"Science, Faculty of"@en . "Earth, Ocean and Atmospheric Sciences, Department of"@en . "DSpace"@en . "UBCV"@en . "Gurbuz, Behic M."@en . "2011-08-22T20:14:06Z"@en . "1966"@en . "Master of Science - MSc"@en . "University of British Columbia"@en . "This study is undertaken in order to calibrate the continuous velocity logs using the comparision of synthetics and field records. The results refer to the following wells in Alberta.\r\n1. Texaco Arrowhead B-76\r\n60 25' 02\"N, 122 59' 02\" W\r\n2. British American Morrin 7-3\r\nLsd 1, Section 3, Twp 31N, Rge 20 4M\r\n3. Cancrude British American Champion 16-29 Lsd 16/ Section 29, Twp 14, Rge 24 W 4M\r\nThe synthetic records were obtained using a linear filter model. To accomplish the synthesizing process in the laboratory, a magnetic tape function generator is used. The two-way time-depth curves are- plotted for these three wells. From these curves-the time intervals of continuous velocity logs were found in-error by 0.007 seconds to 0.0082 seconds. The possible errors in time scale of synthetic seismograms are discussed in Chapter IV.\r\nThe comparision of synthetics with actual field seismograms recorded corresponding well locations and the main creteria for a \"good match\" and \"poor match\" are discussed."@en . "https://circle.library.ubc.ca/rest/handle/2429/36833?expand=metadata"@en . "CALIBRATION OP CONTINUOUS VELOCITY LOGS USING THE COMPARISON OP SYNTHETIC AND FIELD RECORDS by BEHIC M. GURBUZ B.Sc.j University of Istanbul, 196l A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of GEOPHYSICS We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1966 I n 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 o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e 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 , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e 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 a n d s t u d y . I f u r t h e r a g r e e 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 p u r p o s e s may be g r a n t e d by t h e H e a d o f my D e p a r t m e n t o r 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 o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t 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 D e p a r t m e n t o f G e o p h y s i c s T h e 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 V a n c o u v e r 8, C a n a d a D a t e A p r i l 29 , 1 9 6 6 . i i ABSTRACT This study i s undertaken i r i order to c a l i b r a t e the contirraons v e l o c i t y logs- using the comparision of synthetics and f i e l d records. The r e s u l t s r e f e r to the following wells i n Alberta. 1. Texaco Arrowhead B-76 60 25' 02\"N, 122 59' 02\" W - 2v B r i t i s h American Morrin 7-3 Lsd 1, Section 3, Twp 31N, Rge 20 4M 3. Cancrude B r i t i s h American Champion 16-29 Lsd 16/ Section 29, Twp 14, Rge 24 W 4M The synthetic records were obtained using a,linear f i l t e r model. To accomplish the synthesizing'process i n the g e.net- \u00C2\u00AB * . tor-laboratory, a magnetic tape f u n c t i o n * i s used. The two-way time-depth curves are- plotted f o r these three wells. Prom these curves -the time i n t e r v a l s of continuous v e l o c i t y logs were found in-error by 0,007 seconds to 0,0082 seconds. The possible errors i n time scale of synthetic seismograms are discussed in-Chapter IV. The comparision of synthetics with actual f i e l d seismograms\" recorded corresponding well locations and the main c r e t e r i a f o r a \"good match\" and \"poor match\" are discussed. i i i ACKNOWLEDGMENT Many- people have provided- the -author \"with assistance and counsel during the course- of this research. In particular, ~I- wish-to thank Dr. R. D. Russell for his valuable- discussion and criticism of ~the theoretical part of* this thesis. I am also indebted to Dr. R. M. Ellis for providing many helpfulr suggestions and for. reading the manuscript\" critically. I would like to thank Mr. R. H. Carlyle of the-British -American- Company Limited who- provided i;he author^ irrthr-ttre opportunity- of' working- on this problem with the Bri-bi-srfAraerlcan~0il-Company and Mr. E. F. MahafTy of the abover-company-for his-Interest\" and\" helpful assistance during-the course of this research. \u00E2\u0080\u0094 The sturiy-was -supported\" in~T?art try - research grants made to Professor J. A. Jacobs by the National Research Council of Canada. TABLE OF CONTENTS Page Number ABSTRACT i i ACIOtf OWLEDGMENT \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00C2\u00AB \u00C2\u00AB * \u00C2\u00AB \u00C2\u00AB \u00C2\u00BB 0 \u00C2\u00AB o a \u00C2\u00AB o o a o o e o o o o 6 o o o o o e * o 1- i A. LXS7 OF FIGURES\u00E2\u0080\u00A2 \u00E2\u0080\u00A2 f t \u00C2\u00AB * \u00C2\u00BB * \u00C2\u00BB o e \u00C2\u00BB 0 \u00C2\u00BB \u00C2\u00BB o \u00C2\u00AB o o \u00C2\u00BB o o * o o o e \u00C2\u00BB o o o 0 o \u00C2\u00BB \u00C2\u00AB * XV LIST* OF 7A13LES \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 \u00C2\u00AB * \u00C2\u00AB o o \u00C2\u00AB o \u00C2\u00BB \u00C2\u00AB \u00C2\u00AB o \u00C2\u00BB \u00C2\u00AB e o 0 \u00C2\u00AB a * \u00C2\u00BB o o o o 6 e e e \u00C2\u00BB \u00C2\u00AB \u00C2\u00BB \u00C2\u00BB o Vi CHAPTER I - INTRODUCTION 1 . 1 Well geophone and continuous v e l o c i t y 1 . 1 . 1 Description and operation of continuous v e l o c i t y log sonde and recording devices 1 1 . 1 . 2 The observed time discrepancies between continuous and well geo-phone vel o c i t y surveys.. 4 1 . 2 The synthesis of seismograms from con-tinuous v e l o c i t y log data................. 8 CHAPTER II - THEORY 2 . 1 Theory of the l i n e a r f i l t e r model of Peterson and h i s co-workers............... 1 0 2 . 2 To convert a continuous v e l o c i t y log to the r e f l e c t i v i t y function 1 6 2 . 3 Comparison of synthetic and actual f i e l d 2 . 4 Multiple and ghost r e f l e c t i o n s . . . . . . . . . . . . 1 8 CHAPTER III - CALIBRATION OF CONTINUOUS VELOCITY LOGS USING THE COMPARISON OF SYNTHETIC AND FIELD RECORDS CHAPTER IV - RESULTS 4 . 2 Discussion of the errors i n time scale of r e f l e c t i v i t y function. 2 6 4 . 3 Interpretation of r e s u l t s . . . . . . . . . . . . . . . . . 3 0 CHAPTER IV - CONCLUSION 3 4 i v L IST OP FIGURES A f t e r Page 1. Schematic diagram o f the method by which v e l o c i t y i s d e t e r m i n e d by s h o o t i n g i n a w e l l , and a t y p i c a l i n t e r v a l v e l o c i t y o x i r v3 o I D \" f c & i L n & ( 3 . o \u00C2\u00AB \u00C2\u00AB o \u00C2\u00AB o o o o o o o \u00C2\u00AB \u00C2\u00BB o o * o \u00C2\u00BB \u00C2\u00AB \u00C2\u00AB \u00C2\u00BB o o \u00C2\u00AB o o o o 6 o 1 2. The p r e s e n t a t i o n o f r e s u l t s o f w e l l s h o o t i n g . 1 3 . Schematic diagram o f 4 s x 5 ' c o n t i n u o u s VG l O O \"fcOO\u00C2\u00ABL 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 . Diagram o f c o n t i n u o u s v e l o c i t y l o g g e r . . . . . . . . 2 5 . E f f e c t o f a n i s o t r o p y on c o n v e n t i o n a l w e l l v e l o c i t y s u r v e y . . . e e o o o o o o o o o o o o o o o o o o o o o o o 6. F r o n t view o f magnetic tape f u n c t i o n ^ \u00C2\u00A9 n \u00C2\u00A9 1 0 I* o A e e o o o o o o o o o o o o o o o o o o o o o o e o o o o o e o o o 8 7. Impulse response o f a l i n e a r f i l t e r . . . . . . . . . . 11 8 . Schematic i l l u s t r a t i o n o f the r e f l e c t i o n p r o -c e s s f o r two a c o u s t i c i n t e r f a c e s . . . . . . . . . . . . . 11 9. Schematic i l l u s t r a t i o n o f t h e r e f l e c t i o n p r o c e s s w i t h \u00C2\u00BBn' i n t e r f a c e s 12 10. B l o c k diagram o f the c o n v e r t i o n o f a v e l o c i t y l o g t o t h e r e f l e c t i v i t y f u n c t i o n . . . . . . . 16 11. Two a l t e r n a t i v e ways o f r e p r e s e n t i n g t h e r e f l e c t i o n p r o c e s s I n a l i n e a r f i l t e r . . . . . . . . 16 1 2 o WsXX l o c a t i o n tnd]po 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1^3 13. B.A. Cancrude Champion 16-29 f i e l d r e c o r d . . . . 20 14. B.A. M o r r i n 7-3 f i e l d r e c o r d . . . . . . . . . . . . . . . . . 20 15. B.A. Texaco Arrowhead B-76 f i e l d r e c o r d . . . . . . 20 16. B.A. Texaco Arrowhead B-76 s y n t h e t i c p l a y b a c k 21 17. B.A. M o r r i n 7-3 s y n t h e t i c p l a y b a c k . . . . . . . . . . . 21 18. B.A. Cancrude Champion 16-29 s y n t h e t i c P 1 3 j r b 3 01C o e o o o o o o o o o o o o o o e o v e o o o o o o o e o o o o o o e o o 2 1 V 19. B.A. Texaco Arrowhead B-76 t i m e d . JL S O 37 6 ^ 3 6 \u00C2\u00A310 ^ 6 S \u00C2\u00AB \u00C2\u00BB o 0 \u00C2\u00AB o o 0 O 0 \u00C2\u00AB 9 9 9 o o \u00C2\u00AB o \u00C2\u00BB \u00C2\u00AB \u00C2\u00AB 0 0 0 \u00C2\u00AB 0 \u00C2\u00AB Q e e a o 21 20. B.A. M o r r i n 7-3 t i m e d i s c r e p e n c i e s . . . . . . . . . . . 21 21. B.A. Canerude Champion 16-29 t i m e Cl JL S C 1*6 |D 61*10 t L & S o a * \u00C2\u00AB o o a \u00C2\u00AB 0 e * o o \u00C2\u00AB o a * a a o o o \u00C2\u00BB \u00C2\u00BB o * o Q o o o o 2-L 22. B.A. Texaco Arrowhead B-76 r e f l e c t i v i t y 23. B.A. M o r r i n 7-3 r e f l e c t i v i t y f u n c t i o n Pl3jrOU.t 0 * \u00C2\u00AB o 0 0 e o o o 0 0 0 0 0 0 o \u00C2\u00AB a o o 0 9 O 0 0 0 0 O O O 0 0 0 e 0 e o 22 24. B.A. Cancrude Champion 16-29 r e f l e c t i v i t y 25. B.A. Texaco Arrowhead B-76 two-way t i m e -C l S p ' t / l ' l C U L 3 7 V 6 \u00E2\u0080\u00A2 o O \u00C2\u00BB 0 0 0 0 O 9 e O O O 0 0 \u00C2\u00AB O 0 O 0 0 0 O O O 9 0 0 0 \u00C2\u00AB O 0 O 22 26. B.A. M o r r i n 7-3 two-way t i m e - d e p t h curve....^. 