A Seismic Reflection Survey Over the Wayne-25 Oil Field in

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Master's Theses Graduate College

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A Seismic Reflection Survey Over the Wayne-25 Oil Field in Cass A Seismic Reflection Survey Over the Wayne-25 Oil Field in Cass

County, Michigan County, Michigan

Paul D. Horton

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A SEISMIC REFLECTION SURVEY OVER THE WAYNE-25 OIL FIELDIN CASS COUNTY, MICHIGAN

byPaul D. Horton

A Thesis Submitted to the

Faculty of The Graduate College in partial fulfillment of the

requirements for the Degree of Master of Science

Department of Geology

Western Michigan University Kalamazoo, Michigan

December 1987

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

A SEISMIC REFLECTION SURVEY OVER THE WAYNE-25 OIL FIELDIN CASS COUNTY, MICHIGAN

Paul D. Hor t on , M.S.

Western Michigan U n i v e r s i t y , 1987

The "opt imum window" s e i s m i c r e f l e c t i o n method was

u s e d i n an e n d e a v o r t o f u r t h e r d e f i n e an o i l p r o d u c i n g

s t r u c t u r e i n t h e T r a v e r s e Limes tone . Thi s method e n t a i l s

u s i n g a s o u r c e - g e o p h o n e o f f s e t wh i ch a l l o w s d e s i r e d

r e f l e c t i o n s t o a r r i v e i n an u n d i s t u r b e d t ime zone.

S e v e r a l s o u r c e s i n t h e s t u d y a r e a p r o d u c e d s e i s m i c

p u l s e s wi th r e l a t i v e l y h igh dominant f r e q u e n c y components

r a n g i n g f rom 80 t o 120 h e r t z . Ho wever , o n l y s m a l l c h a r g e s

o f d y n a m i t e p r o d u c e d s u f f i c i e n t e n e r g y t o p e n e t r a t e t h e

g l a c i a l d r i f t in t h e s t u d y a r e a .

P r e l i m i n a r i l y i d e n t i f i e d r e f l e c t i o n a r r i v a l s from t h e

t a r g e t e d h o r i z o n wer e c o n s i s t e n t l y masked i n s e i s m i c

p r o f i l i n g r e c o r d s by h igh a m p l i t u d e , low v e l o c i t y s e i s m i c

a r r i v a l s . V a r i e d s o u r c e o f f s e t s , d i g i t a l f i l t e r i n g and

s e i s m i c t r a c e s t a c k i n g f a i l e d t o unmask d e s i r e d r e f l e c t i o n s .

W e l l l o g and s e i s m i c r e f r a c t i o n d a t a c o u p l e d w i t h

s e i s m i c m o d e l i n g s u g g e s t a c l a y l a y e r c a u s e d v e l o c i t y

i n v e r s i o n w i t h i n t h e g l a c i a l d r i f t wh i ch g e n e r a t e d h i g h

a m p l i t u d e , low v e l o c i t y m u l t i p l e phenomena, t h e r e b y masking

r e f l e c t i o n s from t h e t a r g e t e d h o r i z o n .


ACKNOWLEDGEMENTS

I am g r a t e f u l t o Dr. Ger ry C l a r k s o n f o r h i s guidance

and s u p p o r t d u r i n g t h e f u l l l e n g t h o f t h i s r e s e a r c h

p r o j e c t . I a l s o w i s h t o t h a n k Mannes O i l Co. and Ward

K e l l n e r f o r t h e i r c o o p e r a t i o n .

B i l l H e n d e r s o n d e s e r v e s s p e c i a l t h a n k s f o r h i s

m o n u m e n t a l h e l p i n t h e f i e l d work i n v o l v e d i n t h i s

p r o j e c t . A l s o , J e f f r e y S. B r o w n , B i l l M o r s e , E r i c

Montgomery, Dennis T r i p p , and o t h e r s c o n t r i b u t e d g r e a t l y

i n o b t a i n i n g s e i s m i c d a t a .

O t h e r s t o whom I am i n d e b t e d i n c l u d e Dean Bojahanen,

Angus Mann, and Doug D a n i e l s f o r t h e i r a v a i l a b i l i t y and

h e l p f u l n e s s in v o l u n t e r r i n g i n f o r m a t i o n .

F i n a l l y , I w i s h t o t h a n k my w i f e , J i l l , f o r h e r

e n d u r i n g f i n a n c i a l and m o r a l s u p p o r t t h r o u g h o u t t h e

e n t i r e r e s e a r c h p r o j e c t .

Th i s s tu dy was s u p p o r t e d i n p a r t by a r e s e a r c h g r a n t

from The Gr adu a t e C o l l e g e o f Western Michigan U n i v e r s i t y

and t h e Western Michigan U n i v e r s i t y Geology Depar tment .

P au l D. Hor ton

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A seismic reflection survey over the Wayne-25 oil field in Cass County, Michigan

Horton, Paul D., M.S.Western Michigan University, 1987

U M I300 N. Zeeb Rd.Ann Arbor, MI 48106



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TABLE OF CONTENTS

ACKNOWLEDGEMENTS........................................................................................ i i

LIST OF TABLES............................................................................................. v i

LIST OF FIGURES.......................................................................................... v i i

INTRODUCTION.................................................................................................. 1

P u r p o s e .................................................................................................. 1

L o c a t io n and Ge ology ................................................................... 2

P r e v i o u s Work ................................................................................. 7

Rev i ew o f S e l e c t e d L i t e r a t u r e .................................... 11

REFLECTION SURVEY METHOD THEORY..................................................... 13

High R e s o l u t i o n in R e f l e c t i o n P r o f i l i n g ...................... 13

The Source I m p u l s e ............................................................ 14

The E a r t h ' s Response ....................................................... 19

The Geophone R es pon se .................................................... 20

P r o c e s s i n g E f f e c t s ............................................................ 21

P r o f i l i n g Method ............................................................................ 22

The Optimum Window....................... 24

Time Domain C o r r e c t i o n s ............................................................ 27

FIELD SURVEY.................................................................................................. 29

I n s t r u m e n t a t i o n ............................................................................... 29

F i e l d P a r a m e t e r s ............................................................................ 30

Sour ce and Geophone A r r a y ........................................... 31

Source P a r a m e t e r s .............................................................. 32

Se i smograph P a r a m e t e r s .................................................. 32

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Table of Contents— Continued

S i g n a l P r o c e s s i n g .............................................................. 34

SOURCE ANALYSIS........................................................................................... 36

S t a c k i n g T e s t s ................................................................................. 36

Frequency A n a l y s i s ....................................................................... 36

ANALYSIS OF WALK AWAY DATA................................................................ 43

R e f r a c t i o n A n a l y s i s ..................................................................... 43

R e f r a c t i o n A n a l y s i s o f S le dg e Hammer D a t a . . . 46

R e f r a c t i o n A n a l y s i s o f Dynamite Da ta .................. 53

Summary o f R e s u l t s o f R e f r a c t i o n A n a l y s e s , . . 59

R e f l e c t i o n A n a l y s i s ..................................................................... 67

R e f l e c t i o n A n a l y s i s o f S le dge Hammer D a t a . . . 72

R e f l e c t i o n A n a l y s i s o f Dynamite D a t a . . 73

Summary o f R e s u l t s o f R e f l e c t i o n A n a l y s e s . . . 80

INTERPRETATION OF PROFILING RECORDS.......................................... 81

V e l o c i t y A n a l y s i s .......................................................................... 81

Summary o f V e l o c i t y A n a l y s e s .................... 89

Ampl i tude A n a l y s i s ....................................................................... 92

Raypath Mo de l i ng ............................................................................ 95

Near S u r f a c e M u l t i p l e s .................................................. 100

I n t e r f o r m a t i o n a l M u l t i p l e s ........................................ 101

REMOVING THE MULTIPLES.......................................................................... 104

CONCLUSIONS.................................................................................................... 108

APPENDIX ......................................................................................................... 110

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Table o f C o n t e n t s — Cont inued

BIBLIOGRAPHY....................... 112

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r ~ ~ r ■ ■Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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LIST OF TABLES

1. Geo l og ic Column i n Study A r e a ............................................ 5

2. Frequency A n a l y s i s R e s u l t s ................................................... 41

3. T-X A n a l y s i s R e s u l t s For Walk Away Survey S - 1 . . . 48

4. T-X A na l ys i s R e s u l t s For Walk Away Survey S - 2 . . . 54

5. T-X A n a l y s i s R e s u l t s For Walk Away Survey D - 2 . . . 56

6. T-X A na l ys i s R e s u l t s For Walk Away Survey D - 1 . . . 58

7 . Comparison o f Water Table D e p t h s ......................... 60

8. S y n t h e t i c R e f r a c t i o n Walk Away P a r a m e t e r s . . . . . . . 60

9. T-X A n a l y s i s R e s u l t s For S y n t h e t i c R e f r a c t i o nWalk Away.......................................................................................... 65

10. S y n t h e t i c R e f l e c t i o n Walk Away P a r a m e t e r s ................ 69

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LIST OF FIGURES

1. L o c a t i o n Map o f Study A r e a .................................. ................. 3

2. Ba s em en t •P rov ince Map From Kel logg ( 1 9 7 1 ) ................ 4

3. S e i smi c Line PP1-82-1 Over S tudy Area byHosking G e o p h y s i c a l ................................................................... 8

4 . S t r u c t u r a l Contours on t h e T r a v e r s e Limes t o n e as I n t e r p r e t e d by K e l l n e r ( 1 9 8 6 ) ...................... 9

5. Cross S e c t i o n K-K' C r os s in g t h e S t r u c t u r e in t h e T r a v e r s e Limestone as I n t e r p r e t e dby K e l l n e r ( 1 986 ) ........................................................................ 10

6. Ske t ch o f B u f f a lo Gun Shotgun S o u r c e ............................ 17

7 . Common O f f s e t P r o f i l i n g Raypath DiagramBased on Well Log Depths in t h e Study A r e a 23

8. R e f l e c t i o n Model and T i me - Di s t an ce GraphShowing t h e P o s i t i o n o f t h e Optimum w in dow Geophone A r r a y ..................................................................... 25

9. Raypath Diagram Showing S u b s ur f ac e Coverage Obta ined Dur ing a Walk AwayNoise T e s t ........................................................................................ 26

10. Seismograms o f S l edge Hammer S t ack T e s t Showing E f f e c t of M u l t i p l e S t a c k s inReducing N o i s e ............................................................................... 37

11. Seismograms o f Shotgun Slug S t a ck T e s t Showing E f f e c t o f M u l t i p l e S t a c k s inReducing N o i s e ............................................................................... 38

12. I d e a l i z e d Frequency Response Curve of t h e 7 and 1000 Her tz B u t t e r w o r t h F i l t e r s ont he Bison GeoPro S e i s mo g r a p h .............................................. 38

13. S e i smi c P u l s e Recorded by a Geophone o f f s e t From t h e Source 10 f e e t ................................................ 41

14. L o c a t i o n Map o f Four Walk Away NoiseT e s t s Conducted in t h e Study A r e a .................................. 44

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List of Figures— Continued

15. S y n t h e t i c T ime- Di s t anc e Graph For a ThreeLayer Cas e ........................................................................................ 45

16. Seismograms From Walk Away Survey S-1 P r e s e n t e d As a Time- Dis t ance Graph With I n t e r p r e t a t i o no f A r r i v a l s as a Three Layer C a s e ................................. 47

17* Time D i s t a nc e Graph o f F i r s t A r r i v a l s ForWalk Away Survey S - 1 ................................................................ 48

18. Seismograms From Walk Away Survey S-2 (Forward)P r e s e n t e d As a T i m e -D is t a nc e Graph With I n t e r p r e t a t i o n o f A r r i v a l s as a 3 - L a y e r Cas e . . 50

19. Seismograms From Walk Away Survey S-2 (Rever se )P r e s e n t e d As a T i me- Di s t an ce Graph With I n t e r p r e t a t i o n o f A r r i v a l s as a 3-Layer C a s e . . . . 51

20 . T i me- Di s t ance Graph o f F i r s t A r r i v a l s ForForward and Reverse Walk Away Sur veys S - 2 .............. 52

2 1 . V e l o c i t y Layer P r o f i l e C a l c u l a t e d From Time- D i s t a n c e Graph o f F i r s t A r r i v a l s From WalkAway Survey S - 2 ............................................................................ 52

22 . Seismograms From Walk Away Survey D-2 P r e s e n t e dAs a T i me- Dis t ance Graph With I n t e r p r e t a t i o n of F i r s t A r r i v a l s as a Three Layer C a s e .......................... 55

23 . T ime- Di s t anc e Graph o f F i r s t A r r i v a l s FromWalk Away Survey D-2................................................................. 56

24. Seismograms From Walk Away S ur vey D-1 P r e s e n t e dAs a T i me- Di s t anc e Graph With I n t e r p r e t a t i o n of F i r s t A r r i v a l s as a Three Layer Ca s e .......................... 57

25. T i me- Di s t anc e Graph o f F i r s t A r r i v a l s FromWalk Away Survey D-1 ................................................................ 58

26. Geol og i c Cross S e c t i o n o f . G l a c i a l D r i f t AcrossStudy Area Showing a Cont inuous Clay L a y e r 62

27. S y n t h e t i c Walk Away Seismograms Model ing the Se i smi c R e f r a c t i o n Response i n t h e G l a c i a lD r i f t of t h e S tudy A r e a ......................................................... 64

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28. T im e- Di s t anc e Graph of F i r s t A r r i v a l s From S y n t h e t i c Walk Away Seismograms Model ing t h eG l a c i a l D r i f t i n t h e Study A r e a 65 .

29. Geolog i c and V e l o c i t y P r o f i l e Model o f G l a c i a l D r i f t i n t h e Study Area Based on I n t e r p r e t a t i o no f Walk Away Surveys and Well L o g s ..................... 66

30. S y n t h e t i c Walk Away Seismograms Model ing t h e Se i smic R e f l e c t i o n and R e f r a c t i o n Response int h e G l a c i a l D r i f t o f t h e Study A r e a ............................. 70

31. Time S q u a r e d - D i s t a n c e Squared Graph o f T r a v e r s eLimes tone R e f l e c t i o n A r r i v a l Times Computed by S y n t h e t i c Seismogram Program............................................. 71

32. Seismograms From Walk Away D-1 Trace-Mixed andD i g i t a l l y B a n d - P a s s F i l t e r e d 7 5 - 2 00 H e r t z P r e s e n t e d as a T i me- Di s t an ce Graph With I n t e r p r e t a t i o n of R e f l e c t i o n A r r i v a l s ........................ 7**

33. Time S q u a r e d - D i s t a n c e S q u a r e d Graph o f I n t e r p r e t e d T r a v e r s e Limes tone R e f l e c t i o nA r r i v a l s From Walk Away D - 1 . . . . , ...................................... 76

34. T ime- Di s t an ce Graph of High Ampli tude EventsShowing V e l o c i t i e s S i m i l a r To R e f r a c t e d Wave V e l o c i t y ............................................................................................. 76

35. Time S q u a r e d - D i s t a n c e Squared Graph o f HighAmpl i tude E v e n t s .......................................................................... 78

36. Seismograms From Walk Away D-2 Trace-Mixedand D i g i t a l l y Band-Pass F i l t e r e d 75-200 Her tz P r e s e n t e d as a T i me- Di s t an ce Graph With I n t r e p r e t a t i o n of R e f l e c t i o n A r r i v a l s ........................ 79

37. Time S q u a r e d - D i s t a n c e Squared Graph of I n t r e p r e t e d T r a v e r s e Limes tone R e f l e c t i o nA r r i v a l s From Walk Away D-2 ................................................ 78

38. Dynamite Source P r o f i l i n g Seismograms FromM a r c e l l u s Road.............................................................................. 82

39. Dynamite Source P r o f i l i n g Seismograms FromMckenzie Road ......................................................................... 82

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40. T i m e -D i s t an c e Graph o f Se i smic A r r i v a l s From Record 17 o f M a r c e l l u s Road P r o f i l i n g Se i smograms ...................................................................................... 83

41. T i me- Di s t anc e Graph o f S y n t h e t i c T r a v e r s e Limes tone R e f l e c t i o n A r r i v a l s Showing Normal Moveout C u r v a t u r e ....................................................................... 83

42. Time S q u a r e d - D i s t a n c e Squared Graph o f High Ampl i tude Events From M a r c e l l u s RoadP r o f i l i n g Se i smogramso ............................................................ 85

43. Dynamite Source P r o f i l i n g Seismograms From M a r c e l l u s Road Time C o r r e c t e d t o F i r s tA r r i v a l s ............................................................................................. 86

44. Dynamite Source P r o f i l i n g Seismograms From Mckenzie Road Time C o r r e c t e d t o F i r s tA r r i v a l s ............................................................................................. 86

45. S ledge Hammer Source P r o f i l i n g Seismograms From Mckenzie Road Time C o r r e c t e d t o F i r s t A r r i v a l s ............................................................................................. 87

46. Shotgun Source P r o f i l i n g Seismograms From Mckenzie Road Time C o r r e c t e d t o F i r s tA r r i v a l s ............................................................................................. 88

4 7 . Dynamite Source P r o f i l i n g Seismograms From Mckenzie Road ( s o u r c e o f f s e t = 415 f t . ) Time C o r r e c t e d t o F i r s t A r r i v a l s ................................................ 90

