofVarsek et al. (1993) of a crustal root beneath the Eastern Coast Belt, nor does it reinforcetheir argument for crustal thinning to the east of SBC18, our results do not preclude eitherpossibility. Reprocessing of reflection lines SBC13, SBC14, and SBC17, all located onthe west side of the Fraser fault (see Figure 1.1 for locations), is currently in progress atthe UBC Department of Geophysics and Astronomy; additionally, reprocessing of linesSBC11 and SBC12 lying to the east of the fault has been proposed. These efforts willlikely assist in providing definitive answers with regard to Moho structure, as well asfurther elucidation of regional tectonic processes.167Chapter 9 SUMMARY AND FINAL DISCUSSION9.1 Crooked line processingThe quality of the preliminary processing is excellent, and as a general statementthe application of advanced processing techniques yielded a modest improvement overthe contract-processed result.Application of predictive deconvolution apparently succeeded in removing short-period multiple reflections. Although strictly speaking, this type of deconvolution isfounded on the assumption of a minimum phase wavelet, we showed that for a predictiongap sufficiently large so as to encompass the effective width of the Klauder wavelet,the method is relatively insensitive to the zero-phase properties of the Vibroseis sourcesignature.Statics were successfully treated through employment of a refraction-based procedurewhich honoured both long and short wavelength static variations. Success was due largelyto the excellent algorithm available in REFSTAT2, but the use of the surface stackingcharts in diagnosing and correcting systematic error also contributed significantly towardshoning the final statics solution. Had the REFSTAT2 algorithm been used as a "blackbox", with the systematic errors going unchecked, it is likely that the results would havesuffered some appreciable degradation. By far the most significant correction from theviewpoint of the number of affected first break picks was that for "side lobe" error. Still,the number of picks that suffered from this phase misidentification accounted for lessthan 1% of the total. The inclusion of a 3--D statics algorithm (e.g., the Hampson andRussell algorithm) in the processing flow would likely improve results, especially alongvery crooked portions of the line. Thus we envision an improved statics stream consistingof (i) the application of a preliminary run of REFSTAT2 in order to extract delay time168information; (ii) construction of surface stacking charts (SSCs) for first break systematicerror identification and correction; and (iii) a final pass with the 3—D refraction staticsalgorithm.Dip moveout correction (DMO) has succeeded in enhancing the subsurface imagenear the Pasayten fault. On the other hand, application of DMO actually degraded thequality of the output stack along several other portions of the line, probably because the2—D assumptions underlying the algorithm were violated.We derived a 3—D common midpoint (CMP) bin reflection traveltime expressionwhich explicitly separates the inline dip and crossdip effects. Examination of this equationrevealed that the crossdip effect may be considered as a perturbation in the zero-offsettraveltime, and consequently, that a first order correction may be implemented by useof slant stack techniques. The method we developed for crossdip slowness estimationshowed promise in the synthetic environment but performed poorly when we applied it toour real data. We attribute the disappointing results to an error in model specification: ifthe geology were less complex (i.e., the interfaces were adequately approximated by oursimple 3—D model), this might represent a viable means of efficient crossdip parameterestimation.The creation of several CMP bin swaths through the midpoint scatter in the vicinity ofthe undershoot enabled a "pseudo 3—D" characterization of the subsurface near the Fraserfault. In this region where the statics were deemed to be complex, cascaded applicationof crossdip correction and residual statics improved the image relative