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A crustal study using teleseismic P Phases recorded near Port Authur, Ontario Deas, Alec T. 1969

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A CRUSTAL STUDY USING TELESEISMIC P PHASES RECORDED NEAR PORT ARTHUR, ONTARIO by ALEC T. DEAS B . S c , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e D e p a r t m e n t o f GEOPHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d The U n i v e r s i t y o f B r i t i s h C o l u m b i a A u g u s t , 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C olumbia, I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and Study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g or p u b l i c a t i o n of t h i s thes,is f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f G E O P H Y S I C S The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada D a t e Ju ly 30, 1969 ABSTRACT The crustal thickness and P velocities in the Port Arthur, Ontario region of the Canadian Shield have been previously determined by seismic refraction techniques during the Lake Superior Experiment and Project Early Rise. In this study, the P phases of eleven teleseismic earthquakes recorded near Port Arthur have been studied by computing azimuths, angles of incidence, and spectral ratios to ascertain some crustal proper-ties and compare these values with the refraction results. A P velocity at the surface of 6.1 ± 08 km/sec and a crustal thickness of 40 ± 5 km determined from the earthquakes are similar to but less precise than the refraction estimates of 6.3 km/sec and 38 km respectively. Transverse motions generated by the earthquake signal passing through the crust were observed and contributed to the uncertainty. 11 TABLE OF CONTENTS Introduction 1 Data Acquisition 3 Geophysical and Geological Setting of the Port Arthur Region 9 Theoretical and Experimental Analysis 12 Summary and Discussion ' 29 Bibliography 30 Appendix A Calibration Procedure 32 Appendix B Calibration Results 41 Appendix C Special Hints for Field Operation 46 I l l LIST OF TABLES Table I Station Description II List of Earthquakes iv LIST OF FIGURES Figure 1 Standard velocity sensitivity 4 2 Station location and local geology 5 3 Crustal profiles in the Port Arthur region 10 4 Azimuth deviations 14 5 Particle motion diagrams in the horizontal plane 16 6 Apparent angle of incidence determinations 18 • 7 Theoretical spectral ratio curves 21,22 8 Experimental spectral ratio curves 23,24 9 Coherency versus epicentral distance and station separation 27 10 Seismograph block diagram 33 11 Calibration circuitry and typical K-test record 37 12 Time variation of calculated K and system calibration pulse height 42 13 Velocity sensitivity curves 44 V ACKNOWLEDGEMENTS The a s s i s t a n c e and s t i m u l a t i o n by the p e o p l e i n the Department of Geophys ic s i s a p p r e c i a t e d . S p e c i f i c a l l y , I w i sh to thank D r . R. M. E l l i s , my s u p e r v i s o r , f o r h i s a s s i s t a n c e , a d v i c e , and c r i t i c a l r ev i ew o f the t h e s i s and D r . R. D . R u s s e l l and M e s s r s . Michalow and Isherwood f o r c o n s t r u c t i n g the a n a l o g -t o - d i g i t a l sy s t em. D r . R u s s e l l a l s o a s s i s t e d w i t h the se i smo-graph c a l i b r a t i o n . The f i e l d program was suppor ted by the A r c t i c I n s t i t u t e o f N o r t h A m e r i c a w i t h a U n i t e d S t a t e s A i r f o r c e O f f i c e o f S c i e n t i f i c Research Grant AF-AFOSR-702-67 . The f i r s t y e a r o f s tudy was u n d e r t a k e n w i t h a N a t i o n a l Research C o u n c i l B u r s a r y and subsequent a n a l y s i s s u p p o r t e d by the Defense Research Board and the N a t i o n a l Research C o u n c i l . 1 INTRODUCTION A number of recent studies in earthquake seismology have been devoted to an examination of the earth's crustal structure beneath a recording s i t e . From array data, Niazi (1966) cal-culated earthquake azimuths on the basis of particle motions and determined deviations from the great circle azimuth. The deviations were interpreted as a dipping Mohorovicic discontinuity beneath the array. Phinney (1964) compared the vertical-horizontal spectral ratio of long period P waves to theoretical ratios determined from the Haskell matrix formulation to delineate crustal structure. The depth to the Mohorovicic discontinuity and lower crustal velocities were estimated beneath recording sites in New Mexico, U.S.A., and Bermuda. Using similar methods, E l l i s and Basham (1968) compared experimental and theoretical spectral ratios as a test of the Haskell matrix at short periods. Using events recorded on the plains of Alberta and the well documented P velocities and layer thicknesses in the sedimentary rocks only limited agreement was observed between theory and experiment. Anomalously large P to SV conversion and scattering near the base of the sedimentary rocks was believed to cause the differences. This thesis describes a comparison between a variety of earthquake parameters and the theoretical equivalents in an area where the crust is thought to be relatively simple. Azimuths, angles of incidence, vertical-horizontal spectral ratios and 2 coherency are calculated from the P coda for a group of earth-quakes recorded with short period instruments on the Canadian Shield i n the v i c i n i t y of Port Arthur, Ontario. The c r u s t a l structure i n this area has been delineated by seismic r e f r a c t i o n techniques permitting t h e o r e t i c a l comparisons to be made. The general agreement between t h e o r e t i c a l and experimental results and experimental d i f f i c u l t i e s are discussed. 