48. Unprocessed Seismograms Obta ined i n Nor the rn Michigan by Hosking G e o p h y s i c a l ...................................... 91

49. R e l a t i v e Ampl i tude (Ao/Ai) Versus Angle o f I n c i d e n c e (Oi) For t h e Model Case of V1/V2 =. 522 , D e n s i t y R a t i o o f .757» C r i t i c a l Angleo f 31 .5 Degrees (From McCamy e t a l . , 1 9 6 2 ) ............ 93

50. V e l o c i t y D i s t r i b u t i o n Model o f G l a c i a l D r i f t i n t h e Study Area With Raypaths o f P-Waves I n c i d e n t a t 30 and 35 D e g r e e s ........................................... 96

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51. V e l o c i t y D i s t r i b u t i o n Model o f G l a c i a l D r i f t i n t h e Study Area With Raypath3 o f Conver tedWaves i n c i d e n t a t 35 and 55 D e g r e e s ............................. 97

52. V e l o c i t y D i s t r i b u t i o n Model o f G l a c i a l D r i f ti n t h e Study Area With Raypa ths o f P o s s i b l e Ne a r - S u r f a c e and I n t e r f o r m a t i o n a l M u l t i p l e s I n c i d e n t a t 35 D e g r e e s ............................................................ 99

53* V e l o c i t y D i s t r i b u t i o n Model o f G l a c i a l D r i f tin t h e Study Area With Raypaths o f P o s s i b l e M u l t i p l e I n c i d e n t a t 20 D e g r e e s ...................................... 103

54. R e c i p r o c a l o f Wavelength (K) Versus Frequency(F) Ca l l ed an F/K P l o t (From Dobr i n , 197 6) ............ 106


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INTRODUCTION

Purpose

The Wayne-25 o i l f i e l d i n Cass Co un t y , M i c h i g a n

p r o d u c e s from a s m a l l dome i n t h e Midd le Devonian T r a v e r s e

Limes tone . O i l w e l l l o g s and p r o d u c t i o n d a t a c oup led w i t h

a s e i s m i c l i n e r un o v e r t h e s t r u c t u r e a r e i n t e r p r e t e d t o

i n d i c a t e t h e p r e s e n c e o f a n o r m a l f a u l t t r e n d i n g

n o r t h e a s t , b o u n d i n g t h e dome on t h e w e s t . D e t e r m i n a t i o n

o f t he a c t u a l l o c a t i o n and o r i e n t a t i o n of t h e f a u l t c o u l d

be c r u c i a l i n f u t u r e d ev e l op me nt o f t h e o i l f i e l d . Thi s

i n f o r m a t i o n p r o v i d e d t h e j u s t i f i c a t i o n f o r a s e i s m i c s t u d y

o f t h e o i l f i e l d . The p r i m a r y o b j e c t i v e o f t h i s s t u d y was

t o u s e t h e "opt imum window" s h a l l o w s e i s m i c r e f l e c t i o n

t e c h n i q u e t o g e n e r a t e a s e i s m i c p r o f i l e o f t h e T r a v e r s e

Limes tone i n t r a - b e d r o c k r e f l e c t o r . A secondary g o a l was

t o compare t h e r e l a t i v e e f f e c t i v e n e s s o f a s l e d g e hammer,

s h o t gu n , and a s m a l l ch ar ge o f dynami te as h igh f r e q u e n c y

s e i s m i c ene rgy s o u r c e s i n a g l a c i a l d r i f t - c o v e r e d t e r r a n e .

1


2

L o c a t i o n and Geology

The s t u d y a r e a i s l o c a t e d in s e c t i o n s 25 and 36 o f

Wayne To wnsh ip i n C a s s C o u n t y , M i c h i g a n ( F i g u r e 1). The

P recamb r i an basement c o n s i s t s o f g r a n i t e , f e l s i c and maf ic

g n e i s s e s , e x t r u s i v e s , and m e t a s e d i m e n t s , and h a s been

a s s i g n e d t o t h e c e n t r a l b a s e m e n t p r o v i n c e by K e l l o g g

(1971) ( F i g u r e 2). O v e r l y i n g t h e Precambr ian basement i s

t h e P a l e o z o i c s e q u e n c e o f s e d i m e n t a r y r o c k s which a r e

o v e r l a i n by Q u a t e r n a r y g l a c i a l d r i f t d e p o s i t s ( Ta b l e 1).

The Wayne-25 o i l f i e l d p r oduces gas and o i l from t h e

m i d d l e D e v o n i a n T r a v e r s e L i m e s t o n e . The T r a v e r s e

L i m e s t o n e i n t h e s o u t h w e s t e r n p a r t o f M i c h i g a n i s

p r e d o m i n a n t l y p u r e l i m e s t o n e w i t h some b e d s o f d o l o m i t e

and a r g i l l a c e o u s d o l o m i t i c l i m e s t o n e s . Some l i t h o g r a p h i c

l i m e s t o n e beds as w e l l as abundant c h e r t i n t he lower p a r t

o f t h e p u r e l i m e s t o n e a l s o o c c u r s . The T r a v e r s e i s

t h i n n e s t i n t h e s o u t h w e s t e r n p a r t o f Michigan, somet imes

l e s s than 100 f e e t t h i c k .

The T r a v e r s e L i m e s t o n e i s o v e r l a i n by t h e T r a v e r s e

F o r m a t i o n s h a l e wh i ch i s composed o f g r a y s h a l e i n t h e

upper p o r t i o n and g r a d u a l l y g r ades t o more c a l c a r o u s and

a r g i l l a c e o u s l i m e s t o n e n e a r t h e b a s e . The T r a v e r s e

F o r m a t i o n i s c o n s i d e r e d t o be a t r a n s i t i o n z on e b e t w e e n

t h e o v e r l y i n g Antr im S h a l e and t h e T r a v e r s e Limes tone .


p%

3

S tu d y A rea

Wayne

36

Figure 1. Location Map of Study Area.


MAFICVOLCANO

43 # 00 ’ *

4 4 * 0 0 * +

4 3 * 0 0 * +

4 2 * 0 0 4

BASEMENT PR OVINCE MAP

MAFIC \urmjsivcs a n o i n - * \TNU3IVC3

s c a l e

2 0 M I L E S

4 4 3 * 0 0 *

4 4 4 * 0 0

V E T A V O L C A N iC SMSTASC&uCftrS A N O O N E lS S C S

e x t w j sives, /u a / i c I N T R U S I V E * /

N E I S S E S / ' A M /

M E T * - / COI MENTS

M E T A S E O IM E N T S . U E T A V O l C AN IC S . .a n o g n e i s s e s x

METAVOLCANICS

AMOM AR iC GNEISSES

MA RI C l ' s S ^ ? —' 7 I N T R U S I V E * , | G N E I S S E S AMO

C N A N U L I T E

G R A N I T E , r E L S l C ANO U A R IC G N E I S S E S , E X - T R U S I V E S ANO \a i e t a s e o i m e n t s

\ \

I . N T B U S t v t S'Eatru T/i | S l V t S A M I V f ~ 1 ~

u a R iC / — f - j j 3 H E I S S E 3

• 2 * 3 0 *a s * 3 0 *PREDOMINANTsrnucruNALTACNO

442*00*

♦ T ' , - ,0 » * 3 0 0 9 * 3 0 • * * 3 0

r i n o r e a n i i . * * i o a . r . ) C 3 k e <*e e n a « a n ( i . o s - i i 3 0 t )

c e n t r a l ( u - i s o t I b o n e n v i l l C ( o o - i i o . t. )

Figure 2. Basement Province Map From Kellogg (1971).


Table 1

Geo lo g i c Column in Study Area

Format ion Age

GLACIAL DRIFT PLEISTOCENE

COLDWATER SHALE MISSISSIPPIAN

ELLSWORTH SHALETRAVERSE FROMATIONTRAVERSE LIMESTONEDUNDEE LIMESTONE DEVONIANDETROITSYLVANIA

C UNITNIAGARAN SERIESCLINTON SILURIANCABOT HEAD SHALEMANITOULIN DOLOMITE

CINCINNATIAN SERIESUTICA SHALETRENTON FORMATIONBLACK RIVER GROUP ORDOVICIANGLENWOOD SHALEST. PETER SANDSTONEPRAIRE DU CHEIN

TREMPEALEAU FORMATIONFRANCONIA SANDSTONEDRESBACH SANDSTONE CAMBRIANEAU CLAIREMT. SIMON


6

The Antr im S h a l e i s p r e d o m i n a n t l y da r k g r ay t o b l a c k

and brown, ha r d , t h i n - b e d d e d , b r i t t l e , c a r bon aceou s s h a l e

i n t e r b e d d e d wi th l i g h t e r gray s h a l e i n the l ower p a r t . In

s o u t h w e s t e r n Michigan t h e Antr im i s somet imes d i v i d e d i n t o

t h e u p p e r d a r k A n t r i m S h a l e and t h e l o w e r l i g h t A n t r i m

S h a l e . The Antr im r a n g e s in t h i c k n e s s from 120 f e e t where

i t h a s b e e n e r o d e d d u r i n g t h e P l e i s t o c e n e t o 600 f e e t i n

p a r t s o f n o r t h e r n Michigan .

The Antr im s h a l e s a r e o v e r l a i n by the E l l s w o r t h S h a l e

which i s t h e uppermost Devonian Format ion e n c o u n t e r e d i n

M i c h i g a n . The E l l s w o r t h i s g r e e n i s h - g r a y w i t h a

c o n s i d e r a b l e amount of i n t e r b e d e d s i l t s t o n e . In we s te rn

Michigan t h e E l l s w o r t h r an g es from 250 t o 700 f e e t t h i c k .

The E l l s w o r t h i s o v e r l a i n by t h e M i s s i s s i p p i a n Col dwat er

S h a l e .

The Coldwater S h a l e i s p r e d o m i n a n t l y g r ay t o b l u i s h -

g ray s h a l e w i t h some l i m e s t o n e , d o l o m i t e , s i l t s t o n e , and

s a n d s t o n e . At t h e b a s e o f t h e C o l d w a t e r S h a l e i s a t h i n

bed (<20 f e e t t h i c k ) o f r e d a r g i l l a c e o u s l i m e s t o n e o r

d o l o m i t e known as t h e “C o l d w a t e r Red Rock. " On t h e

w e s t e r n s i d e o f t h e M i c h i g a n b a s i n t h e C o l d w a t e r a l s o

c o n t a i n s an a r g i l l a c e o u s d o l o m i t e zone known as t h e

“C o l d wa te r Lime“. The Co l dw at e r t h i n s c o n s i d e r a b l y from

i t s t h i c k n e s s o f 1 0 0 0 - 1 1 0 0 f e e t in c e n t r a l and e a s t e r n

M i c h i g a n t o 5 0 0 - 6 0 0 f e e t i n w e s t e r n M i c h i g a n . The


7

C o l d w a t e r S h a l e i s c o n s i d e r a b l y t h i n n e r i n t h e s t ud y a r ea

due t o P l e i s t o c e n e e r o s i o n .

O v e r l y i n g t h e C o l d w a t e r S h a l e i s 275 t o 350 f e e t o f

Q u a t e r n a r y G l a c i a l D r i f t D e p o s i t s . The lower p o r t i o n of

t h e d r i f t i s p r e d o m i n a n t l y ground moraine d e p o s i t s . The

ground mora ine i s o v e r l a i n by i c e - c o n t a c t s t r a t i f i e d d r i f t

i n kames and kame mo ra ine s of t he I n d i a na Lagro Format ion

kame f a c i e s ( S c h ne i d e r & K e l l e r , 1970).

P r e v i o u s Work

K e l l n e r (1986) o f Mannes Oi l Company i s i n v o l v e d in

t h e d eve l opm en t of t h e Wayne-25 o i l f i e l d . Based on o i l

w e l l l o g s , p r o d u c t i o n d a t a , and a s e i s m i c l i n e r u n by

Hosking Geop hys ica l ( F i g u r e 3), K e l l n e r (1986) i n t e r p r e t s

t h e s t r u c t u r e as a n o r t h e a s t t r e n d i n g normal f a u l t (west

s i d e down) bounding a dome on t h e west ( F i g u r e 4 , 5 ) .

D a n i e l s (1986) o f t h e Michigan Depar tment o f N a t u r a l

Resources (DNR) i s i n v o l v e d i n a s tu dy f or t h e DNR o f the

T r a v e r s e L i m e s t o n e t h r o u g h o u t M i c h i g a n . D a n i e l s ( 1986)

has mapped s e v e r a l l i n e a m e n t s t r e n d i n g bo th n o r t h e a s t and

n o r t h w e s t t h ro u gh ou t t h e Michigan ba s in based on o i l w e l l

l o g s and p r o d u c t i o n d a t a .

A n a l y s i s o f o i l w e l l l o g s , p r o d u c t i o n d a t a , and t h e

s e i s m i c l i n e s u p p o r t s t h e i n t e r p r e t a t i o n by K e l l n e r

( 1 9 8 6 ) . However , p r e l i m i n a r y i n t e r p r e t a t i o n does n o t

r ................Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

8

90 85 80 75 70 65 60I I | I I I I I I I I I I I I I I I I I I I I II I I I M I I I

Hunter Rice• ^

55 50 fISI I I I I I I I I I I I I I I

T r a v e r s e L im e s to n e R e fl,

.» m - t ' w * ^ w m m r s m n _r~~Tlt~—T T " " * — - W s M t V WW * ~*-±. • • • ~-■~m m i i ‘ i > i ' » v v v « i«j #4lf < ‘i ’

-*,S. . • « , . rf=.h» '• • 'h-s- — r i ] I»•■* '* . . i *itj^'yim nsarH avsair***. «99mm xm M im * *■+I • < W « » * N » W W W « ' M

Figure 3. Seismc Line PP1-82-1 Over Study Area by Hosking Geophysical.


LEGENDC.I. * 10 Faat

Datum Elov. • S ta . Laval

SYMBOLS

Contour Lino

* Oil Wall

^ Oil a Qat Wall Dry Wall

/ FAULT

U Upthrovm Block

D Downthtown Block

F i g u r e 4. S t r u c t u r a l Contours On t h e T r a v e r s e Limes tone as I n t r e p r e t e d by K e l l n e r ( 1 98 6 ) .


10

CROSS SECTION K- K'

K K'JONES HOLBURY SHEUNE

. \T IIHIW

GLACIAL DRIFT

6 0 0

COLO WATER SHALE500

4 0 0

ELLSWORTH SHALE3 0 0

200

LIGHT ANTRIM SHALE100

DARK ANTRIM SHALE

— - TRAVERSE-FORMATION

r-O^TD-68-r.l ,1,1J—I - I i 1 i ‘ J , 1 , 1, TRAVERSE LIMESTONE100

TO- 8TD -110

Figure 5. Cross Section K-K' Crossing the Structure in the Traverse Limestone as interpreted bv Kellner (1986). 3


p r e c l u d e the p o s s i b i l i t y o f more t han one f a u l t i n v o l v e d

i n t h e s t r u c t u r e .

Review o f S e l e c t e d L i t e r a t u r e

A p p l i c a t i o n s o f e n g i n e e r i n g s e i s m o g r a p h s i n

c o m p r e h e n s i v e r e f l e c t i o n s u r v e y s h a s i n c r e a s e d w i t h t h e

a d v e n t o f m i c r o - c o m p u t e r s . In t h e a r e a o f h y d r o l o g y ,

Hunter e t a l . (1982b) have d e v e l o p e d an "Optimum Window

T e c h n i q u e " o f s h a l l o w s e i s m i c common o f f s e t r e f l e c t i o n

p r o f i l i n g of s p e c i f i c t a r g e t e d r e f l e c t o r s . Hunter e t a l .

(1982b) used a s l e d g e hammer s ou rce i n mapping i n t r a - d r i f t

and bedr ock r e f l e c t o r s in g l a c i a l t e r r a n e s , p r i m a r i l y in

l o c a t i n g b u r ie d r i v e r c h a n n e l s . Luby (1982) used a s l e d g e

hammer s ou rc e t o o b t a i n c o h e r e n t r e f l e c t i o n s from i n t r a

d r i f t a n d b e d r o c k r e f l e c t o r s i n s e v e r a l g l a c i a l

e n v i r o n m e n t s r a n g i n g i n d ep t h from 80 t o 500 f e e t .

In m i n i n g a p p l i c a t i o n s , S i n g h ( 19 83) d e v e l o p e d a

p r o c e d u r e u s in g a s l e d g e hammer and a s i g n a l enhancement

s e i s m o g r a p h t o i d e n t i f y r e f l e c t i o n s f rom an i r r e g u l a r

bedr ock topo gra phy t h ro u g h a l l u v i u m t o d e p t h s o f 250 f e e t .

S i n g h ’s r e s u l t s were used i n p l a c e r t i n r e s e r v e e v a l u a t i o n

i n t h e t i n f i e l d s of t h e K i n t a V a l l e y , M a l a y s i a .

M o r e r e c e n t l y , K n a p p a n d S t e e p l e s ( 1 9 8 6 c )

s u c c e s s f u l l y u s e d an e n g i n e e r i n g s e i s m o g r a p h and a h i g h

e x p l o s i v e s ou rce in a common dep t h p o i n t r e f l e c t i o n s u r v e y


o v e r s i n k h o l e s a l o n g I n t e r s t a t e 70 i n Kansas. Knapp and

S t e e p l e s ( 198 6c ) d e l i n e a t e d t h e s u b s u r f a c e v e r t i c a l and

h o r i z o n t a l e x t e n t o f t h e s i n k h o l e s b e c a u s e o f t h e

e x c e l l e n t a c o u s t i c s o f an a n h y d r i t e marker bed i n t h e nea r

s u r f a c e .