to our brute stack,although the time-term residual statics algorithm used in the contract processing alsoappeared to yield an acceptable result.Migration yielded disappointing results. Degradation of migrated section quality inthe shallower portion of the line (above - 5 s) was probably owing to the low S/N, the169crookedness of the profile and the fact that our migration algorithm did not honour lateralvelocity variations. Contamination of the deeper sections by smiles, a phenomenon whichis expected in the deep crustal environment, was observed. In spite of such shortcomings,migration represents a necessary component of the processing stream; thus our approachwas to first positively identify events on the zero-offset section, then to examine themigrated section in order to obtain a crude sense of true subsurface reflector geometries.9.2 InterpretationParticularly significant aspects of our revised interpretation include:i) inference of a deep crustal extent (or possible crustal penetration) for the Fraser fault;ii) correlation of two northeast-dipping reflectors, not visible on the sections producedby preliminary processing, with southwest-directed thrusting along the Pasayten fault;iii) correlation of two east-dipping homoclines near the western edge of the profile withroots of the Coast Belt Thrust System (CBTS), leading to a revision of (deeper levelsof) the CBTS structural section;iv) inference of an essentially flat Moho (crust-mantle boundary) across the entire line.It is important to note that our interpretation of a deep crustal extent (crustalpenetration (?)) for the Fraser fault represents a suggestion based on a lack of evidencefor mid-crustal continuity of reflectors across the fault zone and on the juxtapositionof different structural styles at depth on either side of the Fraser Canyon, rather than adefinitive statement. Additional reprocessing preserving relative amplitude variations willlikely be performed so as to better define the precise nature of the discrepancy between thetwo crustal fabrics. Our work and that of Varsek et al. (1993) are pioneering efforts in thesense that they represent the first-ever attempts at characterizing any of the several majorright-lateral strike-slip fault systems of the Cordillera using seismic reflection techniques.As part of the proposed Lithoprobe Slave-Northern Cordillera Lithospheric Evolution170(SNORCLE) transect, two reflection profiles across the Tintina fault in the south-centralYukon are planned. These lines will cross the fault at high angle on continuous roads,and thus will not suffer from the same complications in acquisition (i.e., undershoot) andline crookedness which plague SBC18. 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Program, 19, 809.Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., 1986, Numerical Recipes,Cambridge University Press, Cambridge, 1986, 818 pp.Riddihough, R.P., and Seeman, D.A., 1982, Juan de Fuca Plate Map: JFP-8 GravityAnomaly, Pacific Geoscience Centre, scale 1:2 000 000.Ristow, D., and Jurczyk, D., 1975, Vibroseis deconvolution: Geophys. Prosp., 23,363-379.Robinson, E. A., and Treitel, S., 1980, Geophysical Signal Analysis, Prentice-Hall, NewJersey, 466 pp.Ronen, J., 1985, Spatial antialiasing of synthetic log-stretched multichannel data: Centrefor Wave Phenomena Research Report number CWP-069.Ronen, J., and Claerbout, J.F., 1985, Surface-consistent residual statics estimation bystack-power maximization: Geophysics, 50, 2759-2767.Ronen, J., and Liner, C. L., 1987, Theory of spatial antialiasing of synthetic log-stretchedmultichannel data: 57th Ann. Mtg., Soc. Expl. Geophys., Expanded Abstracts,729-733.Steinhart, J.S., 1967, Mohorovicic discontinuity, In International Dictionary of Geo-physics, Edited by S.K. Runcorn, Oxford, 2 991-994.Taner, M. T., and Koehler, F., 1969, Velocity specra—digital computer derivation andapplications of velocity functions: Geophysics, 39, 859-881.176Ulrych, T.J., and Matsuoka, T., 1991, The output of predictive deconvolution: Geo-physics, 56, 371-377.van der Heyden, P., 1992, A middle Jurassic to early