3 DATA ACQUISITION Instrumentation A brief description of the seismographs and the calibration procedure is given in Appendix A. The standard velocity sensitivity curve to which the seismographs were calibrated to is show in figure 1. The computation of this curve is described in Appendix B. Unfortunately, a dependable time record was not maintained because of power interruptions and chronometer failures. Field Program Three stations were occupied with one fixed seismograph and a second moved midway through the program. Station locations are shown in figure 2 while table I gives a brief description of each s i t e . The detector separation was 27 km in the f i r s t portion of the program and 69 km for the second portion. Events Recorded A total of eleven earthquakes suitable for analysis were recorded by both seismographs. Table II provides information for these events. Earthquake dates, times, locations, magni- -tudes, and depths are those given by the United States Coast and Geodetic Survey Seismological Bulletin. Epicentral distances and azimuths were determined from the earthquake coordinates and station DOT coordinates (with one exception as noted on the table). Errors less than 1.2° in azimuth and 0.6° in epicentral distance are introduced by substitution of DOT coordinates for stations YMH and FISH. The determination of the angle of 4 F I G U R E 1 Standard Velocity Sensitivity to which the Seismographs were Scaled 0 90°W 89° 88° FIGURE 2 Port Arthur Region Showing Station Location and Surface Geology STATION SYMBOL STATION LOCATION OPERATING INTERVAL SITE DESCRIPTION DOT 48U26.0'N 89°18.1'W 6 km West of Port Arthur June 9-August 5, 1967 Seismometers set upon concrete floor of DOT Belrose Road antenna site atop a 150 foot high h i l l . Overburden estimated to be less than 5 feet thick. y w u 4 8 ° 2 9 1 ' N June 12-July 1 0 , 1 9 6 7 A concrete floor of a farm shed 8 9 ° 3 9 3'W s e t * n u n c o n s°lidated overburden 27 km West of supported the seismometers. A C f B + . „ n n r p nearby well 40 foot deep did not Station DOT / . ... , £ , . encounter solid rock. Topographic °* re l i e f of 250 feet over several miles is common. FISH 48°50.4'N July 15-August 6, 196 88°36.2 'W 69 km Northeast of Station DOT 7 Seismometers set in concrete base-ment of vacant hatchery building. Overburden thickness estimated at less than 5 feet. Topography is gently rolling with an occasional sharp canyon. TABLE I STATION DESCRIPTION EVENT STATION DATE T I M E ( U . T ) MAG. EPICENTRAL DEPTH A Z I M . LOCATION L A T . LONG, i ( ° ) * NO. YR.MO.DAY HR.MIN.SEC D I S T A N C E ( ° ) (KM) ( ° ) ( ° ) ( ° ) ° 1 YMH 67 06 21 06 49 57 5 .3 51.4 49 165.0 Peru 2.7S 77.6W 31.8 2 YMH 67 06 26 02 22 35 5 .0 32 .6 45 208.8 Mex. Coast 18.4N 105.2W 38 .0 3 YMH 67 07 04 14 16 52 5.4 87 .3 28 167 .5 C h i l e 38 . IS 73.4W 20 .0 4 YMH 67 07 04 23 42 14 5 .6 78 .0 160 324 .0 Hokkaido 43.2N 142 .5E 22.6 5 YMH 67 07 06 13 42 22 5.9 48 .0 14 306.3 Fox I s . 52 .6N 168 .2W 32 .7 6 FISH 67 07 20 13 11 35 5 .3 78 .8 157 159 .9 A r g e n t i n a 28 . IS 66.9W 22.4 7 FISH 67 07 21 09 14 49 3.9 11 .0 35 ** M i s s . 37.5N 90.4W -8 FISH 67 07 22 16 56 53 6 .0 76 .7 4 42.5 Turkey 40.7N 30 .8E 23.2 9 FISH 67 07 29 10 24 25 6 .0 43 .7 161 156 .2 Co lumbia 6 .8N 73 .OW 34 .0 10 FISH 67 07 29 23 59 59 6 .2 42 .0 10 146.6 V e n e z u e l a 10.6N 67 .3W 34.5 11 FISH 67 07 30 01 31 02 5 .6 76.5 16 47 .8 Turkey 40.7N 30 .4E 23.2 A l l E v e n t s Recorded a t S t a t i o n DOT * A n g l e o f I n c i d e n c e at the base o f the c r u s t * * 184.6 at S t a t i o n DOT 187.3 a t S t a t i o n FISH TABLE II LIST OF EARTHQUAKES 8 incidence at the base of the crust is discussed in a following section. Digitization The three components of ground motion and the time channel were simultaneously digitized with the analog-to-digital conversion system described by Isherwood (1969). Approximately twelve minutes of each event were digitized beginning approximately 100 seconds prior to onset at a sampling rate of 20 ± .06 samples per second. GEOPHYSICAL AND GEOLOGICAL SETTING OF THE PORT ARTHUR AREA The Lake Superior Experiment (1963) and Project Early Rise (1966) were devoted, in part, to mapping the refracting horizons beneath Lake Superior and northward from Port Arthur to Churchill, Manitoba. A portion of the results from these experi-ments are shown in figure 3. Analysis of the Lake Superior data by Berry and West (1966) and O'Brien (1968) show that the v ^ Mohorovicic discontinuity under Lake Superior drops from a depth of 28 km in the west to a maximum depth of 55 km near the eastern shore. The range in velocities shown in figure 2 reflect some variation in interpretive methods. Mereu and Hunter (1969) , presenting an analysis of the Early Rise data, show a nearly horizontal Mohorovicic discontinuity at a depth of 32 km north of Lake Superior. The thicker crust beneath Lake Superior is restricted to the v i c i n i t y of the lake, at least in the northerly direction. The crustal thickness from Early Rise compares favorably with an average Canadian Shield crustal thickness of 35 km deduced by Brune and Dorman (1963) from surface wave work. A dip on the Mohorovicic discontinuity of 4 ° to the south and a depth of 38 km is estimated beneath Port Arthur. A structural difference between Lake Superior and the area north of the lake is the absence of an upper refractor in the northern region. Halls (1966) in a review of geology in the Lake Superior region, states that the Keeweenawan and Aminikean sediments and volcanics occupy a large synclinal basin with the major axis 1 0 FIGURE 3 Crustal Profiles in Lake Superior Locations and the Outline of Lake also shown Region. Superior