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Calibration of continuous velocity logs using the comparison of synthetic and field records Gurbuz, Behic M. 1966-12-31

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CALIBRATION OP CONTINUOUS VELOCITY LOGS USING THE COMPARISON OP SYNTHETIC AND FIELD RECORDS by BEHIC M. GURBUZ  B.Sc.j U n i v e r s i t y o f I s t a n b u l ,  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 t h e s i s as conforming t o the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA April,  1966  In  presenting  requirements Columbia, for  agree  reference  extensive granted It  I  for  is  by  Department  the  gain  in  partial  advanced  degree  at  the  the  Library  study.  I  of  thesis  this of  that  shall  my  for  Department  copying not  of  be  or  British  29,  make  agree  allowed  Columbia  1966.  fulfilment  University it  that  scholarly or  by  his  publication  Canada  April  shall  further  Geophysics  of  8,  thesis  that  Head  University  Vancouver Date  copying  understood  financial  The  and  an  this  without  of  of  of  British  freely  available  permission purposes  the  for  may  be  representatives. this  thesis  my w r i t t e n  for  permission  ii ABSTRACT  T h i s study i s undertaken  i r i order t o c a l i b r a t e  the  contirraons v e l o c i t y logs- u s i n g t h e comparision of s y n t h e t i c s and f i e l d r e c o r d s .  The r e s u l t s r e f e r t o the f o l l o w i n g w e l l s  in Alberta. 1.  Texaco Arrowhead  B-76  60 25' 02"N, 122 59' 02" W -  2v  L s d 1, 3.  S e c t i o n 3,  Twp  31N,  Rge  20  4M  Cancrude B r i t i s h American Champion L s d 16/  The  7-3  B r i t i s h American M o r r i n  S e c t i o n 29, Twp  14, Rge  16-29  24 W  4M  s y n t h e t i c r e c o r d s were obtained u s i n g a , l i n e a r f i l t e r  model.  To accomplish the s y n t h e s i z i n g ' p r o c e s s i n the ge.net-«*.  tor-  l a b o r a t o r y , a magnetic tape f u n c t i o n * i s used. time-depth  The two-way  curves are- p l o t t e d f o r these three w e l l s .  Prom  these c u r v e s t h e time i n t e r v a l s of continuous v e l o c i t y l o g s -  were found i n - e r r o r by 0,007 seconds to 0,0082 seconds.  The  p o s s i b l e e r r o r s i n time s c a l e of s y n t h e t i c seismograms are d i s c u s s e d in-Chapter  IV.  The comparision of s y n t h e t i c s w i t h a c t u a l  field  seismograms" recorded 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 and the main c r e t e r i a f o r a "good match" and  "poor match" are d i s c u s s e d .  iii  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. —  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  LXS7 OF FIGURES• • LIST* OF 7A13LES •  f t « * » * » o e » 0 » » o « o o » o o * o o o e » o o o 0 o » « *  • • « * « o o « o » « « o » « e o 0 « a * » o o o o 6 e e e » « » » o  1- i XV  Vi  CHAPTER I - INTRODUCTION 1.1  Well geophone and continuous v e l o c i t y 1.1.1  1.1.2  1.2  D e s c r i p t i o n and o p e r a t i o n of continuous v e l o c i t y l o g sonde and r e c o r d i n g d e v i c e s  1  The observed time d i s c r e p a n c i e s between continuous and w e l l geophone v e l o c i t y surveys..  4  The s y n t h e s i s of seismograms from continuous v e l o c i t y l o g data.................  8  CHAPTER I I - THEORY 2.1  Theory o f the l i n e a r f i l t e r model of P e t e r s o n and h i s co-workers...............  10  2.2  To convert a continuous v e l o c i t y l o g to the r e f l e c t i v i t y f u n c t i o n  1 6  2.3  Comparison of s y n t h e t i c and a c t u a l  2.4  M u l t i p l e and ghost r e f l e c t i o n s . . . . . . . . . . . .  field 18  CHAPTER I I I - CALIBRATION OF CONTINUOUS VELOCITY LOGS USING THE COMPARISON OF SYNTHETIC AND FIELD RECORDS  CHAPTER IV - RESULTS  4.2  D i s c u s s i o n of the e r r o r s i n time s c a l e of r e f l e c t i v i t y function.  26  4.3  I n t e r p r e t a t i o n of r e s u l t s . . . . . . . . . . . . . . . . .  30  CHAPTER IV - CONCLUSION  A.  34  iv  L I S T OP FIGURES After Page 1.  Schematic d i a g r a m o f t h e method b y w h i c h v e l o c i t y i s determined 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 oxirv3  oID"fc&iLn&(3.o««o«ooooooo«»oo*o»««»oo«oooo6o  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 .  3.  Schematic  4.  Diagram o f continuous v e l o c i t y l o g g e r . . . . . . . .  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 survey... e e o o o o o o o o o o o o o o o o o o o o o o  "fcOO«L  VG l O O  6.  of 4 x5'  diagram 0  0  0  0  0  0  0  0  0  F r o n t view o f magnetic ^©n©  10  0  0  0  1  continuous  s  0  1  0  0  tape  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  2  o  function  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  8.  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 proc 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  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 log to the r e f l e c t i v i t y function.......  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 process In a l i n e a r f i l t e r . . . . . . . .  16  12o  WsXX l o c a t i o n  1^3  13.  B.A. C a n c r u d e C h a m p i o n 16-29  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. T e x a c o A r r o w h e a d B - 7 6 f i e l d r e c o r d . . . . . .  20  16.  B.A. T e x a c o A r r o w h e a d B - 7 6 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  21  18.  B.A. C a n c r u d e C h a m p i o n 16-29  10.  response  of a linear f i l t e r . . . . . . . . . .  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  f i e l d record....  synthetic playback...........  11  20  synthetic  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. T e x a c o A r r o w h e a d 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.  B.A. C a n e r u d e C h a m p i o n 16-29 t i m e  22.  B.A. T e x a c o A r r o w h e a d 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  C l 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  Pl3jrOU.t  B.A. C a n c r u d e C h a m p i o n 16-29 r e f l e c t i v i t y  25.  B.A. T e x a c o A r r o w h e a d B-76 two-way CUL37V6 •  o  O  »  0  0  0  0  O  9  e  O  O  O  0  0  «  22  O  0  O  0  0  0  time-  O  O  O  9  0  0  0  «  O  0  22  O  26.  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 . . . . ^ .  27.  B.A. C a n c r u d e C h a m p i o n 16-29 two-way ClG^thl  28. 29.  CU37V6  30.  time-  record with synthetic  Comparison of f i e l d  record with synthetic  a  * 0  0  22 22  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  Comparison o f f i e l d record  276COjt7Clo  0  0  0  0  0  a  *  32  0 0 9 9  Comparison o f f i e l d  9 0 9 e 0 9 0 » 0 » 0 0 o e 0  0  0 » 0 a o 0  9  Comparison o f f i e l d  32  record with synthetic  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.  Comparison o f f i e l d 376 C O 37Cl o  33.  o  o  o  o  0  »  0  «  9  0  o  9  0  0 9 0 0 0 a  0  32  record with synthetic  a  0  Comparison o f f i e l d 376C037CL«oo  32  record with synthetic  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  31.  2-L  function  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  24.  ClSp't/l'l  21  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  record with synthetic 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  vi  LIST OP TABLES  After Page 1.  Two-way r e f l e c t i o n times a t c o r r e s ponding g e o l o g i c a l f o r m a t i o n s .  B.A. 26  Texaco Arrowhead B-76 2.  Two-way r e f l e c t i o n times a t c o r r e s ponding g e o l o g i c a l f o r m a t i o n s . M o r r i n 7-3  B.A.  •  •  26 3.  Two-way r e f l e c t i o n times at c o r r e s ponding g e o l o g i c a l f o r m a t i o n s . Cancrude Champion  B.A.  16-29 . . . . . . . . . . . . . . . . . .  26  1  CHAPTER I  INTRODUCTION  1.1  Well Geophone ^nd"Continuous " V e l o c i t y Surveys Tfre-Tjra-jorlty" of- w e l l  s i n c e 1955  ve-loclty^surveys-"carried"out  brave "used" t w o d i f f e r e n t - methods.  The f i r s t  method~"foT7 v e l o c i t y - me a^urements' i s tor explode • c h a r g e s o f -  dynamite i n ' a shallow d r i l l t o r y bore hole  hole- alongside"- a "deep - e x p l o r a -  and tt) r e c o r d the a r r i v a l - t i m e s of waves  received- b y an: i n - h o l e d e t e c t o r a t a number of depths which are d i s t r i b u t e d f r o m top t o bottom. 1 U l u s t r a t e i s t h e setup and" shows i n t e r v a l  Figure and  average- v e l o c i t y - c u r v e s ~ of ~ the "type t h a t are obtained  from t h i s procedure.  The-interval-velocity- is-the  between-successive d e t e c t o r p o s i t i o n s i n the w e l l , by t h e d i f f e r e n c e -  ( F i g . 2)  distance  divided  i n a r r i v a l time's a t t h e "two depths, a f t e r  c o r r e c t i o n from- s l a n t - p a t b r t o v e r t i c a l a n d ' a d j u s t i n g datum*;.  distance  The average v e l o c i t y i s t h e t o t a l  to a vertical  d i v i d e d 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 L o g Sonde and- R e c o r d i n g D e v i c e s . contIripous-velocity-logging, type o f I n s t r u m e n t . - F i g u r e -  t h i s t o o l which i n c o r p o r a t e s  The-second method,  i s c a r r i e d out with a s p e c i a l 3 shows a schematic s k e t c h of an a c c o u s t i c - s i g n a l g e n e r a t o r  VELOCITY FT/SEC  AMP LI E R AND RECORDER  3000 4000  — i  2000  1  5000 1  —»  6000 7000 1  8000 1  9000  —+  []—  •^-INTERVAL VELOCITY ELECTRIC CABLE  DETECTOR  3000  [J-  4000  []  5000  []  6000  []  7000  DETECTOR POSITION  Cu  FIGURE Schematic diagram of the method by which v e l o c i t y i s determined by shooting 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 curve o b t a i n e d  WELL  ELEVATION SHOT ^__SHOT  L  DATUM  HOLE  ELEVATION  ELEVATION PLANE  ELEVATION  F I G URE 2 fl  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 17  Geophone d e p t h m e a s u r e d f r o m d a t u m  L  D i f f e r e n c e i n e l e v a t i o n between s h o t and datum p l a n e .  