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Calibration of continuous velocity logs using the comparison of synthetic and field records 1966

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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- « * . 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 author̂  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. — 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 • • • • • • « « * « « » 0 « o a « o o a o o e o o o o 6 o o o o o e * o 1- i A. LXS7 OF FIGURES• • f t « * » * » o e » 0 » » o « o o » o o * o o o e » o o o 0 o » « * XV LIST* OF 7A13LES • • • « * « o o « o » « « o » « e o 0 « a * » o o o o 6 e e e » « » » 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 « « o « o o o o o o o « » o o * o » « « » o o « 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«L 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 ^ © n © 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 »n' 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 £10 ^ 6 S « » o 0 « o o 0 O 0 « 9 9 9 o o « o » « « 0 0 0 « 0 « 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 * « o o a « 0 e * o o « o a * a a o o o » » 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 * « o 0 0 e o o o 0 0 0 0 0 0 o « 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 • o O » 0 0 0 0 O 9 e O O O 0 0 « O 0 O 0 0 0 O O O 9 0 0 0 « 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 » 0 0 t t 0 0 o « 0 0 O Q 0 e o o a o 0 o o o » 0 o o « 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 » 0 » 0 0 o e 0 0 0 » 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 • a r » a « 6 o 0 0 0 0 9 0 O 9 O O O 0 0 0 O e O 0 O O 0 » 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 » a « 0 » o o o o 0 < » o * « * » « o 0 c o o 0 < » ( i o o o o o © » 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 » 0 « 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 « 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«oo 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 • • 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-• 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 • 1 • 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 [ ] — 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 — i 1 1 —» 1 1 —+ •̂ -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 £ 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 -- • 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„ 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 „" 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. --•---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£ 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;±me-'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 — 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„ - The usual-procedure i s to survey- a well with both- methods„ 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 • 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„ 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—the 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 ^ « 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—ground' 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—is- 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)-»0 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 ° 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— o_ R E F L E C T I O N , R• f Ct-tO A M P L I T U D E , R. P . DE L A Y T l M E , t = ± ° 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» 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- % ) • 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: « « 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 « „ w r + i l (18b) °L_ [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 . — > 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 ) *»— 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 • 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° 25' 02" N; 122° 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°59'02" 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 « 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. A., C o r r e l a t i o n T e c h n i q u e s , A Review By, Seismograph S e r v i c e C o r p o r a t i o n , T u l s a , Oklahoma. Backus, M. M., Water R e v e r b e r a t i o n s , T h e i r N a ture and E l i m i n a t i o n , G e o p h y s i c s , V o l . 24, 233-261, 1959. Berryman, L. H., P. L. G o u p i l l a u d and K. H. Weters, R e f l e c t i o n Prom M u l t i p l e T r a n s i t i o n L a y e r s , P a r t I , T h e r i c a l R e s u l t s , G e o p h y s i c s , V o l . 23, 223-243, 1958. B i r c h , P., and B a n c r o f t , E l a s t i c i t y and I n t e r n a l F r i c t i o n i n a Long Column of G r a n i t e , B u l l . S e i s . Soc. Amer., V o l . 23. Bruckshaw, J . M., and P. C. Mahanta, The V a r i a t i o n o f the E l a s t i c C o n t e n t s o f Rocks w i t h F requency, Mimeographed C i r c u l a r o f t h e E.A.E.G., 1952. C h o l e t , J . , and H. 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