Many o t h e r s h a v e done s i g n i f i c a n t work i n s h a l l o w

( l e s s t h a n 500 f e e t ) r e f l e c t i o n s e i s m i c s i n h y d r o l o g y ,

m i n i n g , and e n g i n e e r i n g a p p l i c a t i o n s (See f o r e x a m p l e ,

Hobson ( 1 9 7 0 ) , Nunn and B o t z a s (1977)» Meidav ( 1969 ) and

W a r r i c k and Wins l ow (1969))* However , t h e r e i s v e r y

l i t t l e l i t e r a t u r e on p r o c e d u r e s f o r d ee pe r h igh r e s o l u t i o n

s e i s m i c p r o f i l i n g u s i n g e n g i n e e r i n g se i s mogra ph s .


REFLECTION SURVEY METHOD THEORY

High R e s o l u t i o n In R e f l e c t i o n P r o f i l i n g

The r e f l e c t i o n w a v e l e t seen on t h e s e i s mograph r eco rd

i s n e a r l y a lways a compos i te of v a r i o u s r e f l e c t i o n s caused

by a s e t o f c l o s e l y s p a c e d l a y e r s . H ig h r e s o l u t i o n

r e f l e c t i o n work i s aimed a t s e p a r a t i n g t h e c o n s t i t u e n t s of

t h e s e c o m p o s i t e r e f l e c t i o n s i n t o d i s t i n c t s e p a r a t e

r e f l e c t i o n w a v e l e t s .

The a b i l i t y t o s e p a r a t e o u t t h e c o n s t i t u e n t s , t h a t

i s , o b t a i n h i gh r e s o l u t i o n of t h e r e f l e c t i n g h o r i z o n s , i s

l a r g e l y de t e r mined by t h e f r e q u e n c y c o n t e n t o f t h e source

and r e f l e c t i o n w a v e l e t s . The r e s o l u t i o n o b t a i n a b l e

d e p e n d s on t h e d i s t a n c e b e t w e e n r e f l e c t i n g h o r i z o n s

c om p ar e d t o t h e w a v e l e n g t h o f t h e s e i s m i c p u l s e . Thus ,

t h e s h o r t e r t h e w a v e l e n g t h o f t h e s e i s m i c p u l s e , t h e

h i g h e r t h e r e s o l v i n g p ower . D e c r e a s i n g t h e w a v e l e n g t h

demands a h i g h e r f r e q u e n c y c o n t e n t in t h e s e i s m i c p u l s e .

W i d e s s ( 1 9 7 3 ) s h o w e d t h a t b e d s as t h i n a s 1 / 8 t h e

p redominan t w a v e l e n g t h of t h e s e i s m i c p u l s e a r e c a p a b l e of

p r o d u c i n g a r e f l e c t i o n . K a l l w e i t and Wood ( 198 2) p o i n t

o u t t h a t t h e p r a c t i c a l l i m i t o f r e s o l u t i o n , h o w e v e r ,

o c c u r s a t a b o u t 1/4 t h e w a v e l e n g t h o f t h e p r e d o m i n a n t

f r e q u e n c y o f t h e s e i s m i c p u l s e . F a u l t s w i t h a t h ro w

l a r g e r t h a n 1/4 t h e w a v e l e n g t h can t h u s be s e e n f a i r l y

13

FI: -


14

c l e a r l y whereas the e f f e c t s o f s m a l l e r f e a t u r e s would not

be s ee n .

The pr ob lem of r e s o l v i n g t h i n l a y e r s and s m a l l f a u l t s

t h u s becomes a f i e l d o r i e n t e d p r o b l e m d e p e n d i n g on t h e

a b i l i t y t o p r o d u c e , p r o p a g a t e , r e f l e c t w i t h s u f f i c i e n t

a m p l i t u d e , and r e c o r d a s e i s m i c p u l s e wi th a s i g n i f i c a n t

a m o u n t o f e n e r g y i n t h e h i g h f r e q u e n c y e n d o f t h e

s p e c t r u m . T h i s d e p e n d e n c e can be d i v i d e d i n t o f o u r

p h y s i c a l f a c t o r s a f f e c t i n g t h e r e s o l u t i o n o b t a i n a b l e i n a

common o f f s e t c o n v e n t i o n a l c ov e r a g e r e f l e c t i o n s u r v ey : the

s o u r c e i m p u l s e , t h e e a r t h ’s r e s p o n s e , t h e g e o p h o n e

r e s p o n s e , and t h e e f f e c t s o f p r o c e s s i n g .

The Source Impulse

The a m p l i t u d e and f r e q u e n c y c o n t e n t o f a r e f l e c t e d

wave l a r g e l y depends on t h r e e f a c t o r s : t h e s o u r c e i mpulse

a m p l i t u d e and f r e qu e n c y c o n t e n t , g e o m e t r i c a l s p r e a d i n g of

t h e w a v e f r o n t , and d i v i s i o n of e n e r g y a t an i n t e r f a c e

(Mooney, 1984) . Of t h e s e t h r e e f a c t o r s , o n l y t h e s o u r c e

a m p l i t u d e and f r e q u e n c y c o n t e n t can be c o n t r o l l e d in the

f i e l d . I d e a l l y , a t r u l y i m p u l s i v e s o u r c e w i t h a f l a t

a m p l i t u d e spect rum t o h i g h f r e q u e n c i e s i s d e s i r e d (Knapp

& S t e e p l e s , 1986a). For h ig h r e s o l u t i o n r e f l e c t i o n work,

t h i s t r a n s l a t e s i n t o t h e n e e d o f a s o u r c e i m p u l s e

c o n t a i n i n g a s i g n i f i c a n t h i gh f r e qu enc y component .

r................. .. ............... ....................


15

S l e d g e hammer i mpac t s on a l e a d p l a t e f i r m l y embedded

in t h e s o i l can produce s e i s m i c p u l s e s wi th f r e q u e n c i e s up

t o 120 h e r t z ( s e e T a b l e 2) . A h i g h l y r e p e t i t i v e s e i s m i c

p u l s e c a n be o b t a i n e d p r o v i d e d t h e l e a d p l a t e i s s t r u c k

s o l i d l y i n t h e c e n t e r each t i m e , t he hammer i s n o t a l l o w e d

t o b o u n c e on t h e p l a t e , and t h e l e a d p l a t e d o e s n o t become

b u r i e d i n t h e s o i l . Th i s h i g h l y r e p e t i t i v e n a t u r e a l l o w s

s t a c k i n g o f s l e d g e hammer i m p a c t s t o e n h a n c e t h e

a m p l i t u d e s o f the s e i s m i c a r r i v a l s .

The h i g h f r e q u e n c y c o n t e n t o f t h e p u l s e p r o d u c e d by

t h e s l e d g e hammer i s l a r g e l y d ependen t on t h e n e a r s u r f a c e

g e o l o g y o f t h e i m p a c t s i t e . A d e c r e a s e i n t h e h i g h

f r e q u e n c y componen t i s o b s e r v e d i f t h e l e a d p l a t e i s

p ou nded i n t o t h e s o i l by t h e hammer b l o w . When t h i s

o c c u r s , a l a r g e amount o f t h e s l e d g e hammer ' s e n e r g y i s

t a k e n up in compact ion o f t h e s o i l i m m e d i a t e l y b e n e a t h t h e

l e a d p l a t e , r e s u l t i n g i n a p u l s e of l o n g e r d u r a t i o n .

Bison I n s t r u m e n t s Inc . has had s u c c e s s wi th a sho tgun

s o u r c e c a l l e d a " b u f f a l o gun" as a r e l a t i v e l y h i g h

f r e q u e n c y s e i s m i c s o u r c e . The 1 2 - ga ug e s h o t g u n s o u r c e

c o n s i s t s o f 3 / 4 - i n c h s t e e l p i p e wi th s p e c i a l f i t t i n g s on

one end t o h o l d a 1 2 - g u a g e , 1 - o u n c e s l u g s h o t g u n s h e l l . A

s t e e l r o d 5 / 8 of an i n c h i n d i a m e t e r w i t h a f i r i n g p i n

c e n t e r e d on one end and a w e i g h t on t h e o t h e r s e r v e d a s

t h e t r i g g e r f o r t h e b u f f a l o gun. The b u f f a l o gun i s

F-------------------- -


16

d r i v e n and packed i n t o a 1 - inch d i a m e t e r h o l e d r i l l e d t o a

d e p t h o f two f e e t ( F i g u r e 6) . The s l u g i m p a c t p r o d u c e s an

i m p u l s e t h a t i s n o t q u i t e as r i c h i n t h e h i g h f r e q u e n c y

c o mpon en t as t h e s l e d g e hammer i m p a c t , b u t h a s g r e a t e r

e n e r g y . S u c c e s s i v e s l u g i m p a c t s f i r e d i n t h e same h o l e

a r e n o t g r e a t l y r e p e t i t i v e d u e t o d e f o r m a t i o n and

compact ion of t h e s o i l by p r e v i o u s s l u g s and by jumping o f

t h e b u f f a l o gun due t o wear ing o f the s h o t h o l e . S t a c k i n g

o f t h e s l u g i mpac t s w i l l enhance t h e s e i s m i c r e c o r d i f new

s ho t h o l e s a r e d r i l l e d f o r each s h o t .

A b l a s t i n g cap a s a s e i s m i c s o u r c e p r o d u c e s an

i m p u l s e r i c h i n h igh f r e q u e n c i e s and low i n ene rgy making

i t u s e f u l o n l y i n v e r y s h a l l o w , h i g h r e s o l u t i o n r e f l e c t i o n

work. Knapp and S t e e p l e s ( 1986b) c o n d u c t e d an e x p e r i m e n t

u s i n g a b l a s t i n g c a p v e r s u s one gram o f h i g h e x p l o s i v e

known a s d e t a p r i m e . T h e i r r e s u l t s s h o w e d t h a t t h e

b l a s t i n g cap p r o d u c e d a s p e c t r u m w i t h f r e q u e n c i e s up t o

400 h e r t z , w h e r e a s t h e d e t a p r i m e e x p l o s i v e s h o w e d

p r a c t i c a l l y z e r o a m p l i t u d e f o r f r e q u e n c i e s a b o v e 140

h e r t z , and ve r y l i t t l e a p p a r e n t energy above 110 h e r t z .

T r a d i t i o n a l s e i s m i c s o u r c e s such as dynami te produce

a s h o r t , h i g h - e n e r g y p u l s e r i c h i n lower f r e q u e n c i e s , wi th

t h e dominant f r e q u e n c y between 40 and 60 h e r t z (Knapp and

S t e e p l e s , 1986a) . The o n l y o p t i o n t o s h o r t e n t h e d u r a t i o n

o f t h e p u l s e and s h i f t t h e p redomi na n t f r eq u en cy towards

r -iReproduced with permission of the copyright owner. Further reproduction prohibited without permission.

17

i n Q3 » g j i3 w ------------—--------------*j

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SeismographTrigger

F i g u r e 6. S k e t c h o f B u f f a l o Gun Shotgun S o u r c e .


18

t h e h i g h end o f t h e s p e c t r u m i s t o d e c r e a s e t h e c h a r g e

s i z e . The e f f e c t of i n c r e a s e d r e s o l u t i o n wi t h d e c r e a s e d

ch a r g e s i z e was no ted by Sharpe (1944).

Assuming t h a t t h e r a d i a t i o n g e n e r a t e d by an e x p l o s i o n

i s s p h e r i c a l l y symmetr ic , and t h a t t h e f r a c t i o n of t o t a l

e x p l o s i v e e ne r gy which i s c o n v e r t e d i n t o s e i s m i c e ne r gy i s

c o n s t a n t f o r a g i v e n type o f e x p l o s i v e i n a g i v e n medium,

t h e n t h e d u r a t i o n and a m p l i t u d e of t h e p u l s e produced a r e

b o t h p r o p o r t i o n a l t o t h e cubed r o o t o f t h e c h a r g e s i z e

( Z i o l k o w s k i and L e r w i l l , 1979) . T h i s i m p l i e s t h a t t h e

r e d u c t i o n i n c h a r g e s i z e w i l l s h i f t t h e s p e c t r u m o f t h e

p u l s e t o h i g h e r f r e q u e n c i e s and a l s o d e c r e a s e t h e

a m p l i t u d e by t h e same amount . D e c r e a s i n g t h e a m p l i t u d e

w i l l d e c r e a s e t h e s i g n a l / n o i s e r a t i o , and t h u s a d v e r s e l y

a f f e c t t h e r e s o l u t i o n . T h e r e f o r e a c h a r g e s i z e mus t be

f o u n d t h a t i s s m a l l enough t o p r o d u c e t h e d e s i r e d h i g h

f r e q u e n c y c o mp on en t , y e t l a r g e en ou g h t o p r o d u c e an

a c c e p t a b l e s i g n a l / n o i s e r a t i o . Z i o l k o w s k i and L e r w i l l

( 1 97 9) s u c c e s s f u l l y u s e d a s c a l e d down c h a r g e s i z e i n

a t t e m p t s t o g e t h i g h e r r e s o l u t i o n .


The E a r t h ' s Response

The E a r t h ' s r e s p o n s e t o a g e n e r a t e d s e i s m i c p u l s e

c a n n o t be c o n t r o l l e d . The o v e r a l l e f f e c t o f t h e e a r t h on

a s e i s m i c p u l s e t r a v e l l i n g t h r o u g h i t i s t h a t o f a l o w -

p a s s f i l t e r , a t t e n u a t i n g t h e h i g h f r e q u e n c i e s and

b r o a d e n i n g t h e p u l s e .

Many f a c t o r s a f f e c t a s e i s m i c p u l s e t r a v e l l i n g

t h r o u g h t h e e a r t h . S p h e r i c a l d i v e r g e n c e o f t h e s e i s m i c

p u l s e d e c r e a s e s t h e e n e r g y d e n s i t y i n an i n v e r s e

p r o p o r t i o n t o t h e s q u a r e o f t h e d i s t a n c e o v e r which t h e

wave h as t r a v e l l e d . P a r t i t i o n i n g o f energy a t i n t e r f a c e s

d ep en d en t on r e f l e c t i o n c o e f f i c i e n t s and t h e i r v a r i a t i o n

w i t h i n c i d e n t a n g l e s s t r o n g l y a f f e c t s t h e t r a n s m i t t e d and

r e f l e c t e d a m p l i t u d e s . P e g - l e g m u l t i p l e s i n t h i n l a y e r s

d e l a y t h e s e i s m i c p u l s e and add i t on t o t h e o r i g i n a l wave,

l e n g t h e n i n g and chang i ng t h e shape o f t h e wave.

P r o b a b l y t h e mo s t s i g n i f i c a n t f a c t o r l i m i t i n g h i g h

r e s o l u t i o n i s t h e l o s s o f h i g h f r e q u e n c y e n e r g y by

a b s o r p t i o n . As t h e f r e q u e n c y and d i s t a n c e t r a v e l l e d

i n c r e a s e , a b s o r p t i o n l o s s e s i n c r e a s e , r e s u l t i n g i n a

c h a n g e o f wave s h a p e w i t h d i s t a n c e t r a v e l l e d ( T e l f o r d

e t a l . , 1976) . S e m i - s a t u r a t e d , l o o s e l y c omp a c t e d and

u n c o n s o l i d a t e d m a t e r i a l s such as g l a c i a l d r i f t have much

h i g h e r f r e q u e n c y a b s o r p t i o n c o e f f i c i e n t s t h a n d e e p e r


c o n s o l i d a t e d l a y e r s . Frequency a t t e n u a t i o n by a b s o r p t i o n

i s a m a j o r o b s t a c l e t o h i g h r e s o l u t i o n r e f l e c t i o n

p r o f i l i n g u s i n g a h i g h f r e que nc y s o u rc e .

The Geophone Response

Geophones a r e m o t i o n s e n s i t i v e t r a n s d u c e r s t h a t

c o n v e r t g r o u n d m o t i o n t o an e l e c t r i c a l s i g n a l whose

a m p l i t u d e i s p r o p o r t i o n a l t o t h e v e l o c i t y o f mot ion. For

h i g h r e s o l u t i o n w o r k , g e o p h o n e s w i t h a h i g h n a t u r a l

f r e q u e n c y ac t as a p r e - e m p h a s i s , l o w - c u t f i l t e r . The h igh

f r e q u e n c y geo phon e s u p p r e s s e s low f r e q u e n c y n o i s e and

b a l a n c e t h e s p e c t r u m o f t h e i n c o m i n g s i g n a l . Such p r e

emphas i s f i l t e r i n g r e d u c e s t h e d e t r i m e n t a l e f f e c t s o f the

l o w - p a s s e a r t h f i l t e r , i n c r e a s e s the s i g n i f i c a n c e o f the

r e c o r d e d d a t a , and makes the r e c o r d i n g of h ig h r e s o l u t i o n

d a t a p o s s i b l e by a t t e n u a t i n g t o a manageable l e v e l t h e low

f r e q u e n c y s i g n a l t h a t w ou l d o t h e r w i s e s a t u r a t e a f l a t

r e s p o n s e r e c o r d i n g s y s t e m (Knapp and S t e e p l e s , 1986a).