Station are 11 running east-west in the approximate center of the lake. The sediments and volcanics, although reaching a thickness of 25,000 f t . in Minnesota, are thinning north of Lake Superior and are estimated to be about 500 f t . thick beneath Port Arthur. (Moorhouse 1960) . A general geologic map for the Port Arthur region has been presented in figure 2. The contact between the Lower Keeweenawan and Archean is not precisely mapped in the v i c i n i t y of station FISH. On a more local scale, the geology is much more complex. A t least four rock types and numerous fault locations are present in the Archean system. Intrusive diabase s i l l s cap many of the h i l l s about Port Arthur, including the h i l l under station DOT. Mt. MacKay, rising 97 8 feet above the Lake Superior surface and situated 10 km south of station DOT is the most dominant topo-graphic feature in the area. 12 THEORETICAL AND EXPERIMENTAL ANALYSES Azimuths Niazi (1966) has shown that differences between the experi-mentally determined azimuth and the great cir c l e azimuth may be interpretable on the basis of dipping interfaces beneath the recording station. If such in terfaces e x i s t , the experimental azimuths show deviations from the great circle azimuth in a systematic fashion as a function of azimuth. In this study, azimuths calculated from horizontal motions are compared with great c i r c l e azimuths to ascertain whether systematic differences exist. Great circle azimuths are listed in table 2. Calculation of experimental azimuths proceeded in the following manner. The north and east components of ground motion were projected onto two orthogonal axes situated at angles of 4 5 ° on either side of the great cir c l e azimuth. These components were f i l t e r e d with a 0*- 3 Hz corner low-pass Lanczos numeric f i l t e r . For each of the fi l t e r e d components, five seconds of pre-onset noise was examined and the "peak" noise level was determined. The "peak" noise level is defined as that value of the noise such that i t is exceeded 5% of the time (Byrne 1961). Commencing at onset, the value of each of the simultaneously sampled components were compared with their respective "peak" noise levels and, i f the "peak" noise level was exceeded on both components, an angle 9 was calculated using the relation 13 tan e(t) = X(t)/Y(t) where X(t) and Y(t) are the f i l t e r e d components. Whenever three or more consecutive values of both components exceed the noise levels, the average of the calculated values of 6 was determined to yield one estimate of the rotated azimuth. Five seconds of the P coda were analysed in this fashion. The estimates of the rotated azimuth were averaged and standard deviation determined. The effect of axis projection was removed to determine the deviation from the great circle azimuth. The azimuth deviations for a l l earthquakes at a l l sites are shown in figure 4. Two observations are evident. There is scatter of points at the same azimuth and the magnitude of the standard deviations are comparable to the azimuth deviations. The scattering of estimates and a lack of events at certain azimuths prohibits interpretation on the basis of dipping inter-faces beneath the recording sites. The distribution of estimates may be caused by scattering of incident radiation by crustal structures or calibration uncertainties. Calibration uncertain-ties of ± 10% could introduce azimuth deviation of ± 6°. The N-S dip of 4° on the crust mantle boundary in this area would result in a maximum expected azimuth deviation of 4° for events used in this study (Niazi 1966) . While abandoning any hope of interpretation on the basis of crustal structure, the source of the large standard deviations may be examined. Two reasons are suggested. The f i r s t is the low signal-to-noise ratio often found on horizontal components. The method of azimuth determination insures that the f i l t e r e d 20 _ ~ 10 o H < > W Q OS H 1 < 0 10 09 5 -20 0 100 200 GREAT CIRCLE AZIMUTH (°) CLOCKWISE FROM NORTH 300 360 FIGURE 4 Azimuth Deviation and Corresponding Standard Deviations versus Great Circle Azimuth. A Positive Deviation indicates that the Calculated Azimuth is larger than the Great Circle Azimuth 15 signal to "peak" noise ratio be greater than unity at least 95% o f the time. An example of contamination of the earthquake signal to noise is shown in figure 5a. For some events, large standard deviations arise because of transverse motion in the horizontal plane. Examples are shown in figures 5b and c. Here, records of the same earthquake from stations DOT and YMH show distinct transverse motion in the f i r s t 2% seconds. Angles of Incidence The angle of incidence at a recording station for an incoming earthquake depends upon the source parameters, the mantle path and the crust beneath the recording site. Variations in the angle of incidence due to variations at the source such as earthquake depth or crustal structure are not significant for the events studied here. Assuming the earth to be spherically symmetric, the angle of incidence at the base of the crust becomes a function o f epicentral distance only. The angle of incidence at the base o f the crust as listed in table 2 was determined from a curve of Ichikawa shown by Basham (1967). The angle of incidence at the base of the crust was not determined for event 7 since the curve becomes unreliable at small epicentral distances. Once the angle of incidence at the base of the crust, i Q , is known, determination of the angle of incidence at the free sur-face, i , may be easily calculated i f any layers in the crust are horizontally layered. Let V R be the P velocity beneath the free surface and V 1 the P