22 27. B.A. Cancrude Champion 16-29 two-way t i m e -C l G ^ t h l C U 3 7 V 6 0 s \u00C2\u00BB 0 0 t t 0 0 o \u00C2\u00AB 0 0 O Q 0 e o o a o 0 o o o \u00C2\u00BB 0 o o \u00C2\u00AB e o o e o 22 28. Comparison o f f i e l d r e c o r d w i t h s y n t h e t i c r e c o r d 32 29. Comparison of f i e l d r e c o r d w i t h s y n t h e t i c 276COjt7Clo a * 0 0 0 0 0 0 0 a * 0 0 9 9 9 0 9 e 0 9 0 \u00C2\u00BB 0 \u00C2\u00BB 0 0 o e 0 0 0 \u00C2\u00BB 0 a o 0 9 32 30. Comparison o f f i e l d r e c o r d w i t h s y n t h e t i c 276 C O 17 CL \u00E2\u0080\u00A2 a r \u00C2\u00BB a \u00C2\u00AB 6 o 0 0 0 0 9 0 O 9 O O O 0 0 0 O e O 0 O O 0 \u00C2\u00BB O 0 0 O O 0 O O 0 0 32 31. Comparison o f f i e l d r e c o r d w i t h s y n t h e t i c 376 C O } 7 C l o o o o o 0 o \u00C2\u00BB a \u00C2\u00AB 0 \u00C2\u00BB o o o o 0 < \u00C2\u00BB o * \u00C2\u00AB * \u00C2\u00BB \u00C2\u00AB o 0 c o o 0 < \u00C2\u00BB ( i o o o o o \u00C2\u00A9 \u00C2\u00BB 32 32. Comparison of f i e l d r e c o r d w i t h s y n t h e t i c 376 C O 37Cl o o o o o 0 \u00C2\u00BB 0 \u00C2\u00AB 9 0 o a 0 Q 9 Q o o o o 0 O 0 O Q O 0 o o o o o a o o a \u00C2\u00AB o O 2 33. Comparison o f f i e l d r e c o r d w i t h s y n t h e t i c 376C037CL\u00C2\u00ABoo 9 0 0 9 0 0 0 a 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 v i LIST OP TABLES After Page 1. Two-way r e f l e c t i o n times at corres-ponding geological formations. B.A. Texaco Arrowhead B-76 26 2. Two-way r e f l e c t i o n times at corres-ponding geological formations. B.A. Morrin 7-3 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 26 3. Two-way r e f l e c t i o n times at corres-ponding geological formations. B.A. Cancrude Champion 16-29 . . . . . . . . . . . . . . . . . . 26 1 CHAPTER I INTRODUCTION 1.1 Well Geophone ^nd\"Continuous \"Velocity Surveys Tfre-Tjra-jorlty\" of -well ve-loclty^surveys-\"carried\"out since 1955 brave \"used\" tw o d i f f e r e n t - methods. The f i r s t method~\"foT7 velocity- me a^urements' i s tor explode-\u00E2\u0080\u00A2 charges of dynamite i n ' a shallow d r i l l hole- alongside\"- a \"deep - explora-tory bore hole and tt) record the arrival- times of waves received- by an: in-hole detector at a number of depths which are d i s t r i b u t e d from top t o bottom. Figure 1 U l u s t r a t e i s the setup and\" shows i n t e r v a l and average- velocity-curves~ of ~ the \"type that are obtained from t h i s procedure. The-interval-velocity- is-the distance between-successive detector p o s i t i o n s i n the well, divided by t h e - d i f f e r e n c e i n a r r i v a l time's at the \"two depths, a f t e r correction from- slant-patbrto v e r t i c a l and'adjusting to a datum*;. (Fig. 2) The average v e l o c i t y i s t h e t o t a l v e r t i c a l distance divided by the t o t a l time. 1 \u00E2\u0080\u00A2 1 \u00E2\u0080\u00A2 1 De sc r i p t i on and Ope r a t i on of Cont inuous V e l o c i t y Log Sonde and- Recording Devices. The-second method, contIripous-velocity-logging, i s c a r r i e d out with a special type of -Instrument.- Figure 3 shows a schematic sketch of t h i s t o o l which incorporates an accoustic- signal generator AMP LI E R AND RECORDER ELECTRIC CABLE DETECTOR 2 0 0 0 [ ] \u00E2\u0080\u0094 3 0 0 0 [ J -4 0 0 0 [ ] 5 0 0 0 [ ] FIGURE 7000 Cu VELOCITY FT/SEC 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 9 0 0 0 \u00E2\u0080\u0094 i 1 1 \u00E2\u0080\u0094\u00C2\u00BB 1 1 \u00E2\u0080\u0094+ \u00E2\u0080\u00A2^ -INTERVAL VELOCITY DETECTOR POSITION 6000 [] Schematic diagram of the method by which v e l o c i t y i s determined by shooting i n a well, and a t y p i c a l i n t e r v a l v e l o c i t y curve obtained WELL E L E V A T I O N SHOT H O L E E L E V A T I O N ^ _ _ S H O T E L E V A T I O N L D A T U M P L A N E E L E V A T I O N 17 L U + L c \u00C2\u00A3 A t s t e T U + L Ac T F I G URE fl2 The p r e s e n t a t i o n o f r e s u l t s o f w e l l s h o o t i n g Geophone depth measured f r o m datum e l e v a t i o n . D i f f e r e n c e i n e l e v a t i o n between shot and datum p l a n e . Geophone depth measured f r o m shot e l e v a t i o n . Geophone depth measured f r o m w e l l e l e v a t i o n . S t r a i g h t l i n e t r a v e l p a t h f r o m shot t o w e l l geophone. H o r i z o n t a l d i s t a n c e f r o m w e l l t o shot p o i n t . Depth o f s h o t . Uphole t i m e a t shot o r o t h e r s u r f a c e r e f e r e n c e t i m e . L = V e r t i c a l t i me f r o m shot t o datum p l a n e . Observed time f r o m shot t o w e l l geophone. C - A - A e D i f f e r e n c e i n e l e v a t i o n between w e l l and shot p o i n t , = V e r t , t r a v e l time f r o m datum p l a n e t o geophone. COQ'J ~[ = V e r t , t r a v e l t i m e f r o m shot e l e v a t i o n t o geophone. Va = Average v e l o c i t y = ^ y . = I n t e r v a l v e l o c i t y = ATc Ve = Topmost v e l o c i t y i n c o n s o l i d a t e d l a y e r . V = d - ( K e l l y B u s h i n g e l e v a t i o n - E l e v a t i o n Datum). C A B L E B U M P E R ^ Z w 2 n < j RECEIVER - r A C O U S T I C I N S U L A T O R I s t R E C E I V E R - 7 ACOUSTIC I N S U L A T O R T R A N S M I T T E R --\u00E2\u0080\u00A2 1 ~ F | G U R E # 3 Schematic d i a g r a m of 4'X5' c o n t i n u o u s v e l o c i t y t o o l . 2 (transmitter) \"-whichemits pulses -ttrartr-travel through- \"the formation- side wall s to \"thereceivers, -The- -transmitter's and receivers are spaced v e r t i c a l l y about 5 feet apart and- are insulated from each other by acoustic insulation\u00E2\u0080\u009E The d i stance \"belween^ must be large enoughso that the f i r s t signal to reach t h i s receiver\" t r a v e l s through at least a small part of the formation which is- to be m e a s u r e d . T h i s c o n d i t i o n obviously cannot b e s a t i s f l e d i n - f ormat1ons i n whic h t h e - v e l o c i t i e s are slower than\" i n \"the mud \u00E2\u0080\u009E\" When formation\" velocl-ty -exceeds mud v e l o c i t y ; the- minimum -required- \"spaclngbetrween-trans-mit ter-and\" t h e f i r s t receiver i s proportional to the stand-off ( i . e . t h e s e p a r a t i o n between the wall of t h e h o l e and the tranducers)- and- is-w f u n c t i o n o f t h e r a t i o of mud \"velo-c i t y -to-f ormatlon v e l o c i t y T h e relationship\" may be derived by straightforward\" computation of the t o t a l time f o r an acoustic pulse to t r a v e l from transmitter to receiver. The r e s u l t i s dmin = p - \ / I + OC s v i - a where dmi n\" = and receiver S =\" stand-off OC = r a t i o of \"mudvelocity to formation -velocity The f i r s t \"arrivals- of- the acoustic signals at the two-receivers are r e c o r d e d d i r e c t l y on the f i l m . F i g u r e 4 i s s i m p l i f i e d Diagram o f c o n t i n u o u s v e l o c i t y l o g g e r . 3. diagram o f t h e continuous v e l o c i t y logger f o r the\"single receiver pulse system. At the pulse Instant, -switch S-^ closesy s t a r t i n g the sawtooth generator Gen, which develops a voltage p r o p o r t i o n a l t o time. --\u00E2\u0080\u00A2---When-'i^e-^coustlc-'Slgnals a r r i v e s a t receiver Rec^, switch\" Sg i s closed discharging the generator voltage, as of t h a l r l r r s t a T i t , - \" ^ on gal 'vanometer Gal^- the -pointer of w h i c h\"traces\"the value of t\u00C2\u00A3 on the l o g a t t h e i n d i c a t e d d e p t h . The~i;\u00C2\u00B1me-'lTistajr^ i t ^ - a r r i v a l at receiver Rec a r e d i s p l a c e d o n a n oscilloscope. - T;The ' l T T t e r g r a t o r \"provides _the~-over-all trav\"el~tlme _ f o r the i n t e r v a l logged by continuous integration of t h e t ^ curve. - The\"contlTiuous\" v e l o c i t y l o g s \"then-consist-of \"two curves: - (a) The I n t e r v a l v e l o c i t y cxirve This\"curve I s \"the-contirraoxts\" recording of the i n t e r v a l time I n -raicTOsecTDnds through i n d i v i d u a l formations along the entire v e r t i c a l extent of the - well; and\" can; be read\" as I n t e r v a l v e l o c i t y on the approp-ri a t e \u00E2\u0080\u0094 s c a l e a t t h e t o p o f t h e l o g . (b) The integrated\"curve. This curve\" i s derived by d i r e c t summationof \" t h e i n t e r v a l \" v e l o c i t y curve, and i s c a l i -brated: to-the geophone s u r v e y s . T o t a l t r a v e l times over any section of the log may be obtained from i t . 4. The -re s u i t s erf time tteterainations surveyed by both h methods- do not - -agree \"and: disc\"repancies up to several \"tents of milliseconds f o r tteep wells occur\u00E2\u0080\u009E - The usual-procedure i s to survey- a well with both- methods\u00E2\u0080\u009E When the survey i s i n -terpreted; the continuous v e l o c i t y data adjusted t o the well geophone survey; - The usual \"argument f o r this\" procedure i s that the\" well geophone'survey simulates-more c l o s e l y the conditions' encountered i n seismic\" shooting. The i n t e r v a l v e l o c i t y curve-is therefore l a t e r a l l y displaced, \"and the slope of the - i n t egrated: curve is- adjusted before f i n a l d rafting, using a corrected time. The ref lection\" horizons -\" are not always\" obvious from h a continuous v e l o c i t y \"log. \"They ref lect\" the l i t b l o g y and are often - very s i m i l a r to r e s i s t i v i t y logs. The r e f l e c t i o n h o r i -zons \"versus v e l o c i t y - c o n t r a s t s can be-correlated from well to well i n a given area. 1.1.2 The\" Observed Time' Discrepancies Between C ont irruous and- -Velocity- Surveys. - The- -re suits\" of - the s t a t i s t i c a l analysis of the observed time discrepancies between continuous and v e l o c i t y surveys showed\" that there is\" both a~ normal random discrepancy-and-a systematic deviation between the observed time of the velocity-and the well geophone surveys (Oretener 1963). It I s found - that certain\" Important fac t o r s strongly influence the deviation found between the two\" types of surveys. \"The\"study of continuous-velocity surveys Is subject t o t h r e e s o u r c e s of e r r o r s . F i r s t o f a l l a p r o blem a r i s e s i n t h e - p r e s e n c e - o f non i d e a ! t o o l geometry. L a b o r a t o r y s t u d i e s ' a n d s u r v e y s i n w e l l s ( H i c k s 1959* Kokesk and P l i z a r d 1959, W y l l i e , G r e g o r y and Gardener 1958), showed t h a t i n t h e i n v a d e d ( p e n e t r a t e d by d r i l l i n g f l u i d ) zone a-round a w e l l , t h e apparent v e l o c i t y i s l o w e r t h a n i n t h e v i r g i n f o r m a t i o n . The major f a c t o r s e f f e c t i n g t h e t h i c k n e s s of t h e low v e l o c i t y zone are the c o n s o l i d a t i o n , p o r o s i t y ; and' m i n e r a l c o m p o s i t i o n of t h e f o r m a t i o n b e i n g p e n e t r a t e d . The c o n t i n u o u s v e l o c i t y measurements a c q u i r e t h e c h a r a c t e r o f r e -f r a c t i o n s u r v e y s and u n l e s s the s p a c i n g ( d i s t a n c e between r e c e i v e r and t r a n s m i t t e r ) i s s u f f i c i e n t l y l a r g e ( F i g . 