Another f a c t o r t o c o n s i d e r i n h i g h f r e q u e n c y s e i s m i c

r e c o r d i n g i s t h e e f f e c t o f geophone ground c o u p l i n g on t h e

incoming s i g n a l . Geophone ground c o u p l i n g i s t h e a ccu racy

wi th which the geophones measure t h e a c t u a l ground mot ion.

G eo pho nes a c c u r a t e l y f o l l o w t h e g r oun d m o t i o n when t h e

f r e q u e n c i e s i n c o m i n g a r e much l e s s t h a n t h e c o u p l i n g

r e s o n a n t f r e q u e n c y o f t h e p l a n t e d g e o p h o n e . H i g h e r

r— --------------------


21

f r e q u e n c y s i g n a l s can be a l t e r e d i n b o t h a m p l i t u d e and

p h a s e . Krohn (1984) f o u n d t h a t f o r a f i r m l y p l a n t e d

g e o p h o n e w i t h a l o n g s p i k e , t h e c o u p l i n g r e s o n a n t

f r e q u e n c y i s k e p t as h i g h a s p o s s i b l e . I n c r e a s i n g t h e

c o u p l i n g r e s o n a n t f r e q u e n c y o u t s i d e t he b an d - p a s s o f t h e

a n a l o g t o d i g i t a l c o n v e r s i o n a l l o w s a f l a t r e s p o n s e from

the geophone’s n a t u r a l f r e q u e n c y t o t h e ground c o u p l i n g

r e s o n a n t f r e q u e n c y . Thus f o r h i g h r e s o l u t i o n , a h i g h

n a t u r a l f r e q u e n c y g e o p h o n e w i t h a l o n g s p i k e p l a n t e d i n

f i r m s o i l b e n e a t h t he l o o s e s u r f a c e m a t e r i a l w i l l r e s u l t

i n t h e b e s t s e i s m i c r e c o r d o f t h e d e s i r e d h i g h f r e q u e n c y

s i g n a l s .

P r o c e s s i n g E f f e c t s

B e s i d e s u s i n g t h e n a t u r a l f r e q u e n c y o f t h e g e o ph o ne

as a p r e - e m p h a s i s , l o w - c u t f i l t e r , t h e se i smograph band

p a s s f i l t e r f i l t e r s t h e a n a l o g s i g n a l f ro m t h e geop h on e

p r i o r t o d i g i t i z i n g and r e c o r d i n g t h e s i g n a l . The b a n d

p a s s f i l t e r i s a l s o a p r e - e m p h a s i s f i l t e r , and f o r h i g h

r e s o l u t i o n s h o u l d be s e t as h i g h as 7 5 - 1 0 0 H e r t z on t h e

l o w - c u t s i d e . The b an d -p as s f i l t e r a i d s i n a t t e n u a t i o n o f

high a m p l i t u d e low f r e q u e n c y a r r i v a l s t h a t might o t h e r w i s e

swamp t h e d i g i t i z i n g s y s t e m and s a t u r a t e t h e memory,

l e a v i n g no t r a c e o f h i g h f r e q u e n c y r e f l e c t i o n s .

A n o t h e r f a c t o r i m p o r t a n t t o h i g h r e s o l u t i o n i s t h a t

r --------------------------------I


22

t h e c o m b i n i n g o f g e o p h o n e o u t p u t s i n common d e p t h p o i n t

s h o o t i n g t e n d s t o a t t e n u a t e h i g h e r f r e q u e n c i e s .

T h e r e f o r e , h i g h r e s o u l t i o n i s o b t a i n e d u s i n g s i n g l e

g e o p h o n e s in a c o n v e n t i o n a l s i n g l e - f o l d , c o n t i n u o u s

c o v e r a g e survey than wi th common d e p t h p o i n t s h o o t i n g .

P r o f i l i n g Method

The c o n v e n t i o n a l me t ho d o f r e c o r d i n g s e i s m i c d a t a

u t i l i z e d i n t h i s s t u d y i s c o n t i n u o u s c o v e r a g e , s i n g l e - f o l d

s h o o t i n g . In t h i s method each geophone or geophone group

s a m p l e s a un i que a r e a i n t h e s u b s u r f a c e ; t h e r e s p o n s e s o f

s e p a r a t e geophones a r e n o t combined.

An "end o n - i n l i n e o f f s e t " s o u r c e and geophone a r r a y

a l l o w s c o n t i n u o u s , s i n g l e - f o l d c o v e r a g e o f t h e t a r g e t e d

r e f l e c t o r . The r e f l e c t i o n s f r o m a s i n g l e s h o t a r e

r e c o r d e d by e q u a l l y s p a c e d g e o p h o n e s l a i d o u t i n a l i n e

w i t h t h e s h o t p o i n t .

The p o r t i o n o f t h e r e f l e c t o r b e i n g s a m p l e d i s h a l f

t h e l e n g t h of t h e g e o p h o n e s p r e a d . C o n t i n u o u s c o v e r a g e

p r o f i l i n g then r e q u i r e s a s h i f t o f t h e s h o t and geophone

a r r a y by h a l f t h e d i s t a n c e o f t h e g e o p h o n e s p r e a d f o r

s u c c e s s i v e s h o t s ( F i g u r e 7 ) .

The s h o t p o i n t i s o f f s e t from t h e geophones a s p e c i f i c

d i s t a n c e t o a l l o w d e s i r e d r e f l e c t i o n s t o a r r i v e d u r i n g a


Reproduced

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shot 1 geophone 1 geophone 12depth f t . 700 f t 335 ft -

100

G lacial D rift200

300

Coldwater Shale400

500

Ellsworth Shale600

700Light Antrim Shale

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F i g u r e 7 . Common O f f s e t P r o f i l i n g R aypath D iagram Based on W ell Log D epths i n th e S tudy Ar ea .

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t ime i n t e r v a l t h a t does n o t o v e r l a p s u r f a c e and r e f r a c t e d

w a v e s . T h i s zone o f t i m e i s c a l l e d t h e ’' op t imum window"

and can be de t e r min ed by a "walk away" n o i s e t e s t .

The Optimum Window

The opt imum window i s t h e r e g i o n on a t i m e v e r s u s

d i s t a n c e d i a g r a m w h e r e r e f l e c t i o n s f r o m a t a r g e t e d

r e f l e c t o r can a r r i v e u n d i s t u r b e d by s u r f a c e and r e f r a c t e d

wa ve s ( F i g u r e 8) . The window s h o u l d be c h o s e n i n an a r e a

as c l o s e as p o s s i b l e t o t h e l e a d i n g edge of t h e s u r f a c e

wave a r r i v a l s , spann ing a zone where the r e f l e c t o r shows

maximum c u r v a t u r e , y e t n o t e x t e n d i n g t h e window i n t o t h e

w i d e - a n g l e zone wher e p o s s i b l e i n t e r f e r e n c e a f f e c t s may

o c c u r ( H u n t e r e t a l . , 1982 a) . I d e n t i f y i n g t h i s opt imum

window a l l o w s a means o f s e l e c t i n g s o u r c e o f f s e t and

geophone s p a c i n g t o r e c o r d t h e d e s i r e d r e f l e c t i o n s i n a

c l e a r t im e i n t e r v a l .

The mos t e f f e c t i v e me t hod f o r d e f i n i n g t h e opt imum

window i s a w a l k away n o i s e t e s t . A wa lk away n o i s e t e s t

i s conduc ted by t a k i n g s h o t s a t i n c r e a s e d i n t e r v a l s wi th

t h e g e o p h o n e s i n a f i x e d l o c a t i o n ( F i g u r e 9) . The w a l k

away n o i s e t e s t p r o v i d e s a measurement of s e i s m i c r e s p o n s e

a t a l a r g e number of s o u rc e - g eo ph o ne o f f s e t s , and g i v e s a

t i m e vs . d i s t a n c e d i a g r a m f rom w h i c h t h e opt imum window

( s o u r c e o f f s e t and g e o ph o ne s p r e a d ) f o r t h e t a r g e t e d

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F i g u r e 8 . R e f l e c t i o n Model and T i m e -D is t a nc e GraphShowing t h e P o s i t i o n o f t h e Optimum Window Geophone Array (From Hu nt e r e t a l . v 1982b) .


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F i g u r e 9. Raypath Diagram Showing S u b s u r f a c e Coverage O b t a i ned Dur ing a Walk Away Noise T e s t .

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r e f l e c t o r can be chosen . For c a s e s where t h e r e a r e l a r g e

l a t e r a l d i s c o n t i n u i t i e s i n t h e n e a r s u r f a c e , s o u r c e and

g e o p h o n e a r r a y s may n e e d t o c h a n g e t o a c c o m m o d a t e

d i f f e r e n t c o n d i t i o n s . In t h i s c a s e , s e v e r a l w a l k away

n o i s e t e s t s s h o u l d be done i n d i f f e r e n t z o n e s o f t h e

s u r v e y a r e a t o d e f i n e any change i n p a r a m e t e r s needed.

Time Domain C o r r e c t i o n s

Two t i m e domai n c o r r e c t i o n s a p p l i e d t o s e i s m i c

p r o f i l i n g d a t a a r e s t a t i c a n d n o r m a l m o v e o u t (NMO)

c o r r e c t i o n s . S t a t i c c o r r e c t i o n s a r e a p p l i e d t o c o r r e c t

t h e e f f e c t s o f i r r e g u l a r i t i e s i n t h e n e a r s u r f a c e on

a r r i v a l t i me s of s e i s m i c e v e n t s . These i r r e g u l a r i t i e s a r e

p r i m a r i l y v a r i a t i o n s i n e l e v a t i o n f rom s h o t t o s h o t and

l o c a l v a r i a t i o n s i n t h e n e a r s u r f a c e v e l o c i t i e s . I n

g l a c i a l t e r r a n e s where t h e r e i s a t h i c k , low v e l o c i t y zone

and s i g n i f i c a n t l a t e r a l d i s c o n t i n u i t i e s i n t h e n e a r

s u r f a c e v e l o c i t i e s , s t a t i c s can become a p romi nen t s ou rce

o f m i s - t i e s i n c o r r e l a t i n g r e f l e c t i o n s from s h o t t o s h o t .

NMO c o r r e c t i o n s a cc o u n t f o r t h e d i f f e r e n c e s between

r e f l e c t i o n t r a v e l t i m e due t o t h e v a r y i n g h o r i z o n t a l

o f f s e t s o f g e o p h o n e s or geoph.one g r o u p s f rom t h e s o u r c e .

NMO c o r r e c t i o n s can be c a l c u l a t e d w i t h s y n t h e t i c model s ,

o r can be d e r i v e d by v e l o c i t y a n a l y s e s o f t h e t a r g e t e d

r e f l e c t o r s . S ince NMO c o r r e c t i o n s a r e dynamic in n a t u r e ,


28

i n v o l v i n g a d i f f e r e n t c o r r e c t i o n v e l o c i t y f o r s u c c e s s i v e

r e f l e c t o r s , NMO c o r r e c t i o n s u s i n g t h e GeoPro se i smograph

can o n l y be made f o r a s p e c i f i c r e f l e c t o r . The GeoPro

se i smog ra ph does not a l l o w movement o f s e p a r a t e r e f l e c t e d

e v e n t s w i t h i n a s i n g l e t r a c e .


FIELD SURVEY

I n s t r u m e n t a t i o n

I n s t r u m e n t a t i o n i n t h i s s t u d y was d i c t a t e d p r i m a r i l y

by a v a i l a b i l i t y . The se i smograph i s a Bison GeoPro 8012A

1 2- c ha nn e l s i g n a l p r o c e s s i n g s e i s mograph . The GeoPro i s a

microcomputer c o n t r o l l e d s e i s m o g r a p h f o r r e f l e c t i o n and

r e f r a c t i o n s e i s mol og y . I t s programmable o p e r a t i n g sys tem

p r o v i d e s a v a r i e t y o f o p t i o n s f o r t h e a c q u i s i t i o n ,

d i s p l a y , p r o c e s s i n g , and s t o r a g e o f s e i s m i c d a t a . The

GeoPro system i n c o r p o r a t e s a n o n - s a t u r a t i n g form o f b l o c k

f l o a t i n g p o i n t s i g n a l enhancement , and i s powered by a 12-

v o l t b a t t e r y .

C a p a b i l i t i e s i n c l u d e : r e m o v a l o f n o i s y o r

u n d e s i r a b l e w a v e f o r m s f ro m e n h a n c e d d a t a by w a v e f o r m

s u b t r a c t i o n ; keyboard c o n t r o l o f i n p u t g a i n s , sweep t i me s ,

p o l a r i t y of geophones , d e l a y e d t r i g g e r i n g , programmed ga i n

r a n g i n g , and p r e - e m p h a s i s d i g i t a l f i l t e r i n g ; au t om at i c or

m a n u a l t r i g g e r a r m i n g ; c a l i b r a t e d d i s p l a y c o n t r o l o f

i n d i v i d u a l waveform s i z e and p o s i t i o n ; and two i ndependen t

t i m e m a r k e r c u r s o r s w i t h i n d e p e n d e n t d i s p l a y o f t i m e

l o c a t i o n s f o r i n d i v i d u a l waveforms.

A d d i t i o n a l c a p a b i l i t i e s t h r ough a p p l i c a t i o n s programs

i n c l u d e waveform m a t h em a t i c s , d i g i t a l f i l t e r i n g d u r i n g or

29


30

of t h e se i smograph r e c o r d can be o b t a i n e d from t h e GeoPro

p r i n t e r o r an o f f i c e p r i n t e r . An IBM c o m p a t i b l e

microcomputer wi th a n u l l modem c a b l e f o r i n t e r f a c i n g wi th

t h e GeoPro , and " M i r r o r ” c o m m u n i c a t i o n s s o f t w a r e a l l o w

p e r m a n e n t s t o r a g e o f s e i s m o g r a p h r e c o r d s on c o m p u t e r

d i s k s .

G e o p h o n e s a r e Mark P r o d u c t s , 60 h e r t z n a t u r a l

f r e q u e n c y , v e r t i c a l componen t g e o p h o n e s w i t h a 3 - i n c h

s p i k e . The Mark P r o d u c t s g e o p h o n e c a b l e h a s 12 g e o ph on e

t a k e - o u t s a t 30.5 f o o t (10 m e t e r ) i n t e r v a l s .

For s l e d g e hammer and b u f f a l o gun s o u r c e s , an impact

s w i t c h c o n n e c t e d t o t h e G e o P r o by 2 - c o n d u c t o r w i r e

p r o v i d e s t h e t r i g g e r i m p u l s e . Fo r a d y n a m i t e s o u r c e , a

d e t o n a t o r c o m p l e t e s t h e 2 - c o n d u c t o r c i r c u i t t o t r i g g e r t he

se i smograph a t t h e t ime of d e t o n a t i o n .

F i e l d P a r a m e t e r s

F i e l d p a r a m e t e r s in a r e f l e c t i o n s u r v e y a r e l a r g e l y

de t e r mine d by two f a c t o r s : t h e r e f l e c t i o n s u r v e y method

and t h e d e s i r e d r e s u l t s combined w i t h t he l o c a l c o n d i t i o n s

o f t h e s u r v e y a r e a . The s u r v e y method c o n t r o l s p a r a m e t e r s

o f s o u r c e and g eo p ho n e a r r a y and t h e t y p e o f s u b s u r f a c e

c o v e r a g e , as d i s c u s s e d i n t h e r e f l e c t i o n p r o f i l i n g s e c t i o n .


31

Source and Geophone Array

For t h i s s t u d y an end o n - i n l i n e o f f s e t s o u r c e and

g e o p h o n e a r r a y was u t i l i z e d w i t h s i n g l e g e o p h o n e s p e r

t r a c e . The med i um d e p t h o f t h e t a r g e t e d r e f l e c t o r

d i c t a t e s a l a r g e r g e o p h o n e s p a c i n g t h a n u s e d i n s h a l l o w

s e i s m i c r e f l e c t i o n p r o f i l i n g . A v a i l a b l e equipment l i m i t e d

t h e maximum g eop ho n e s p a c i n g t o 30.5 f e e t (10 m e t e r s ) f o r

12 g e o p h o n e s . T hu s , f o r e a s e i n t h e f i e l d t h e maximum

g e o p h o n e s p a c i n g o f 30.5 f e e t was u s e d g i v i n g a t o t a l

g e o p h o n e s p r e a d l e n g t h o f 335.5 f e e t , an i n i t i a l s o u r c e

o f f s e t o f 610 f e e t was de t e r mi ne d by r e f r a c t i o n a n a l y s i s

o f w a l k away n o i s e t e s t s and s y n t h e t i c m o d e l i n g . S i n c e

t h e sampled s u b s u r f a c e i s r o u g h l y h a l f t h e l e n g t h of t h e

geophone s p r e a d , c o n t i n u o u s co v er a ge r e q u i r e s a s h i f t o f

t h e s h o t p o i n t and g e o p h o n e s p r e a d by h a l f t h e l e n g t h o f

335 . 5 f e e t (167.25 f e e t ) f o r e a c h s u c c e s s i v e s h o t . To

a l l o w some o v e r l a p o f s u b s u r f a c e c o v e r a g e from s h o t p o i n t

t o s h o t p o i n t , t h e s h o t p o i n t and geo ph o ne s p r e a d were

s h i f t e d f i v e g e o p h o n e s p a c i n g s ( 152 .5 f e e t ) f o r e a ch

s u c c e s s i v e s h o t .

&Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

32

Source P ar amet er s

T h r e e d i f f e r e n t s o u r c e s were u s e d i n t h i s s t u d y . The

s l e d g e hammer source c o n s i s t e d o f a 16-pound s l e d g e hammer

impacted on a l e a d p l a t e f i r m l y s e a t e d i n t h e s o i l on t h e

edge of the road . The b u f f a l o gun was t i g h t l y f i t t e d i n t o

a 2 - f o o t deep, o n e - i n c h d i a m e t e r h o l e d r i l l e d wi t h a one-

inch hand auger . The b l a s t i n g cap and dynami te c h a r g e s of

80 g r a m s 40% n i t r o g l y c e r i n w e r e t a m p e d i n t o 2 - i n c h

d i a m e t e r h o l e s 3.5 t o 4 f e e t deep, and d e t o n a t e d .

Sei smograph P ar amet er s

S e i s m o g r a p h p a r a m e t e r s i n c l u d e r e c o r d sweep t i m e ,

r e c o r d d e l a y , f i l t e r s e t t i n g s , and g a i n s e t t i n g s . For

w a l k away n o i s e t e s t s and r e f l e c t i o n p r o f i l i n g , sweep

t i me s o f both 960 and 480 m i l l i s e c o n d s were used. The 960

m i l l i s e c o n d s w e e p t i m e g i v e s a s a m p l i n g r a t e o f 1

m i l l i s e c o n d and t h e 480 m i l l i s e c o n d sweep s a m p l e s a t 2

m i l l i s e c o n d i n t e r v a l s . A c o n c l u s i o n from s a mp l i n g t h e o r y

c o n s i d e r a t i o n s i s t h a t no i n f o r m a t i o n i s l o s t by r e g u l a r

s a m p l i n g p r o v id e d t h e s a mp l in g f r e q u e n c y i s g r e a t e r than

t h e h i g h e s t f r e q u e n c y component b e i ng sampled ( T e l f o r d e t

a l . , 1976) . The sweep t i m e s o f 960 and 480 m i l l i s e c o n d s

h a v e s a m p l i n g f r e q u e n c i e s o f 5 00 and 1000 h e r t z ,

r •LReproduced with permission of the copyright owner. Further reproduction prohibited without permission.

33

r e s p e c t i v e l y . H a l f o f t h e s a m p l i n g f r e q u e n c y i s c a l l e d

t h e " N y q u i s t f r e q u e n c y . " Any f r e q u e n c y p r e s e n t i n t h e

s i g n a l which i s g r e a t e r than t h e Nyqu i s t f requency ( fn) by

t h e amount ( f ) w i l l be i n d i s t i n g u i s h a b l e f rom t h e l o w e r

f r e q u e n c y f n - f ( T e l f o r d e t a l . f 1976) . T h i s e f f e c t i s

c a l l e d " a l i a s i n g " and must be c o n s i d e r e d i n a t t e m p t s a t

r e c o r d i n g h i g h e r f r e q u e n c y w a v e f o r m s . The N y q u i s t

f r e q u e n c i e s f o r t h e 960 and 480 m i l l i s e c o n d sweep t i m e s

a r e 250 and 500 h e r t z . These Ny qu i s t f r e q u e n c i e s a r e h i g h

en ou g h t o p r e v e n t s i g n i f i c a n t a l i a s i n g o f t h e s e i s m i c

s i g n a l i n the d e s i r e d r e c o r d i n g r ange o f 100-200 h e r t z .

D ynami t e s o u r c e w a l k away s u r v e y s u t i l i z e d a 960

m i l l i s e c o n d sweep t i m e , and t h u s a l i a s i n g o f s e i s m i c

s i g n a l s c o u l d be a p roblem i f t h e dynami te s ou rc e produced

a s i g n i f i c a n t f r e q u e n c y c om po n en t a b o v e t h e N y q u i s t

f r e q u e n c y of 250 h e r t z . Frequency a n a l y s i s in t h i s s t ud y

s u g g e s t s a d o m i n a n t f r e q u e n c y f o r t h e d y n a m i t e s o u r c e o f

80 h e r t z (See T a b l e 2). A s i g n i f i c a n t component above 250

h e r t z i s u n l i k e l y .

F i l t e r s e t t i n g s f o r h igh r e s o l u t i o n of h igh f r e qu e n c y

r e f l e c t i o n s w e r e s e t a t 3 5 - 2 0 0 h e r t z b a n d - p a s s f o r

d y n a m i t e s h o t s , and 7 5 - 3 7 5 h e r t z b a n d - p a s s f o r s l e d g e

hammer and sho tgun s h o t s . A b a n d - r e j e c t (no tch) f i l t e r o f

60 h e r t z was a p p l i e d f o r a l l s h o t s t o s u p p r e s s power l i n e

g e n e r a t e d n o i s e . Gains were s e t by e x p e r i m e n t a t i o n i n t h e


34

f i e l d s o t h a t d e s i r e d s i g n a l s were n o t s a t u r a t i n g t h e

memory o f t h e se i s mo gra ph .

S i g n a l P r o c e s s i n g

P r o c e s s i n g o f s e i s m i c d a t a i s aimed a t enhanc ing t h e

d e s i r e d r e f l e c t i o n s w h i l e d e c r e a s i n g t h e e f f e c t s o f n o i s e

such as u n d e s i r a b l e s e i s m i c a r r i v a l s , low f r e qu enc y ground

n o i s e ( c a r s , t r e e r o o t s , e t c . ) , h i g h f r e qu e n c y wind n o i s e ,

and power l i n e n o i s e . Two p r o c e s s i n g s t e p s were a p p l i e d

t o t h e s e i s m i c r e c o r d s : t r a c e m i x i n g a n d d i g i t a l

f i l t e r i n g .

T r a c e m i x i n g i s s i m p l y a m a t h e m a t i c a l a d d i t i o n o f

e a c h g e o p h o n e r e s p o n s e t o t h e s u c c e s s i v e g e o p h o n e

r e s p o n s e . For example , t r a c e 1 = t r a c e 1 + t r a c e 2, t r a c e

2 = t r a c e 2 + t r a c e 3> e t c . T r a c e m i x i n g e n h a n c e s t h e

s e i s m i c r e c o r d s by c a n c e l l i n g o u t - o f - p h a s e random n o i s e ,

w h i l e e n h a n c i n g t h e h i g h v e l o c i t y r e f l e c t e d p - w a ve

a r r i v a l s . T r a c e m i x i n g r e s u l t s i n b e t t e r o v e r a l l

c o r r e l a t i o n o f t h e r e f l e c t i o n w a v e l e t from s h o t t o s h o t .

Walk away r e f l e c t i o n a n a l y s i s r e v e a l s t h a t a d v e r s e e f f e c t s

on t h e h i g h f r e q u e n c y co mponen t o f t h e r e f l e c t i o n s by

t r a c e m i x i n g a r e o u t w e i g h e d b y t h e i n c r e a s e i n

c o r r e l a t a b i l i t y o f t h e r e f l e c t e d a r r i v a l s ( see R e f l e c t i o n

A n a l y s i s of Walk Away Data) .

r------------ : ......... """ 'h' .


L

35

D i g i t a l f i l t e r i n g can a l s o i n c r e a s e r e c o r d q u a l i t y .

In h i g h f r e q u e n c y work a b a n d - p a s s f i l t e r can be a p p l i e d

t o d e c r e a s e t h e e f f e c t s o f low f r e q u e n c y u n d e s i r a b l e

a r r i v a l s o u t s i d e t h e b and -pas s f r e q u e n c y range .


SOURCE ANALYSIS

S t a c k i n g T e s t s

I n i t i a l work u s i n g t h e s l e d g e hammer and b u f f a l o gun

s o u r c e s i n v o l v e d d e t e r m i n i n g t he number o f s t a c k s r e q u i r e d

t o c a n c e l o u t - o f - p h a s e random n o i s e and e n h a n c e d e s i r e d

s e i s m i c e v e n t s . A s l e d g e hammer s t a c k t e s t ( F i gu r e 10) on

Mckenzie Road showed t h a t a f t e r 10 s t a c k e d s l e d g e hammer

i mp ac t s , a d d i t i o n a l i mpac t s do n o t s i g n i f i c a n t l y i n c r e a s e

r e c o r d q u a l i t y .

Two s t a c k s o f b u f f a l o gun s h o t s u s i n g 1 - o u n c e , 12-

g au ge s l u g s ( F i g u r e 11) a r e s u f f i c i e n t t o c l e a n up most

random n o i s e p r o v i d i n g a new s h o t h o l e i s u s e d f o r t h e

s e c o n d s h o t . More t h a n two s t a c k s o f 1 2 - g a u g e , 1 - o u n c e

s l u g s becomes more e x p e n s i v e , and more work t h a n t h e

h i g h e r e ne r gy s ou rce o f dynami te .

Frequency A n a l y s i s

The Bison GeoPro has a f r e q u e n c y range c a p a b i l i t y of

7 - 1 0 0 0 h e r t z . For a n a l y s i s o f t h e d o m i n a n t f r e q u e n c y of

t h e s e i s m i c s o u r c e s i n t h e s t u d y a r e a , l o w n a t u r a l

f r e q u e n c y 6 h e r t z phones were u se d . I d e a l i z e d f requ en cy

r e s p o n s e c u r v e s ( F i g u r e 12) o f t h e 7 and 1000 h e r t z

B u t t e r w o r t h f i l t e r s i n d i c a t e a f l a t r e s p o n s e t o s e i s m i c

s i g n a l s b e t w e e n 10 and 900 h e r t z f o r t h e t o t a l s e i s m i c

36

r -------------------------------: ■*........................ts.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

A A. A " A A A -V < C V v V

* * * . .A

.» ; A; A A A ^ n A-Av^. a^ -CÂ-'a a a '

V-AÂAvA ^ ^ A v vVaA

(b) 20 Stacks________.. a 1.1 l i A A I i.i A A i _ T ~ . J- 1 | l i l lA ^ A *AvA >;^ -- . . : a T a Xa * •> ' a .Aw- ^ .a a. a ,

w ._av»A. >'.'v*-Is A Â"A- a.*. .^ ^ vv^ ^ A -^ vA \A -^ A * AÂ;■ ^ v ■„• V v ' A ^ ^ a a - A i' ... <A- v )/“ v " \ .* '- ‘*~''^s^*

(c) 30 Stacks

r ^ V A i t M ^ A A ; — A W ^ A * ‘ v*sA ^-~-

\ \ i V A ^ * £ c r r r

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• : M vAA.A^ ■\AAA-*

(d) 40 Stacks

F i g u r e 10 . Seisraograms o f s l e d g e Hammer S t a ck T e s t Showing E f f e c t o f M u l t i p l e S t a c k s i n Reducing No i se .


38

(a) 1 Slug StackA A

1 * J A A ~ —■ a t

(b) 2 Slug Stacks

F i g u r e 11. Seismograms of Shotgun S l ug S t ack T e s t Showing E f f e c t o f M u l t i p l e S t a c k s i n Reducing Noi se .

- 5

-10

-15

-20

10 100 1000FREQUENCY (HZ)

F i g u r e 12. I d e a l i z e d Frequency Response Curve o f t h e7 and 1000 H e r t z B u t t e r w o r t h F i l t e r s on t h e Bison GeoPro Se i smograph.


sys tem.

Frequency a n a l y s i s i s based on t h e as sumpt ion t h a t a

g eo ph o ne o f f s e t 10-15 f e e t f rom t h e s o u r c e w i l l m e a s u r e

t h e s e i s m i c s i g n a l which r e p r e s e n t s t h e dominant f r e qu e n c y

o f t h e i n i t i a l l y p r o d u c e d P - wa ve p a r t i c u l a r t o t h e n e a r

s u r f a c e c o n d i t i o n s o f t h e s t u d y a r e a . At t h e s m a l l o f f s e t

o f 10-15 f e e t , l o s s e s i n t he ener gy and f r e q u e n c y c o n t e n t

o f t h e s e i s m i c p u l s e a r e due p r i m a r i l y t o a b s o r p t i o n i n

t h e l o o s e l y c o n s o l i d a t e d n e a r s u r f a c e l a y e r . F o r a

s h o t p o i n t a t t h e s u r f a c e , t h e d o m i n a n t f r e q u e n c y o f t h e

s e i s m i c p u l s e a f t e r i t h a s p as s ed t h r ou gh t h e low v e l o c i t y

l a y e r i s t h e p a r a m e t e r o f i n t e r e s t . O f f s e t t i n g t h e

g e o p h o n e s a s m a l l d i s t a n c e i n f r e q u e n c y a n a l y s i s a l l o w s

r e c o r d i n g o f a p u l s e t h a t i s a b e t t e r a p p r o x i m a t i o n o f t h e

t r u e s e i s m i c p u l s e t h a t h as t r a v e l l e d t h r o u g h t h e t h i n ,

u n s a t u r a t e d , l o w - v e l o c i t y l a y e r .

I d e a l l y , t h e f i r s t s i g n a l t o a r r i v e a t a geo ph o ne a

s m a l l d i s t a n c e f ro m t h e s o u r c e i s a d i r e c t P - w a v e . The

p u l s e r e c o r d e d by t h e geophone i s r e p r e s e n t e d as a w a v e l e t

wi th a s p e c i f i c a p p a r e n t f r e q u e n c y . With a f l a t r e s p o n s e

r e c o r d i n g s y s t e m , t h e a p p a r e n t f r e q u e n c y w i l l r e p r e s e n t

t h e d o m i n a n t f r e q u e n c y c omp onen t p r o d u c e d by t h e s o u r c e .


40

F r e q u e n c i e s wer e t a k e n f rom m e a s u r e m e n t o f t h e p e r i o d o f

t h e f i r s t s e i s m i c p u l s e r e c o r d e d ( F i g u r e 13)» where t h e

f r e q u e n c y in c y c l e s p e r s e c o n d ( h e r t z ) i s e q u a l t o t h e

r e c i p r o c a l o f t h e p e r i o d .

The d o m i n a n t f r e q u e n c i e s ( T a b l e 2) a r e a p p l i c a b l e

s p e c i f i c a l l y t o t h e s t u d y a r e a , and may be g e n e r a l l y

a p p l i c a b l e f o r t h e s e s o u r c e s i n g l a c i a l d r i f t d e p o s i t s .

A l l f r e q u e n c i e s a r e r e l a t i v e l y h i gh as r e q u i r e d f o r h i g h

r e s o l u t i o n r e f l e c t i o n p r o f i l i n g . The dominant f r e q u e n c y

o f 80 h e r t z f o r t h e 80 g r a m c h a r g e o f d y n a m i t e i s

s i g n i f i c a n t i n t h a t t r a d i t i o n a l l a r g e ch ar ge s i z e s produce

a dominant f r e qu e n c y between 40-60 h e r t z . T h e r e f o r e , t h e

r e d u c e d c h a r g e s i z e i n c r e a s e s t h e e n e r g y i n t h e h i g h

f r e q u e n c y c o m p o n e n t o f t h e i m p u l s e , a l l o w i n g t h e

p o s s i b i l i t y o f h i g h e r r e s o l u t i o n i n s e i s m i c p r o f i l i n g

u s i n g an e x p l o s i v e s o u r c e .

E x p e r i m e n t a l e v i d e n c e s u g g e s t s t h a t a b s o r p t i o n

c o e f f i c i e n t s a r e a p p r o x i m a t e l y p r o p o r t i o n a l t o f r e qu e n c y

( T e l f o r d , 1976) . F o r e l a s t i c waves i n r o c k s , l o s s o f

e n e r g y i s a p p r o x i m a t e l y e x p o n e n t i a l w i t h d i s t a n c e

t r a v e l l e d wher e ( I o ) i s t h e i n i t i a l e n e r g y i n t e n s i t y i n

d e c i b a l s , (§) i s t h e a b s o r p t i o n c o e f f i c i e n t , and I i s t h e

e n e r g y i n t e n s i t y i n d e c i b a l s a f t e r t h e s e i s m i c p u l s e

t r a v e l s a d i s t a n c e (x).

I = Io e -§x T e l f o r d e t a l (1976)


41

Pe.f i p j Ct) f r t < p u * n t , y { i r y

Figure 13. Seismic Pulse Recorded by a Geophone Offset From the Source 10 Feet.

T a b l e 2

F re qu en cy A n a l y s i s R e s u l t s

So u rc e O f f s e t ( f t )

DominantF requency

A b s o r p t i o n(db)

1 6 - l b . S l e d ge 10 120 . 88

B u f f a l o Gun 10 100 .73

B l a s t i n g Cap 10 90 .66

Dynamite (80gm) 15 80 .88


42

An a r b i t r a r y v a l u e o f t h e a b s o r p t i o n c o e f f i c i e n t

t h o u g h t t o be t y p i c a l i s 0 .25 d e c i b a l s p e r w a v e l e n g t h

( T e l f o r d e t a l . f 1976) . U s i ng t h e s e r e l a t i o n s , t h e

r e s u l t s o f f r e q u e n c y a n a l y s i s and as summing a I o o f 1 .0 ,

l o s s of e ne r gy i n t e n s i t y by a b s o r p t i o n was c a l c u l a t e d f o r

each s ou rce s e i s m i c p u l s e t r a v e l l i n g t h r ou g h nea r s u r f a c e

g l a c i a l d r i f t ( T a b l e 2). Based on t h e s e c a l c u l a t i o n s , t he

s l e d g e hammer and d y n a m i t e s o u r c e i m p u l s e s r e t a i n t h e i r

e n e r g y i n t e n s i t y t o a g r e a t e r d e g r e e . The s l e d g e hammer

and dynami te s ou rc e i m p u l s e s would o n l y l o s e 12 p e r c e n t o f

e n e r g y i n t e n s i t y compar ed t o 17 and 24 p e r c e n t f o r t h e

s ho tgun and b l a s t i n g cap s ou rc e i m p u l s e s , r e s p e c t i v e l y .