velocity below the crust. Then, by Snell's Law sin i = R sin i • where R = V N / V ] _ (b) EVENT 4 STATION DOT FIGURE 5 Particle Motion Diagrams in the Horizontal Plane. Four Consecutive 2% Second Intervals beginning 2% Seconds before Onset are Shown. Small Circles indicate Start of Each Interval. Arrows indicate Great Circle Azimuths 17 The free surface reflects both P and S waves from the surface. The motion caused by the incident P and outgoing P and S is recorded by the seismograph. From this motion, an apparent angle of incidence i may be calculated which is related to i by Wiechert's relation (Bullen 1963) cos i = l - - sin^ l assuming Poisson's ratio equals \. Taking Poisson's ratio to be 0.30, typically alters the apparent angle of incidence by 2°. Figure 6 shows the variation of i with i Q for a variety of R assuming horizontal layering throughout the crus t. Experimental determinations of the apparent angle of i n c i -dence were calculated from motions recorded in the plane containing the vertical component and the horizontal component in the azimuthal direction. (The latter is termed the radial component). Except for two modifications, the apparent angles of incidence were calculated in an identical fashion to the azimuths. The f i r s t change is the substitution of the vertical and radial components for the north and east components. Secondly, the apparent angle of incidence was roughly estimated and this angle was used in place of the great circle azimuth s when the axes were projected. The results for a l l events (except event 7) at a l l sites are shown in figure 6. The large standard deviations are the result of SV motion and noise contamination. Since SV phases are generated at velocity contrasts and since SV motion is observed in the f i r s t 2h seconds for some events at a l l stations, u. 18 FIGURE 6 Apparent Angles of Incidence Standard Deviations for Expe and Theoretical Curves for a at the Surface versus i . rimental Determinations Variety 0 f R are shown 19 crustal inhomogenieties are present beneath the recording area. SV motion observed at \h seconds after onset originates at distances of about 13 km from the detector. Comparing this distance to the known crustal thickness of 38 km shows that the SV source is not associated with the crust-mantle boundary. Comparing theoretical curves of horizontally layered models with experimental results suggests a best f i t at R = .75 ± .10. Assuming a P velocity of 8.1 km/sec beneath the crust implies a surface P velocity of 6.1 + .8 km/sec beneath the recording sites. This estimate is closer to the 6.3 km/sec velocity determined from Early Rise data than to the 4.68 - 5.5 km/sec velocity observed for the upper refractor beneath Lake Superior. No definite conclusions may be drawn on the nature of crustal structure other than an estimate of the surface velocity. This estimate requires an assumption of horizontal velocity contrasts and is quite imprecise due to large standard deviations and, as in the case with azimuth determinations, calibration uncertainties. Some sort of velocity structures must be present in the crust, however, to account for the SV conversion. Spectral Studies In a study of long period seismic body waves, Phinney (1964) demonstrated that the square root of the vertical-horizontal power spectral ratio could be interpreted on the basis of horizontal crustal layering. In this study, experimental results in two frequency ranges are compared with theoretical curves determined from the Haskell matrix formulation. Theoretical analysis requires estimates of the angle of incidence at the base of the 20 crust and the layer parameters of P velocity, S velocity, density and thickness. Theoretical curves are shown in figure 7 for a number of crustal models. The P velocities were chosen from the Early Rise estimate and an estimate of the surface velocity beneath Lake Superior. S wave velocities were calculated assuming Poisson's ratio is equal to ht while densities were determined from the velocity-density relationship of Nafe and Drake (Grant and West 1965). The theoretical curves show a series of peaks due to resonant effects in the crust. Variations in the angle of incidence cause a change in the average amplitude of the curves and a shifting of peak positions. The curves in the frequency range .05 - .30 Hz have much larger peaks and are more sensitive to variation in crustal thickness. The effect of a 2.0 km surface layer in the frequency range 0.1 - 3.0 Hz may be seen by comparing figures 7a and 7b. Quefrencies of 4 cycles per hertz are observed on both curves but a smaller quefrency is superposed upon the surface layer model curve. For the frequency range 0.1 - 3.0 Hz, the experimental curves were determined by calculating the square root of the ratio of vertical to radial spectra for each event (except event 7) commencing at onset and continuing for 20 seconds. These events were separated into two categories on the basis of their angle of incidence at the base of the crust. Values of the spectral ratios in each category were averaged at 0.1 Hz intervals in a frequency band 0.2 - 2.5 Hz. Standard deviations were also calculated. The results are shown in figure 8a and b. 21 4.01 3 . a 2.0-1.0 0.0 (a) 4.0-i = 25v o i = 35 o MODEL LAYER THICKNESS AND P VELOCITIES 2 KM 5.6 KM/SEC o 28 KM 6.3 KM/SEC — i 1 1 1.0 2.0 3.0 Hz 8.1 KM/SEC 3.0-2.0-1.0 ^ m j ^ m M ^ - « ° 3 0 K M 6 - 3 K M / S E C 0.0 (b) 4.0. 