3), the f i r s t a r r i v a l s w i l l n o t have t r a v e l l e d t h r o u g h the v i r g i n f o r -m a t i o n . I t i s t h u s d e s i r a b l e t o e x t e n d the s p a c i n g t o the maximum p o s s i b l e l e n g t h . A f u r t h e r \" p o t e n t i a l source o f e r r o r a r i s e s f r o m the problem\" o f the i m p r o p e r c e n t e r i n g o f the t o o l i n t h e h o l e . The t o o l i s equipped w i t h removable r u b b e r bumpers and cen-t r a l i z e r s o f a p p r o x i m a t e l y 5 i n c h e s i n d i a m e t e r . W i t h \" t h e h i g h l o g g i n g speeds, t h e f l o w o f mud\" around the t o o l w i l l a l s o t e n d t o keep th e t o o l c e n t r a l i z e d . T h e r e f o r e , a s y s -t e m a t i c d e v i a t i o n due t o a c o n s t a n t i n c l i n a t i o n o f the t o o l i n the\" h o l e , seems i m p r o b a b l e . I t i s f u r t h e r - f o u n d t h a t t h e r e s u l t s may be a f f e c t e d by p o s s i b l e wave d i s p e r s i o n i n t h e f r e q u e n c y range 50-12,000 c.p.s. We have l i t t l e a v a i l a b l e i n f o r m a t i o n c o n c e r n i n g wave d i s p e r s i o n . B i r c h and B a n c r o f t (1958) have i n v e s t i g a t e d t h i s 6. phenomenon i n g r a n i t e i n the range 140 t o 4,500 c.p.s. They have measured t h e f T e x u r a l \" ^ t o r s i o n a l and l o n g i t u d i n a l modes. The f i r s t \"two\" modes-do\" n o t I n d i c a t e any I n c r e a s e \" I n v e l o c i t y , w h i l e t h e l a s t one -shows an I n c r e a s e i n v e l o c i t y of about 0.5$ o v e r t h e range 850 t o 4,300 c.p.s., w h i c h l i e s w e l l w i t h i n \" t h e l i m i t of e r r o r . They have c o n c l u d e d ' t h a t - f o r t h e s e f r e q u e n c i e s , t h e v e l o c i t i e s were independent of f r e -quency t o w i t h i n 1$ o r l e s s . . Bruckshaw and Mahanta (1952) have a l s o s t u d i e d t h i s p r o b l em i n t h e range of 40 t o 120 c , p t s . f o r v a r i o u s r o c k t y p e s such as d i o r i t e , d o l e r i t e , l i m e s t o n e and sandstone. The v e l o c i t y - f r e q u e n c y c u r v e s o f the s e r o c k s a r e q u i t e s i m i l a r , showing an i n c r e a s e of t h e wave v e l o c i t y w i t h f r e -quency of about 1.5$ i n t h e range of 40 t o 120 c.p.s. These c u r v e s I n d i c a t e t h a t t h e r a t e o f i n c r e a s e d i m i n i s h e s w i t h h i g h e r f r e q u e n c i e s . One\" can c o n c l u d e \"that t h e r e i s e v i d e n c e t h a t the wave v e l o c i t y i n c r e a s e s s l i g h t l y w i t h \u00E2\u0080\u00A2 f r e q u e n c y . A l t h o u g h t h e r e a re two major s o u r c e s o f e r r o r s i n the w e l l geophone s u r v e y s , i t i s - a l s o f o u n d t h a t t h e r e a re many p o s s i b l e e f f e c t s which\" c o u l d cause a degree o f randomness i n t h e ' o b s e r v e d \"data. The most I m p o r t a n t s i n g l e source o f e r r o r i s t h e d e l a y o f t h e s i g n a l due t o t h e c h a n g i n g e l e c t r i c a l p r o p e r t i e s o f t h e setup d u r i n g the s u r v e y . F o r s h a l l o w s h o t s , an u n s h i e l d e d w e l l geophone c a b l e h a v i n g a h i g h i n d u c t a n c e and low c a p a c i t a n c e \" I s wound on\" t h e drum w h i l e f o r deep check 7. shots - the capacitance i s high and inductarte i s low. This, of course, \"might introduce a lag into the we IT geophone survey. An attempt has been made to - eliminate t h i s possibility\u00E2\u0080\u009E An experiment was set\" up whereby a pulse was recorded d i r e c t l y and also a f t e r going through the\" cable and the downhole geo-phone; The r e s u l t s of t h i s experiment\"have not shown\" any delay. However, i i ; \"has been\" noticed that In\" the case of poor breaks,' some kind of later\" event might be picked rather than the\" true\" f i r s t a r r i v a l s . Studies-at d i f f e r e n t locations \"indlcated\"i;ftat\" ani so-trophy i s indeed a rather common phenomenon, i n a simple case or-anisotropy, ~the\" v e l o c i t y p a r a l l e l to the surface w i l l be greater than that at right angles to i t . If \"the beds are undistributed,\" the hoTizontal v e l o c i t y i s greaterl;han\u00E2\u0080\u0094the v e r t i c a l v e l o c i t y i n the medium above the geophone l e v e l . The ani sotropy fac tor -may be \"given by the r a t i o of the horizont a l v e l o c i t y t o the- v e r t i c a l v e l o c i t y . ~ I n any intermediate direction- the v e l o c i t y \"has a value Vg, whereby ^ \u00C2\u00AB Figure 5 shows the a f f e c t of anisotropy i n the shallow layers on a well geophone v e l o c i t y survey. For the v e r y shallow check-shot l e v e l s , the angle i s large-and the ray t r a v e l s at a v e l o c i t y V , which is\" about (V^ + V z ) / 2 , while f o r the deep levels\"the angle becomes\" small-and \"the:ray-travelsthrough-the same shallow layers at a v e l o c i t y very close to V z . Consequently;- an-error I s committed -when- correcting the shallow check-shot times' to v e r t i c a l time by a mere W E L L SHOT POINT E f f e c t of anisotropy on conventional well v e l o c i t y survey 8. multiplication'with cos tp . The times f o r the shallow check-shot l e v e l s w i l l be short I f no allowance i s made f o r aniso-tropyr^whiie the times f o r the\" deep l e v e l s w i l l be correct. For anisotropy fa c t o r of 1.1 and various v e l o c i t i e s the error i s zero at-*the surface'and increases to a maximum for signals a r r i v i n g at 45 degrees. I t -should- be taken into consideration that a cur-vature i n the raypath'will cause the same type of error. I f we do\" not have- available continuous- v e l o c i t y data\" from the surface downwards, i t w i l l i n most cases be impossible to determine- whether such\" an-error i s due t o true anisotropy, or curvature of the\" raypath- or combination of both. 1.2 The~Synthesis--of Seismograms\" from Continuous V e l o c i t y Log Data. Recent developments\" of continuous- v e l o c i t y l o g sur-veying \"and i t s logging devices and a c q u i s i t i o n of\"sub-stantial amounts-of- data-have m a t e r i a l l y increased the p o t e n t i a l i t i e s of such Investigations-.- - \"Under- s i m p l i f i e d hut - r e a l i s t i c p h y s i c a l assumptions, the basic data from continuous v e l o c i t y surveys i n wells-can be\" used-to\" simulate-the v a r i a t i o n s i n acoustic impedance in- the\u00E2\u0080\u0094ground' which gives r i s e to\" seismic-ref l e c t i o n s . ThIs argument\" - has - been- put -forward by\"Pete rson et a l . (1954), who they describe -an-analogue- computer which' makes use of the basic w e l l data to procedure synthetic seismic records re-sembling actual f i e l d seismograms. To accomplish \"this synthe-sizing-process- i n the laboratory magnetic- tape function generator i s being used (Fig. 6 ) . FIGURE # 6 F r o n t view o f magnetic tape f u n c t i o n g e n e r a t o r 9. - Corre^pondrarrce between the synthesized\" record and actual\" seismic record made over-the w e l l i s quite good i n many cases; even-though some-of the conditions-which occur i n nature (noise, multiple r e f l e c t i o n s , f o r example) are not simulated - In \"the synthesis r The technique i s p a r t i c u l a r l y useful-Tor showinig the e f f ect of -small - changes i n v e l o c i t y or l a y e r thickness upon ~fche wave form- of a -reflection. Mo re recent\"studies have been\" made\"Berryman (1958)-and Wuenschel (I960) who have \"described mo dels\" which\" contain a l l \" multiples. Backus (1959) \"tntraduced\"water reverbations into the model. Lindsey \"(i960) introduced ghosts i n the same way \"that Backus introduced reverbations. Up~tc- t h i s p-oint-j, we \"have-briefly- outlined the -process- of two well velocity-survey methods and have discussed possible causes f o r time\" discrepancies between \"continuous v e l o c i t y and\"~well -geophone- surveys-and the - c a l i b r a t i o n of continuous velocity-logs-according-to the well geophone data. F i n a l l y ; we have mentioned\"the sythesis of selsmo-grams. - In- our\" studies, we have attempted to c a l i b r a t e con-tinuous v e l o c i t y logs using-comparisions\" of - syntheilcs and f i e l d records rather than well geophone survey. 10. CHAPTER I I THEORY 2.1 Theory of the L i n e a r F i l t e r Model of Peterson and h i s Co-Workers. In- t h e ^ ^ made i r r order t o make the problem t r a c t a b l e . The model ea r t h i s assumed to be t r a n s v e r s l y i s o t r o p i c , a n d i s c h a r a c t e r i z e d i n t h e ' \" v e r t i c a l ~ d l r e c t i ^ ^ v(z) -7 \"that\u00E2\u0080\u0094is- obtained-from a -continuous-Telocity l o g . The d e n s i t y f u n c t i o n p ( z ) o f the model i s r e l a t e d by any general expression of the form P(z) = k where k and m a r e constants. The s h o t p u l s e propagates i n the v e r t i c a l d i r e c t i o n as a planewave, thus s t r i k i n g the l a y e r s at normal incidence and r e f l e c t i o n s r e s u l t e x c l u s i v e l y from v e l o c i t y changes due to the - -assumed: r e l a t i o n s h i p ^ \"between \"density and \" v e l o c i t y . Furthermore\" o n l y p r i m a r y - r e f l e c t i o n s a r e inc l u d e d , a l l types of \"noise\" such as ground r o l l , m u l t i p l e s and ghosts are e x c l u d e d . T h e shot pulse wave form I s t i m e - i n v a r i a n t (the p r o p e r t i e s o f \" t h e f i l t e r \"are --Independent\" of \"time)- i t s s h a p e and a m p l i t u d e a r e constant -and do not - change w i t h t r a v e 1 time. One g e n e r a l l y accepted standard method of f i l t e r V tf.) 11. c h a r a c t e r i z a t i o n i s i t s i m p u l s e r e s p o n s e . ( P i g . 