Tertiary Andean-Sierran arc modelfor the Coast belt of British Columbia: Tectonics, 11, 82-97.Varsek, J.L., Cook, F.A., Clowes, R.M., Journeay, M., Monger, J.W.H., Parrish, R.R.,Kanasewich, E.R., and Spencer, C.S., 1993, Lithoprobe crustal reflection structure ofthe southern Canadian Cordillera II: Coast mountains transect: Tectonics, 12, 334-360.Wang, W., 1990, Stacking processing of crooked lines using the SUN/INSIGHT system:LSPF Newsletter, 4, (1), 13-17.Warner, M., 1987, Migration—why doesn't it work for deep continental data: Geophys.J. R. astr. Soc, 89, 21-26.Wiggins, R. A., Larner, K., and Wisecup, R. D., 1976, Residual statics analysis as ageneral linear inverse problem: Geophysics, 41, 922-938.Yilmaz, 0., 1987, Seismic Data Processing, S.E.G., Tulsa, 526 pp.Yorath, C.J., 1990, Where Terranes Collide, Orca, Victoria, 231 pp.Zelt, B.C., Ellis, R.M., and Clowes, R.M., 1993, Crustal Velocity Structure in the EasternInsular and Southernmost Coast Belts, Canadian Cordillera: Can. J. Earth Sci. (inpress).177Appendix A: Derivation of the 3—D CMP bin reflection traveltimeexpression (equation (5.7))We begin the analysis by considering the general reflection traveltime expressionof Levin (1971) for a 3—D dipping planar interface embedded in a constant velocityhalfspace. With reference to Figure A.1, he showed that the traveltime t for a source atthe origin and a receiver at position (x,0,0) is given byt2 (2D) 2 x2 (1 — sin2 cos2 0)V^V2where D is the perpendicular distance between the source-receiver midpoint and theinterface, V is the (constant) medium velocity, 0 is the dip angle, and 9 is the dip lineazimuth, measured clockwise from the x-axis to the dip line.This expression may be massaged to obtain the general traveltime expression for anarbitrary source and receiver location in terms of the perpendicular distance d betweenthe origin and the interface, and the associated direction cosines a, /3, and 0. These threeangles are measured between the line d and the x, y and z coordinate axes, respectively(Figure A.1a). Angles a and )3 are defined on the open interval [0°, 1801, and 0 isdefined on the open interval [0°, 90°]. We consider a source at some arbitrary positionon the surface, say (x,y,z)=(x,0,0) (Figure A.2). We express the (arbitrary) receiverlocation in terms of the absolute value of the source-receiver offset, B, and the source-receiver azimuth, p . This azimuth is measured clockwise from a line parallel to thex—axis (0 p .360°). It is convenient to introduce a new set of coordinate axes (x',y',z')as shown in the figure. In terms of the primed coordinate system, the traveltime for thenew source-receiver pair 1' may be written as/2^213' 2 B2 (1 - sin2 01 cos2 99(t = ^(V ) V2where all primed quantities are defined analogously to their unprimed counterparts.(A.1)(A.2)178(0, 0, 0) (x/2 o, 0) (x, 0, 0).4/ I^"frFigure A.1. (a) three-dimensional model consisting of a single dipping layer over ahalfspace; (b) definition of the dip line azimuth, 0.17-9Figure A.2. A new source-receiver pair has been introduced to the modelshown in Fig. A.1. The source is located at (X, xi', 0); the receiver positionis defined by the source-receiver azimuth, p, and the absolute value ofthe source-receiver offset, B. In terms of the rotated coordinate system shownin the figure, the receiver is located at the point (x', y', z ,). (B, 0, 0).1 80The first step in the analysis involves expressing the primed quantities D', 4', and 9' interms of unprimed parameters. Because lines d and d' are parallel, as are the vertical axesof the two coordinate systems under consideration, it is easy to see from Figure A.2 that01 = 0,^ (A.3)and moreover thatO' = 0 — p.^ (A.4)The calculation for D' is somewhat more involved. D' is related to d',the perpendic-ular distance measured from the primed origin down to the interface, byd' = D' + —B cos a' ,^ (A.5)where a' is the direction cosine measured between the x' axis and the line d'. Becaused runs between the primed origin, (x,y,z)=(x,0,0), and a point on the interface, say(x,y,z)=(xo,Y0hz,0) we may writedi . NA x — xof + ( P — y 0 ) 2 + 4, ,^ (A.6)andxo cos a -I- yo cos ,8 + zo cos 0 = d ,^(A.7)the latter expression arising from the fact that the equation for the reflecting plane isx cos a -I- y cos Q+ z cos 0= d .