3.0 2.0-1 1.0 2.0 Hz 3.0 8.1 KM/SEC 1.0 i. = 25° 2 0 K M 6 - 3 KM/SEC o i = 35' Q 0.0 (c) 4.0-1.0 2.0 Hz 3.0 8.1 KM/SEC 3.0 2 .0 1.0 A y \ A A / V V V W V A A A y i 0 = 25 V V \ A A A A A A A A A A / i 0 - 35° o 40 KM 6.3 KM/SEC 0.0 1.0 2.0 Hz 3.0 8.1 KM/SEC FIGURE 7 a, b, c, d Theoretical Spectral Ratios in Frequency Range .05 - 2.5 Hz 22 V H MODEL LAYER THICKNESS AND P VELOCITY 30 KM 6.3 KM/SEC 250 = 35° 8.1 KM/SEC V H V H 5.0 4.0 3.0 2.0 l.Oi-0.0 ( f ) 5.0, 4.G 3.0 2.0 40 KM 6.3 KM/SEC = 3Sl 0.1 0.2 Hz 0.3 8.1 KM/SEC l . O -35' 50 KM 6.3 KM/SEC 8.1 KM/SEC 0.0 •(g) 0.1 0.2 Hz 0.3 FIGURE 7 e,' f, g Theoretical Spectral Ratios in Frequency Range .04 - .28 Hz 23 V H 4.0i 3.0 2.0 1.0 0.0 ) 0.0 1.0 2.0 Hz 3.0 (a) ANGLES OF INCIDENCE LESS THAN 30( V H 4.0 3.0 2.0-1.0 0.0 0.0 1.0 2.0 Hz 3 .0 (b) ANGLES OF INCIDENCE GREATER THAN 30( FIGURES 8 a, b Averaged Experimental Spectral Ratios and Standard Deviations in Frequency Range 0.4 - 2.5 Hz 24 V H 7.On 6.0 5.0-4.0-3.0-2.0-l.o-0.0-0.0 0 . 1 0.2 (c) ANGLE OF INCIDENCE LESS THAN 30 i = 2 5 0 FOR THEORETICAL RATIO o 0.3 o \J . u-j 1 , 1 0.0 0 . 1 0.2 0 . 3 (d) ANGLES OF INCIDENCE GREATER THAN 30° i = 3 5 0 FOR THEORETICAL RATIO 0 FIGURE 8 c, d Averaged Experimental Spectral Ratios and Standard Deviations in Frequency Range 1 . 2 or 0.8 to 0.3 Hz. Theoretical Ratios from 40 km Crust is Dashed 25 In this frequency range the experimental curves are quite featureless. The general decrease in amplitude beginning at 2 Hz is likely due to noise appearing predominantly on the horizontal components. The experimental curves are most similar to theoretical curves derived from models having no surface layers and a crustal thickness in excess of 30 km. The experimental spectral ratios in the frequency band 0.1 - 0.3 Hz were calculated in a slightly different manner because of the long record sections . Commencing at onset and continuing for 150 seconds, the vertical and radial components of the four events of magnitude 6.0 or larger were f i l t e r e d with a low pass 2 Hz corner Lanczos f i l t e r . The filtered components were numerically redigitized by retaining every third point in the record and rejecting the remainder. The retention of every third point reduced the folding frequency from 10to 3.33 Hz while the f i l t e r i n g eliminated aliasing d i f f i c u l t i e s . The square root of the vertical to radial ratio was calculated from the shortened record section. The four events were separated, as before, into two categories, based on the angle of incidence at the base of the crust. Three events, nos. 9, 10 and 11 were characterized by angles greater than 30° leaving only event 8 in the less than 30° class. Similar to before, a l l estimates of the spectral ratio at a given frequency were averaged in each category and standard deviations calculated. The experimental curves determined at frequency intervals of .01 Hz are shown in figure 8c and d. 26 These experimental curves are closely approximated by theoretical curves derived from a one layer crust of thickness 40 km and a P velocity of 6.3 km/sec. More exact model f i t t i n g was not attempted because i t is not certain that, for the small number of events analyzed, the experimental curves are truly representative. A single earthquake may not possess earthquake signal in the entire frequency band. Thus, when a small number of events are averaged, the complete frequency band may not be representative. The uncerta inty in crustal thickness is e s t i -mated at ± 5 km. It is expected that an earthquake recorded at one site w i l l appear similar to the record of the same earthquake recorded at a nearby s i t e . The degree of similarity was investigated by computing the coherence of the vertical components of corresponding station pairs. The same events and the same record sections as used in the spectral ratio calculations were used. The coherency estimates for the events were averaged over the frequency bands 0.3 - 1.2 Hz and .16 - .30 Hz and plotted as a function of epicentral distance (figure 9a). The average coherency of these events were averaged for each of the DOT-YMH and DOT-FISH station pairs. The coherency versus station separation is shown in figure 9b. Also shown in this diagram is the average coherency in the frequency range 0.3 - 1.2 Hz for the events used in the longer period coherency calculations. E l l i s and Basham (1968) observed an increase in coherence with epicentral distance in the frequency range .25 - 1.58 Hz in central Alberta. No such trend is evident in a similar frequency 27 w u w OS w as o u 1.0-0.5-El 0.0-0 — 1 1 1 1 25 50 75 100 EPICENTRAL DISTANCE (°) (a) FREQUENCY RANGE 0.3 - 1.2 Hz INDICATED BY • FREQUENCY RANGE 0.16 - 0.3 Hz INDICATED BY o l . O - i w u w oi w as o u 0.5' 0.0 I 0 20 40 60 80 DETECTOR SEPARATION (KM) (b) FREQUENCY RANGE 0.3 - 1.2 Hz ALL EVENTS (EXCEPT 7) INDICATED BY • FREQUENCY RANGE 0.16 - 0.3 Hz EVENTS 8, 9 § 10 INDICATED BY o FREQUENCY RANGE 0.3 - 1.2 Hz EVENTS 8, 9 § 10 INDICATED BY x FIGURE 9 Station Pair Coherence versus Event Epicentral Distance and Detector Separation 28 band for the region studied here. At longer periods a decrease in coherence with epicentral distance is observed although a small number of events are analyzed. Also, the coherence is generally larger at longer periods suggesting that the longer period energy is less affected by crustal inhomogenieties whose effects have been observed at shorter periods in angles of incidence determinations. The coherency versus station separation suggests, despite lack of estimates, that the coherence is significantly reduced for a station separation of 27 km at 1 second periods while remaining relatively large at .2 second periods up to station separations of 67 km. A rough estimate of a relationship between coherence, station separation and signal wavelengths is made assuming straight lines connect the coherence estimates. (A detector separation of zero is assumed to yield a coherence of one.) Signals of frequency 2.0 and 0.2 Hz have wavelengths of about 3 and 30 km respectively where the P velocity is 6.3 km/sec. A coherence of .75 is estimated for station separations of about 3 X for 2 Hz signals and 7 X for 0.2 Hz signals. 