7.) An i n p u t i m p u l s e of u n i t a r e a w i l l p r o c e d u r e a c h a r a c t e r i s t i c t r a n s i e n t o u t p u t waveform u ( t ) . There a r e t w o r e s t r i c -t i o n s o f t h e f u n c t i o n u ( t ) i n any p h y s i c a l l y r e a l i z a b l e f i l t e r : UCt) = 0 for t< o ( 2 ) U(t)-\u00C2\u00BB0 for t -> oo An a r b i t a r y i n p u t f ( t ) w i l l be m o d i f i e d i n passing- through\" t h e f i l t e r \"and g i v e a n o u t p u t which w i l l be a f u n c t i o n of b o t h f ( t ) and u ( t ) . The- m a t h e m a t i c a l e x p r e s s i o n o f t h i s o u t p u t w i l l be g i v e n b y c o n v o l v i n g f ( t ) w i t h u ( t ) . T h e m a t h e m a t i c a l o p e r a t i o n o f c o n v u l a t i o n i s d e s i g n a t e d by a s t a r , a n d i s d e f i n e d b y t h e f o l l o w i n g r e l a t i o n s h i p : S(t) = f ( t J * U C t ) = f f (t)U ( .L-T)dT ( 3 ) -Jo F i g u r e 8 shows a s i n g l e i n t e r f a c e s e p a r a t i n g two s e m i - i n f i n i t e media. The v e l o c i t y above the i n t e r f a c e i s v 1 and the v e l o c i t y b e l o w i s V g . T h e d e n s i t i e s a b o v e and below the i n t e r f a c e p^ and p^ . T h e d e n s i t y - v e l o c i t y p r o d u c t between two r o c k l a y e r s w i l l be P ( v]_ a n d P 2 V 2 \u00C2\u00B0 The p u l s e - p r o p a g a t e s d o w n w a r d as a p l a n e wave w i t h normal i n c i d e n c e i n t e r f a c e s . The r e f l e c t i o n c o e f f i c i e n t i s d e f i n e d as t h e r a t i o o f t h e r e f l e c t e d wave a m p l i t u d e t o the i n c i d e n t wave a m p l i t u d e . I t i s e q u a l t o P2V2-P1V1 ( 4 ) P 2 V 2 + A V , I M P U L S E FI6URE #7 Impulse response o f a l i n e a r f i l t e r D E P T H S T R I P G R A P H OF A C O U S T I C I M P E D A N C E V E L O C I T Y V, R E F L E C T I O N C O E F F I C I E N T o v2 R _ A^-A X _ A r i t SHOT P U L S E f(t) UN IT A M P L I T U D E x i\u00E2\u0080\u0094 o_ R E F L E C T I O N , R\u00E2\u0080\u00A2 f Ct-tO A M P L I T U D E , R. P . DE L A Y T l M E , t = \u00C2\u00B1 \u00C2\u00B0 L o F I G U R E W 8 or >-< MED I U M I P, V, M E D I U M 2 J R A N S M I T T E D W A V E I M P U L S E Schematic i l l u s t r a t i o n of the r e f l e c t i o n process f o r two acoustic i n t e r f a c e s 12. assuming--the\"density to-be-constant, we can write t h i s re-lati o n s h i p as follows: portional to some power of the v e l o c i t y . The r e f l e c t e d pulse h a s - i d e n t i c a l l y the same- shape -and iare-adth as the i n -cident pulse, but d i f f e r s i n amplitude\". When the incident wave propagates from a medium of low velocity, the r e f l e c t i o n c o e f f i c i e n t i s - p o s i t i v e -and i t s p o l a r i t y w i l l be the same as the~shot pulse. On the other hard, when\" the incident wave t r a v e l s from a medium of high v e l o c i t y into one of lower v e l o c i t y , the corresponding r e f l e c t i o n c o e f f i c i e n t i s negative and\"its p o l a r i t y - w i l l be reversed\u00C2\u00BB The beginning of the reflection\"occurs at the time 7/ , which i s the two-way t r a v e l time to the int e r f a c e . Thus, i f one designs the shot pulse f(t)- , the~ r e f lection-can be written R.jf(t- % ) \u00E2\u0080\u00A2 This model can be extended to -velocity\"interfaces occurring at i n f i n i t i s i m a l l y small depth-intervals (Fig. 9 ) . Each r e f l e c t i o n has-its- own- polarity,\" amplitude and time delay, but has the same wave-form-as the time-invariant shot pulse. The sum of a l l the r e f l e c t i o n s w i l l be the output of t h i s model. R = V 2 ~ V 1 (5) v2i-v, As was mentioned i n the discussion of the properties of t h i s model, the density ( p ) i s assumed constant or pro-S C t ^ R f C t - p + f ^ f C l - p t - (6) If written as a summation: n (7) BLACK BOX SHOT PULSE Schematic i l l u s t r a t i o n of the r e f l e c t i o n process with 'n1 interfaces 13. The e q u a t i o n (7) d e s c r i b e s t h e r e f l e c t i o n - p r o c e s s i n t h e \" n \" l a y e r e d model. T h i s e q u a t i o n shows\" \"that t h e r e f l e c t i o n p r o c e s s o f P e t e r s o n ' s model i s a l i n e a r f i l t e r p r o c e s s . The e a r t h c a n b e assumed as a f i l t e r w h ich im-p u l s e r e s p o n s e i s the s e t of r e f l e c t i o n c o e f f i c i e n t s spaced\" \" s u i t a b l y in'time\". The\" m o d e l c a n be \"extended\"from \"n\" l a y e r s t o a c o n t i n u o u s v e l o c i t y - d i s t r i b u t i o n a s t h e l a y e r t h i c k n e s s a p p r o a c h e s z e r o . Then e q u a t i o n (7) be-comes c o n v o l u t i o n I n t e g r a l . \" \" T h e \" c o n t i n u o u s v e l o c i t y - l o g g i v e s the c o m p l i -c a t e d l a y e r i n g o f t h e e a r t h ; a n d i t can be sampled t o g i v e a m a n y l a y e r e d model. T h e r e f l e c t i o n c o e f f i c i e n t s c a n b e c a l c u l a t e d u s i n g e q u a t i o n ( 5 ) . P e t e r s o n i n t r o d u c e d a s i m p l i f i c a t i o n by u s i n g a n a p p r o x i m a t e expre s s i o n f o r t h e r e f l e c t i o n c o e f f i c i e n t s . I n e q u a t i o n ( 5 ) , v g can be wr i t t e n as p v^+ /\ ( p v ) . Then e q u a t i o n (5) becomes: [pv.VACP^-pv, (.8) - 1 ~ [Pv ( T-A(Pv)]tPM R - A C P V ) (9) 1 2PX+ACPV) I f a c o n t i n u o u s ve1oc11y l o g i s sampled a t s u f f i c i e n t l y s m a l l - I n t e r v a l s , t h e e q u a t i o n (9) can be w r i t t e n as f o l l o w s : R g l A C P V ) ( 1 0 ) 1 2 P V , or, 1 R^_LA.Log(PV) (11) 2 14. T h i s a p p r o x i m a t i o n g i v e s r e a s o n a b l e r e s u l t s f o r r e f l e c t i o n c o e f f i c i e n t s l e s s t h a n + 0 . 4 . I n t h i s model, t h e d e n s i t y i s c o n s i d e r e d c o n s t a n t , so t h a t t h e above r e l a t i o n s h i p (11) can be- f u r t h e r s i m p l i f i e d t o g i v e : R . L L A l o g V , ] (12) T h i s e x p r e s s i o n s t a t e s t h a t the a m p l i t u d e o f t h e wave r e -f l e c t e d by each i n c r e m e n t a l change o r \" s t e p \" i n a c o u s t i c impedance i s p r o p o r t i o n a l t o the c o r r e s p o n d i n g i n c r e m e n t a l change i n t h e v a l u e o f t h e l o g a r i t h of a c o u s t i c impedance. I n r e l a t i o n s h i p (1) i f k and m are c o n s t a n t s , the a c o u s t i c - impedance can be e x p r e s s e d as f o l l o w s : p v = k v n w (13) When s u b s t i t u t i n g t h e above v a l u e i n e q u a t i o n (11), t h e r e f l e c t i o n c o e f f i c i e n t becomes: R ^ - i - A U g k V m + ' (14) 2 \ ' T h i s can a l s o be w r i t t e n as f o l l o w s : 2 A Log k-Km+ Q ALonV (15) s i n c e k I s a c o n s t a n t , t h e e q u a t i o n (15) can be w r i t t e n i n t he form. R ^ J H t L A L o g V (16) ~ 2 I n the above e x p r e s s i o n (16) the r e f l e c t i o n c o e f f i c i e n t I s a l s o p r o p o r t i o n a l t o t h e change i n the l o g a r i t h m o f v e l o c i t y 15. The c o n t i n u o u s v e l o c i t y l o g shows the v e l o c i t y d i s t r i b u t i o n w i t h r e s p e c t t o d e p t h . T h i s i s c o n v e r t e d t o v e l o c i t y as a f u n c t i o n of two-way t r a v e l t i m e . I n t h e d i s c r e t e l a y e r c a s e / t h e r e f l e c t i o n a m p l i t u d e i s determined\" by the r e -f l e c t i o n c o e f f i c i e n t s , u s i n g e q u a t i o n (5) o r a p p r o x i m a t i o n (11). Otherwise t h e c o n t i n u o u s s e t of r e f l e c t i o n c o e f -f i c i e n t s i s r e p l a c e d by the r e f l e c t i v i t y f u n c t i o n r ( t ) . The r e f l e c t i v i t y f u n c t i o n can be made more u s e f u l I n r e l a t i o n s h i p (9) by l e t t i n g A t approach z e r o as a l i m i t . T h i s can be done by f o l l o w i n g t h e s t e p s as shown below: \u00C2\u00AB \u00C2\u00AB L i m _ ^ _ = L i m I : LUO A t At-o A t ow / AV \ A t I 2V dv At (18a) dt d i l \u00C2\u00AB \u00E2\u0080\u009E w r + i l (18b) \u00C2\u00B0L_ [Log V ( t ) l it L J 2 v d; The c o n s t a n t 1/2 on the r i g h t s i d e of t h i s e q u a t i o n i s m e r e l y a g a i n f a c t o r and i t can be I g n o r e d . The l o g a r i t h m of v e l o c i t y as a f u n c t i o n of time i s c a l l e d t h e v e l o c i t y f u n c t i o n . Then the f i r s t d e r i v a t i v e o f the v e l o c i t y f u n c t i o n w i t h r e s p e c t t o time i s d e f i n e d as t h e r e f l e c t i v i t y f u n c t i o n : A d Log V CD , -r = Jl ( 1 9 ) a t 16. 2.2 To Co n v e r t a C o n t i n u o u s V e l o c i t y Log t o t h e R e f l e c t i v i t y F u n c t i o n F i g u r e (10) i s a b l o c k diagram which shows how t o c o n v e r t a c o n t i n u o u s v e l o c i t y l o g t o the r e f l e c t i v i t y f u n c t i o n . S i n c e the r e f l e c t i o n p r o c e s s i s a f i l t e r p r o c e s s , t h e r e - a r e two a l t e r n a t e w a y s t o a c c o m p l i s h t h e f i l t e r i n g p r o -c e s s i n P e t e r s o n ' s model ( F i g u r e 11). The f i r s t normal way f o r t h e r e f l e c t i o n p r o c e s s i s t o c o n s i d e r t h e shot p u l s e as the i n p u t and the r e f l e c t i v i t y f u n c t i o n as the impu l s e response o f the f i l t e r . As i t has been mentioned i n t h e p r e v i o u s d i s c u s s i o n s , t h e m a t h e m a t i c a l t h e o r y of t h i s model i s depen-dent upon c o n v o l u t i o n . We know t h a t the c o n v o l u t i o n has com-m u t a t i v e o p e r a t i o n , ( i . e . f ( t ) ^ g ( t ) = g ( t ) # f (t)) t h e r e f o r e , t h e i n p u t and the f i l t e r can be i n t e r c h a n g e d , u s i n g the r e f l e c t i v i t y f u n c t i o n as an i n p u t and t h e shot p u l s e as t h e im p u l s e r e s -onse of the f i l t e r . T h i s i s P e t e r s o n ' s analogue method of p r e p a r i n g s y n t h e t i c seisinograms. The f i l t e r s e t t i n g s t h a t a c t upon t h e r e f l e c t i v i t y f u n c t i o n have been d i v i d e d i n t o two p a r t s , namely the shot p u l s e and the f i l t e r i n g e x t e r n a l t o the e a r t h . The l a t t e r i n c l u d e s t h e combined e f f e c t o f a l l i n s t r u -ments p l u s geophone c o u p l i n g ( F i g u r e 11). 