^(A.8)Because the line d' is perpendicular to the plane, and therefore parallel to the planenormal n=(cosa, cos/3, cos4), we haveX — xo = A cos a ,'P — yo = A cos fl ,^ (A.9)—zo = A cos 0 ,181where A is some arbitrary scalar. Recalling thatcost a + cos2 /3 + cos2 ck = 1 ,manipulation of (A.7) and (A.9) givesA = Xcosa-l-Wcos# — d .Substituting (A.9) into (A.6) yieldsct = iAi •(A.10)(A.11)(A.12)We arrive at the expression for d in terms of unprimed parameters by considering(A.11) and (A.12):= Id — X cos a — ‘11 cos #1 •^(A.13)To resolve the ambiguity of sign in (A.13), note that the surface projection of the reflectoris a line satisfying the relationx cos a + y cos /3 = d .^(A.14)Hence, in order that the new source and receiver not lie "beyond" the surface trace, werequire thatX cos a + W cos /3 < d ,^(A.15)and consequently that= d — X cos a — W cos /3 .^(A.16)The next step in the analysis is to express cosa' in terms of the unprimed quantities.Note that the direction cosine angle a' depends only on the rotation of the primed182coordinate system relative to the original system, and not on its translation. Hence,we may use the standard transformation equations for a rotated coordinate system:x= x' cos p — yt sin py = x i sin p yl cos p^ (A.17)z = z .From Figure A.3, it is apparent thatxp xp cos p yp sin pcos —and sincex pcos a = —Lcos /3 = YPLthat(A.18)(A.19)cos a' = cos a cos p + cos )3 sin p .^(A.20)We obtain the desired expression for D' from (A.5), (A.16) and (A.20):= d — X cos a — 'P cos # ——B (cos a cos p + cos fl sin p) .^(A.21)Finally, we may rewrite (A.2) in terms of unprimed parameters, using (A.3), (A.4) and(A.21):2i i2 = :72^— X cos a —'Y cos /3 — (cos a cos p + cos /3 sin p))}VB2 (1 — sin2 cos2 (9 — p)) .(A.22)Although (A.22) gives the general result for the reflection traveltime for an arbitrarilylocated source-receiver couplet in terms of the unprimed parameters, it is not yet in a183Figure A.3. A line of length L extending from the origin to some termination point P. Fordisplay purposes, we have translated the primed coordinate system defined inFigure A.2 to the unprimed origin.tan Ccos # =+ tang / tan2 C(A.28)form amenable to an analysis of the crossdip problem. We now seek to express t' in termsof the inline dip angle, I, and the angle of crossdip, C (Figure A.4). In the followinganalysis, we assume that I and C may take on both positive and negative values on theclosed interval (0°, 90°) (the corresponding restrictions imposed on the direction cosinesa, 13, and 0 ensure that no singularities arise in manipulating the system of equations{ (A.10), (A.23) and (A.24)) below).From the figure it is easy to see thatand thatcos atan / =cos(A.23)costan C = cos 0 • (A.24)From these last two expressions and (A.10), we obtain tan I(A.25)cos a =tang / t an2 CNote that we have used the fact thatsgn (cos a) = sgn (tan I) ,^ (A.26)wheresgn (x) = +1, x > 0(A.27)—1, x <0 .In writing equation (A.26), we have considered (A.23) together with the fact that cosq?. 0 for the domain of definition of 0.Similarly, the corresponding expression for the y direction cosine is found to be185(dcosa, dcosj3, dcos4)Figure A.4: Definition of the crossdip angle, C, and the inline angle, I ./ ii‘sincos acos 0 = (A.30)(tan / cos p + tan C sin p) 2 cost (0 — p) =tan2 I + tan2 C (A.35)while the dip angle 0 is related to the inline dip and crossdip bysin k =  ^tang I + tan2 C 1 +tan2 /+tan2 C(A.29)Having expressed the direction cosines in terms of the angles of inline dip andcrossdip, we perform a similar analysis for the dip line azimuth, 9. From Figure A.1,we see thatandsin 0 = cos 13sin 0 (A.31)We may use equations (A.25), (A.28) and (A.29) to rewrite these last two expressions:cos 0 =  tan I,^ (A.32)Vtan2 I + tan2 Candsin 9 =Using the double angle formulacos (9 — p) = cos° cos p + sin 9 sin ptogether with (A.32) and (A.33), we find thattan CVtan2I tanz c (A.33)(A.34)By substituting these expressions for cosa, cosi3, sing, and cos 2(0—p) (equations(A.25), (A.28), (A.29) and (A.35), respectively) into (A.22), we obtain, after some187simplification,2t12 = tc — (-2 ) (X tan/ -1- W tan C B6^+72ii327.1 (1 ( 7) )where we have defined(A.36)7^tan2 I + tan2 C ,^(A.37)andtan I cos p -I- tan C sin p ,2dt, -=^.