U +L c  Geophone d e p t h m e a s u r e d f r o m s h o t  elevation.  Geophone d e p t h m e a s u r e d f r o m w e l l  elevation.  Straight  Depth o f shot.  T +  C-A-Ae  Uphole  L  shot t o w e l l  geophone.  point.  time 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 . = V e r t i c a l t i m e f r o m s h o t t o datum p l a n e .  Observed  L  t r a v e l path from  d i s t a n c e from w e l l t o shot  A t te  s  U  line  Horizontal  £  elevation.  time from shot t o w e l l  geophone.  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  point,  = V e r t , t r a v e l t i m e f r o m datum p l a n e t o  Ac  geophone. COQ'J ~[ = V e r t , t r a v e l t i m e f r o m s h o t e l e v a t i o n t o geophone.  T  Va  = Average v e l o c i t y =  y.  = Interval  V  = Topmost v e l o c i t y  V  = d - (Kelly Bushing elevation  e  velocity  ^ =  ATc  i n consolidated  layer.  - Elevation  Datum).  CABLE  BUMPER  ^ Z w 2  n < j  ACOUSTIC  I  -r  RECEIVER  INSULATOR  RECEIVER  st  ACOUSTIC  - 7  INSULATOR  --  TRANSMITTER  •  ~F|GURE 3  1  #  Schematic  d i a g r a m o f 4'X5'  continuous v e l o c i t y  tool.  2 ( t r a n s m i t t e r ) "-whichemits p u l s e s  -ttrartr-travel through- "the  formation- s i d e w a l l s t o " t h e r e c e i v e r s ,  -The- -transmitter's  r e c e i v e r s are spaced v e r t i c a l l y about 5 f e e t apart  and  i n s u l a t e d from each other by a c o u s t i c insulation„  The  and  are  -  d i stance " b e l w e e n ^ must be l a r g e e n o u g h s o t h a t the f i r s t  s i g n a l to reach  t h i s r e c e i v e r " t r a v e l s through at l e a s t a small p a r t o f 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  the  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 „"  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 off  r e c e i v e r i s p r o p o r t i o n a l t o the  (i.e. theseparation  the tranducers)- and  When formation" velocl-ty -exceeds  between the w a l l of t h e h o l e  is-w f u n c t i o n o f t h e  -  c i t y -to-f ormatlon v e l o c i t y T h e by  standand  r a t i o of mud " v e l o -  r e l a t i o n s h i p " may  be  derived  straightforward" computation of the t o t a l time f o r an  a c o u s t i c p u l s e to t r a v e l from t r a n s m i t t e r to r e c e i v e r .  The  result i s  dmin  =  s  where  p-\/ v  I + OC  i-a  dmi n" = and S  receiver  =" s t a n d - o f f  OC = r a t i o of " m u d v e l o c i t y t o f o r m a t i o n - v e l o c i t y The  f i r s t " a r r i v a l s - of- the a c o u s t i c  s i g n a l s 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 of continuous v e l o c i t y  logger.  3.  diagram o f t h e  continuous v e l o c i t y l o g g e r f o r t h e " s i n g l e  receiver pulse  system.  c l o s e s y s t a r t i n g the  At the p u l s e I n s t a n t , -switch  sawtooth generator  Gen,  S-^  which develops  a v o l t a g e 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  switch" Sg i s c l o s e d d i s c h a r g i n g the generator of  voltage,  as  thalrlrrstaTit,-"^  on gal'vanometer Gal^- the -pointer of w h i c h " t r a c e s " t h e of  Rec^,  t£  on the l o g a t  theindicateddepth. i t ^ - a r r i v a l at  The~i;±me-'lTistajr^ r e c e i v e r Rec  value  aredisplaced onan oscilloscope.  - T ; T h e ' l T T t e r g r a t o r " p r o v i d e s t h e ~ - o v e r - a l l trav"el~tlme _  f o r the i n t e r v a l logged  by continuous i n t e g r a t i o n 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  T h i s " c u r v e I s "the-  contirraoxts" r e c o r d i n g o f the i n t e r v a l time I n -raicTOsecTDnds through i n d i v i d u a l f o r m a t i o n s  along the e n t i r e v e r t i c a l  of the w e l l ; and" can; be read" a s I n t e r v a l v e l o c i t y on the -  riate—scale a t t h e t o p (b)  The  integrated"curve.  geophone s u r v e y s . T o t a l  s e c t i o n of the l o g may  approp-  ofthelog. T h i s curve" i s d e r i v e d  d i r e c t s u m m a t i o n o f " t h e i n t e r v a l " v e l o c i t y curve, brated: to-the  extent  be o b t a i n e d  and  iscali-  t r a v e l times over  from i t .  by  any  4.  The -re s u i t s erf time t t e t e r a i n a t i o n s surveyed by both h  methods do not agree "and: disc"repancies up to s e v e r a l "tents -  --  of m i l l i s e c o n d s f o r tteep w e l l s occur„ - The usual-procedure i s to survey- a w e l l w i t h both- methods„  When t h e survey i s i n -  t e r p r e t e d ; the c o n t i n u o u s v e l o c i t y data a d j u s t e d t o the w e l l geophone survey; - The u s u a l "argument f o r t h i s " procedure i s that the" w e l l geophone'survey simulates-more  c l o s e l y the  c o n d i t i o n s ' encountered i n seismic" s h o o t i n g .  The  interval  v e l o c i t y c u r v e - i s t h e r e f o r e l a t e r a l l y d i s p l a c e d , "and the s l o p e of the - i n t egrated: curve i s - a d j u s t e d b e f o r e f i n a l  drafting,  u s i n g a corrected time. The r e f l e c t i o n " horizons " are n o t always" obvious from -  h  a c o n t i n u o u s v e l o c i t y "log. " T h e y r e f l e c t " t h e 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  hori-  zons "versus v e l o c i t y - c o n t r a s t s can b e - c o r r e l a t e d from w e l l to well i n a given area. 1.1.2  The" Observed  Time' D i s c r e p a n c i e s Between  C ont irruous and- -Velocity- Surveys. - The- -re s u i t s " o f the -  statistical  a n a l y s i s o f the observed time d i s c r e p a n c i e s between continuous and v e l o c i t y surveys showed" t h a t t h e r e i s " both a~ normal random discrepancy-and-a s y s t e m a t i c d e v i a t i o n between the observed of the v e l o c i t y - a n d the w e l l geophone surveys (Oretener  time  1963).  I t I s found t h a t c e r t a i n " Important f a c t o r s s t r o n g l y i n f l u e n c e -  the d e v i a t i o n found between the two" types of surveys. "The"study of c o n t i n u o u s - v e l o c i t y s u r v e y s Is s u b j e c t  to  three  sources  in  the presence of -  non  -  studies'and Plizard  of e r r o r s .  surveys  1959,  that i n the  invaded  Kokesk  Gardener  and  1958),  showed  f l u i d ) zone  a-  inthe  major f a c t o r s e f f e c t i n g the  thickness  v e l o c i t y zone a r e t h e c o n s o l i d a t i o n , p o r o s i t y ;  continuous  of the f o r m a t i o n b e i n g p e n e t r a t e d .  and'  The  v e l o c i t y measurements a c q u i r e the c h a r a c t e r of r e -  surveys  r e c e i v e r and  and u n l e s s t h e  spacing  ( d i s t a n c e between  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),  a r r i v a l s w i l l not  mation.  1959*  ( p e n e t r a t e d by d r i l l i n g  The  mineral composition  first  i n wells (Hicks  Laboratory  the apparent v e l o c i t y i s lower than  v i r g i n formation.  fraction  of a l l a problem a r i s e s  i d e a ! t o o l geometry.  W y l l i e , G r e g o r y and  round a w e l l ,  of the low  First  have t r a v e l l e d t h r o u g h  I t i s thus d e s i r a b l e to extend  the  the  the v i r g i n  spacing to  for-  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  of e r r o r a r i s e s from  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 the The  t o o l i s equipped w i t h removable rubber  t r a l i z e r s of approximately  hole.  b u m p e r s and  5 inches i n diameter.  keep the t o o l c e n t r a l i z e d .  t e m a t i c d e v i a t i o n due in  the" h o l e , seems It  to a constant  Therefore,  We  dispersion.  will a  sys-  i n c l i n a t i o n of the  tool  improbable.  i s f u r t h e r - f o u n d t h a t the  r e s u l t s may  b y 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 c.p.s.  cen-  With"the  h i g h l o g g i n g s p e e d s , t h e f l o w o f mud" a r o u n d t h e t o o l also t e n d t o  the  have l i t t l e B i r c h and  range  be a f f e c t e d  50-12,000  a v a i l a b l e information concerning Bancroft  (1958)  wave  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 t h e r a n g e 140 t o  4,500  c.p.s.  They  h a v e m e a s u r e d t h e f T e x u r a l " ^ t o r s i o n a l a n d 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 a n y 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 a n I n c r e a s e  0.5$  850  over t h e range  within" the l i m i t  to  4,300  of e r r o r .  i n v e l o c i t y of about  c.p.s., which l i e s w e l l  They have  concluded'that-for  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 i n d e p e n d e n t o f f r e q u e n c y 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  p r o b l e m i n t h e r a n g e o f 40 t o 120 c , p s . f o r v a r i o u s t  types The  such as d i o r i t e ,  dolerite,  velocity-frequency curves  similar,  limestone  o f these  and sandstone.  rocks are quite  i n t h e r a n g e o f 40 t o 120  c.p.s.  curves I n d i c a t e that the rate of increase diminishes higher  rock  s h o w i n g a n i n c r e a s e o f t h e wave v e l o c i t y w i t h  q u e n c y o f a b o u t 1.5$  this  freThese  with  frequencies. One" c a n c o n c l u d e " t h a t t h e r e i s e v i d e n c e  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 Although  with•frequency.  