ANALYSIS OF WALK AWAY DATA

R e f r a c t i o n An a l y s i s

Walk away s u r v e y s p r o v i d e two k i n d s o f i m p o r t a n t

i n f o r m a t i o n : near s u r f a c e s e i s m i c r e s p o n s e and d e f i n i t i o n

of t h e optimum window f o r d e s i r e d r e f l e c t i o n s . R e f r a c t i o n

a n a l y s i s o f walk away d a t a i n v o l v e d use of microcomputer

s o f t w a r e "HRASSD" p r o d u c e d by t h e New J e r s e y G e o l o g i c a l

S u r v e y . T h i s s o f t w a r e i n c l u d e s a p r o g r a m f o r t h e

t r a n s f e r e n c e o f d a t a f rom t h e B i s o n GeoPro t o d a t a d i s k

a n d p r o g r a m s f o r t h e a n a l y s i s o f r e f r a c t i o n s a n d

r e f l e c t i o n s , a s w e l l a s f o r c r e a t i n g s y n t h e t i c

s e i s m o g r a m s . C o mm er c i a l s o f t w a r e "REFRACT" p r o d u c e d by

G e o - L o g i c I n c . was a l s o u s e d i n r e f r a c t i o n a n a l y s i s o f

some o f t h e d a t a .

L o c a t i o n s of f o u r walk away s u r v e y s ( F i gu r e 14) were

l a r g e l y d i c t a t e d by t o p o g r a p h i c r e l i e f . A r e a s o f low

t o p o g r a p h i c r e l i e f were chosen t o r educe c o m p l i c a t i o n s in

a n a l y s i s o f t h e d a t a . S and D p r e c e d i n g l o c a t i o n l a b e l s

d e n o t e s s l e d g e hammer and dynami te s o u r c e s , r e s p e c t i v e l y .

In r e f r a c t i o n a n a l y s e s , f i r s t a r r i v a l t i m e s p l o t t e d

v e r s u s d i s t a n c e s from t h e souce g i v e a Time- Dis t ance (T-X)

graph . F i g u r e 15 shows a s y n t h e t i c T-X graph wi t h the d a t a

p o i n t s ( s h o w n by + ' s ) l y i n g on a p p r o x i m a t e l y t h r e e

43


44

sOJ£

D-lMarcel! 14s Rd.

Secti on 25

McKenzie Rd.

S-l

Secti on 36

Dutch Settlement Rd. R15W R14W

F i g u r e 14. L o c a t i on Map o f Four Walk Away Noise T e s t s Conducted i n t h e Study Area.


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Time (ms)

200

150

100

0 200 400 600 800 1000 1200 1400Distance ( f t )

F i g u r e 15. S y n t h e t i c T im e- D i s t a n c e Grapn For a Three Layer Case.

<j i

i

46

s t r a i g h t l i n e s . The r e c i p r o c a l o f t h e . s l o p e (m) o f t h e s e

l i n e s r e p r e s e n t s t h r e e s u c c e s s i v e l a y e r v e l o c i t i e s . The

t i m e a t wh i ch t h e s e l i n e s i n t e r c e p t t h e 0 f o o t s o u r c e

o f f s e t l i n e i s c a l l e d t h e i n t e r c e p t t ime (Ti ) and i s used

i n c a l c u l a t i n g the d e p t h s t o t he r e f r a c t i n g l a y e r s . Using

S n e l l ' s l aw and t h e s i m p l e g e o m e t r y o f a h o r i z o n t a l l y

l a y e r e d s i t u a t i o n , t h e f o l l o w i n g e q u a t i o n s can be d e r i v e d

f o r c a l c u l a t i n g t h e l a y e r t h i c k n e s s e s .

S n e l l ' s Law s in01/V1 = s in02/V2

D1 = V1Ti2 [1 /2{V2/ (V22-V12 ) 1 /2}] (1)

D2 = 1 /2[Ti3-2D1{(V32-V12)1/2/V3V1}][Q]

where Q = [ V3V2/(V32-V22 ) 1/2] (2)

(Mooney, 1984)

The d e p t h s c a l c u l a t e d by t h i s method r e p r e s e n t t h e

a v e r a g e d e p t h o f t h e s u b s u r f a c e t h a t i s s a m p l e d by t h e

p a r t i c u l a r s o u r c e and g e o p h o n e a r r a y . The s e c o n d and

t h i r d l a y e r v e l o c i t i e s a r e a p p a r e n t v e l o c i t i e s , and c o u l d

be d i f f e r e n t f rom a c t u a l v e l o c i t i e s i f t h e r e f r a c t i n g

h o r i z o n d i p s s i g n i f i c a n t l y .

R e f r a c t i o n A n a l y s i s o f Sledge Hammer Walk Away Data

The s e i s m o g r a m f rom s l e d g e hammer w a l k away S - 1

( F i gu r e 16) shows a 3 - l a y e r r e f r a c t i o n case . T-X a n a l y s i s

r e s u l t s o f walk away S-1 ( F i g u r e 17» T a b l e 3) e x h i b i t t h e

g e n e r a l c a s e w h e r e V1 r e p r e s e n t s t h e v e l o c i t y o f


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ITIME (milliseconds)

DISTANCE (feet)

F i g u r e 16. Seismograms From Walk Away Survey S-1 P r e s e n t e d As a T im e- Di s t an c e Graph With I n t e r p r e t a t i o n o f A r r i v a l s as a Three Layer Case.

j=-3

48

Time (m il l i seconds)

m=l/v,150 _

m=l/v100 -

Ti 3

50 -Ti 2

1000800600200 4000Distance ( f t )

F i g u r e 17. Time D i s t a n c e Graph o f F i r s t A r r i v a l s For Walk Away Survey S-1 .

T a b l e 3

T - X A n a l y s i s R e s u l t s For Walk Away S u r v e y S-1

V e l o c i t i e s( f t / s e c )

I n t e r c e p t Times (Ti ) ( s e c o n d s )

C a l c u l a t e d Depths ( f e e t )

v i = 1133 T i i = *048 Di = 27 . 5

v 2 = 5985 T i 2 = .097 D2 = 1 8 6 . 5

v 3 = 9524


u n s a t u r a t e d , g l a c i a l t i l l ( see Ta b le 7); V2 r e p r e s e n t s t h e

v e l o c i t y o f s a t u r a t e d , g l a c i a l t i l l ; and V3 r e p r e s e n t s

e i t h e r a c l a y l a y e r w i t h i n t h e t i l l , o r t h e b e d r o c k

( Co ld wa t e r S h a l e ) . The a n a l y s i s of t h e V3 l a y e r w i l l be

c o n s i d e r e d b e l o w . D1 r e p r e s e n t s t h e w a t e r t a b l e d e p t h ,

and D2 r e p r e s e n t s t h e d e p t h t o t h e V3 l a y e r . S c a t t e r o f

p o i n t s on T-X g r a p h s can be a t t r i b u t e d t o v a r i a t i o n s i n

t h e t h i c k n e s s o f t h e low v e l o c i t y l a y e r and t o t h e f a c t

t h a t t h e p o r t i o n o f t h e s u b s u r f a c e b e i n g s a m p l e d i s

d i f f e r e n t f o r s u c c e s s i v e s h o t s in t h e w a l k away n o i s e

t e s t s .

Seismograms from a fo rwar d and r e v e r s e s l e d g e hammer

w a l k away a t l o c a t i o n S- 2 on McKenzie Road ( F i g u r e 18,

F i g u r e 19) show a 3 - l a y e r c a s e . T-X a n a l y s i s o f t h e S - 2

f o rw ar d and r e v e r s e d a t a ( F i g u r e 20) i s i n t e r p r e t e d u s i n g

t h e •'REFRACT1' program. REFRACT a n a l y s i s i s based on f i r s t

a r r i v a l t i m e s of t h e r e f r a c t e d s e i s m i c i m p u l s e s . A f i l e

o f t i m e - d i s t a n c e d a t a d e f i n e d by t h e f i r s t a r r i v a l s i s

c r e a t e d and s a v e d on d i s k . From t h e t i m e - d i s t a n c e d a t a ,

i t i s p o s s i b l e t o s o l v e a g e o l o g i c mode l h a v i n g s e v e r a l

d i f f e r e n t l a y e r s . The number o f l a y e r s i n t h e m o d e l , as

w e l l as s p e c i f i c c r o s s - o v e r d i s t a n c e s can be s p e c i f i e d t o

c o n s t r a i n t h e s o l u t i o n o f t h e model t o i n c l u d e t h e s e

p o i n t s as known v a l u e s . The REFRACT program l e a s t square


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without

permission.

Tine

300-

(m illiseconds) ___ii i.i in <;i jwlimp,i "*1'1 Id to L jld ij <to«to Ju«iK* y fo .*< p «j»to ^ to m f o i v i c b j m }

m * f r ■ ■ * m & &t t ;> &A 1 ii n \ £ i j> 1 i n 14- piS< '•_% rf*—* * 1 5 ■ > /i I <■ 4 > ■*. j 4 < , i /* -> ■ ..< i \ \ i ' j i J, <.*., ^ j is ^ / \ «;.' > } ^ } ■ j i - t - . t «: i ; < a , t L*

) & % : i > t i l ? :*-* * v.f-T— • J J ' < 5 : j> 1 1 . J \ I <• S

200 -

> > ?•

30.5 36b 701.5 D istance ( f t )

1037 1372.5

F i g u r e 18. Seisraograras From Walk Away Survey S-2 (Forward) P r e s e n t e d As a T i m e- D i s t a nc e Graph With I n t e r p r e t a t i o n o f A r r i v a l s a s a 3 - L a y e r Cas e .

U1o

51

!

I


Figu

re

19.

Seis

raog

ram

s Fr

om

Walk

Aw

ay

Surv

ey

S-2

(Rev

erse

) Pr

esen

ted

As a

Tim

e-D

ista

nce

Grap

h W

ith

Inte

rpre

tati

on

of A

rriv

als

as a

3-La

yer

Cas

e.

52

Time (ms)

360

280

200

120

1400800 1000 1200 Forward Shot ( f t )

600400Distance From

200

F i g u r e 20. T im e- Di s t anc e Graph o f F i r s t A r r i v a l s For Forward and Reve r se Walk Away S ur vey s S - 2 .

Depth ( f t )44W- f t / s e c

4499 f t / s e c120

160

200240

i t i i i / / / ' / / ' / i i i / / i / / i i i / / / i> / / / / / / / /' / / / / / ’ / / / : 7308 f t / s e c ........ ....................../ i f t i i i t t t t t t t t t i i i i i i ! fi t t i / / / / / / / / / / / / / / '

280 •My// / / / / / / / / / / / /r t t t f t t t t t t t t t t f f i f t t i t i t t t t f t t t t t r t t t t t t t t t t t t / t t t r t t t fi ll ! / / / / / f f / f i f f / i f if if i f i f f i f f / i f if if i f f i f f i f / / / / / / i f / i f / i f i f f /

1200 1400800600 1000400200Distance From Forward Shot ( f t )

F i g u r e 21. V e l o c i t y Layer P r o f i l e C a l c u l a t e d From Time- Di s t a n c e Graph o f F i r s t A r r i v a l s From Walk Away Survey S-2 .


53

f i t s N l i n e s e g m e n t s t o t h e d a t a p o i n t s s u b j e c t t o t h e s e

c o n s t r a i n t s : t h e N=1 l i n e must p as s t h r ou gh t h e o r i g i n ,

a p p a r e n t v e l o c i t i e s must i n c r e a s e , and t h e c o n d i t i o n o f

r e c i p r o c i t y mus t be met . The c o n d i t i o n o f r e c i p r o c i t y

s i m p l y s t a t e d i s t h a t t h e f o r war d and r e v e r s e t r a v e l t i me s

mus t be e q u a l f o r e a c h l i n e s e g m e n t . V a r i a n c e o f t h e

o v e r a l l f i t s o f t h e l i n e s e g m e n t s t o t h e d a t a p o i n t s i s

c a l c u l a t e d by t h e REFRACT program. Reve r se t i m e - d i s t a n c e

d a t a can be used t o s o l v e f o r t h e a v e r a g e a p p a r e n t d i p of

t h e l a y e r s . The r e s u l t s o f t h e T-X i n t e r p r e t a t i o n a r e

used by REFRACT t o c a l c u l a t e t r u e l a y e r v e l o c i t i e s , l a y e r

t h i c k n e s s e s , and l a y e r d ip p r e s e n t e d as a g e o l o g i c l a y e r

p r o f i l e ( F i g u r e 21) . T a b l e 4 i s a summat i on o f t h e

r e s u l t s o f t h e REFRACT a n a l y s i s o f t h e S - 2 w a l k away.

D e r i v a t i o n o f f o r m u l a s used i n s o l v i n g m u l t i p l e - d i p p i n g -

l a y e r r e f r a c t i o n problems i s c o n t a i n e d i n Mooney ( 1984) .

R e f r a c t i o n A n a l y s i s o f Dynamite Data

Seismograms from a dynami te walk away a t l o c a t i o n D-2

( F i g u r e s 2 2 , 23, & T a b l e 5) g i v e d e p t h s and v e l o c i t i e s

c o n s i s t e n t wi t h t h e r e v e r s e s l e d g e hammer walk away, S-2,

a t t h e same l o c a t i o n .

Seismograms from t h e dynami te walk away a t l o c a t i o n

D-1 on M a r c e l l u s Road ( F i g u r e 24) a g a i n show a 3 - l a y e r

case . T-X a n a l y s i s (F igur e 25, Ta b l e 6) g i v e s dep ths and


54

T a b le 4

T-X a n a l y s i s R e s u l t s For Walk Away Survey S-2

Layer Forward Shot Reverse Shot Layer Dip

V e l o c i t i e s Layer Layer

( f t / s e c ) T h i c k n e s s ( f t ) T h i c k n e s s ( f t ) ( d e g r e e s )

1341 41 26 0 . 6

4923 164 132 1.8

6978

r _ _ „ _ . . . . . .


55

n f> |r•15*11

’. ' fj. ' i

a a>

to -P

•dcpUT V3 l i t :r) B

f(0 0)tlO-H <

3. CO TO COtU 10

CO < u*

M * |*MT”


56

Time (m i l l i s econ d s )

m=l/v250

200m=l/v

150 “

m=l/v, 100 -

200 4000 600 1000 1200 1400800Distance ( f t )

F i g u r e 23* T im e- Di s t an c e Graph o f F i r s t A r r i v a l s From Walk Away Survey D-2.

Table 5T - X Analysis Results For Walk Away Survey D-2

Velocities(ft/sec)

Intercept Times (Ti) (seconds)

Calculated Depths (feet)

vi = 1017 Tii == .046 Di = 23.8v2 = 5016 Ti2 =* .120 D2 = 188.6v3 = 9211


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with perm

ission of the

copyright ow

ner. Further


without

permission.

TOE900

(im“ W’jw iS r l^ lll l ltd til |U1 AjJ |ui U jllJ |U1 |Ul',lll ‘Ul'tu tiÛl lliJJllm m_v... in in rv m it. to k £%)] w » m 'in jr-. jm m to h

* * ** '* 1 | * ‘ i i ~ "T —f — ■■ m m

s s H ,< <•- :i ! V - C - « <;•> < « . < . £- I I I 1 1 - H <.«.;< j -'m .

500

i

366 701.5 DISTANCE ( f e e t )

1372.5

F i g u r e 24. Seisraograms From Walk Away S u rv ey D-1 P r e s e n t e d As a Time-Dis tance . Graph With I n t e r p r e t a t i o n o f F i r s t A r r i v a l s as a Three Layer Case. <ji-j

Time (milliseconds)

250m=l/v m=l/v,

200 -i

m=l/v150 -

1003

2

200 400 1200 14000 600 800 1000Distance ( f t )

F i g u r e 2 5 . T i me- Di s t an ce Graph o f F i r s t A r r i v a l s From Walk Away Survey D-1.

Table 6T - X Analysis Results For Walk Away Survey D-1

Velocities (ft/sec)

Intercept Times (Ti) (seconds)

Calculated Depths (feet)

vi = 1131 Ti]_ == .058 Dx = 34.2v2 = 4236 Ti2 == .114 D2 = 188.2v3 = 8242

F ' .Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

59

v e l o c i t i e s c o m p a t i b l e wi th r e s u l t s o f walk away s u r v e y s on

McKenzie Road.

Summary o f R e s u l t s o f R e f r a c t i o n Analyses

W a t e r t a b l e d e p t h s c a l c u l a t e d f r o m r e f r a c t i o n

a n a l y s e s c o r r e s p o n d w e l l w i t h s t a t i c w a t e r l e v e l s (SWL)

r e c o r d e d i n wa t e r w e l l l o g s from t h e s t u d y a r e a ( Tab l e 7).