29 SUMMARY AND DISCUSSION The model of the crust beneath the Canadian Shield north of Lake Superior as delineated by refraction seismology features a P velocity of 6.3 km/sec in a single layer 38 km thick in the vici n i t y of Port Arthur. In this study, an estimate of crustal thickness based upon the Haskell matrix formulation of a single layer of P velocity 6.3 km/sec places the base of the crust at 40 ± 5 km beneath the Port Arthur region. The small number of suitable events recorded in a two-month period and the forcing of an unambiguous inter-pretation by the assumption of a P velocity limit the value of such techniques. No indication of near surface horizontal layering was observed. As estimate of the P velocity at the surface is 6.1 ± .8 km/sec -based upon angle of incidence determinations assuming any crustal layering is horizontal. The generation of transverse motion in this region of the crust complicates crustal analysis in the time domain. Frequency domain studies indicate that, for the area studied earthquake signals retain a coherence of .75 up to detector separation of about 5 times the wavelength of the signal. Neither the sources of the transverse motion generated by the signal passing through the crust nor the coherence of the signal generated transverse motion were investigated. Scattering by topographic features or localized velocity contrasts near the surface or at depth are suggested as origins of the former and may be detected by techniques such as the latter. 30 BIBLIOGRAPHY Bancroft, A.M. and P.W. Basham (1967). An F.M. Magnetic tape recording seismograph, Pub. Dom. Obs. 3_5_, 199-217. Basham, P.W. (1967). Time domain studies of short period tele-seismic P phases, M.Sc. thesis, Department of Geophysics, University of British Columbia. Berry, M.J. and G.F. West (1966). A time term interpretation of the f i r s t arrival data of the 1963 Lake Superior experiment, Am. Geophys. Union Monograph 10, 166-180, ed. by J.S. Steinhart and T.J. Smith. Brune, J. and J. Dorman (1963). Seismic waves and earth structure in the Canadian Shield, Bull. Seism. Soc. Am. 5_3_, 167-209 . Bullen, K.E. (1963). An Introduction to the Theory of Seismology, Cambridge University Press, 3rd ed. Byrne, C.J. (1961). Instrument noise in seismometers, Bull. Seism. Soc. Am. 5_1, 69-84. E l l i s , R.M. and P.W. Basham (1968). Crustal characteristics from short-period P waves, Bull. Seism. Soc. Am. 5_8_, 1681-1700. Grant, F.S. and G.F. West (1965). Interpretation Theory in Applied Geophysics, McGraw-Hill. Halls, H.C. (1966). A review of the Keeweenawan geology of the Lake Superior region, Am. Geophys. Union Monograph 10_, 3-27, ed. by J.S. Steinhart and T.J. Smith. Isherwood, B. (1969). Electronic analog-to-digital converters, B.Sc. thesis, Department of Geophysics, University of British Columbia. Moorhouse, W.W. (1960). Gunflint iron range in the vi c i n i t y of Port Arthur, Ontario Department of Mines, LXIX, part 7, 1-40. Mereu, R.F. and J.A. Hunter (1969). Crustal and upper mantle structure under the Canadian Shield from Project Early Rise data, Bull. Seism. Soc. Am. 5_9 , 147-165 . Niazi, M. (1966). Corrections to apparent azimuths and travel-time gradients for a dipping Mohorovicic discontinuity, Bull. Seism. Soc. Am. 56, 491-509. 31 O'Brien, P.N.S. (1968). Lake Superior crustal structure - A reinterpretation of the 1963 seismic experiment, J. Geophys. Res. 73, 2669-2689. Phinney, R.A. (1964). Structure of the Earth's crust from spectral behavior of long-period body waves, J. Geophys. Res. 69, 2997-3017. 32 APPENDIX A - CALIBRATION OF THE U.B.C. SEISMOGRAPHS NOS. 1 AND 2 (FORMERLY A.I.N.A. SEISMOGRAPHS NOS. 1 AND 2) BY A PULSE METHOD (THEORY). Introduction The seismographs used in the 1967 f i e l d season were designed to detect and record three components of ground motion in the frequency range 1.0 Hz to 10.0 Hz. Each seismometer, oriented to detect either the vertical north or east component of ground motion was followed by a phototube amplifier. The amplifier out-put passed through a control panel where the signal was divided into two output levels separated by 12 db. The signals were then recorded on a seven channel slow speed F.M. tape recorder. A chronometer provided timing marks which were recorded on the seventh channel. The overall gain of each component was adjustable by an attenuator at the amplifier input. A simplified block diagram of a seismograph is shown in figure 10. A complete description of these seismographs is given by Bancroft and Basham (1967). The calibration procedure determines the velocity sensitivity of each channel of the seismograph as a function of frequency of ground motion. Variations in the shape of the velocity sensitivity curve are not expected because the frequency response of the seismometer-amplifier galvanometer system are the same from channel to channel. Variations in the amplitude of the curves are expected to vary since the overall gain varies from amplifier to amplifier. These amplitude variations must be SEISMOMETERS AMPLIFIERS CONTROL PANEL WITH HIGH-LOW GAIN SEPARATION V V CHRONOMETER a TAPE RECORDER Q_0 FIGURE 10 Seismograph Bl ock Diagram 34 determined before intercomponent or interstation calculations are made. The portion of the calibration procedure that is completed in the f i e l d consists of two separate operations - the system calibration and the "K test". During the system calibration a step function in ground acceleration is simulated