t h e r e a r e two m a j o r s o u r c e s  t h e w e l l geophone s u r v e y s ,  that the  of errors i n  i ti s - a l s o found that there are  many p o s s i b l e e f f e c t s which" c o u l d c a u s e a d e g r e e o f r a n d o m n e s s i n the'observed "data.  The most I m p o r t a n t  single  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 p r o p e r t i e s o f t h e setup d u r i n g the survey. 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  electrical  For shallow  shots,  a h i g h i n d u c t a n c e and  l o w 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 c h e c k  7.  shots the c a p a c i t a n c e -  i s h i g h and inductarte i s low.  This,  of course, "might i n t r o d u c e a l a g i n t o the we I T geophone  survey.  An attempt has been made to e l i m i n a t e t h i s possibility„ -  experiment was  set" up  whereby a p u l s e was  recorded  An  directly  and a l s o a f t e r going through the" c a b l e and the downhole geophone;  The r e s u l t s of t h i s experiment"have not shown" any  delay.  However, i i ; "has been" n o t i c e d t h a t I n " the case  of  poor breaks,' some k i n d of l a t e r " event might be p i c k e d r a t h e r than the" true" f i r s t  arrivals.  S t u d i e s - a t d i f f e r e n t l o c a t i o n s "indlcated"i;ftat" a n i sotrophy i s indeed a r a t h e r common phenomenon,  in a  case o r - a n i s o t r o p y , ~the" v e l o c i t y p a r a l l e l to t h e  simple  surface  w i l l be g r e a t e r than t h a t at r i g h t a n g l e s to i t .  I f "the beds  are u n d i s t r i b u t e d , " the hoTizontal v e l o c i t y i s g r e a t e r l ; h a n — t h e 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 . a n i s o t r o p y f a c t o r -may  be "given b y the r a t i o of the h o r i z o n t a l  v e l o c i t y t o the- v e r t i c a l ~ I n value  Vg,  The  velocity.  a n y i n t e r m e d i a t e d i r e c t i o n - the v e l o c i t y "has a whereby  ^  «  F i g u r e 5 shows the  affect  of a n i s o t r o p y i n the shallow l a y e r s on a w e l l geophone v e l o c i t y survey.  F o r the v e r y shallow check-shot  i s large-and t h e about  l e v e l s , the  r a y t r a v e l s at a v e l o c i t y  angle  V , which i s "  (V^ + V ) / 2 , while f o r the deep l e v e l s " t h e angle z  becomes" small-and " t h e : r a y - t r a v e l s t h r o u g h - t h e l a y e r s at a v e l o c i t y very c l o s e to  V  z  same  shallow  .  Consequently;- a n - e r r o r I s committed -when- c o r r e c t i n g 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 a n i s o t r o p y on w e l l v e l o c i t y survey  conventional  8.  m u l t i p l i c a t i o n ' w i t h 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 a n i s o t r o p y r ^ w h i i e the times f o r the" deep l e v e l s w i l l be c o r r e c t . For  a n i s o t r o p y f a c t o r of 1.1 and v a r i o u s v e l o c i t i e s the e r r o r  i s zero at-*the surface'and i n c r e a s e s t o a maximum f o r s i g n a l s a r r i v i n g a t 45 degrees. I t -should- be taken i n t o c o n s i d e r a t i o n t h a t a c u r vature i n the r a y p a t h ' w i l l cause the same type of e r r o r .  If  we do" not have a v a i l a b l e continuous- v e l o c i t y data" from the -  s u r f a c e downwards, i t w i l l i n most cases be i m p o s s i b l e t o determine- whether such" a n - e r r o r i s due t o t r u e a n i s o t r o p y , or  c u r v a t u r e of the" raypath- o r combination of both.  1.2  The~Synthesis--of Seismograms" from Continuous V e l o c i t y Log  Data. Recent  developments" o f continuous- v e l o c i t y l o g s u r -  v e y i n g "and i t s l o g g i n g d e v i c e s and a c q u i s i t i o n o f " s u b - s t a n t i a l amounts-of- data-have of  m a t e r i a l l y i n c r e a s e d the p o t e n t i a l i t i e s  such Investigations-.- - "Under- s i m p l i f i e d hut - r e a l i s t i c  assumptions,  the b a s i c data from continuous v e l o c i t y  physical  surveys  i n w e l l s - c a n be" used-to" simulate-the v a r i a t i o n s i n a c o u s t i c impedance in- the—ground' which g i v e s r i s e to" s e i s m i c - r e f l e c t i o n s . ThIs argument" - has been- put -forward by"Pete rson e t a l . (1954), -  who they d e s c r i b e -an-analogue- computer which' makes use of t h e b a s i c w e l l data t o procedure s y n t h e t i c sembling a c t u a l f i e l d  seismograms.  seismic records r e -  To accomplish " t h i s synthe-  s i z i n g - p r o c e s s - i n the l a b o r a t o r y magnetic- tape f u n c t i o n generator i s b e i n g used  (Fig. 6 ) .  FIGURE 6 #  Front view of magnetic tape f u n c t i o n generator  9.  - Corre^pondrarrce between t h e synthesized" r e c o r d and a c t u a l " s e i s m i c r e c o r d made over-the w e l l i s q u i t e good i n many cases; even-though some-of the c o n d i t i o n s - w h i c h  occur i n  n a t u r e (noise, m u l t i p l e r e f l e c t i o n s , f o r example) are not simulated  -  I n "the s y n t h e s i s r  The t e c h n i q u e i s p a r t i c u l a r l y  u s e f u l - T o r showinig t h e e f f e c t of -small - changes i n v e l o c i t y or l a y e r t h i c k n e s s upon ~fche wave form- of a  -reflection.  Mo re  r e c e n t " s t u d i e s have been" made"Berryman (1958)-and Wuenschel (I960) who have " d e s c r i b e d mo d e l s " which" c o n t a i n a l l " m u l t i p l e s . Backus (1959) "tntraduced"water r e v e r b a t i o n s L i n d s e y "(i960) i n t r o d u c e d introduced  i n t o t h e model.  ghosts i n the same way "that Backus  reverbations. Up~tc- t h i s p-oint-j, we "have-briefly- o u t l i n e d the  process- o f two w e l l v e l o c i t y - s u r v e y methods and have  -  discussed  p o s s i b l e causes f o r time" d i s c r e p a n c i e s 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 v e l o c i t y - l o g s - a c c o r d i n g - t o t h e w e l l geophone data.  F i n a l l y ; we have mentioned"the s y t h e s i s o f selsmo-  grams. -  In- our" s t u d i e s , we have attempted t o c a l i b r a t e con-  tinuous v e l o c i t y l o g s using-comparisions"  of - syntheilcs and  f i e l d r e c o r d s r a t h e r than w e l l geophone survey.  10.  CHAPTER I I THEORY  2.1  Theory o f t h e L i n e a r F i l t e r Model o f P e t e r s o n  and h i s  Co-Workers. In-  the^^  made i r r o r d e r t o make t h e p r o b l e m t r a c t a b l e .  The model e a r t h  i s assumed t o 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 in  the'"vertical~dlrecti^^  v ( z ) -7 " t h a t — i s - o b t a i n e d - f r o m a - c o n t i n u o u s - T e l o c i t y l o g . density function  The  p ( z ) o f t h e 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 The  V tf.)  constants.  shotpulse  propagates i n the v e r t i c a l d i r e c t i o n  as a p l a n e w a v e , t h u s s t r i k i n g t h e l a y e r s a t normal i n c i d e n c e 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 f r o m v e l o c i t y changes due  t o the -assumed: r e l a t i o n s h i p ^ "between " d e n s i t y 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 i n c l u d e d , a l l t y p e s of " 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 . T h e shot p u l s e wave form I s t i m e - i n v a r i a n t ( t h e 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  c o n s t a n t -and do not - change w i t h t r a v e 1  One g e n e r a l l y a c c e p t e d s t a n d a r d method o f f i l t e r  time.  11.  c h a r a c t e r i z a t i o n i s i t s impulse  response.  inputimpulse  procedure a c h a r a c t e r i s t i c  of u n i t area w i l l  t r a n s i e n t output waveform tions of the function  u ( t ).  ( P i g . 7.)  There a r e t w o  An  restric-  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  filter: UCt) = 0  t< o  for  (2)  U(t)-»0  for  An a r b i t a r y i n p u t  t -> oo f ( t )will  p a s s i n g - t h r o u g h " t h e f i l t e r "and be  a function of both  expression f(t)  f (t)  withu(t)  i s designated  .  give a n o u t p u t which  and  of t h i s output w i l l  be m o d i f i e d i n  u(t) .  be  will  The- m a t h e m a t i c a l  givenbyconvolving  Themathematical operation of convulation  by a s t a r , a n d  i sdefined b y t h e following  relationship:  S(t) = f ( t J * U C t ) = f f (t)U(.L-T)dT -Jo  ( 3 )  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. and  The v e l o c i t y a b o v e t h e i n t e r f a c e i s v  the v e l o c i t y b e l o w i s Vg . T h e densitiesabove  b e l o w t h e i n t e r f a c e p^ product The  and  p^  .Thedensity-velocity  b e t w e e n two r o c k l a y e r s w i l l  be  pulse-propagatesdownward as a plane  incidence interfaces.  P  v (  ]_  a  n  d  P  2  V  2 °  wave w i t h n o r m a l  The r e f l e c t i o n c o e f f i c i e n t  a s 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 wave a m p l i t u d e .  and  i s defined  the incident  I t i s equal t o  P2V2-P1V1 P2V2+AV,  ( 4 )  1  IMPULSE  FI6URE 7 #  Impulse response of a l i n e a r  filter  REFLECTION  VE LOCITY  DEPTH  COEFFICIENT  V,  A^-A  R _  v  2  o  SHOT  i t  PULSE  f(t)  R E F L E C T I O N , R• f Ct-tO A M P L I T U D E , R. . DE L A Y T l M E , t = ± ° L P  UN IT A M P L I T U D E x  i—  STRIP GRAPH OF ACOUSTIC IMPEDANCE  o_  o  MED I U M or  P,  >-  MED I UM 2  <  FIGURE 8 W  I  V,  JRANSMITTED WAVE IMPULSE  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 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  X _ A r  12.  