(A.38)(A.39)Note that tc is the two-way zero-offset traveltime measured at the unprimed origin.A hypothetical common midpoint scatter plot associated with a single CMP bin ispresented in Figure A.5. We have sketched in two midpoints, both displaying considerabletransverse offset Y. Note that for any midpoint which lies inside the bin, we have therelationX = --2 cos p ,= --2sinp+Y ,so that (A.36) reduces toB 2 S 2t12 = (tc pY)2 + —V2 (1 — (7))where we have defined2tanCP —^ •V7(A.40)(A.41)(A.42)Equation (A.41) is the result presented in Chapter 5, equation (5.7).188Figure A.5. A common midpoint scatter plot. The CMP bin is centre is locatedat the coordinate origin. Two midpoints associated with different shot-receiverpairs are shown in the figure. Both midpoints are substantially offset from thebin centre.cos asin / = ,^cos2 a -F cos2(B. 4)Appendix B: Demonstration that the crossdip-corrected zero-offsetsection effectively images the inline component of dipWe recall from Chapter 5 that the crossdip correction effectively restores reflectiontraveltimes within an NMO-corrected CMP gather to the normal incidence two-waytraveltime measured at the bin centre tc . Hence an expression for the time slope (apparentslowness) of a 3—D dipping event on a crossdip-corrected zero-offset section may bederived by considering the traveltime difference between two normally incident rayswhich intersect the slalom line at different points. With reference to Figure A.1, a simplegeometric argument reveals that d, the perpendicular distance down to the reflecting planemeasured at the origin, differs in length from its counterpart measured at a distance &along the slalom line (i.e., the x-axis) by an amountbx cos a .^ (B. 1)The resulting discrepancy in normal incidence two-way traveltime St is given bySt — 28 x cos aVfrom whence we can determine the time slope:St 2 cos a5x V(B. 2)(B. 3)From Figure A.4,a result we can rewrite using (A.28) and (A.10):sin / = cos a (B. 5)1±tan2 / I1-tang C190From this last expression we see that in the limit of zero crossdip, sin I = cos a.Thus from (13.3) we recover the well-known result for the time slope associated with areflector exhibiting pure inline dip:^( St)^2 sin / (B. 6)45.2 inline^V(e.g. Hale, 1984). Moreover for a significant range of modest crossdips (say,—20°<C<20°, although the range increases with increasing magnitude of inline dip), wesee from equation (B.5) thatsin / cos a ,^ (B. 7)and thus from equation (3.3) that^S ^2 sin /^bx^V (B. 8)In other words, a first order estimate of the inline component of dip angle I may beobtained by simply measuring the time slope on the crossdip-corrected zero-offset section.This result is in harmony with our intuition.As an example, we consider one of the dipping reflectors associated with the obliquetraverse of the Pasayten fault. We orient our coordinate axes such that the x-z planecontains the zero-offset section, with the positive x-axis pointing in the direction ofincreasing station number. By direct inspection of the zero-offset section (Figure 8.6a)and using (13.8), we estimated an inline dip angle I of 40° (we assumed a constant velocityof 5600 m/s in this calculation). The optimum crossdip parameter was determined fromthe CSS analysis to be 0.00013 s/m. From (A.42), we calculated a crossdip angle C of15°. Substitution of these results for C and I into (13.5) revealed that sin I = 0.98 cos a ,suggesting that we were justified in measuring the inline dip angle from the zero-offsetsection. From (A.32) and (A.29) we calculated a dip line azimuth 9 of 18° and a truedip angle (/) of 41°. Taking into account the fact that our x-axis was oriented at [N40°E],we inferred that the feature dips 41° [E30°1•1].191

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