The t h i r d l a y e r , V3, as i n t e r p r e t e d from T-X gr aphs

e x h i b i t s an a v e r a g e v e l o c i t y o f 8372 f t / s e c wh ich i s

s omewhat h i g h e r t h a n an a v e r a g e d r i f t v e l o c i t y g i v e n by

T e l f o r d , e t a l . ( 1 9 7 6 ) , o f 5000 f t / s e c . S o n i c l o g d a t a

f rom A l l e g a n County o i l w e l l s i n d i c a t e t h a t t h e b e d r o c k

( Co l dwat er S h a l e ) has a v e l o c i t y of abou t 9000 f t / s e c .

I n i t i a l a n a l y s i s of t h e V3 l a y e r s u g g e s t s a r e f r a c t e d

w a v e o r i g i n a t i n g f r o m t h e b e d r o c k s u r f a c e . T-X

c a l c u l a t i o n s of t he a v e r a g e d ep t h t o l a y e r V3 f o r t h e walk

away s u r v e y s i s 176 f e e t . The C o l d w a t e r S h a l e , h o w e v e r ,

l i e s a t a d ep t h o f 265-350 f e e t t h r o u g h o u t t h e s t u d y a r ea .

A g e n e r a l r u l e o f thumb b a s e d on a h o r i z o n t a l l y l a y e r e d

s i t u a t i o n s t a t e s t h a t t h e d e p t h t o t h e r e f r a c t o r b e i n g

s a m p l e d i s r o u g h l y e q u a l t o 1 / 3 o f t h e s o u r c e g eo pho ne

a r r a y l e n g t h (Mooney, 1984) . T h e o r e t i c a l l y t h e n , t h e

a r r a y l e n g t h o f 1000 f e e t a c h i e v e d i n a l l w a l k away

s u r v e y s s h o u l d be g r e a t enough t o a l l o w r e c o r d i n g of t h e


Table 7Comparison of Water Table Depths

Walk Away L o c a t i o n

N e a r e s t Water Wel l SWL ( f t )

C a l c u l a t e d Depth ( f t )

S - l 35 28

S-2 43 34

D-1 41 35

T a b l e 8

S y n t h e t i c R e f r a c t i o n Walk Away P a r a m e t e r s

Layer V e l o c i t y T h i c k n e s s Depth( f t / s e c ) ( f e e t ) ( f e e t )

1 1265 30 -

2 4791 155 30

3 8372 15 185

4 4791 95 200

5 9000 — 295


61

bedrock r e f r a c t e d wave as a f i r s t a r r i v a l .

A p o s s i b l e e x p l a n a t i o n o f t h i s anomalous d a t a i s t h e

c l a s s i c v e l o c i t y i n v e r s i o n r e f r a c t i o n p rob lem i n which a

h i g h v e l o c i t y l a y e r i s u n d e r l a i n by a low v e l o c i t y l a y e r .

Assumi ng t h a t s p e c i a l c a s e , a h i g h v e l o c i t y l a y e r w ou ld

l i e i n t h e d r i f t a t a d e p t h o f a b o u t 176 f e e t and be

u n d e r l a i n by a lower v e l o c i t y m a t e r i a l .

T h r e e o i l w e l l l o g s f rom t h e s t u d y a r e a i n c l u d e

d e s c r i p t i o n s o f t h e g l a c i a l d r i f t . They show an

a p p a r e n t l y c o n t i n u o u s c l a y l a y e r a t 1451 155 and 185 f e e t ,

r e s p e c t i v e l y , u n d e r l a i n by s a n d and g r a v e l down t o t h e

bedrock ( F i g u r e 26 ) .

C l a y s e x h i b i t v e l o c i t i e s f ro m 3 0 0 0 - 9 0 0 0 f t / s e c

( J a k o s k y , 1950) . The a v e r a g e v e l o c i t y f o r l a y e r V3 o f

8372 f t / s e c c o u l d be p r o d u c e d by a h a r d - p a c k e d , d e n s e ,

c l a y l a y e r . Assuming t h a t V3 i s t h e v e l o c i t y o f a c l a y

l a y e r , and t h a t t h e v e l o c i t y o f t h e s a n d / g r a v e l l a y e r

between t h e c l a y l a y e r and bedrock i s c o n s i s t e n t w i t h t he

d r i f t a b o ve t h e c l a y l a y e r (V2) , a s y n t h e t i c s e i s m o g r a m

was c a l c u l a t e d u s i n g t h e HRASSD p r o g r a m . The s y n t h e t i c

sei smogram p a r a m e t e r s ( v e l o c i t i e s , d e p t h s ) were o b t a i n e d

from r e f r a c t i o n a n a l y s e s , and w e l l l o g d e p t h s t o t he c l a y

l a y e r and bedrock ( T a b l e 8).

The HRASSD s y n t h e t i c seismogram program c a l c u l a t e s a

t r a v e l - t i m e s y n t h e t i c model c o n t a i n i n g no r e a l a m p l i t u d e


Reproduced

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JONES 1-36 JONES 2 -3 6

sand — gravel

sand —gravel

sandy clay

sand - g ra v e l/c la y

TOY 2 -2 3b ' elev. f t

0 900 ^

600 -

700 -

C l a y - m u d

coldw ater shale600 -

H.S. I - . S m i l e s V.S. l" = 100 f t

F i g u r e 26 . Ge o l og i c Cross S e c t i o n o f G l a c i a l D r i f t Across S tudy Area Showing a Con t i nu ous Clay Layer .

o\ro

m ode l i ng . R e f l e c t i o n a r r i v a l s a r e a r b i t r a r i l y a s s i g n e d a

wave a m p l i t u d e t w i c e t h a t o f r e f r a c t i o n a r r i v a l s . The

program c a l c u l a t e s r e f r a c t i o n s and r e f l e c t i o n s f o r e v e r y

l a y e r s p e c i f i e d , w i t h t h e b o t t o m l a y e r c o n s i d e r e d a s a

h a l f - s p a c e . Formulas a r e d e r i v e d u s i n g S n e l l * s law and th e

s i m p l e g e o m e t r y o f h o r i z o n t a l l a y e r s . Mooney (1984)

d e r i v e s t h e f o r m u l a s f o r t h e m u l t i p l e - h o r i z o n t a l - l a y e r

r e f r a c t i o n c a s e .

The s y n t h e t i c s e i s m o g r a m s h o wi n g o n l y r e f r a c t i o n s

( F i g u r e 27) and t h e T-X a n a l y s i s o f t h e s y n t h e t i c f i r s t

a r r i v a l s ( F i g u r e 2 8 , T a b l e 9) c o r r e l a t e s w e l l w i t h t h e

o b s e r v e d f i e l d d a t a . Note t h a t t h e b e d r o c k r e f r a c t i o n

i s not a f i r s t a r r i v a l e v e n t i n t h i s model . Dynamite walk

away D-1 ( F i g u r e 24) s u p p o r t s t h i s mode l s h o w i n g t h e

bedrock r e f r a c t e d a r r i v a l s as t hey a r r i v e l a t e r t h a n t h e

i n t e r p r e t e d c l a y l a y e r r e f r a c t e d a r r i v a l s i n t h e f a r

o f f s e t d a t a .

A g e o l o g i c and v e l o c i t y l a y e r p r o f i l e of t he d r i f t in

t h e s t u d y a r e a ( F i g u r e 29) i s b a s e d on t h e p r e c e d i n g

a n a l y s e s and models . The most s i g n i f i c a n t d e t a i l o f t h i s

i n t e r p r e t a t i o n i s a v e l o c i t y i n v e r s i o n caused by a h i g h -

v e l o c i t y , t h i n , c l a y l a y e r assumed t o be c o n t i n u o u s in t h e

d r i f t t h r o u g h o u t t h e s t u d y a r e a . T h i s i n t e r p r e t a t i o n o f

n e a r s u r f a c e v e l o c i t i e s and t h i c k n e s s e s w i l l be u s e d i n

r .


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ission of the

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permission.

Time (milliseconds)

j■ ■ 1 H i M i M i i [

v * t : 1 ;! ? • I 1 i ! ; 1 I

M 1 I 1 ! M 1 1 ; 1I j ; ; I ; i i ! : ; j

! 1i t i l

• • »• > t i

! i ; » • •

; d r p u p d - r c i l ^ i : L T ! ji

j ' ' i 1 1 : : ! jB e d ro c R I

• • • * i * * i i • « «i i : . i 1 I l i . . ;

LefrrpqtiQ iji i • • • i • •• |

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4--------.____

J.

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i j |

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I H * * £ £ * t T j i j i j i

W **" i * t V * i i i i i i «: f. > T f ! i i i \ i i I 1 i I

I I ! ! ! I 1 1 icijay i a y e i r1 » ‘ 1 ♦ 1 * ! » •• j ‘ I i

a____

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cd------------A!-.

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i q n j

! 1 i* i t ! ! j j iI * i

i : i- t- > r i ; i i I ; t ! i i 1 i 1* £ f : M \ 1 ! i : i ! i M i ! iw i ! : ' w a t e r ’ T kbjld R e f r k d t i o f i

i l l ! ! • ' ! i !

i i ! i !. i f f *

! ! ; i !

* ! ! ! ? ! » ♦ * 1 i » * * * ? 5 » * • I 1 5 i ! ! ! ! ! ! : : l i i i i t t iM M ! ! ! !

M U Mi I ! 1 i 1■ ! ! ! ! I

t t •

i i Ii 1 i • f I

I i :

400

300

200

100

30.5 366 732Distance ( feet )

1098

F i g u r e 27 . S y n t h e t i c Walk Away Seismograms Model ing t h e S e i sm ic R e f r a c t i o n Response i n t h e G l a c i a l D r i f t o f t h e S tudy Area .

o\XT

65

Time (ms)

200

1003

2

1000 1200 1400200 400 600 8000Distance ( f t )

F i g u r e 28 . T im e - Di s t a n c e Graph o f F i r s t A r r i v a l s FromS y n t h e t i c Walk Away Seisraograms Model ing t h e G l a c i a l D r i f t i n t h e S tudy Area.

Table 9T - X Analysis Results For Synthetic Refraction Walk Away

Velocities(ft/sec)

Intercept Times (seconds)

(Ti) Calculated Depths (feet)

V! = 1260 Tii = .050 Di = 30.0V2 = 4976 Ti2 = .088 D2 = 185.0V3 = 8337

F : ' ~ ........


Reproduced

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ission of the

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permission.

Depth ( f t )

Weathered Zone V = 1265 Ft/sec- 50 -

— Sand & Gravel Some Clay V = 4791 Ft/sec 100 _

- 150 _

u a v v = ud/z i-t/sec “ 200 _

- Sand & Gravel Some Clay V = 4791 Ft/sec 250 .

**nn

- Coldwater Shale V = 9G00 Ft/sec

Vertical Scale = Horizontal Scale 1" = 100'

350 -

F i g u r e 29. G e o l o g i c and V e l o c i t y P r o f i l e Model o f G l a c i a lD r i f t i n t h e Study Area Based on I n t r e p r e t a t i o n o f Walk Away Surveys and Wel l Logs.

67

f u r t h e r s y n t h e t i c m o d e l i n g and i n i n t e r p r e t a t i o n o f

s e i s m i c e v e n t s r e c o r d e d on r e f l e c t i o n p r o f i l i n g

se ismograms.

R e f l e c t i o n A n a l y s i s

R e f l e c t i o n s on t h e w a l k away s e i s m o g r a m s a r e

d i f f i c u l t t o r e c o g n i z e and i n t e r p r e t due t o power l i n e

g e n e r a t e d n o i s e and l a c k of a p p a r e n t m o v e o u t . T r a c e

m i x i n g and d i g i t a l f i l t e r i n g e n h a n c e t h e r e f l e c t e d

a r r i v a l s a l l o w i n g b e t t e r c o r r e l a t i o n . The f i r s t s t e p in

i d e n t i f y i n g r e f l e c t i o n s was t o c r e a t e a r e f l e c t i o n

s y n t h e t i c seismogram u s i n g t he HRASSD s y n t h e t i c program.

C a l c u l a t i o n o f t h e s y n t h e t i c s e i s m o g r a m , a n d

i n t e r p r e t a t i o n of r e f l e c t i o n s i n a c t u a l r e c o r d s a r e based

on t h e a s s u m p t i o n t h a t t r a v e l - t i m e ( t ) f o r a r e f l e c t i o n

and s o u r c e - d e t e c t o r s e p a r a t i o n (x) a r e r e l a t e d by t h e

s i m p l e e q u a t i o n :

t 2 = t 0 2+(x2/ V 2 ) (3)

where t o i s t h e two- way t r a v e l t i m e f o r a c o i n c i d e n t

s o u r c e and d e t e c t o r and V i s a v e l o c i t y . Dix ( 1955)

showed t h a t f o r a s e c t i o n c o n s i s t i n g o f o n l y h o r i z o n t a l

beds , e q u a t i o n 3 g i v e s a s a t i s f a c t o r y f i t t o the d a t a f o r

r e l a t i v e l y s m a l l v a l u e s o f x (<5000 f t ) , and t h a t V in t h e

e q u a t i o n r e p r e s e n t s a RMS v e l o c i t y (Vrms) where

Vrms2 = « .Vi2/ t i ) / « . t i > («)


68

wh er e t ^ i s t h e t r a v e l t i m e i n t h e i t h l a y e r and Vi i s t h e

a v e r a g e v e l o c i t y w i t h wh i c h a wave t r a v e l s i n t h e i t h

l a y e r ( T e l f o r d e t a l . , 1976) .

The l a y e r t h i c k n e s s e s and v e l o c i t i e s c a l c u l a t e d by

r e f r a c t i o n a n a l y s i s f o r t h e d r i f t l a y e r , c o u p l e d w i t h

s o n i c l o g d a t a f r o m A l l e g a n C o u n t y o i l w e l l s a nd

f o r m a t i o n d e p t h s f rom o i l w e l l s i n t h e s t u d y a r e a were

used t o d e f i n e t h e p a r a m e t e r s o f t h e s y n t h e t i c r e f l e c t i o n

walk away ( Ta b l e 10). The s y n t h e t i c walk away ( F i gu r e 30)

shows r e f r a c t e d and r e f l e c t e d a r r i v a l s , and s h o u l d be a

f a i r l y a c c u r a t e r e p r e s e n t a t i o n o f t h e t r u e s e i s m i c

r e f l e c t i o n r e s p o n s e i n t h e s t u d y a r e a w i t h r e s p e c t t o

t r a v e l t i m e s and RMS v e l o c i t i e s .

The T r a v e r s e F o r m a t i o n a n d T r a v e r s e L i m e s t o n e

r e f l e c t i o n s form a c o u p l e t and a r e t h e l a t e s t r e f l e c t i o n s

on t h e s y n t h e t i c s e i s m o g r a m . The i n t e r c e p t t i m e f o r t h e

T r a v e r s e L i m e s t o n e r e f l e c t i o n i s 275 m i l l i s e c o n d s . The

opt imum window f o r t h e T r a v e r s e L i m e s t o n e r e f l e c t i o n

o c c u r s a t a s o u r c e o f f s e t o f 366 t o 1000 f e e t . A HRASSD

t i m e s q u a r e d v s . d i s t a n c e s q u a r e d (T2-X2 ) g r a p h ( F i g u r e

31) o f a r r i v a l t i m e s of t h e T r a v e r s e Limestone r e f l e c t i o n

w i t h i n t h e opt imum window zone g i v e s a r e f l e c t i o n RMS

v e l o c i t y o f 7340 f t / s e c . I n t e r p r e t a t i o n o f r e f l e c t i o n s i s

b a s e d on e q u a t i o n 3 where t 2 p l o t t e d v e r s u s x 2 y i e l d s a

f .


69

Table 10S y n t h e t i c R e f l e c t i o n Walk Away P a r a m e t e r s

Layer V e l o c i t y( f t / s e c )

T h i c k n e s s( f e e t )

Depth ( f e e t )

1 1265 30 -

2 4791 155 30

3 8372 15 185

4 4791 95 200

5 9000 132 295

6 10000 258 427

7 9500 198 685

8 11400 43 883

9 14000 ' — 926


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ission of the

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permission.

Tine (milliseconds)

400-

j |

i i ■

30aL L :. I i i a^ *■ • • r a • • a a

. \ I .. L L > i»

200-

; i i i i i i . i .

I I t U i- l> I I j 1, y k V s ?• »

r r r r f ? : ; : i \ i ! \ 1 i * i. ?r • t «L l > !

? i J a* a ♦ aL * > ?-

i i

100*

m- r r r r r n : i-.............. 5. V

I i ii i! ! i I i

L L ! ! I *

i ii i i I

i * ;t > ii i !

; i il i t !

0 30.5 3GG 732Distance ( feet)

1098

F i g u r e 30. S y n t h e t i c Walk Away Seismograms Model ing t h e S e i s mi c R e f l e c t i o n and R e f r a c t i o n Response i n t h e G l a c i a l D r i f t o f t h e Study Area .

—j o

Reproduced

with perm

ission of the

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permission.

Tine2 (ins)2 100000

50000

m s = 7340 f t / s ec

10000Distance2 (ft)*-

1200000

F i g u r e 31. Time S q u a r e d - D i s t a n c e Squared Graph o f T r a v e r s e Limes tone R e f l e c t i o n A r r i v a l Times Computed by S y n t h e t i c Seismogram Program.