assuming--the"density t o - b e - c o n s t a n t , we can w r i t e t h i s r e lationship  as f o l l o w s :  R  V  =  2 ~  V  1  (5)  v i-v, 2  As was mentioned i n the d i s c u s s i o n of t h e p r o p e r t i e s of t h i s model, t h e d e n s i t y portional  ( p ) i s assumed constant o r p r o -  t o some power of the v e l o c i t y .  pulse h a s - i d e n t i c a l l y  The r e f l e c t e d  the same- shape -and iare-adth as the i n -  c i d e n t p u l s e , but d i f f e r s i n amplitude".  When t h e i n c i d e n t  wave propagates from a medium o f low v e l o c i t y ,  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 t h e same -  as the~shot p u l s e .  On the o t h e r hard, when" t h e  wave t r a v e l s from a medium o f h i g h v e l o c i t y lower v e l o c i t y ,  i n t o one o f  the c o r r e s p o n d i n g r e f l e c t i o n c o e f f i c i e n t i s  n e g a t i v e a n d " i t s p o l a r i t y - w i l l be reversed» of t h e r e f l e c t i o n " o c c u r s  a t t h e time 7/  way t r a v e l t i m e t o the i n t e r f a c e . shot p u l s e  incident  The b e g i n n i n g  , which i s the two-  Thus, i f one d e s i g n s the  f ( t ) - , the~ r e f l e c t i o n - c a n  be w r i t t e n  T h i s model can be extended t o - v e l o c i t y " i n t e r f a c e s at i n f i n i t i s i m a l l y s m a l l d e p t h - i n t e r v a l s ( F i g . 9 ) .  R.jf(t- %  ) •  occurring Each  r e f l e c t i o n h a s - i t s - own- p o l a r i t y , " amplitude and time delay, but  has t h e same wave-form-as the t i m e - i n v a r i a n t shot p u l s e .  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.  SCt^RfCt-p+f^fCl-ptIf  (6)  w r i t t e n as a summation: n  (7)  BLACK BOX  SHOT PULSE  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 process with 'n i n t e r f a c e s 1  13.  The in  the"n"  equation  (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  l a y e r e d model.  This equation  r e f l e c t i o n p r o c e s s of Peterson's process.  shows" " t h a t t h e  model i s a l i n e a r  filter  The e a r t h c a n b e assumed a s a f i l t e r w h i c h i m -  pulse response i s the s e t of r e f l e c t i o n spaced" " s u i t a b l y i n ' t i m e " .  coefficients  The" m o d e l c a n b e " e x t e n d e d " f r o m  "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 the  layer thickness approacheszero.  Then e q u a t i o n  (7) b e -  comes c o n v o l u t i o n I n t e g r a l . ""  The"continuous v e l o c i t y - l o g gives the compli-  catedlayering oftheearth;and give a m a n y l a y e r e d model.  Thereflection coefficients  can b e c a l c u l a t e d u s i n g equation a s i m p l i f i c a t i o n by u s i n g a n reflection coefficients.  wr i t t e n a s p v^+ /\  i t c a n be s a m p l e d t o  (5).  introduced  approximate expre s s i o n f o r t h e  I n equation  ( pv).  Peterson  (5),  Then equation  [pv.VACP^-pv,  v  g  c a n be  ( 5 ) becomes:  .  ( 8)  - ~ [Pv(T-A(Pv)]tPM 1  R  -  ACPV)  If  a continuous  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 equation  Rgl 1  or,  (9)  2PX+ACPV)  1  2  A  CPV)  ( 9 ) c a n be w r i t t e n a s f o l l o w s :  ( 1 0 )  PV, 1  R^_LA.Log(PV) 2  (11)  14.  This approximation  givesreasonable  c o e f f i c i e n t s less than + 0 . 4 . is consideredconstant,  results f o r reflection  I n t h i s model, t h e d e n s i t y  so t h a t t h e above r e l a t i o n s h i p  (11)  c a n be- f u r t h e r s i m p l i f i e d t o g i v e : (12)  R.LLAlogV,] This expression states that the amplitudeof  t h e wave r e -  f l e c t e d by e a c h 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 t h e c o r r e s p o n d i n g change i n t h e v a l u e  ofthe  In relationship  l o g a r i t h o f a c o u s t i c impedance. (1)  i f k  and  t h e a c o u s t i c - i m p e d a n c e c a n be e x p r e s s e d  p v = k v  n  m  are constants,  as f o l l o w s :  (13)  w  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 reflection coefficient  incremental  (11),  the  becomes:  R^-i-AU kV g  m +  (14)  '  2  \  '  T h i s c a n a l s o be w r i t t e n a s f o l l o w s :  2 since  k  A Log k - K m + Q A L o n V  I s a constant, the equation  (15)  (15) c a n be w r i t t e n  i n the form. R^JHtLALogV  ~  2  I n t h e above e x p r e s s i o n (16)  (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 t h e 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 t h e v e l o c i t y with respect to depth. function  T h i s i s converted t o v e l o c i t y as a  o f two-way t r a v e l t i m e .  case/ the r e f l e c t i o n amplitude  In the discrete  Otherwise  or approximation  the continuous set of r e f l e c t i o n coef-  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 The r e f l e c t i v i t y f u n c t i o n  c a n be made more u s e f u l  (9) b y l e t t i n g A t  relationship  layer  i s determined" by 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 , u s i n g e q u a t i o n (5) (11).  distribution  T h i s c a n be done b y f o l l o w i n g  approach zero as a  r(t)  .  In limit.  t h e s t e p s a s shown b e l o w : ««  _ ^ _  L i m  LUO  =  L  i m  I  At-o A t  At  ow / AV \ At  dv  I  2V  :  At  dt d i l « „ wV r( t )i ll °L_ [Log it d;  (18b)  +  2 v  L  The c o n s t a n t 1/2 on t h e r i g h t merely a gain f a c t o r of  function. function  J  side  of t h i s equation i s  a n d i t c a n be I g n o r e d .  v e l o c i t y as a f u n c t i o n Then t h e f i r s t  (18a)  The l o g a r i t h m  of time i s c a l l e d the v e l o c i t y derivative  of the v e l o c i t y  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  function: A r  =  d Log Jl V CD  at  , ( 1 9 )  -  16.  2.2 To C o n v e r t  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 Figure how t o c o n v e r t function.  (10) i s a b l o c k d i a g r a m w h i c h  a continuous  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  Since the r e f l e c t i o n process  i sa filter  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 -  c e s s i n P e t e r s o n ' s model ( F i g u r e 11). for  shows  process,  the f i l t e r i n g pro-  The f i r s t n o r m a l way  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 t h e r e f l e c t i v i t y of the f i l t e r .  response  As i t h a s been m e n t i o n e d i n t h e p r e v i o u s  d i s c u s s i o n s , the mathematical dent upon c o n v o l u t i o n . mutative  f u n c t i o n as t h e impulse  t h e o r y o f t h i s model i s depen-  We know t h a t t h e c o n v o l u t i o n h a s com-  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 t h e f i l t e r  c a n be i n t e r c h a n g e d , u s i n g t h e 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 i m p u l s e r e s onse o f t h e f i l t e r .  This i s Peterson's  p r e p a r i n g s y n t h e t i c seisinograms. act  a n a l o g u e method o f  The f i l t e r  settings that  u p o n t h e r e f l e c t i v i t y f u n c t i o n h a v e b e e n d i v i d e d i n t o two  p a r t s , namely t h e shot p u l s e and t h e f i l t e r i n g e x t e r n a l t o t h e earth.  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 -  m e n t s p l u s geophone c o u p l i n g ( F i g u r e 1 1 ) . 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 Before  attempting  Seismograms  t o a p p r o a c h o u r p r o b l e m , we  have s t u d i e d t h e c o m p a r i s o n o f 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 . shows t h e a r e a s t u d i e d .  F i g . 12  voo  CON VERT D E P T H TO TRAVELTIME  VCO  CONVERT V E L O C I T Y TO L O G A R I T H OF VELOC1Y  R E F L E C T 1 V-ITY FUNCTION Log  VCt) DI F F E R E N T I A T E  TWO-WAY  rOt)* JL_ l o g v(tj  dt  FlGURE 10 #  B l o c k diagram of the c o n v e r t i o n o f a l o g to the r e f l e c t i v i t y f u n c t i o n  velocity  rCt)  Fl SHOT  P U L S E  a. —  >  LTER  REFLECTI VITY FUNCTION  r(t)  NPUT  Fl L T E R E X T E R N A L TO EARTH e(t)  OCf)  ^ OUTPUT  S Y N T H E T I C  set)  REF LECTI  VIY  FUNCTION r(t)  1 NPUT  F I L T E R SHOT  P U L S E  OCt)  *»—  F|  LTER  E X T E R N A L TO EARTH e(+)  OUTPUT El  GURE*II  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 process i n a l i n e a r f i l t e r  the  reflection  As a r e s u l t o f t h e s e s t u d i e s , t i o n s -were o b t a i n e d  reasonable c o r r e l a -  at thirteen different locations,  while"  a f e w l o c a t i o n s showed " p o o r " m a t c h e s . There are three 1.  The s y n t h e t i c character.  main c r i t e r i a  and a c t u a l f i e l d  f o r a good m a t c h .  record  s h o u l d match i n  B o t h r e c o r d s s h o u l d h a v e t h e 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 " d e a d " z o n e s . 2 . ' When " t h e - f i e l d a n d s y n t h e t i c character  r e c o r d s have t h e b e s t  m a t c h , t h e y s h o u l d a l s o h a v e t h e same  filter  delay. 3.  The p o l a r i t i e s o f b o t h r e c o r d s s h o u l d be If  the p o l a r i t y of the f i e l d  making t h e ' i n i t i a l  from low t o h i g h  In a r e f l e c t i o n that record.  velocity  velocity will  The p o l a r i t y o f t h e s y n t h e t i c  an i s o l a t e d step  result  i n i t i a l l y b r e a k s down o n t h e a c t u a l  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  . the i n i t i a l  i s e s t a b l i s h e d by  s i g n a l break-down, a step  change i n t h e e a r t h  field  record  consistent.  