2.3 Comparison o f S y n t h e t i c and A c t u a l F i e l d Seismograms B e f o r e a t t e m p t i n g t o approach our problem, we have s t u d i e d t h e comparison of s y n t h e t i c s w i t h a c t u a l f i e l d seismograms r e c o r d e d a t c o r r e s p o n d i n g w e l l l o c a t i o n s . F i g . 12 shows the a r e a s t u d i e d . v o o C O N V E R T D E P T H TO T R A V E L T I M E TWO-WAY VCO C O N V E R T V E L O C I T Y TO L O G A R I T H OF V E L O C 1 Y Log VCt) DI F F E R E N T I A T E R E F L E C T 1 V-ITY F U N C T I O N rCt) rOt)* JL_ log v(tj dt F l G U R E # 1 0 Block diagram of the convertion of a v e l o c i t y log to the r e f l e c t i v i t y function F l L T E R S H O T P U L S E a . \u00E2\u0080\u0094 > N P U T R E F L E C T I V I T Y F U N C T I O N r ( t ) OCf) ^ O U T P U T F l L T E R E X T E R N A L T O E A R T H e( t ) R E F L E C T I V I Y F U N C T I O N F I L T E R r ( t ) S H O T P U L S E O C t ) *\u00C2\u00BB\u00E2\u0080\u0094 F | L T E R E X T E R N A L T O E A R T H 1 N P U T O U T P U T e(+) E l G U R E * I I S Y N T H E T I C set) Two a l t e r n a t i v e ways of r e p r e s e n t i n g the r e f l e c t i o n p r ocess i n a l i n e a r f i l t e r As a r e s u l t o f t h e s e s t u d i e s , r e a s o n a b l e c o r r e l a -t i o n s -were o b t a i n e d a t t h i r t e e n d i f f e r e n t l o c a t i o n s , while\" a few l o c a t i o n s showed \"poor\" matches. There are t h r e e main c r i t e r i a f o r a good match. 1. The s y n t h e t i c and a c t u a l f i e l d r e c o r d s h o u l d match i n c h a r a c t e r . B o t h r e c o r d s s h o u l d have the same i n t e r v a l time between l a r g e r e f l e c t i o n e v e n t s and have a l s o t h e same \"dead\" zones. 2 . ' When \" t h e - f i e l d a nd s y n t h e t i c r e c o r d s have t h e b e s t c h a r a c t e r match, t h e y s h o u l d a l s o have t h e same f i l t e r d e l a y . 3. The p o l a r i t i e s of b o t h r e c o r d s s h o u l d be c o n s i s t e n t . I f t h e p o l a r i t y o f t h e f i e l d r e c o r d i s e s t a b l i s h e d by m a k i n g t h e ' i n i t i a l s i g n a l break-down, a s t e p v e l o c i t y change i n t h e e a r t h f r om low t o h i g h v e l o c i t y w i l l r e s u l t I n a r e f l e c t i o n t h a t i n i t i a l l y b r e a k s down on t h e a c t u a l f i e l d r e c o r d . The p o l a r i t y o f t h e s y n t h e t i c r e c o r d can be s e t ' t o t h e p o l a r i t y o f t h e f i e l d r e c o r d by p l a c i n g an i s o l a t e d s t e p on the v e l o c i t y f u n c t i o n and o b s e r v i n g . the i n i t i a l b r e a k of I t s r e f l e c t i o n . I n g e n e r a l , t h e r e are t h r e e p o s s i b l e r e a s o n s f o r a poor match i n comparison w i t h t h e s y n t h e t i c and a c t u a l f i e l d r e c o r d s . 1. The f i l t e r i n g on t h e s y n t h e t i c may n o t d u p l i c a t e the f i l -t e r i n g on the a c t u a l f i e l d r e c o r d . I t s h o u l d be t a k e n i n t o a ccount t h a t the' a c t u a l f i e l d r e c o r d c o n t a i n s a shot p u l s e f i l t e r as w e l l as a l l f i l t e r i n g e x t e r n a l t o 18. t h e e a r t h - such as, geophone c o u p l i n g , a m p l i f i e r f i l t e r , geophone re s p o n s e , (Automatic G a i n C o n t r o l ) and so on. 2. The o r i g i n a l c o n t i n u o u s v e l o c i t y l o g i s s u b j e c t t o e r r o r - i n some o f the f o r m a t i o n s . The most i m p o r t a n t ones are due t o washouts i n s a l t and s h a l e f o r m a t i o n s . 3. The a s s u m p t i o n made i n t h e t h e o r y of t h i s model may n o t h o l d s u f f i c i e n t l y w e l l i n the a c t u a l e a r t h . The p r i m a r y poor a s s u m p t i o n i s t h a t t h e r e c o r d o n l y i n c l u d e s p r i m a r y r e f l e c t i o n s . A l l t y p e s o f n o i s e such as ground r o l l , m u l t i p l e s and g h o s t s a r e e x c l u d e d . The second poor a s s u m p t i o n i s t h a t t h e d e n s i t y as constant\" o r p r o p o r t i o n a l t o v e l o c i t y . T h i s a ssumption i s poor i n some f o r m a t i o n s such as s a l t and a n h y d r i t e . 2.4 M u l t i p l e and Ghost R e f l e c t i o n s : Based on e x p e r i e n c e and p h y s i c a l r e a s o n i n g , c o n d i t i o n s c o n d u c i v e t o the f o r m a t i o n of m u l t i p l e r e f l e c t i o n s a r e : (a) \" t h e \" e x i s t a n c e of s t r a t a which r e f l e c t s a l a r g e p e r c e n t a g e o f t h e \" i n c i d e n t energy o r f o r m a t i o n s h a v i n g minumum a t t e n u a t i o n and a b s o r p t i o n of s e i s m i c e n e r g y by secondary e f f e c t s ( d i f f r a c t i o n , d i f f u s i o n e t c . ) . (b) s u r f a c e c o n d i t i o n s \"such t h a t e x p l o s i v e c h a r g e s are e f f i c i e n t and a l a r g e p e r c e n t a g e of the emergent energy i s r e f l e c t e d f r o m t h e ground s u r f a c e . The s i g n i f i c a n c e o f m u l t i p l e s t o t h e t o t a l r e f l e c t e d s i g n a l depends on t h e v e r t i c a l d i s t r i b u t i o n o f a c o u s t i c imped-ance. F o r s m a l l c o n t r a s t s i n a c o u s t i c impedance, m u l t i p l e s 19. can produce d i s c r e t e e v e n t s , cause phase s h i f t s i n l a r g e a m p l i t u d e , d i r e c t r e f l e c t i o n s , and a l t e r t h e f r e q u e n c y o f weak, d i r e c t , r e f l e c t e d s i g n a l s . I f the nea r s u r f a c e con-t r a s t s a r e l a r g e , t h e n m u l t i p l e s w i t h i n t h e s e l a y e r s can mask a d i r e c t r e f l e c t e d s i g n a l f r o m d e p t h by p r o d u c i n g \" r i n g i n g \" o r \"wave t r a i n i n g \" . M u l t i p l e s cause d i s t o r t i o n s . The magnitude of d i s t o r t i o n cannot be o b s e r v e d on t h e seismo-grams. The e x i s t a n c e of a l a r g e v e l o c i t y d i s c o n t i n u i t y above a s e i s m i c shot can be r e c o g n i z e d as t h e source of \"g h o s t \" r e f l e c t i o n s appearing\" on t h e seismogram. I n such i n s t a n c e s , the downgoing wave f r o n t s e t up by the shot i s c h a r a c t e r i z e d b y energy moving d i r e c t l y downward f r o m t h e shot p o i n t f o l l o w e d i n space and time- b y energy r e f l e c t e d f r o m t h e o v e r l y i n g d i s c o n t i n u i t y . When d e t e c t e d t h i s down-g o i n g wave f r o n t appears as two w a v e l e t s d i s p l a c e d i n time by a p p r o x i m a t e l y t w i c e the t r a v e l time f r o m the shot t o the d i s c o n t i n u i t y and w i t h p o s s i b l e d i f f e r e n c e s I n shape. Any d i f f e r e n c e i n shape may be a t t r i b u t e d t o resonance e f f e c t s o f the ground between t h e shot and the d i s c o n t i n u i t y and the s p h e r i c i t y o f t h e i n c i d e n t wave f r o n t a t t h e d i s c o n -t i n u i t y . Recent s t u d i e s have made p o s s i b l e the e l i m i n a t i n g of the- ghost r e f l e c t i o n s on m a g n e t i c a l l y r e c o r d e d seismograms by means of a l i n e a r f i l t e r . T h i s a d d i t i o n a l f i l t e r I n c l u d e s b o t h t h e v e l o c i t y l a y e r i n g above t h e shot and t h e a d d i t i o n a l a t t e n u a t i o n i n t h e ghost p a t h . The a p p l i c a t i o n of t h i s f i l t e r does n ot a l t e r s i g n i f i c a n t l y the c h a r a c t e r o f p r i m a r y r e f l e c t i o n s a l t h o u g h e l i m i n a t i n g t h e ghost r e f l e c t i o n s . 20. CHAPTER I I I CALIBRATION- OP CONTINUOUS VELOCITY LOGS USING COMPARISON OP SYNTHETIC AND FIELD RECORDS RATHER THAN WELL GEOPHONE SURVEY DATA 3.1 P r o c e d u r e The w r i t e r has attemp t e d t o c a l i b r a t e c o n t i n u o u s v e l o c i t y l o g s by comparing s y n t h e t i c s and f i e l d r e c o r d s as f o l l o w s : 1. F i r s t , the f u n c t i o n g e n e r a t o r t a p e s and t h e i r p l a y o u t s are made fr o m t h e u n c a l i b r a t e d c o n t i n u o u s v e l o c i t y l o g s f o l l o w i n g the same t h r e e s t e p s which a re shown i n F i g u r e 10. 2. The f i l t e r i n g u s ed i n making s y n t h e t i c s i s g e n e r a l l y d e t e r m i n e d e m p i r i c a l l y , u s i n g two band pass f i l t e r s -one m a t c h i n g the f i l t e r used on the f i e l d r e c o r d ( i n s t r u m e n t f i l t e r ) and t h e o t h e r s i m u l a t i n g the f i l t e r i n g a c t i o n of the shot p u l s e ( e a r t h f i l t e r ) . The i n s t r u m e n t f i l t e r i s known ( o b t a i n e d f r o m a c t u a l f i e l d d a t a ) , t h e r e f o r e , the second f i l t e r i s v a r i e d t o g i v e the b e s t c h a r a c t e r match between a c t u a l f i e l d and s y t h e t i c r e c o r d s . T h i s can be done by ch a n g i n g the low and h i g h c u t - o f f f r e q u e n c y ranges o f the e a r t h f i l t e r u n t i l t he b e s t c o r r e l a t i o n between them i s o b t a i n e d . 3. The time i n t e r v a l s are s e t on b o t h r e c o r d s a t e v e r y 100 m i l l i s e c o n d s . The time i n t e r v a l s s h o u l d be s e t on t h e f i e l d r e c o r d a f t e r making the time c o r r e c t i o n f o r w e a t h e r i n g and e l e v a t i o n v a r i a t i o n s ( F i g u r e s 13, B.A. Cancrude Champion 16-29 f i e l d record B.A. Morrin 7-3 f i e l d record B.A. Texaco Arrowhead B-76 f i e l d record 21. 