by the rapid termination of a current through the seismometer. The response of the system to the simulated acceleration step is recorded on the tape recorder and is later used in the determination of the velocity sensitivity. The seismometer constant K is determined from the chart recorder strips recorded during the K test. K is the ratio, relating the velocity of the seismometer mass to the voltage appearing across the seismometer terminals as a result of this velocity. The K test strips record a voltage proportional to the voltage across the seismometer both when the seismometer mass is displaced from the equilibrium position by a current through the coil and when the seismometer freely oscillates after the current is terminated. During the K test, the seismometer is separated from the remainder of the seismograph. The magnitude of the system calibration step is determined from the calculated value of K. Transfer function and velocity sensitivity The velocity sensitivity is simply related to the system transfer function. Generally, the transfer function may be determined for a linear system whenever the output function can be determined for a given input. The transfer function S(u) may be defined as 35 S(w) = Fourier Transform of output Fourier Transform of input In the present case, the input signal is a simulated ground acceleration step function of magnitude A microns/sec 2. (Since the input is a simulated acceleration, S(to) is also called the acceleration response of the seismograph). The output signal is the voltage recorded during the system calibration, v(t), multiplied by the difference between normal station operation amplifier attenuation and the amplifier during calibration. The attenuation ratio D, may be determined by com-parison with the following example: If normal station operation is 6 db, and a particular channel is calibrated at 36 db, then (36-6) D = 10 2 0 =31.6 Let F represent the Fourier transform. Then for a step input, F {input signal) = F {step function of height A} A = 10) F {output signal} = F{D-v(t)} = D.F{v(t)} The transfer function becomes S ( w ) = 5|£L F{v(t)} Since, in this case, the transfer function is also the acceleration sensitivity, the velocity sensitivity may be determined using the following relationship F{*x#} = - i wF{x} 36 The transfer function and the velocity sensitivity, S v e ^ o ( o j ) are related by c r \ - or V F{x} _ t o 2 D Development of equations leading to acceleration step height The acceleration step height is computed from the seismometer constant K and the calibration circutry elements. The following l i s t of symbols (M.K.S . units throughout) w i l l be used in the derivation. e(t) - voltage across seismometer terminals - volts x(t) - velocity of seismometer mass relative to frame - m/sec K . - seismometer transducer constant volt-sec/m M - mass of seismometer pendulum - kgm F x - force on seismometer mass during K test loading condition - newtons F c - force on seismometer mass during system calibration loading condition - newtons 1^  - current through seismometer co i l during K test coating condition - amperes I c - current through seismometer c o i l during system calibration loading - amperes V - voltage of calibration c e l l in system calibration circuit - volts d - a damping coefficient - sec" 1 e<j>ei»e2 - measurements from K test strips (Figure 11c) - volts RSEIS - resistance of seismometer in channel being calibrated - ohms R29,R32,R27,R30 - resistance of cir c u i t elements in control panel (Figure 11 a and b) - ohms R32 R33 CHART RECORDER r -• 1 RSEI! R2! (a) K TEST LOAD CIRCUIT RSEIS\ R27 R30 V (b) SYSTEM CALIBRATION LOAD CIRCUIT FIGURE 11 Calibration Circuitry and Typical K Test Record 38 Evaluation of K-test data. The seismometer transducer constant K may be defined by two equivalent equations e = Kx or F = KI During the K test loading, a current 1^  is passed through the seismometer c o i l producing a force F^ on the mass given by F k - K IK-The current 1^  is determined from an analysis of the K test load circuit (Figure 11a). It may be shown that h " e d / R X where RX = RSEIS + R32 (1+RSEIS/R29) The termination of 1^  results in an acceleration step A applied to the seismometer given by Newton's second law A = KIk/M Solution of the differe n t i a l equation describing the seismometer results in the expression for the velocity resulting from this step x =(KI k /u)M)e" d t sin wt The voltage across the seismometer as recorded on the K test strip is 'e(t) = Kx = K 2 l k e" d t sin tot coM The frequency co may be determined from the K test strips as shown in figure 11c. Also shown on this diagram are the quantities Tf 3 TT ei and e 2 which are values of v(t) at t = — and t = — ' respectively. Thus, ej and e 2 are given by 39 C l = (K 2l k/ UM) e _ C d i r / 2 a i ) e 2 = (K2l k /«M) e " ( d 3 T r / 2 ^ Consider the following manipulation e i 3 / 2 e 2 " 1 / 2 - ( K 2 l k A , M ) 3 / V l ^ = (K2l k/«M) Thus, i t may be seen that K2 = (( o M e 1 3 / 2 e 2 " 1 / 2 ) / I k Determination of the acceleration step height. When the value of K has been determined for a particular seismometer, the acceleration step height may be easily determined. During the system calibration loading operation, a current, I c , is passed through the seismometer c o i l . The resulting force on the mass, by analogy with equations above, is given by F = I K c c The sudden termination of the current results in a simulated acceleration step of height A applied to the seismometer given by the above equation and Newton's second law A = F /M = I K/M c c The amount I is determined from the system calibration loading operation shown in figure l i b . Analysis yields I = V.R27/R30(RSEIS+R27) Calculation of the Fourier Transform of the system calibration  pulse The system calibration pulse v(t) is recorded on magnetic tape in the f i e l d . When the pulse is digitized, the Fourier 40 Transform may be conveniently calculated using the formula N-l ri2'ir'ta>^  F{v(t) } = At £ v(t)e l N t=0 where N is the number of estimates of v(t) and At is the digitiza-tion interval. 