record  record can  by p l a c i n g  on t h e v e l o c i t y f u n c t i o n and  observing  break of I t s r e f l e c t i o n .  In general,  there  are three  possible  poor match i n comparison w i t h t h e s y n t h e t i c  reasons f o r a  and a c t u a l  field  records. 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  t e r i n g on t h e a c t u a l f i e l d  record.  I t s h o u l d be t a k e n  i n t o account that  the' a c t u a l f i e l d  shot pulse  as w e l l as a l l f i l t e r i n g  filter  the f i l -  record  contains  a  external to  18. the  earth  -  s u c h a s , geophone c o u p l i n g ,  geophone r e s p o n s e , 2.  amplifier  (Automatic Gain Control)  filter,  a n d so o n .  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 - i n some o f t h e f o r m a t i o n s . due  3.  The m o s t i m p o r t a n t o n e s a r e  t o washouts i n s a l t and s h a l e  formations.  The a s s u m p t i o n made i n t h e t h e o r y hold  o f t h i s m o d e l may n o t  s u f f i c i e n t l y w e l l i n the actual earth.  poor assumption i s that the record reflections.  to error  A l l types of noise  The p r i m a r y  only includes  such as ground  primary roll,  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 assumption 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 . i n some f o r m a t i o n s 2.4  This  assumption i s poor  such as s a l t and a n h y d r i t e .  M u l t i p l e and Ghost R e f l e c t i o n s : B a s e d o n 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 ,  conducive t o the formation (a) " t h e " e x i s t a n c e  attenuation  (b)  of multiple r e f l e c t i o n s are:  of s t r a t a which r e f l e c t s a large  of t h e " i n c i d e n t  energy o r formations  and a b s o r p t i o n  having  of seismic  effects  (diffraction,  surface  c o n d i t i o n s "such t h a t e x p l o s i v e  efficient  percentage  minumum  e n e r g y by secondary  diffusion etc.). charges are  and a l a r g e p e r c e n t a g e o f the emergent energy  i s r e f l e c t e d from t h e ground The  conditions  surface.  significance of multiples to the 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 ance.  For small contrasts  i n acoustic  impedance,  imped-  multiples  19.  can produce  discrete  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 . trasts are large,  I f the near  then m u l t i p l e s  within  s u r f a c e con-  these l a y e r s  c a n mask  a d i r e c t r e f l e c t e d s i g n a l from depth by producing  "ringing"  or  The  "wave t r a i n i n g " .  Multiples  cause  distortions.  m a g n i t u d e o f d i s t o r t i o n c a n n o t be o b s e r v e d o n t h e s e i s m o grams. The  existance of a large  above a s e i s m i c  velocity  discontinuity  s h o t c a n be r e c o g n i z e d a s t h e s o u r c e o f  "ghost" r e f l e c t i o n s appearing" on t h e seismogram. instances,  t h e d o w n g o i n g wave f r o n t  characterized shot p o i n t  I n such  s e t up b y t h e s h o t i s  b y e n e r g y m o v i n g d i r e c t l y downward f r o m t h e  followed  from t h e o v e r l y i n g g o i n g wave f r o n t  i n s p a c e a n d time- b y e n e r g y discontinuity.  appears  reflected  When d e t e c t e d t h i s down-  a s 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 t h e t r a v e l time f r o m t h e s h o t t o t h e d i s c o n t i n u i t y and w i t h difference  possible  Recent  the- g h o s t  Any  effects  between t h e shot and t h e 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 of the i n c i d e n t  of  I n shape.  i n shape may be a t t r i b u t e d t o r e s o n a n c e  of t h e ground  tinuity.  differences  studies  wave f r o n t  at the discon-  h a v e made p o s s i b l e  the eliminating  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  by means o f a l i n e a r f i l t e r .  seismograms  This additional f i l t e r  Includes  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 s h o t and t h e a d d i t i o n a l attenuation filter  i n t h e ghost path.  The a p p l i c a t i o n o f t h i s  does n o t a l t e r s i g n i f i c a n t l y t h e 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 although eliminating  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 F I E L D RECORDS RATHER THAN WELL GEOPHONE SURVEY DATA  3.1  Procedure The  w r i t e r has attempted  to calibrate  continuous  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  records as  follows: 1.  First,  the f u n c t i o n generator  t a p e s and t h e i r  a r e made f r 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 l o g s f o l l o w i n g t h e same t h r e e in Figure 2.  one  e m p i r i c a l l y , u s i n g two b a n d p a s s f i l t e r s -  (instrument f i l t e r )  The  used on t h e f i e l d  and t h e o t h e r  a c t i o n of t h e shot p u l s e  instrument  field  s t e p s w h i c h a r e shown  used i n making s y n t h e t i c s i s g e n e r a l l y  matching the f i l t e r  filtering  velocity  10.  The f i l t e r i n g determined  playouts  filter  record  simulating the (earth 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  d a t a ) , t h e r e f o r e , t h e second f i l t e r  i svaried to  g i v e t h e 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 sythetic records.  T h i s c a n be done b y c h a n g i n g  and high c u t - o f f frequency  ranges o f the e a r t h  thelow filter  u n t i l t h e 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 t i m e  i n t e r v a l s a r e s e t on b o t h  100 m i l l i s e c o n d s . on t h e f i e l d for  The t i m e  records at every  i n t e r v a l s s h o u l d be s e t  r e c o r d a f t e r making t h e time c o r r e c t i o n  weathering  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.  M o r r i n 7-3  f i e l d record  B.A.  Texaco Arrowhead B-76  field  record  21.  14,  1 5 ) . When m a k i n g 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 o f t h e w e l l d a t a  s h o u l d be u s e d .  I t i s arbit-  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 t h e s y n thetic  t r a c e i s zero time.  A s i t c a n be s e e n ,  a r e two t r a c e s o n t h e s y n t h e t i c p l a y b a c k  there  record  ( F i g u r e s 1 6 , 1 7 , 1 8 ) . The u p p e r one i s t h e s y n thetic  trace.  function.  The l o w e r one shows t h e v e l o c i t y  I f one c o n s i d e r s t h e  correspondence  between t h e 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 trace,  i t i snot surprising that the r e s u l t i n g  thetic  t r a c e w i l l h a v e 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 time.  This  ""simply a f i l t e r d e l a y .  syn-  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 t h e i m p u l s e response  wave f o r m ,  which,  i n t h e case  of the synthetic  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 step ocity function. set  Therefore,  the zero time  vel-  interval Is  on t h e s t a r t i n g p o i n t o f t h e s y n t h e t i c t r a c e , n o t  on t h e 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 , b e cause t h e c o r r e l a t i o n r e s u l t s o f t h e s y n t h e t i c and field  r e c o r d time  i n t e r v a l s w i l l be u s e d a n d n o t t h e  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 record. In  this  s t e p , t h e s y n t h e t i c and a c t u a l f i e l d  are c o r r e l a t e d . apparent  records  The c o r r e l a t i o n c a n be made b e t w e e n  r e f l e c t i o n p e a k s ( F i g u r e s 1 9 , 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 m a t c h , 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 b e t w e e n them.  Therefore,  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. C a n c r u d e C h a m p i o n 16-29 s y n t h e t i c  playback  B.A.  T e x a c o A r r o w h e a d B-76  time  dlscrepencies  ^AAA  8 A MORRIN 7-3 7-3-3IN-20W4  @ 05  FIOURE *Z0  B.A.  M o r r i n 7-3  time d i s c r e p e n c i e s  SYNTHETIC FIELD  TIME  RECORD  TIME  INTERVALS INTERVALS  V\C-  @ 02  B.A.  Cancrude Champion 16-29  time d i s c r e o e n c i e s  SYNTHETIC FIELD  TIME  RECORD  TIME  2-1  INTERVALS INTERVALS  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 records, the time i n t e r v a l s of the f i e l d  field  r e c o r d c a n be  irransferred t o the synthetic record. 5.  On t h e p l a y o u t s o f 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 , t h e t i m e i n t e r v a l s f o r a h u n d r e d m i l l i s e c o n d s a r e shown at  the top of the graph  (Figures 2 2 , 2 3 , 24).  d e p t h i n t e r v a l s f o r e a c h 1000 f e e t a r e a l s o on t h e d e p t h s c a l e . intervals, 26, 27).  shown  U s i n g t h e same t i m e a n d d e p t h  a t i m e - d e p t h g r a p h c a n be made ( F i g u r e s 2 5 , On t h i s g r a p h , d e p t h i s t h e o r d i n a t e a n d t h e  two-way t i m e i s t h e a b s c i s s a . graph,  The  At the o r i g i n of t h i s  t i m e w i l l be a s s u m e d z e r o a n d t h e d e p t h w i l l  -s t a r t i n g depth value of the l o g . c a n a l s o be p l o t t e d on t h e d e p t h  The t i m e scale,  assuming t h a t the o r i g i n i s zero time. the s t r a i g h t l i n e  be  intervals  similarly In Figure 2 5 ,  (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 , a s s u m i n g t h a t t h e s t a r t of the v e l o c i t y f u n c t i o n i s zero time. second  straight line  The  ( B ) , i n d i c a t e d by c r o s s p o i n t s ,  shows t h e a c t u a l two-way t i m e - d e p t h  curve.  