14, 1 5 ) . When making t h i s c o r r e c t i o n , t h e e l e v a t i o n datum of the w e l l d a t a s h o u l d be us e d . I t i s a r b i t -r a r i l y assumed t h a t t h e s t a r t i n g p o i n t o f the syn-t h e t i c t r a c e i s z e r o t i m e . As i t can be seen, t h e r e are two t r a c e s on t h e s y n t h e t i c p l a y b a c k r e c o r d ( F i g u r e s 16, 17, 1 8 ) . The upper one i s the syn-t h e t i c t r a c e . The l o w e r one shows t h e v e l o c i t y f u n c t i o n . I f one c o n s i d e r s the cor r e s p o n d e n c e between the v e l o c i t y f u n c t i o n and t h e s y n t h e t i c t r a c e , i t i s not s u r p r i s i n g t h a t the r e s u l t i n g s y n -t h e t i c t r a c e w i l l have s i m i l a r c h a r a c t e r , b u t w i l l be l a t e r i n t i m e . T h i s \"\"simply a f i l t e r d e l a y . The amount o f t h i s f i l t e r d e l a y i s r e l a t e d t o the i m p u l s e response wave form, which, i n t h e case o f t h e s y n t h e t i c seismogram i s g i v e n by t h e r e f l e c t i o n f r o m a s t e p v e l -o c i t y f u n c t i o n . T h e r e f o r e , t h e z e r o t i m e i n t e r v a l I s se t on the s t a r t i n g p o i n t o f the s y n t h e t i c t r a c e , n o t on the s t a r t i n g p o i n t o f t h e v e l o c i t y f u n c t i o n , be-cause the c o r r e l a t i o n r e s u l t s of the s y n t h e t i c and f i e l d r e c o r d time i n t e r v a l s w i l l be used and not the c o r r e l a t i o n between t h e v e l o c i t y f u n c t i o n and f i e l d r e c o r d . I n t h i s s t e p , the s y n t h e t i c and a c t u a l f i e l d r e c o r d s a r e c o r r e l a t e d . The c o r r e l a t i o n can be made between apparent r e f l e c t i o n peaks ( F i g u r e s 19, 20, 2 1 ) . I t i s known t h a t when t h e f i e l d and s y n t h e t i c r e c o r d s show t h e b e s t c h a r a c t e r match, t h e r e s h o u l d be no r e l a t i v e t i m e - s h i f t between them. T h e r e f o r e , i f one o b t a i n s B.A. Texaco Arrowhead B-76 synthetic playback B.A. Morrin 7-3 synthetic playback B.A. Cancrude Champion 16-29 s y n t h e t i c p l a y b a c k B.A. Texaco Arrowhead B-76 time d l s c r e p e n c i e s ^ A A A 8 A MORRIN 7-3 7-3-3IN-20W4 @ S Y N T H E T I C T I M E I N T E R V A L S 05 F I E L D R E C O R D T I M E I N T E R V A L S FIOURE *Z0 B.A. Morrin 7-3 time discrepencies V\C- 2-1 @ S Y N T H E T I C T I M E I N T E R V A L S 02 F I E L D R E C O R D T I M E I N T E R V A L S B.A. Cancrude Champion 16-29 time discreoencies the b e s t c h a r a c t e r match between s y n t h e t i c and f i e l d r e c o r d s , t h e time i n t e r v a l s o f t h e f i e l d r e c o r d can be i r r a n s f e r r e d t o the s y n t h e t i c r e c o r d . 5 . On the p l a y o u t s of the f u n c t i o n g e n e r a t o r t a p e s , t h e time i n t e r v a l s f o r a hundred m i l l i s e c o n d s a re shown at t h e t o p o f t h e graph ( F i g u r e s 2 2 , 2 3 , 2 4 ) . The de p t h i n t e r v a l s f o r each 1000 f e e t a re a l s o shown on t h e d e p t h s c a l e . U s i n g the same t i m e and d e p t h i n t e r v a l s , a t i m e - d e p t h graph can be made ( F i g u r e s 2 5 , 2 6 , 2 7 ) . On t h i s graph, depth i s the o r d i n a t e and t h e two-way time i s t h e a b s c i s s a . At t h e o r i g i n o f t h i s g raph, time w i l l be assumed z e r o and t h e d e p t h w i l l be - s t a r t i n g d e pth v a l u e of t h e l o g . The t i m e i n t e r v a l s c a n a l s o be p l o t t e d on t h e d e p t h s c a l e , s i m i l a r l y assuming t h a t the o r i g i n i s z e r o t i m e . I n F i g u r e 2 5 , the s t r a i g h t l i n e (A) p a s s i n g t h r o u g h t h e o r i g i n , shows a two-way t i m e - d e p t h c u r v e , assuming t h a t t h e s t a r t of t h e v e l o c i t y f u n c t i o n i s z e r o t i m e . The second s t r a i g h t l i n e ( B ) , i n d i c a t e d by c r o s s p o i n t s , shows the a c t u a l two-way t i m e - d e p t h c u r v e . The a c t u a l two-way t i m e - d e p t h c u r v e can be o b t a i n e d i n t h e - f o l l o w i n g manner. F i r s t , t he s y n t h e t i c time i n t e r v a l s a r e p l o t t e d on the two-way time s c a l e , t a k i n g i n t o c o n s i d -e r a t i o n - t h e time d i f f e r e n c e s between s y n t h e t i c and f i e l d r e c o r d s . At t h i s p o i n t i t s h o u l d be n o t e d t h a t the time i n t e r v a l on t h e s y n t h e t i c r e c o r d i s not e q u a l t o t h e time i n t e r v a l on the v e l o c i t y f u n c t i o n which i s shown a t t h e top B.A. Texaco Arrowhead B-76 r e f l e c t i v i t y function playout B.A. Morrin 7-3 r e f l e c t i v i t y function playout ! B.A. Osnnrude Champion 16-29 r e f l e c t i v i t y f u n c t i o n playout B.A. Cancrude Champion 16-29 two way t i m e - d e p t h c u r v e B.A. M o r r i n 7-3 two-way t i m e - d e p t h c u r v e B.A. Texaco Arrowhead B - 7 6 two-way t i m e - d e p t h c u r v e 23. o f t h e \u00E2\u0080\u00A2 p l a y o u t s of t h e f u n c t i o n g e n e r a t o r t a p e s ( F i g u r e s 22, 23, 2 4 ) . T h i s d i s c r e p a n c y i s f o u r m i l l i s e c o n d s . T h i s m a t t e r s h o u l d b e ' c o n s i d e r e d b e f o r e p l o t t i n g t h e syn-t h e t i c time i n t e r v a l p o i n t s on t h e two-way t i m e s c a l e . Then, i f t h e s e - s y n t h e t i c time i n t e r v a l p o i n t s are extended v e r -t i c a l l y and t h e c o r r e s p o n d i n g t i m e i n t e r v a l s on t h e d e p t h s c a l e a re extended h o r i z o n t a l l y , t h e y w i l l i n t e r s e c t a t c r o s s - p o i n t s . The s t r a i g h t l i n e p a s s i n g t h r o u g h t h e s e p o i n t s w i l l r e s u l t i n t h e a c t u a l two-way t i m e - d e p t h c u r v e . To i l l u s t r a t e t h i s p o i n t , l e t us c o n s i d e r the f o l l o w i n g example. I n F i g u r e 19 the time d i f f e r e n c e between t h e syn-t h e t i c time (0.8 seconds) and t h e f i e l d t i m e (1.0 seconds) i s 0.012 seconds. As i t can be seen i n F i g u r e 19, t h e f i e l d t ime a c c o r d i n g - t o - t h e s y n t h e t i c t i m e i s 0.012 seconds l a t e r i n t i m e ; so t h a t the e x a c t p l a c e o f t h e s y n t h e t i c t ime on the two-way time s c a l e ( F i g u r e 25) i s O.988 seconds ( d e s i g -n a t e d by a l e t t e r a ) . I f t h i s p o i n t i s extended v e r t i c a l l y and t h e c o r r e s p o n d i n g time of 0.8 seconds ( d e s i g n a t e d by a l e t t e r b) i s extended h o r i z o n t a l l y , t h e y w i l l i n t e r s e c t a t c r o s s p o i n t c. The o t h e r c r o s s p o i n t s on t h i s graph can be f o u n d i n the same manner. 24. CHAPTER IV RESULTS 4 . 1 Data U s i n g t h e s e s t e p s , i t was attemp t e d t o c a l i b r a t e t h e c o n t i n u o u s v e l o c i t y l o g s . The s t u d i e s were c a r r i e d out a t t h r e e d i f f e r e n t w e l l s . F o l l o w i n g are the names and l o c a t i o n s o f t h e s e w e l l s : 1. Texaco Arrowhead B - 7 6 60\u00C2\u00B0 25' 02\" N; 122\u00C2\u00B0 5 9 ' 02\" W 2. B.A. M o r r i n 7 - 3 L s d . 7, S e c t i o n 3 , Twp. 31N, Rge. 20, W4M 3 . Cancrude B.A. Champion 16-29 L s d . 16, S e c t i o n 29, Twp. 14, Rge. 24, W4M The l o c a t i o n s o f the w e l l s u s e d i n t h i s work are shown I n F i g u r e 12. The f u n c t i o n g e n e r a t o r t a p e s and t h e i r p l a y o u t s are o b t a i n e d f r o m the u n c a l i b r a t e d c o n t i n u o u s v e l o c i t y l o g s o f t h e s e t h r e e w e l l s . From t h e s e f u n c t i o n g e n e r a t o r t a p e s , s y n t h e t i c r e c o r d s were produced r e s u l t i n g i n t h e b e s t c o r -r e l a t i o n s w i t h the f i e l d r e c o r d s . The f i l t e r s used i n p r o d u c i n g t h e s y n t h e t i c r e c o r d s a t t h e s e t h r e e w e l l s were as f o l l o w s : 25. (a) B.A. Texaco Arrowhead B-76 S l o p e s ( i n Db/oct. a t $5 amp.) LC HC LC HC ( c . p . s . ) ( c . p . s . ) I n s t r u m e n t F i l t e r 22 62 16 22 E a r t h F i l t e r 25 25 (b) B.A. M o r r i n 7-3 I n s t r u m e n t F i l t e r 28 8l 18 20 E a r t h F i l t e r 25 25 (c) B.A. Cancrude Champion 16-29 I n s t r u m e n t F i l t e r 28 8l 18 20 E a r t h F i l t e r 35 35 The t ime i n t e r v a l l i n e s a r e drawn on bo t h r e c o r d s a t e v e r y 100 m i l l i s e c o n d s . B e f o r e s e t t i n g t h e time i n -t e r v a l s on the f i e l d r e c o r d s , the time c o r r e c t i o n s were made u s i n g t h e f o l l o w i n g d a t a : B.A. Texaco Arrowhead Shot P o i n t E l e v a t i o n = 1275' E l e v a t i o n Datum = 1150' W e a t h e r i n g C o r r e c t i o n = 0.014 Shot Hole Depth = 40' E l e v a t i o n C o r r e c t i o n V e l o c i t y , = 6000'/sec. T o t a l Time C o r r e c t i o n = 0.049 s e c . B.A. M o r r i n 7-3 Shot P o i n t E l e v a t i o n = 2702' E l e v a t i o n Datum = 2650' W e a t h e r i n g C o r r e c t i o n = 0.0273 Shot Hole Depth = 70\" E l e v a t i o n C o r r e c t i o n V e l o c i t y = 6500*/sec. T o t a l Time C o r r e c t i o n = 0.027915 s e c . 26. Cancrude B.A. Chamption 16-29 Shot P o i n t E l e v a t i o n = 3 2 4 3 ' E l e v a t i o n Datum = 3 1 5 0 ' W e a t h e r i n g C o r r e c t i o n = 0 . 0 1 8 Shot Hole Depth = 7 1 ' E l e v a t i o n C o r r e c t i o n V e l o c i t y = 1 1 0 0 0 ' / s e c . T o t a l Time C o r r e c t i o n = 0 . 0 3 2 Then t h e s y n t h e t i c and f i e l d r e c o r d s a re c o r r e -l a t e d ( F i g u r e s 19, 20, 21). The time d i f f e r e n c e between' s y n t h e t i c and f i e l d r e c o r d t ime i n t e r v a l s a r e i n the range of 0.01 - 0.065 s e c . a t Cancrude B.A. Champion, f r o m 0.002 seconds t o 0.02 seconds a t B.A. M o r r i n , and between 0.003 and 0.032 seconds a t B.A. Texaco Arrowhead. As a f i n a l s t e p , t he two-way t i m e - d e p t h c u r v e s were p l o t t e d f o r t h e s e t h r e e w e l l s ( F i g u r e s 25, 26, 27). From t h e s e c u r v e s the time i n t e r v a l s of c o n t i n u o u s v e l o c i t y l o g s were d e t e r m i n e d t o be i n e r r o r by + 0.007 seconds t o + O . O O 8 2 5 seconds. I n t a b l e s 1 t o 3, the v e l o c i t y a n a l y s i s d a t a a t the s e t h r e e w e l l s are t a b u l a t e d . The r e s u l t s o f t h i s s t u d y can be checked w i t h t h e v a l u e s shown I n t h e s e t a b l e s . 