41 APPENDIX B - CALIBRATION OF THE U.B.C. SEISMOGRAPHS NOS. 1 AND 2, 1967 FIELD SEASON The f i e l d portion of the calibration procedure was repeated every five days for each system. From the K test strips recorded in the f i e l d the values of K were determined. The time variations in the calculated value of K for each system are shown in figure 12 a and b. Variations in K such as are shown on these diagrams are a superposition of two effects. The f i r s t is a small general decrease in K over the two month period. This decrease was not further investigated. The second is a scattering of estimates of K. Ambient temperature fluctuations affecting the seismometers are not expected since the seismometers have an exceedingly small temperature dependence at one second natural period. Also, system two was located in a temperature controlled building and large variations in K are observed for that system. The scattering of estimates of K are caused by the d i f f i c u l t i e s in picking the K test strips and the failure of the chart recorder to accurately reproduce f u l l scale deflections. Because a ratio of two voltages are taken from the K test strips, the absolute gain of the chart recorder is not directly important. Indirectly, however, fluctuations in the gain from day to day may cause a f u l l scale deflection to be recorded. On the other hand, picking errors are minimized with f u l l scale deflections. CO f— o J rH O H > CQ H 2.0 1.5 < rH 1.0 2.0 VERTICAL NORTH EAST ^-VERTICAL HIGH GAIN LOW GAIN NORTH • ac UJ w t - CO tO - J >" 1 5-( c) 1.0"1 1 1 1 1 ' 1 0 10 20 30 10 20 30 JUNE JULY STATION DOT SYSTEM TWO EAST (b) (d) 2.2n 2 .0-1.8 2.2" 2.0-1.8 2.2-2 .0" 1.8 2 .0 0 VERTICAL NORTH EAST VERTICAL ^—7-j? NORTH i i i i i i 10 20 30 10 20 30 JUNE JULY STATION YMH - HX3- STATION FISH SYSTEM ONE FIGURE 12 Time Variation of Calculated K and System Calibration Pulse Height The value of K for each component at each site was the average of a l l available values of K for that component at that si t e . From the values of K, values of A were calculated. Each system calibration pulse recorded in the f i e l d was played back on a chart recorder and the maximum excursion of each pulse was measured. The time variations of the pulse heights are shown in figure 12 c and d. The average pulse height for the high gain channels and the high-low channel separation for each component at each site was determined. Variations of ±S% are typical and limit the accuracy of the calibration. Two calibration pulses per component per seismograph were chosen for digitization. A total of 8.25 seconds at a sampling rate of .04 seconds were digitized commencing at the pulse onset. A typical velocity sensitivity curve as determined from the digitized pulse is shown in figure 13. Also shown is a theoretical velocity sensitivity as deduced from seismometer and galvanometer characteristics. A l l twelve velocity sensitivities are similar in shape at periods exceeding 0.8 seconds. The short period scatter is due to a combination of the relatively small amount of high frequency energy contained in a step function and d i g i t i z -ation noise. Since the curve shapes are similar, i t is possible to scale each channel to a common sensitivity by a multiplicative scaling factor. The parameters used in the standard sensitivity are (1) a digitized system calibration pulse scaled to a maximum excursion of 1.0 volt C(v(t) x =1.0) (2) acceleration step height A = 150 microns/sec 2 VELOCITY SENSITIVITY (VOLT SEC/MICRON) SCALE VALUE ARBITRARY 45 (3 ) o p e r a t i n g a t t e n u a t i o n 0 d b , c a l i b r a t i o n a t t e n u a t i o n 36 db (D = 6 4 ) U s i n g these p a r a m e t e r s , a v e l o c i t y s e n s i t i v i t y curve was c a l c u l a t e d . The s h o r t p e r i o d p o r t i o n of the curve was r e p l a c e d w i t h t h a t from the t h e o r e t i c a l curve to produce the s t a n d a r d v e l o c i t y s e n s i t i v i t y shown i n f i g u r e 13. To s c a l e a h i g h g a i n channe l t o the s t andard r e s p o n s e , the q u a n t i t y D - v ( t ) / A 'max f o r the s t a n d a r d curve was d i v i d e d by the same q u a n t i t y f o r the c h a n n e l under c o n s i d e r a t i o n . The r e s u l t i s the m u l t i p l i c a t i v e s c a l i n g f a c t o r f o r t h a t c h a n n e l . F o r low g a i n c h a n n e l s , the c o r r e s p o n d i n g h i g h g a i n c h a n n e l s c a l i n g f a c t o r i s m u l t i p l i e d by the h i g h - l o w channe l s e p a r a t i o n to produce the s c a l i n g f a c t o r . The u n c e r t a i n t y o f the c a l i b r a t i o n i s e s t i m a t e d at ±10% based upon ±5% v a r i a t i o n s i n each o f the a c c e l e r a t i o n s t e p h e i g h t and maximum e x c u r s i o n o f the system c a l i b r a t i o n p u l s e . 46 APPENDIX C - SPECIAL HINTS FOR THE USE OF THE SEISMOGRAPHS Prior to f i e l d operation one should adjust ( i f necessary) and measure resistors in K test, system calibration, high-low separation and seismometer damping circuits and determine resistance of seismometers. During f i e l d operation, the seismometers should be careful aligned and oriented. The value of a complete log should not be underestimated. 


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