The a c t u a l two-way t i m e - d e p t h c u r v e c a n be o b t a i n e d in are  t h e - f o l l o w i n g manner.  First,  the s y n t h e t i c time  p l o t t e d o n t h e two-way t i m e s c a l e ,  taking into consid-  e r a t i o n - t h e t i m e d i f f e r e n c e s between s y n t h e t i c and records.  intervals  field  A t 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 t h e t i m e  i n t e r v a l on t h e s y n t h e t i c  record i s not equal t o the time  i n t e r v a l on t h e v e l o c i t y f u n c t i o n w h i c h  i s shown a t t h e t o p  B.A.  Texaco Arrowhead B-76  r e f l e c t i v i t y f u n c t i o n playout  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 playout  !  B.A.  O s n n r u d e C h a m p i o n 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  time-depth  curve  B.A.  M o r r i n 7-3  two-way t i m e - d e p t h  curve  B.A.  T e x a c o A r r o w h e a d B - 7 6 two-way t i m e - d e p t h  curve  23. of 22,  the•playouts of the f u n c t i o n generator tapes (Figures 23,  24).  This discrepancy i s four milliseconds.  T h i s matter should be'considered before p l o t t i n g the synthetic if  t i m e i n t e r v a l p o i n t s on t h e two-way t i m e  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  tically  cross-points. points w i l l  example.  i s 0.012  they w i l l  ver-  intersect at  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  result  To i l l u s t r a t e  thetic  Then,  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  scale are extended h o r i z o n t a l l y ,  these  i n t h e a c t u a l two-way t i m e - d e p t h  curve.  t h i s point, l e t us consider the f o l l o w i n g  I n F i g u r e 19 t h e t i m e d i f f e r e n c e b e t w e e n t h e s y n -  time  (0.8  seconds) and t h e f i e l d  seconds.  (1.0  time  seconds)  A s i t c a n be s e e n i n F i g u r e 19,  t i m e 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 in  scale.  the f i e l d  seconds  later  t i m e ; so t h a t t h e 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 i m e o n  t h e two-way t i m e  scale  n a t e d by a l e t t e r a ) .  (Figure  25)  c r o s s p o i n t c.  O.988  seconds  I f t h i s p o i n t i s extended  and t h e c o r r e s p o n d i n g t i m e o f 0.8 l e t t e r b) i s e x t e n d e d  i s  (desig-  vertically  seconds ( d e s i g n a t e d by a  horizontally,  they w i l l  intersect at  The o t h e r c r o s s p o i n t s o n t h i s g r a p h c a n  be f o u n d i n t h e same m a n n e r .  24.  CHAPTER I V  RESULTS  4.1  Data Using these  the continuous  s t e p s , i t was a t t e m p t e d  velocity logs.  out a t t h r e e d i f f e r e n t  to calibrate  The s t u d i e s were  carried  wells.  F o l l o w i n g a r e t h e names a n d l o c a t i o n s o f t h e s e wells: 1.  Texaco Arrowhead  B-76  60° 25' 0 2 " N; 122° 5 9 ' 0 2 " W 2.  B.A. M o r r i n L s d . 7,  3.  7-3  S e c t i o n 3 , Twp. 31N, R g e . 20,  W4M  C a n c r u d e B.A. C h a m p i o n 16-29 Lsd.  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 t h e w e l l s u s e d i n t h i s w o r k a r e  shown I n F i g u r e 1 2 . The f u n c t i o n g e n e r a t o r  tapes  and t h e i r  are o b t a i n e d from the u n c a l i b r a t e d continuous of these synthetic  three wells.  r e c o r d s were p r o d u c e d r e s u l t i n g i n t h e b e s t  logs  tapes, cor-  records.  The f i l t e r s u s e d i n p r o d u c i n g these  velocity  From t h e s e f u n c t i o n g e n e r a t o r  r e l a t i o n s with the f i e l d  at  playouts  t h r e e w e l l s were a s f o l l o w s :  the synthetic records  25. Slopes ( i n Db/oct. a t $5 amp.) LC HC (c.p.s.)  LC HC (c.p.s.) (a)  B.A. T e x a c o A r r o w h e a d  B-76  Instrument F i l t e r Earth F i l t e r (b)  B.A. M o r r i n  Instrument F i l t e r Earth F i l t e r  a t e v e r y 100  22  28 25  8l 25  18  20  28 35  8l 35  18  20  t i m e i n t e r v a l l i n e s a r e drawn on b o t h milliseconds.  the following  records  Before s e t t i n g t h e time i n -  t e r v a l s on t h e f i e l d r e c o r d s , made u s i n g  16  16-29  B.A. C a n c r u d e C h a m p i o n  The  62 25  7-3  Instrument F i l t e r Earth F i l t e r (c)  22 25  t h e t i m e c o r r e c t i o n s were  data:  B.A. T e x a c o A r r o w h e a d 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'  Weathering Correction  =  0.014  Shot Hole Depth  =  40'  , =  6000'/sec.  =  0.049 s e c .  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'  Weathering C o r r e c t i o n  =  0.0273  Shot Hole Depth  =  70"  Elevation Correction Velocity  =  6500*/sec.  T o t a l Time C o r r e c t i o n  =  0.027915 s e c .  Elevation Correction Velocity T o t a l Time C o r r e c t i o n B.A. M o r r i n  7-3  26.  16-29  C a n c r u d e B.A. C h a m p t i o n Shot P o i n t E l e v a t i o n  =  3243'  E l e v a t i o n Datum  =  3 1 5 0 '  Weathering C o r r e c t i o n  =  0 . 0 1 8  Shot Hole Depth  =  7 1 '  Elevation Correction Velocity  =  11000'/sec.  T o t a l Time C o r r e c t i o n  =  0.032  Then t h e s y n t h e t i c lated  (Figures  synthetic  19,  20, 21).  and f i e l d  o f 0.01 - 0.065 s e c .  record  and f i e l d  The t i m e d i f f e r e n c e  between'  time i n t e r v a l s a r e i n t h e range  a t C a n c r u d e B.A. C h a m p i o n , f r o m 0.002  s e c o n d s t o 0.02 s e c o n d s a t B.A. M o r r i n , and  records are corre-  a n d b e t w e e n 0.003  0.032 s e c o n d s a t B.A. T e x a c o A r r o w h e a d . As  a final  step,  t h e two-way t i m e - d e p t h  were p l o t t e d f o r t h e s e t h r e e  wells  (Figures  25,  curves  26,  From t h e s e c u r v e s t h e time i n t e r v a l s o f c o n t i n u o u s  27). velocity  l o g s w e r e d e t e r m i n e d t o be i n e r r o r b y + 0.007 s e c o n d s t o + O.OO825  seconds. I n t a b l e s 1 t o 3,  these three can 4.2  the v e l o c i t y analysis data at  wells are tabulated.  The r e s u l t s o f t h i s  be c h e c k e d w i t h t h e v a l u e s shown I n t h e s e The D i s c u s s i o n s  thetic  of theErrors  study  tables.  i n Time S c a l e  o f Syn-  Seismograms Over a p e r i o d  lines for synthetic  o f time, non u n i f o r m i t y  of timing  seismograms h a s been r e c o g n i z e d  symptom o f e r r o r , w i t h  as a  q u e s t i o n s as t o t h e nature o f such  WELL  N60 25'02"WI22°59'02" NAME B.A.TEXACO ARROWHEAD B-76  AREA  FT. SIMPSON  LOCATION  o  K 8 -J265  GEOLOGIC FORMATION  SCATTER L. BUCKING HORSE FLETT. BNFF. EX. KOTCHO F. LIME TETCHO TROUT RIVER KAKISA RED KNIFE FORT SIMSON MUSKWA SLAVE POINT WATT PINE PT. DOLOMITE T.D.  DEPTH FROM  K.B  ELEVATION FROM  REFLECTION SECS  173 76 -356 -2007 -3566 -3611 -3934 -4854 -4964 -5232  .218 .2390 .326 .576 .872 .882 .924 1.086 1.1032 1.142  6548  -5297  1.149  8448 8479 8790  -7197 -7228 -7539  1.4586 1.464 1.492  8823  -7572  1.4923  9805  -8554  1.59  TABLE * l  TIME  (TWO-WAY)  1078 1175 1607 3258 4817 4862 5185 6105 6215 6482  I  i  FT  S E A LEVEL  7 - 3 - 3 1 - 2 0 W.4  LOCATION WELL A  R  c  NAME  ^JWOJRJRJN  MORRIN  A  K B -S=11P~G L -2705 GEOLOGIC FORMATION  DEPTH FROM  ELEVATION  K 8  FROM  SEA  FT  REFLECTION SECS  LEVEL  (TWO-WAY)  L.P.  2060  659  .472  COLO.  2553  166  "5666  2 WS  3420  -701  .744  B.F.S.  3696  -977  .802  VIK.  3814  MANV.  4072  -1350  PEK.  4498  -1779  BNFF.  4676  -1957  EX.  4970  -2251  _|  WAB.  4985  -2266  i  STET.  5018  -2299  1.012  CAL.  5495  -2776  1.062  NIS.  5506  -2787  IRE.  5651  -2932  1.0802  LED.  5688  -2969  1.0856  6390  -3671  1.16  -3881"  1. 1816  j  TIME  .82  -1095 L  "  .87  GLAUC. ~ ~ 9 4 6 ~  t  .964  !  1.0073 1.008  1.064  NIS. P O R .  DUV. E Q U I N . CK. L . B.H.L  "6600  "  EP.  7202  -4483  1.2430  T.D.  7264  -4545  1.248 *  i  i  TABLE *2  LOCATION  WELL A  R  E  16-29-14-24-W. 4  NAME  CANCRUDE  B.A. CHAMPION  CHAMPION  A  K B  3256  G L  3243.3 GEOLOGIC FORMATION  DEPTH FROM  ELEVATION  K B  FROM  SEA  FT LEVEL  R E F L E C T I O N TIME SECS  (TWO-WAY)  B.P.  1378  1878  .243  B.R.  1950  1306  .362  PAK.  2933  323  .544  MR.  3082  174  .5710  COLO.  3471  -215  .6302  2WS.  4479  -1223  .803  BFS.  4802  -1546  .855  B. IS.  4862  -1606  .865  BL.  5278  -2022  .931  OST.  5693  -2437  .992  BSL. QTZ.  5748  -2492  .9996  SWIFT.  5780  -2524  1.004  RIER.  5808  -2552  1.0084  5906  -2650  1.023  5958  -2702  1.028  L.POR.  6002  -2746  1.0322  SHUNDA  6216  -2960  1.054  PEK.  6296  -3040  1.061  BNFF.  6496  -3240  1.0824  EX.  7072  -3816  1.141  WAB.  7082  -3826  1.142  FAIR.  7590  -4334  1.194  CK. L .  8283  -5027  1.261  B.H.L.  8467  -5211  1.2796  ER  8877  -5621  1.321  CAMB.  8896  -5640  1.3232  T.D.  8973  -5717  TV. M.  UPOR. DENSE  TABLE * 3  27.  error being  r a i s e d i n consequence.  I n l a r g e degree, any  errors are d i r e c t l y related to error i n the basic l o g and a n a l y s i s The  velocity  thereof.  s t a r t i n g point of the r e f l e c t i v i t y  function  i s a r b i t a r i l y chosen a s z e r o t i m e and 1 0 0 m i l l i s e c o n d s a r e placed  on t h e r e c o r d .  (See F i g u r e s  2 2 , 2 3 , 24.)  I ti 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 and  the actual timing l i n e s  should  be t h e same.  can  be s e e n 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  lines  But I t differ-  ences change i r r e g u l a r l y t h r o u g h o u t t h e r e c o r d . -  We h a v e 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 the 1.  data.  More s p e c i f i c a l l y ,  Field and  a r e human e r r o r s i n t r e a t i n g  the basic  limitations are:  and l a b o r a t o r y systems a s o p e r a t e d  d i s p l a y data  with limited f i d e l i t y .  