4.2 The D i s c u s s i o n s of t h e E r r o r s i n Time S c a l e of Syn- t h e t i c Seismograms Over a p e r i o d o f t i m e , non u n i f o r m i t y of t i m i n g l i n e s f o r s y n t h e t i c seismograms has been r e c o g n i z e d as a symptom o f e r r o r , w i t h q u e s t i o n s as t o the n a t u r e of such L O C A T I O N N60o25'02\"WI22\u00C2\u00B059'02\" W E L L N A M E B.A.TEXACO ARROWHEAD B-76 A R E A FT. SIMPSON K 8 -J265 G E O L O G I C F O R M A T I O N D E P T H F R O M K . B E L E V A T I O N F T F R O M S E A L E V E L R E F L E C T I O N TIME S E C S (TWO-WAY) SCATTER 1078 173 .218 L. BUCKING HORSE 1175 76 .2390 FLETT. 1607 -356 .326 BNFF. 3258 -2007 .576 EX. 4817 -3566 .872 KOTCHO 4862 -3611 .882 F. LIME 5185 -3934 .924 TETCHO 6105 -4854 1.086 TROUT RIVER 6215 -4964 1.1032 KAKISA 6482 -5232 1.142 RED KNIFE FORT SIMSON 6548 -5297 1.149 MUSKWA 8448 -7197 1.4586 SLAVE POINT 8479 -7228 1.464 WATT 8790 -7539 1.492 PINE PT. DOLOMITE 8823 -7572 1.4923 T.D. 9805 -8554 1.59 I i T A B L E * l L O C A T I O N 7 - 3 - 3 1 - 2 0 W.4 W E L L N A M E ^ J W O J R J R J N A R c A MORRIN K B -S=11P~-G L - 2 7 0 5 GEOLOGIC DEPTH ELEVATION FT REFLECTION TIME FORMATION FROM K 8 FROM SEA LEVEL SECS ( T W O - W A Y ) L.P. 2 0 6 0 659 .472 COLO. 2553 166 \"5666 2 WS 3 4 2 0 -701 . 7 4 4 B.F.S. 3696 - 9 7 7 .802 VIK. 3814 j -1095 .82 MANV. 4 0 7 2 -1350 L \" . 8 7 GLAUC. PEK. 4 4 9 8 - 1 7 7 9 ~ ~ 9 4 6 ~ t BNFF. 4 6 7 6 -1957 .964 EX. 4 9 7 0 -2251 _| 1.0073 WAB. 4985 - 2 2 6 6 i 1.008 STET. 5018 - 2 2 9 9 1.012 C A L . 5495 - 2 7 7 6 1.062 NIS. 5506 - 2 7 8 7 ! 1.064 NIS. POR. IRE. 5651 - 2 9 3 2 1.0802 L E D . 5688 - 2 9 6 9 1.0856 DUV. EQUIN. CK. L . 6 3 9 0 -3671 1.16 B.H.L \" 6 6 0 0 \" - 3 8 8 1 \" 1. 1816 EP . 7 2 0 2 - 4 4 8 3 1.2430 T.D. 7264 - 4 5 4 5 1.248 * i i TABLE *2 L O C A T I O N 16-29-14-24-W. 4 W E L L N A M E CANCRUDE B.A. CHAMPION A R E A CHAMPION K B 3256 G L 3243 .3 GEOLOGIC FORMATION DEPTH FROM K B ELEVATION FT FROM SEA LEVEL REFLECTION TIME SECS (TWO-WAY) B.P. 1378 1878 .243 B.R. 1950 1306 .362 PAK. 2 9 3 3 3 2 3 .544 MR. 3082 174 .5710 COLO. 3471 -215 . 6 3 0 2 2WS. 4479 -1223 .803 BFS . 4 8 0 2 - 1 5 4 6 .855 B. IS. 4 8 6 2 -1606 . 8 6 5 B L . 5278 - 2 0 2 2 .931 OST. 5693 - 2 4 3 7 .992 BSL. QTZ. 5748 - 2 4 9 2 .9996 SWIFT. 5 7 8 0 - 2 5 2 4 1.004 RIER. 5 8 0 8 - 2 5 5 2 1.0084 T V . UPOR. 5906 - 2 6 5 0 1.023 M. DENSE 5958 - 2 7 0 2 1.028 L.POR. 6 0 0 2 - 2 7 4 6 1.0322 SHUNDA 6216 - 2 9 6 0 1.054 PEK. 6296 - 3 0 4 0 1.061 BNFF. 6 4 9 6 - 3 2 4 0 1.0824 E X . 7 0 7 2 -3816 1.141 WAB. 7 0 8 2 - 3 8 2 6 1.142 FAIR. 7 5 9 0 - 4 3 3 4 1.194 CK. L. 8283 - 5 0 2 7 1.261 B.H.L. 8 4 6 7 -5211 1.2796 ER 8 8 7 7 -5621 1.321 CAMB. 8896 - 5 6 4 0 1.3232 T.D. 8 9 7 3 - 5 7 1 7 TABLE * 3 2 7 . e r r o r b e i n g r a i s e d i n consequence. I n l a r g e degree, any e r r o r s a r e d i r e c t l y r e l a t e d t o e r r o r i n t h e b a s i c v e l o c i t y l o g and a n a l y s i s t h e r e o f . The s t a r t i n g p o i n t o f the r e f l e c t i v i t y f u n c t i o n i s a r b i t a r i l y chosen as z e r o t ime and 1 0 0 m i l l i s e c o n d s a r e p l a c e d on the r e c o r d . (See F i g u r e s 2 2 , 2 3 , 24.) I t i s c l e a r t h a t t h e time d i f f e r e n c e s between t h e s e t i m i n g l i n e s and the a c t u a l t i m i n g l i n e s s h o u l d be t h e same. But I t can be seen f r o m t h e s e f i g u r e s ( 2 2 , 2 3 , 24) t h a t d i f f e r -ences - change i r r e g u l a r l y t h r o u g h o u t the r e c o r d . We have c o n c l u d e d t h a t a c c u r a c y l i m i t a t i o n s i n -h e r e n t i n i n t e g r a t i n g equipment and i t s o p e r a t i o n r e s u l t i n d i s c r e p a n c i e s and t h a t t h e r e a re human e r r o r s i n t r e a t i n g the d a t a . More s p e c i f i c a l l y , t he b a s i c l i m i t a t i o n s a r e : 1 . F i e l d and l a b o r a t o r y systems as o p e r a t e d i n t e g r a t e and d i s p l a y d a t a w i t h l i m i t e d f i d e l i t y . One conse-quence i s t h a t the i n t e g r a t i o n o f the v e l o c i t y l o g c a r r i e d o u t a t magnetic tape f u n c t i o n g e n e r a t o r some-t i m e s d i f f e r s f r o m the f i e l d i n t e g r a t i o n . The i n t e -g r a t i o n \"systems a t magnetic tape f u n c t i o n g e n e r a t o r has an a c c u r a c y under normal o p e r a t i n g c o n d i t i o n s o f + 1 $ and presumably the f i e l d i n t e g r a t i o n systems have a s i m i l a r a c c u r a c y . V e l o c i t y l o g s p r e s e n t e d w i t h o n l y v e l o c i t y s c a l e i n v o l v e and r e q u i r e a d d i t i o n a l p r o c e s s i n g w i t h consequent u n a v o i d a b l e d e g r a d a t i o n a c c u r a c y . These l i m i t a t i o n s a re i n t r i n s i c i n the s y n t h e t i c seismograms produced f r o m t h e 28. l o g s and are i n p a r t i n s t r u m e n t a l and i n p a r t human. The c o m p a r a t i v e l y minor sou r c e o f non u n i f o r m i t y s u b j e c t t o c o r r e c t i o n i s : 2. E n t i r e l y human e r r o r i n d r a f t i n g and p r e s e n t a t i o n i n -c l u d i n g i mproper t r a n s f e r o f t i m e s f r o m the c a l i b r a t e d l i n e a r d e p t h l o g t o the new l i n e a r t i m e l o g . The d i f f e r e n c e s between f i e l d and magnetic tape f u n c t i o n g e n e r a t o r i n t e g r a t i o n s i s a most i m p o r t a n t source of d i s c r e p a n c i e s . I n p r o d u c i n g a s y n t h e t i c seismogram, the l i n e a r d e p t h v e r t i c a l s c a l e o f the c a l i b r a t e d v e l o c i t y l o g i s c o n v e r t e d t o a l i n e a r t i m e v e r t i c a l s c a l e . T h i s o p e r a t i o n r e q u i r e s an i n t e g r a t i o n of t h e c a l i b r a t e d l o g . The p r o b l e m i s t o m a i n t a i n c o r r e c t a s s o c i a t i o n o f i n t e -g r a t e d t i m e s w i t h t h e a p p r o p r i a t e d i s c r e t e v e l o c i t y measure-ments. I f t h e new i n t e g r a t i o n r e p e a t s t h e c o r r e c t e d f i e l d i n t e g r a t i o n ( I . e . , i f the a s s o c i a t i o n o f v e l o c i t y mea-surements w i t h i n t e g r a t e d t i m e s on t h e new l i n e a r t ime l o g d u p l i c a t e s t h e a s s o c i a t i o n of v e l o c i t y measurements a t t h e s e same t i m e s on the c a l i b r a t e d l i n e a r d e p t h l o g ) , e q u a l time i n t e r v a l s w i l l i n f a c t be l i n e a r l y spaced on the l i n e a r time l o g . However, a disagreement between the two i n t e -g r a t i o n s w i l l be e v i d e n c e d by t h e f a c t t h a t t i m i n g l i n e s on the l a b o r a t o r y i n t e g r a t e d l i n e a r time l o g w i l l be a s s o c i -a t e d w i t h d i f f e r e n t v e l o c i t y measurements t h a n t h o s e a p p e a r i n g a t t h e s e same t i m e s on the c a l i b r a t e d l i n e a r d e p th f i e l d l o g . As the f i e l d i n t e g r a t i o n i s computed d i r e c t l y i n l o g g i n g d e v i c e , whereas magnetic tape f u n c t i o n g e n e r a t o r i n t e g r a t i o n d e r i v e s f r o m a d d i t i o n a l c u r v e p l o t t i n g 2 9 . and t r a c i n g s t e p s , the a s s o c i a t i o n of v e r t i c a l i n t e g r a t e d t i m e s - and d i s c r e t e v e l o c i t y measurements on the c a l i b r a t e d f i e l d l o g i s adopted. As a r e s u l t , the time i n t e r v a l s t r a n s f e r r e d f r o m the c a l i b r a t e d f i e l d l o g onto the l i n e a r time l o g w i l l g e n e r a l l y n o t be of t h e same l e n g t h . The l a c k of f i d e l i t y o r m a l f u n c t i o n of f i e l d i n t e g r a t i n g equipment o r h a n d l i n g r e q u i r e s one t o r e c a l i b r a t e the l o g . The second source o f the d i s c r e p a n c i e s i s due t o t i m e - t o - l i n e a r v e l o c i t y c o n v e r s i o n of h o r i z o n t a l s c a l e . T h i s t y p e I s p e c u l i a r t o v e l o c i t y l o g s which are o n l y w i t h a l i n e a r v e l o c i t y h o r i z o n t a l s c a l e i n s t e a d o f t h e more b a s i c l i n e a r time h o r i z o n t a l s c a l e . The i n t e g r a t i o n of t h e s e l o g s can be done by r e c o n v e r t i n g f r o m a l i n e a r v e l o c i t y s c a l e t o a l i n e a r time s c a l e . A f t e r t h i s , n ormal i n t e g r a t i o n p r o c e s s e s are us e d . C o n s e q u e n t l y , the l o g has two a d d i t i o n a l t i m e s . Such i n t e g r a t i o n s , when completed, commonly d i f -f e r f r o m the c a l i b r a t i o n t i m e s and o f t e n a p p r e c i a b l y . I n p r a c t i c e , i t i s f e l t t h a t t h e s e a d d i t i o n a l c o n v e r s i o n p r o c e s s e s , f r o m l i n e a r time t o l i n e a r v e l o c i t y and t h e n back f r o m l i n e a r v e l o c i t y t o l i n e a r t i m e , compound the d i s c r e p a n c i e s . I t i s p o s t u l a t e d t h a t t h e r e a s o n f o r t h i s i s d i f f i c u l t y i n o b t a i n i n g l i n e a r i t y i n the e l e c t r i c a l c i r c u i t s i m u l a t i n g the c o n v e r s i o n . 30. 4.3 I n t e r p r e t a t i o n o f R e s u l t s : a. B.A. Texaco Arrowhead The w e l l was s t a r t e d i n B u c k i n g h o r s e f o r m a t i o n a t IO78 f t . and bottomed i n P i n e P o i n t D o l o m i t e a t a p p r o x i -m a t e l y 8800 f t . The s y n t h e t i c r e c o r d s are compared w i t h a f i e l d r e c o r d t a k e n n e a r t h e w e l l . The o b j e c t o f t h i s c o m p a r i s o n w i l l be t o d e t e r m i n e w h i c h s y n t h e t i c r e c o r d more c l o s e l y r e s embles the r e f l e c t e d s i g n a l on t h e f i e l d r e c o r d . The s y n t h e t i c r e c o r d which a g r e e s most c l o s e l y w i t h the r e f l e c t i o n r e c o r d shows th e b e s t c o r r e s p o n d e n c e a t t i m e s n e a r 0.37 s e c , O.58 s e c . and 1.13 s e c . (as shown i n c i r c l e s i n F i g u r e 19). The f i e l d r e c o r d shows t h a t a m u l t i p l e comes f r o m the f i r s t r e f l e c t i o n a t 1.5-1.6 s e c . The h i g h v e l o c i t y d i s t r i b u t i o n o c c u r s between 0.3-0.5 s e c . The o s c i l l a t i o n s on t h e s y n t h e t i c r e c o r d v a r y q u i t e smoothly as though the e n t i r e r e c o r d has been p l a y e d t h r o u g h a v e r y narrow band f i l t e r . b. B.A. M o r r i n The c o n t i n u o u s v e l o c i t y l o g c o v e r e d the d e p t h range f r o m a p p r o x i m a t e l y 800 f t . t o 7200 f t . A c o r r e s -pondence between t h e s y n t h e t i c and t h e f i e l d r e c o r d s shows t h a t t h e r e are agreements a t t i m e s 0.45, 0.6, O.85-O.95 s e c . There i s i n t e r f e r e n c e a t 0.8-0.9 s e c . which comes fr o m t h e f i r s t r e f l e c t i o n e v e n t . The s y n t h e t i c r e c o r d has been time s h i f t e d a p p r o x i m a t e l y 0.5 m.s. t o t h e r i g h t t o e s t a b l i s h the c o r r e s p o n d e n c e between h i g h v e l o c i t y zones and peaks on t h e f i e l d r e c o r d . The main e v e n t s 31. v i s i b l e on t h e s e i s m i c record, a r e : (a) weaker r e f l e c t i o n s f r o m deeper h o r i z o n s and (b) v e r y l i t t l e i n t e r f e r e n c e o r n o i s e . The o s c i l l a t i o n s on the s y n t h e t i c r e c o r d show r a p i d changes o f a m p l i t u d e . c. B.A. Conerude Champion: The c o n t i n u o u s v e l o c i t y l o g was r e c o r d e d between 877 f t . and 8973 f t . The s t r o n g r e f l e c t i o n e v e n t s on the f i e l d r e c o r d are matched w i t h t h e s y n t h e t i c r e c o r d a t 0.57-0.9 and 1.05 s e c . The s y n t h e t i c r e c o r d has the same p o l a r i t y as t h e f i e l d r e c o r d , as d e t e r m i n e d from t h e i n i t i a l down br e a k o f the r e f l e c t i o n f r o m t h e a r t i f i c a l s t e p p l a c e d n e a r the b e g i n n i n g of each V e l o c i t y f u n c t i o n . The r e f l e c t i v i t y f u n c t i o n shows much s m a l l e r v e l o c i t y con-t r a s t s t h a n t h a t of the p r e v i o u s two examples. The syn-t h e t i c r e c o r d has been d i s p l a c e d about 4 m i l l i s e c o n d s t o match t h e s t r o n g r e f l e c t i o n e v e n t s . The c o r r e l a t i o n of s y n t h e t i c r e c o r d s w i t h f i e l d r e c o r d s a t d i f f e r e n t l o c a t i o n s i s shown i n F i g u r e s 28 and 33. The s y n t h e t i c r e c o r d s i n each case have the same p o l a r i t y as the f i e l d r e c o r d . The p o l a r i t y i s d e t e r m i n e d f r o m t h e i n i t i a l b r e a k of the r e f l e c t i o n f r o m the a r t i f i -c i a l s t e p p l a c e d near t h e b e g i n n i n g of each r e f l e c t i v i t y f u n c t i o n . (See F i g u r e s 16, 17, 18.) T h i s f u l f i l l s t he t h i r d c r i t e r i o n f o r good match. 32. The s y n t h e t i c and f i e l d r e c o r d s i n F i g u r e s 28 and 33 a r e d i s p l a c e d w i t h z e r o r e l a t i v e time s h i f t , i n accordance w i t h t h e second c r i t e r i o n . The wide peaks c o r r e s p o n d t o \" t h i c k \" bed o r v e l o c i t y zones and narrow peaks c o r r e s p o n d t o \" t h i n \" bed zones. F i g u r e s 28, 29 and 30 are chosen as examples of v e l o c i t y d i s t r i b u t i o n s f o r which m u l t i p l e s a r e not s i g -n i f i c a n t . I n t h e s e examples the i n t e r f a c e s are smooth and p a r a l l e l . The r e c o r d s show t h a t s e i s m i c energy i s r e c e i v e d i n a p p r e c i a b l e amounts a t a l l t i m e s a f t e r t h e t r a n s m i s s i o n o f the i n c i d e n t p u l s e . The l a r g e a m p l i t u d e o s c i l l a t i o n s a r e as apt t o be t h e r e s u l t o f c o n s t r u c t i v e I n t e r f e r e n c e as of prominent i n d i v i d u a l c o n t r a s t s . I t can be seen ( F i g u r e 28) t h a t the l a r g e s t amount of i n c i -dent energy does not n e c e s s a r i l y produce t h e h i g h e s t a m p l i t u d e o s c i l l a t i o n s on the r e c o r d . The a m p l i t u d e of the o s c i l l a t i o n a t 0.84 seconds i s l e s s t h a n t h a t a t 1.12 seconds d e s p i t e t h e f a c t t h a t the i n c i d e n t energy i s than \u00C2\u00AB i t greater*0 . 8 2 seconds. F i g u r e s 31, 32 and 33 are examples w h e r e i n m u l t i p l e s are i m p o r t a n t t h r o u g h o u t the d u r a t i o n o f the r e f l e c t e d s i g n a l . The prominent m u l t i p l e s a r e d e s i g n a t e d by l e t t e r 'M'. The m u l t i p l e s caused c o n s i d e r a b l e phase s h i f t i n the d i r e c t r e f l e c t e d s i g n a l . The d i f f e r e n c e s b e t -ween the s y n t h e t i c and f i e l d r e c o r d are r a t h e r s m a l l e s p e c i a l l y a t t h e e a r l i e r a r r i v a l t i m e s . ( F i g u r e s 31, 32.) At l a t e r t i m e s t h e two r e c o r d s appear t o become a p p r e c i a b l y FIELD RECORD SY NT HETIC RECORD Fl GURE*28 Comparision of f i e l d record with synthetic record 0.6 0.7 0.8 09 1.0 I.I 12 I F I E L D I I , \" . I S Y N T H E T I C R E C O R D F I G U R E * 2 9 C o m p a r i s i o n o f f i e l d r e c o r d w i t h s y n t h e t i c r e c o r d F IE LD R E C O R D F I G U R E * 3 0 C o m p a r i s i o n o f f i e l d r e c o r d w i t h s y n t h e t i c r e c o r d Q5 0.6 0.7 08 0.9 1.0 C o m p a r i s i o n of f i e l d r e c o r d w i t h s y n t h e t i c r e c o r d 0.8 0,9 1,0 1.1 1.2 13 1.4 ECORD C o m p a r i s i o n o f f i e l d r e c o r d w i t h s y n t h e t i c r e c o r d 3 0.4 05 - 0.6 0.7 0.8 0.9 IP FIELD RECORD Comparision of f i e l d record with synthetic record 33. d i f f e r e n t . I f the phase s h i f t due t o the m u l t i p l e s which c a u s e s t h i s a pparent l a c k o f s i m i l a r i t y i s removed, th e c o r r e l a t i o n w i l l be improved. A t h i r d example ( F i g u r e 33) shows a p a i r of m u l t i p l e s r e f l e c t i o n . The r e c o r d s appear v e r y s i m i l a r , but the s u b t r a c t i o n o f one f r o m t h e o t h e r shows t h a t phase s h i f t i s c a u s i n g an i n c r e a s i n g d i v e r g e n c e a t l a t e r t i m e s . 34. CHAPTER V CONCLUSION I n t h i s s t u d y , o n l y a l i m i t e d number o f s y n t h e -t i c s have been p r e p a r e d f o r c o mparison w i t h a c t u a l f i e l d record's o b t a i n e d a t t h e c o r r e s p o n d i n g w e l l l o c a t i o n s . The r e s u l t s o f t h i s s t u d y p r o v e d t h a t t h e r e i s a p o s s i -b i l i t y o f c a l i b r a t i n g c o n t i n u o u s v e l o c i t y l o g s u s i n g the c o m p a r i s o n of s y n t h e t i c and f i e l d r e c o r d s . D u r i n g t h i s r e s e a r c h the b e s t c o r r e l a t i o n s were o b t a i n e d a t t h i r t e e n d i f f e r e n t l o c a t i o n s . I n some c a s e s , poor c o r r e l a t i o n s were o b t a i n e d i n s p i t e of the good q u a l i t y of t h e r e f l e c t i o n r e c o r d . T h i s poor agreement may be p a r t i a l l y e x p l a i n e d by the f a c t t h a t the s y n t h e t i c seismogram produced by P e t e r -son's method o n l y a p p r o x i m a t e s th e t r u e r e f l e c t e d s i g n a l . An improvement i n o b t a i n i n g a \"good match\" would be e x p e c t e d i f the a p p r o x i m a t i o n used by P e t e r s o n c o u l d be a v o i d e d . P e t e r s o n ' s t e c h n i q u e c o n s i s t s of n e g l e c t i n g t r a n s m i s s i o n c o -e f f i c i e n t s , m u l t i p l e s and ghost r e f l e c t i o n s , and assuming t h a t the d e n s i t y i s c o n s t a n t . He f u r t h e r f i n d s a p p r o x i -m a t i o n s f o r the r e f l e c t i o n c o e f f i c i e n t s a t each change i n a c o u s t i c impedance u s i n g one \" h a l f the f r a c t i o n a l d i f f e r e n c e o f t h e v e l o c i t y a c r o s s the c o n t r a s t s . The m a t h e m a t i c a l a p p r o x i m a t i o n w i l l more c l o s e l y approach i d e a l s i t u a t i o n s by i n c l u d i n g m u l t i p l e s and t r a n s m i s s i o n c o e f f i c i e n t s . F u r -t h e r improvement can be o b t a i n e d by computing e x a c t l y the r e f l e c t e d s i g n a l of p l a n e waves i n c i d e n t normal t o t h e s u r f a c e of a m u l t i l a y e r e d h a l f space, i n the case where 35. t h e source i s a u n i t i m p u l s e i n t i m e . I t was f o u n d t h a t the f o l l o w i n g f a c t o r s must be t a k e n i n t o account i n the c a l i b r a t i o n o f c o n t i n u o u s v e l o -c i t y l o g s u s i n g t h i s p r o c e d u r e . 1. When making the ti m e c o r r e c t i o n f o r w e a t h e r i n g and e l e v a t i o n v a r i a t i o n s , t h e e l e v a t i o n datum o f the w e l l d a t a s h o u l d be used f o r t h e a c t u a l s e i s m i c r e c o r d . 2 . The c o r r e l a t i o n between the s y n t h e t i c and f i e l d r e c o r d s s h o u l d be made between s t r o n g r e f l e c t i o n e v e n t s . 3. I t was fo u n d t h a t the time i n t e r v a l on the syn-t h e t i c r e c o r d i s n o t e q u a l t o the time i n t e r v a l on the v e l o c i t y f u n c t i o n p l a y o u t . T h e r e f o r e , the time i n t e r v a l o f the s y n t h e t i c r e c o r d s h o u l d be con-v e r t e d t o t h e time i n t e r v a l o f v e l o c i t y f u n c t i o n b e f o r e p l o t t i n g t h e s y n t h e t i c t i m e i n t e r v a l s on the two-way time depth g r a p h s . 4. A cor r e s p o n d e n c e s h o u l d be e s t a b l i s h e d between t h e s y n t h e t i c r e c o r d and the v e l o c i t y f u n c t i o n by s h i f t i n g t he s y n t h e t i c f o r w a r d i n t i m e . 5. Any s i g n i f i c a n t move-out on the s e i s m i c r e c o r d s h o u l d be removed b e f o r e comparison w i t h the s y n t h e t i c r e c o r d . BIBLIOGRAPHY Au s t e y , N. 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"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "Calibration of continuous velocity logs using the comparison of synthetic and field records"@en . "Text"@en . "http://hdl.handle.net/2429/36833"@en .