integrate One c o n s e -  quence i s t h a t t h e i n t e g r a t i o n o f t h e v e l o c i t y l o g c a r r i e d out a t magnetic tape f u n c t i o n generator  some-  times d i f f e r s from the f i e l d i n t e g r a t i o n .  The  g r a t i o n "systems a t m a g n e t i c t a p e f u n c t i o n  generator  has  an a c c u r a c y u n d e r n o r m a l o p e r a t i n g  + 1 $ and p r e s u m a b l y t h e f i e l d a similar  conditions of  i n t e g r a t i o n systems have  accuracy.  V e l o c i t y logs presented  with only v e l o c i t y  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 unavoidable degradation intrinsic  inte-  accuracy.  with  scale  consequent  These l i m i t a t i o n s a r e  i n t h e s y n t h e t i c seismograms produced from t h e  28. l o g s and a r e i n p a r t  instrumental  and i n p a r t  human.  The c o m p a r a t i v e l y m i n o r s o u r c e o f n o n u n i f o r m i t y subject 2.  to correction i s :  E n t i r e l y human e r r o r i n d r a f t i n g a n d p r e s e n t a t i o n i n c l u d i n g improper t r a n s f e r o f times from 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 t h e 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 b e t w e e n 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 of d i s c r e p a n c i e s .  I n producing a synthetic  the l i n e a r depth v e r t i c a l log  requires  The p r o b l e m grated ments.  seismogram,  scale of the c a l i b r a t e d v e l o c i t y  i s converted t o a l i n e a r time v e r t i c a l  operation  source  scale.  This  an i n t e g r a t i o n o f t h e c a l i b r a t e d l o g .  i s to maintain correct  times with the appropriate  association of i n t e d i s c r e t e v e l o c i t y measure-  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  integration  ( I . e . , i f t h e 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 duplicates  field  integrated  t i m e s o n t h e new l i n e a r t i m e l o g  t h e a s s o c i a t i o n o f v e l o c i t y measurements a t t h e s e  same t i m e s o n t h e 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 intervals will  i n f a c t be l i n e a r l y  t i m e l o g . However,  a disagreement  spaced on t h e l i n e a r b e t w e e n t h e 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 b y t h e f a c t t h a t the l a b o r a t o r y  integrated  time  t i m i n g l i n e s on  l i n e a r t i m e 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  those  a p p e a r i n g a t t h e s e same t i m e s on t h e c a l i b r a t e d l i n e a r depth f i e l d  l o g . As t h e f i e l d  d i r e c t l y i nl o g g i n g  device,  i n t e g r a t i o n i s computed  whereas magnetic  generator i n t e g r a t i o n derives  tape  function  from a d d i t i o n a l curve p l o t t i n g  29.  and  tracing  steps,  t i m e s and d i s c r e t e -  field  the association  As a r e s u l t , t h e t i m e  from the c a l i b r a t e d f i e l d  time l o g w i l l  integrated  v e l o c i t y m e a s u r e m e n t s on t h e c a l i b r a t e d  l o g i s adopted.  transferred  of v e r t i c a l  generally  intervals  l o g onto the l i n e a r  n o t be o f t h e same l e n g t h .  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 equipment o r h a n d l i n g r e q u i r e s  The  integrating  one t o r e c a l i b r a t e t h e  log. The s e c o n d s o u r c e o f t h e d i s c r e p a n c i e s to time-to-linear  v e l o c i t y conversion of h o r i z o n t a l  This type I s p e c u l i a r t o v e l o c i t y logs a linear velocity horizontal  scale  basic  scale.  l i n e a r time h o r i z o n t a l  these logs  two  additional  o f t h e more  from a l i n e a r After this,  normal  Consequently, the l o g has  times.  Such i n t e g r a t i o n s ,  when c o m p l e t e d , commonly  f e r f r o m t h e c a l i b r a t i o n t i m e s and o f t e n practice,  with  The i n t e g r a t i o n o f  t o a l i n e a r time s c a l e .  i n t e g r a t i o n processes are used.  scale.  which are only  instead  c a n be done b y r e c o n v e r t i n g  v e l o c i t y scale  i s due  i ti s felt  that  appreciably.  these a d d i t i o n a l  difIn  conversion  p r o c e s s e s , f r o m l i n e a r t i m e t o l i n e a r v e l o c i t y and t h e n b a c k 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 t h e discrepancies. is difficulty circuit  I t i s postulated i n obtaining  simulating  that  the reason f o r t h i s  l i n e a r i t y i n the e l e c t r i c a l  the conversion.  30. 4.3 a.  I n t e r p r e t a t i o n of Results: B.A. T e x a c o A r r o w h e a d The  w e l l was  IO78 f t . and b o t t o m e d  8800 f t .  mately a field  The  started i n Buckinghorse formation at i n Pine Point Dolomite at approxi-  s y n t h e t i c r e c o r d s a r e compared w i t h  record taken near the w e l l .  The  object of  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 more c l o s e l y r e s e m b l e s t h e r e f l e c t e d record.  The  synthetic  t i m e s n e a r 0.37  r e c o r d w h i c h a g r e e s most  shown i n c i r c l e s i n F i g u r e 19). that a 1.6  0.3-0.5  sec.  sec. (as record  shows 1.5-  r e f l e c t i o n at  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  record vary  smoothly as though the e n t i r e r e c o r d has been p l a y e d  B.A.  filter.  Morrin The  continuous v e l o c i t y l o g covered the depth  range f r o m a p p r o x i m a t e l y  800  7200 f t .  f t . to  p o n d e n c e b e t w e e n t h e s y n t h e t i c and t h e f i e l d t h a t t h e r e are agreements There from the f i r s t  at times  i s interference at r e f l e c t i o n event.  A  corres-  r e c o r d s shows  0.45, 0.6, O.85-O.95 0.8-0.9 The  h a s b e e n t i m e s h i f t e d a p p r o x i m a t e l y 0.5 to  closely  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 b e t w e e n  t h r o u g h a v e r y narrow band b.  field  m u l t i p l e comes f r o m t h e f i r s t  sec.  quite  The  field  correspondence  s e c . and 1.13  s e c , O.58  record  s i g n a l on t h e  w i t h t h e r e f l e c t i o n r e c o r d shows t h e b e s t at  this  s e c . w h i c h comes  synthetic m.s.  record  to the  right  e s t a b l i s h the correspondence between h i g h v e l o c i t y  z o n e s and p e a k s o n t h e f i e l d  record.  The  sec.  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  (b)  very l i t t l e  interference or noise.  on t h e s y n t h e t i c r e c o r d c.  f r o m deeper h o r i z o n s and  show r a p i d c h a n g e s o f  amplitude.  B.A. C o n e r u d e C h a m p i o n : The  continuous  877 f t . a n d 8973 f t . field  velocity  l o g was r e c o r d e d  between  The s t r o n g r e f l e c t i o n e v e n t s on t h e  r e c o r d a r e 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 a n d 1.05 polarity initial  s e c . The s y n t h e t i c r e c o r d h a s t h e same  as t h e f i e l d  record, as determined from the  down b r e a k o f t h e 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  step placed near the beginning The  The o s c i l l a t i o n s  of each V e l o c i t y f u n c t i o n .  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  trasts  than t h a t of t h e p r e v i o u s  thetic  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 The records  correlation  at different  two e x a m p l e s .  The  con-  syn-  events.  of synthetic records with  l o c a t i o n s i s shown i n F i g u r e s  field 28 and  33. The polarity  synthetic records  as the f i e l d  from t h e i n i t i a l cial  record.  i n e a c h c a s e h a v e t h e same The p o l a r i t y  break of the r e f l e c t i o n from the a r t i f i -  step placed near the beginning  function.  i s determined  ( S e e F i g u r e s 16, 17, 18.)  t h i r d c r i t e r i o n f o r good match.  of each  reflectivity  This f u l f i l l s the  32. The and  s y n t h e t i c and f i e l d  33 a r e d i s p l a c e d w i t h z e r o  records  relative  accordance w i t h t h e second c r i t e r i o n .  28  i n Figures  time s h i f t , i n The w i d e p e a k s  c o r r e s p o n d t o " t h i c k " b e d o r v e l o c i t y zones and n a r r o w peaks correspond t o " t h i n " bed zones. Figures  28,  29 and 30 a r e c h o s e n a s e x a m p l e s o f  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 are not s i g nificant. and  I n t h e s e e x a m p l e s t h e i n t e r f a c e s a r e smooth  parallel.  The r e c o r d s  received i n appreciable transmission  show t h a t s e i s m i c  energy i s  amounts a t a l l t i m e s a f t e r t h e  of the incident pulse.  The l a r g e  amplitude  o s c i l l a t i o n s a r e a s a p t 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 Interference  as of prominent i n d i v i d u a l c o n t r a s t s .  c a n be s e e n ( F i g u r e  28)  It  t h a t t h e l a r g e s t amount o f i n c i -  dent energy does n o t 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 t h e r e c o r d . the  o s c i l l a t i o n a t 0.84  seconds d e s p i t e  The a m p l i t u d e o f  seconds i s l e s s than t h a t a t  1.12  the f a c t that the i n c i d e n t energy i s  than « i t  greater*0.82 seconds. Figures  31,  m u l t i p l e s are important reflected  signal.  by  'M'.  letter  shift  32 a n d 33 a r e e x a m p l e s w h e r e i n throughout the duration of the  The p r o m i n e n t m u l t i p l e s a r e  designated  The m u l t i p l e s c a u s e d c o n s i d e r a b l e  i n the d i r e c t r e f l e c t e d s i g n a l .  ween t h e s y n t h e t i c a n d f i e l d  The d i f f e r e n c e s b e t -  record are rather  e s p e c i a l l y at the e a r l i e r a r r i v a l times. A t l a t e r t i m e s t h e two r e c o r d s  phase  small  ( F i g u r e s 31,  a p p e a r t o become  32.)  appreciably  FIELD RECORD  SY NT HETIC RECORD  Fl GURE*28  Comparision of f i e l d r e c o r d with s y n t h e t i c  record  0.6 I  FIELD  0.7 I  0.8 I  09 ,  1.0 .  "  I.I I  12  SYNTHETI C RECORD FIGURE*29  Comparision of f i e l d  record with synthetic  record  F IE LD RECORD FIGURE*30  Comparision of f i e l d  record with synthetic  record  Q5  0.6  0.7  08  Comparision of f i e l d  0.9  1.0  record with synthetic  record  0.8  0,9  1,0  1.1  1.2  13  ECORD Comparision of f i e l d  record with synthetic  record  1.4  3  0.4  05  -  0.6  0.7  0.8  0.9  FIELD  RECORD  Comparision 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  record  IP  33.  different.  I f t h e phase  s h i f t due  to the m u l t i p l e s  which  c a u s e s t h i s a p p a r e n t l a c k o f s i m i l a r i t y i s removed, t h e correlation will  be i m p r o v e d .  shows a p a i r o f m u l t i p l e s very similar,  reflection.  The  (Figure  records  b u t t h e s u b t r a c t i o n o f one f r o m t h e  shows t h a t p h a s e at l a t e r  A t h i r d example  times.  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  33)  appear other  divergence  34.  CHAPTER V  CONCLUSION  In this tics  have been p r e p a r e d  record's o b t a i n e d The  study,  o n l y a l i m i t e d number o f  synthe-  f o r comparison with a c t u a l  field  at the corresponding  r e s u l t s of t h i s  study proved t h a t there  b i l i t y of c a l i b r a t i n g continuous c o m p a r i s o n of research  s y n t h e t i c and  the best  different  field  i s a possi-  velocity logs using records.  During  c o r r e l a t i o n s were o b t a i n e d  locations.  I n some c a s e s ,  obtained  i n s p i t e of the  record.  T h i s p o o r a g r e e m e n t may  the f a c t t h a t the  well locations.  at t h i r t e e n  reflection  p a r t i a l l y explained  s y n t h e t i c s e i s m o g r a m p r o d u c e d by  s o n ' s method o n l y a p p r o x i m a t e s t h e t r u e r e f l e c t e d i m p r o v e m e n t i n o b t a i n i n g a "good m a t c h " w o u l d be  if  the  Peterson's  technique  efficients, t h a t the  expected  avoided.  He  and  co-  assuming  further finds approxi-  r e f l e c t i o n c o e f f i c i e n t s a t e a c h change i n  i m p e d a n c e u s i n g one " h a l f t h e f r a c t i o n a l d i f f e r e n c e  approximation  contrasts.  The  mathematical  w i l l more c l o s e l y a p p r o a c h i d e a l s i t u a t i o n s  i n c l u d i n g m u l t i p l e s and  t h e r improvement can reflected  ghost r e f l e c t i o n s ,  density i s constant.  of the v e l o c i t y across the  by  c o u l d be  Peter-  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  m u l t i p l e s and  m a t i o n s f o r the acoustic  u s e d by P e t e r s o n  by  signal.  An  approximation  this  p o o r c o r r e l a t i o n s were  good q u a l i t y o f t h e be  the  be  transmission coefficients.  obtained  s i g n a l of p l a n e  by c o m p u t i n g e x a c t l y  waves i n c i d e n t n o r m a l t o  Furthe  the  s u r f a c e o f a m u l t i l a y e r e d h a l f s p a c e , i n t h e c a s e where  35.  the source i s a u n i t impulse i n time. I t was f o u n d t h a t t h e f o l l o w i n g f a c t o r s must be taken i n t o account  i n the c a l i b r a t i o n of continuous  city logs using this 1.  velo-  procedure.  When m a k i n g t h e t i 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  t h e w e l l d a t a s h o u l d be u s e d f o r t h e a c t u a l s e i s m i c record. 2.  The c o r r e l a t i o n b e t w e e n t h e s y n t h e t i c a n d f i e l d r e c o r d s s h o u l d be made b e t w e e n s t r o n g r e f l e c t i o n events.  3.  I t was f o u n d t h a t t h e t i m e i n t e r v a l o n t h e s y n thetic  r e c o r d i s n o t e q u a l t o t h e time  on t h e v e l o c i t y f u n c t i o n p l a y o u t .  interval  Therefore, the  t i m e i n t e r v a l o f t h e s y n t h e t i c r e c o r d s h o u l d be c o n verted t o t h e time i n t e r v a l o f v e l o c i t y  function  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 t h e two-way t i m e d e p t h 4.  A correspondence  graphs.  s h o u l d be e s t a b l i s h e d b e t w e e n t h e  s y n t h e t i c r e c o r d and t h e v e l o c i t y f u n c t i o n b y s h i f t i n g the synthetic forward i n time. 5.  Any s i g n i f i c a n t move-out  on t h e s e i s m i c r e c o r d s h o u l d  be r e m o v e d b e f o r e c o m p a r i s o n record.  with the synthetic  BIBLIOGRAPHY  A u 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 R e v i e w B y , 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. B a c k u s , M. M., W a t e r R e v e r b e r a t i o n s , T h e i r N a t u r e 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.  B e r r y m a n , L . H., P. L . G o u p i l l a u d and K. H. W e t e r s , 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 , Part I , T h e r i c a l Results, Geophysics,  V o l . 23, 223-243,  B i r c h , P.,  1958.  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 L o n g Column o f G r a n i t e , B u l l . S e i s . S o c . Amer., V o l . 23.  B r u c k s h a w , J . M., and P. C. M a h a n t a , The V a r i a t i o n o f the E l a s t i c Contents of Rocks w i t h Frequency, M i m e o g r a p h e d C i r c u l a r o f t h e E.A.E.G., 1952. Cholet,  J . , and H. R i c h a r d , A T e s t o n E l a s t i c A n i s o t r o p y Measurements a t B e r r i a n e (North Sahara), G e o p h y s . P r o s p e c t i n g , V o l . 2, No. 3, 1954.  D e l a p l a n e h e , J . , An E x a m p l e o f t h e u s e o f S y n t h e t i c Seismograms, G e o l . ,  V o l . 28,  No. 5,  843,  1963.  D u n o y e r de S e g o n z a c , P., a n d L o h e r r e r e , A p p l i c a t i o n o f the Continuous V e l o c i t y t o Anisotropy M e a s u r e m e n t s i n N o r t h e r n S a h a r a , R e s u l t s and C o n s e q u e n c e s , G e o p h y s . P r o s p e c t i n g , V o l . 7, No.  2.  Gretener,  P. E. F., An A n a l y s i s o f t h e O b s e r v e d Time D i s c r e p a n c i e s Between C o n t i n u o u s and C o n v e n t i o n a l W e l l V e l o c i t y Surveys, J . A l b e r t a Soc. P e t r o . G e o l o g i s t s , V o l . 8, No. 10, 272-286, i960.  H i c k s , W.  G., L a t e r a l V e l o c i t y V a r i a t i o n s N e a r G e o p h y s i c s , V o l . 24, No. 3, 451-464,  K o k e s h , F. P., and R. B. B l i z a r d , G e o m e t r i c a l S o n i c L o g g i n g , G e o p h y s i c s , V o l . 24,  64-76,  1959.  Boreholes,  1959-  Factors i n No. 1,  Lindsey, J . P., E l i m i n a t i o n of Seismic Ghost R e f l e c t i o n s by Means of L i n e a r F i l t e r , Geol. V o l . 25,  No. 1, 130-140,  I960.  Lee, Y. W., S t a t i s t i c a l Theory of Communication, New York, London, John Wiley and Sons I n c . Peterson, R. A., W. R. F i l l i p p o n e , F. B. Coker, The S y n t h e s i s o f Seismograms from Well Log Data, Geophysics, V o l . 20, No. 3, 516-538, 1955. R i c h a r d s , T. C , Wide-Angle R e f l e c t i o n s and T h e i r A p p l i c a t i o n t o F i n d i n g Limestone S t r u c t u r e s i n the F o o t h i l l s o f Western Canada, Geophysics,  V o l . 25, No. 2, 385-407, I960.  R i c k e r , N., Wavelet C o n t r a c t i o n , Wavelet Expansion and the C o n t r o l of Seismic R e s o l u t i o n , Geophysics,  V o l . 18, No. 4, 769-792, 1953.  RIcker, N., The Form and Lows of Propagation o f Seismic Wavelets, Geophysics, V o l . Io, No. 1, 11-40,  1953.  R i c k e r , N., The Form and Nature o f Seismic Waves and the S t r u c t u r e o f Seismograms, Geol., V o l . 5, No. 4,  349-366, 1940.  Sengbush, R. L., P. L . Lawrence, and F. J . McDonal, I n t e r p r e t a t i o n o f S y n t h e t i c Seismograms,  Geophysics, V o l . 26, No. 2, I38-I56, 1961.  Summers, G. C , and R. A. Broding, Continuous V e l o c i t y Logging, Geophysics, V o l . 17, No. 3, 598-614,  1952.  Smith, M. K., A Review of Methods of F i l t e r i n g Seismic Data, Geophysics, V o l .  23,  No.  1, 44-57, 1958.  V o g e l , C. B., A Seismic V e l o c i t y Logging Method, Geophysics,  V o l . 17, No. 3,~587-597, 1952.  White, J . E., Seismic Waves R a d i a t i o n , T r a n s m i s s i o n and A t t e n u a t i o n , McGraw H i l l .  W o l f , A., The Time D e l a y o f a Wave G r o u p i n t h e W e a t h e r e d L a y e r , G e o p h y s i c s , V o l . 5* 367~3725 1940. Wolf,  A., The R e f l e c t i o n o f E l a s t i c Waves P r o m T r a n s i t i o n Layers o f V a r i a b l e V e l o c i t y , Geophysics,  V o l . 2, 357-363, 1937.  Woods, J . P., The C o m p o s i t i o n o f R e f l e c t i o n ,  V o l . 21, No. 2, 261-276, 1956.  Geophysics,  W u e n s c h e l , P. C , S e i s m o g r a m S y n t h e s i s 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 , G e o p h y s i c s , V o l . 25, No. 1, 106-129, i960. Wyllie,  M. R. J . , A. R. G r e g o r y , a n d G. H. P. G a r d n e r , An E x p e r i m e n t a l I n v e s t i g a t i o n o f F a c t o r s A f f e c t i n g E l a s t i c Wave V e l o c i t i e s i n P o r o u s M e d i a , G e o p h y s i c s , V o l . 23, No, 3, 459-493,  1958.  

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