72

s t r a i g h t l i n e whose s l o p e (ra) e q u a l s 1/Vrms2 , and whose y-

i n t e r c e p t e q u a l s t h e two way t r a v e l - t i m e t o . Depths are

then c a l c u l a t e d u s i n g the s i mp l e e q u a t i o n

h = 1 /2 ( Vrms*to) (5)

where h i s t h e d ep t h t o t h e r e f l e c t o r .

T2-X2 a n a l y s i s r e s u l t s can g i v e v e l o c i t i e s and d e p t h s

a c c u r a t e w i t h i n a f ew p e r c e n t w h e r e t h e r e c o r d s a r e good

q u a l i t y and t h e v e l o c i t y d i s t r i b u t i o n i s not s i g n i f i c a n t l y

l a t e r a l l y complex ( T e l f o r d e t a l . , 1976) .

R e f l e c t i o n An a l y s i s o f Sledge Hammer Data

Based on t h e s y n t h e t i c s e i s m o g r a m ( F i g u r e 30) , t h e

T r a v e r s e L i m e s t o n e r e f l e c t i o n i s a n t i c i p a t e d t o o c c u r

somewhere between 250-320 m i l l i s e c o n d s , e x h i b i t i n g an RMS

v e l o c i t y o f 7 0 0 0 - 8 0 0 0 f t / s e c . Walk away s u r v e y S - 1

(F ig ur e 16) does n o t show a c o r r e l a t a b l e r e f l e c t i o n e v e n t

n e a r t h e e x p e c t e d a r r i v a l t i m e , e v e n t h o u g h f i e l d

p a r a m e t e r s and i n s t r u m e n t s e t t i n g s w e r e s e t f o r opt imum

enhancement o f t h e d e s i r e d r e f l e c t i o n s i g n a l .

Walk away s u r v e y S-2 fo rwar d and r e v e r s e seismograms

( F i g u r e 18, F i g u r e 19) a p p e a r t o h a v e a c o r r e l a t a b l e

r e f l e c t i o n i n t h e e x p e c t e d t i m e zone. C l o s e r i n s p e c t i o n

r e v e a l s t h a t t h e s e a r e t h e r e s u l t o f 5 0 - 6 0 h e r t z power

l i n e g e n e r a t e d n o i s e . I n t h i s c a s e , t h e n o t c h and 75

h e r t z l o w - c u t f i l t e r s used in t h e a c q u i s i t i o n o f t he d a t a

- - -

6 ■Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

f a i l e d t o d i m i n i s h t h e power l i n e n o i s e s u f f i c i e n t l y t o

i n c r e a s e t h e s i g n a l / n o i s e r a t i o t o an a c c e p t a b l e l e v e l .

Based on f a i l u r e o f t h e s l e d g e hammer t o p r o d u c e a

s i g n i f i c a n t r e f l e c t i o n e v e n t i n t h e ex pec t ed t ime zone, i t

was assumed t h a t a l a r g e p o r t i o n o f t h e impact e n e r g y was

b e i n g a t t e n u a t e d in t h e t h i c k g l a c i a l d r i f t .

R e f l e c t i o n An al ys i s o f Dynamite Data

I n t h e s e a r c h f o r a s o u r c e w i t h a d e q u a t e e n e r g y t o

p e n e t r a t e t h e g l a c i a l d r i f t , e x p l o s i v e e n e r g y became an

o b v i o u s s o l u t i o n . Seismograms from dynami te walk away D-1

on M a r c e l l u s Road ( F i g u r e 32) h a v e b een t r a c e mi xed and

d i g i t a l l y b and -p as s f i l t e r e d 75-200 h e r t z t o enhance any

r e f l e c t e d a r r i v a l s . The second s e t o f 12 t r a c e s between

3 6 6 - 7 0 1 . 5 f e e t o f f s e t a r e p o o r q u a l i t y due t o i n a d e q u a t e

g a i n s e t t i n g s d u r i n g f i e l d a c q u i s i t i o n .

Loca t ed between 300 and 400 m i l l i s e c o n d s in t h e t h i r d

s e t o f t w e l v e t r a c e s ( F i g u r e 32) a h i g h v e l o c i t y e v e n t

can be seen as t h r e e peaks t h a t i n t e r f e r e w i t h p a r t o f the

lower v e l o c i t y r e f r a c t e d a r r i v a l wave t r a i n . Th i s e v e n t

d o e s n o t e x h i b i t n o r m a l m o v e o u t , b u t a p p e a r s t o h a v e t h e

r e v e r s e h y p e r b o l i c shape c h a r a c t e r i s t i c o f d i f f r a c t i o n s .

C l o s e r i n s p e c t i o n r e v e a l s t h a t t h e r e v e r s e h y p e r b o l i c

s h a p e o f t h e a r r i v a l s can be a t t r i b u t e d t o a b e n d , an


74

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i n c r e a s e i n a p p a r e n t v e l o c i t y , on t h e l a s t f ou r t r a c e s o f

t h e t h i r d s e t of twe lve (F ig ur e 32) .

A l oo k a t t h e e v e n t s between 400 and 600 m i l l i s e c o n d s

on t h e f o u r t h s e t of t w e l v e t r a c e s shows t h e same i n c r e a s e

i n a p p a r e n t v e l o c i t y on the l a s t f o u r t r a c e s ( F i g u r e 32).

The f a c t t h a t t h i s a p p a r e n t v e l o c i t y i n c r e a s e i s e v i d e n t

on two s e p a r a t e s e t s o f r e c o r d s r e c o r d e d from t h e same s e t

o f g e o p h o n e s i n t h e same l o c a t i o n s s u g g e s t s t h a t t h e

r e v e r s e h y p e r b o l i c shape of t he e v e n t s i s an a r t i f a c t o f

n e a r s u r f a c e c o n d i t i o n s l o c a l t o t h e l a s t f o u r geophones

i n t h i s walk away geophone s p r ea d .

T h e r e f o r e , a s s u m i n g t h a t t h e e v e n t b e t w e e n 2 5 0 - 3 5 0

m i l l i s e c o n d s on t h e t h i r d s e t o f t w e l v e t r a c e s i s a

p r i m a r y r e f l e c t i o n ( F i gu r e 32), T^-X^ a n a l y s i s was c a r r i e d

o u t t o d e t e r m i n e a r o u g h e s t i m a t e o f t h e d e p t h o f o r i g i n .

Hof fman ( 1 9 8 5 ) , f o u n d t h a t i f a r e f l e c t i o n d o e s no t

e x h i b i t normal moveout , T^-X^ a n a l y s i s w i l l g i v e a dep th

v a l u e prone t o e r r o r . T^-X^ a n a l y s i s ( F i gu r e 33) g i v e s an

RMS v e l o c i t y o f 6200 f t / s e c and a computed dep th based on

norma l i n c i d e n c e of 1034 f e e t . These c a l c u l a t i o n s and t h e

c l o s e match i n a r r i v a l t i m e s w i t h t h e s y n t h e t i c T r a v e r s e

L i m e s t o n e r e f l e c t i o n ( F i g u r e 30 ) , l e d t o t h e c o n c l u s i o n

t h a t t h i s e v e n t i s e i t h e r t h e T r a v e r s e F o r m a t i o n o r

T r a v e r s e Limes tone r e f l e c t i o n s , or a r e f l e c t i o n from some

o t h e r i n t e r f a c e i n t h e d e s i r e d d e p t h r a n g e o f 9 0 0 - 1 0 0 0

Fk '


Tine2 (ms)2180000

= 6189 f t / secrms

0

50000 Distance'" (ft)*" 1100000

F i g u r e 33. Time S q u a r e d - D i s t a n c e S q u a r e d Graph o f I n t e r p r e t e d T r a v e r s e Limes tone R e f l e c t i o n A r r i v a l s From Walk Away D-1.

Tine (ms)

600

500

400

300

200

10014001200 130011001000

Distance (feet)

F i g u r e 34. Ti r ae-Dis tance Graph o f High Ampl i tude Ev en t s Showing V e l o c i t i e s S i m i l a r To R e f r a c t e d Wave V e l o c i t y .


77

f e e t .

The h i g h a m p l i t u d e e v e n t s b e t w e e n 400 a n d 600

m i l l i s e c o n d s i n t h e f o u r t h s e t o f t w e l v e t r a c e s h a s an

a p p a r e n t v e l o c i t y much s l o w e r t h a n t h e r e f l e c t i o n e v e n t i n

t h e t h i r d s e t o f t w e l v e t r a c e s ( F i g u r e 3 2 ) . A T-X

a n a l y s i s ( F i gu r e 34) o f t h e a r r i v a l t i m e s o f t h e s e e v e n t s

compared t o t h e a r r i v a l t i m e s o f the r e f r a c t e d wave show

a p p a r e n t v e l o c i t i e s and s h a p e m i m i c k i n g t h e r e f r a c t e d

wave. T2-X2 a n a l y s i s o f t h e s e e v e n t s ( F i gu r e 35) g i v e s an

a ve r a g e RMS v e l o c i t y of 4129 f t / s e c . This v e l o c i t y i s t o o

low t o b e l o n g t o t h e T r a v e r s e L i m e s t o n e r e f l e c t i o n , o r

any r e f l e c t i o n s from g r e a t e r dep ths .

S e i s m o g r a m r e c o r d s f ro m d y n a m i t e w a l k away D-2 on

McKenzie Road ( F i g u r e 36) h a v e b e e n t r a c e mixed and

d i g i t a l l y b a n d - p a s s f i l t e r e d 7 5 - 2 0 0 h e r t z . L o c a t e d

b e t w e e n 300 and 350 m i l l i s e c o n d s on t h e s e c o n d and t h i r d

s e t o f t w e l v e t r a c e s , a r e f l e c t i o n i s o b s e r v e d s i m i l a r t o

t he r e f l e c t i o n e v e n t in t h e D-1 walk away ( F i g u r e 36).

Again t h i s e v e n t i s i n t e r f e r e d wi th by the lower v e l o c i t y

r e f r a c t e d a r r i v a l wave t r a i n in t h e l a s t few t r a c e s o f t h e

t h i r d s e t ( F i g u r e 36) . T2- X 2 a n a l y s i s o f t h i s e v e n t

( F i g u r e 37) g i v e s an RMS v e l o c i t y o f 6729 f t / s e c and a

depth o f 1098 f e e t .

The o p t i m u m wi nd o w f o r t h i s r e f l e c t e d e v e n t

r : ■'Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

78

Time (ms 400,000 ‘

Vave = 4129 F t/sec

Distance1' ( feet ) 000,0001,000,000

F i g u r e 35. Time S q u a r e d - D i s t a n c e Squared Graph of High Ampl i tude E v e n t s .

180,000

1 1i J. . J. ■■ »1 * T

Vrms = 6729 Ft/secTo = 326 msZ = 1098 f t

0 N3Gi500,000 Distance1u (feet)*" 1,100,000

F i g u r e 37'• Time S q u a r e d - D i s t a n c e Squared Graph ofI n t r e p r e t e d T r a v e r s e Limes t one R e f l e c t i o n A r r i v a l s From Walk Away D-2.


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c o r r e l a t e s w e l l wi th t h e window produced by t h e s y n t h e t i c

s e i s m o g r a m , and i s l o c a t e d b e t w e e n s o u r c e o f f s e t s o f 450

and 1000 f e e t .

Summary o f R e f l e c t i o n Analyses

S l e d g e hammer w a l k away s e i s m o g r a m s do n o t show a

r e f l e c t i o n i n t h e e x p e c t e d t i m e z o n e . T h i s f a c t i s

a t t r i b u t e d t o s o u r c e e n e r g y a t t e n u a t i o n by a t h i c k

o v e r b u r d e n o f g l a c i a l d r i f t . D y n a m i t e w a l k away

s e i s m o g r a m s a r e c o n s i s t e n t w i t h e a c h o t h e r and e x h i b i t a

r e f l e c t i o n i n t e r p r e t e d a s o r i g i n a t i n g n e a r t h e t a r g e t e d

z on e o f t h e T r a v e r s e L i m e s t o n e . The opt imum window i s

l i m i t e d on t h e f a r o f f s e t s i d e by a l ow RMS v e l o c i t y ,

h i g h - a m p l i t u d e e v e n t r e s e m b l i n g r e f r a c t e d a r r i v a l s .


INTERPRETATION OF PROFILING RECORDS

V e l o c i t y A n a l y s i s

Common o f f s e t , d ynami te s ou rce p r o f i l i n g r e c o r d s f rom

M a r c e l l u s and McKenzie Roads show a h i g h - a m p l i t u d e , low

RMS v e l o c i t y e v e n t c o v e r i n g up t o 250 m i l l i s e c o n d s of t h e

s e i s m o g r a m f o l l o w i n g t h e r e f r a c t e d a r r i v a l ( F i g u r e 38,

F i g u r e 39). The seismogram r e c o r d s shown in f i g u r e s 38 and

39 a r e u npr ocess ed 612 f t source o f f s e t p r o f i l i n g r e c o r d s

from t h e s tu dy a r ea .

T-X p l o t s ( F i g u r e 40) o f t h e a r r i v a l t i m e s of t h e

r e f r a c t e d wave and t h e h i g h a m p l i t u d e e v e n t s t h a t f o l l o w

a r e r e p r e s e n t a t i v e o f t h e p r o f i l i n g d a t a in g e n e r a l . These

l a t e r e v e n t s do n o t e x h i b i t n o r m a l m ov e o u t c u r v a t u r e on

t h e T-X d i a g r a m ( F i g u r e 4 0 ) . I f t h e s e e v e n t s a r e

r e f l e c t i o n s , a p l o t o f a r r i v a l t i m e s v e r s u s d i s t a n c e f rom

t h e s o u r c e s h o u l d a l l o w d e f i n i t i o n o f normal moveout on a

T-X graph . The s y n t h e t i c a l l y c a l c u l a t e d normal moveout

c u r v a t u r e f o r t h e T r a v e r s e Limestone r e f l e c t i o n i s e a s i l y

v i s i b l e on a T-X d i a g r a m ( F i g u r e 4 1 ) . The v e l o c i t i e s o f

j u s t above 8000 f t / s e c f o r t h e s e e v e n t s are s i m i l a r t o t h e

r e f r a c t e d wave v e l o c i t y (V3) o f 8372 f t / s e c as de t e r mi ne d

f o r t h e c l a y l a y e r i n t h e d r i f t . T h e s e v e l o c i t i e s a r e

a l s o c o m p a t i b l e wi th t h e a bedrock r e f r a c t e d wave v e l o c i t y

o f 9000 f t / s e c d e t e r min e d from s o n i c l o g s o f o i l w e l l s in

81


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Tine (ms) 500 T

200

Distance ( feet ) 1000600F i g u r e 40. T i me- Di s t anc e Graph of S e i s m i c A r r i v a l s From

Record 17 o f M a r c e l l u s Road P r o f i l i n g Seismograms.

Time (ms) 300 f

270Distance ( feet ) 1067.5366

F i g u r e 41. T i me- Dis t anc e Graph of S y n t h e t i c T r a v e r s eLimestone R e f l e c t i o n A r r i v a l s Showing Normal Moveout C u r v a t u r e .


84

A l l e g a n County, Mich i gan .

T2-X2 a n a l y s i s ( F ig u re 42) o f t h e s e e v e n t s g i v e s RMS

v e l o c i t i e s o f j u s t a b o v e 4000 f t / s e c . T h e se a r e l o w e r

t h a n e x p e c t e d r e f l e c t i o n v e l o c i t i e s as p r e d i c t e d by

s y n t h e t i c s e i smograms , and t h e walk away i n t e r p r e t a t i o n

o f the T r a v e r s e Li mes t one r e f l e c t i o n RMS v e l o c i t y o f 6000-

7000 f t / s e c .

S e i smi c r e c o r d s from f i g u r e s 38 and 39 t ime c o r r e c t e d

t o the f i r s t a r r i v a l s (F igure 43, F i g u r e 44) , d e m o n s t r a t e

t h e n e a r e q u i v a l e n t v e l o c i t i e s o f t h e q u e s t i o n e d e v e n t s .

The e v e n t s l i n e u p a c r o s s t h e r e c o r d s g i v i n g t h e

i mp r e s s i o n o f c o n t i n u o u s r e f l e c t i o n s . S le dg e hammer and

b u f f a l o gun p r o f i l e r e c o r d s from McKenzie Road have been

t i m e c o r r e c t e d t o t h e f i r s t a r r i v a l s ( F i g u r e 45 , F i g u r e

46) and r e s e m b l e t h e dynami te p r o f i l e r e c o r d s i n t h a t t h e

h i g h a m p l i t u d e e v e n t s h a v i n g s i m i l a r v e l o c i t i e s l i n e up,

g i v i n g t h e i m p r e s s i o n o f h o r i z o n t a l , c o n t i n u o u s

r e f l e c t o r s . P r o f i l i n g r e c o r d s s h o t on M a r c e l l u s and

McKenzie Roads t o t a l i n g o v e r 2 m i l e s o f s u r f a c e c ov e r a g e

f a i l e d t o show any s i g n i f i c a n t s e i s m i c a r r i v a l s o t h e r t han

t h e s e h i g h - a m p l i t u d e , l o w - v e l o c i t y e v e n t s .

The s o u r c e o f f s e t was a l t e r e d w i t h i n t h e opt imum

window t o a v o i d t h e masking o f d e s i r e d r e f l e c t i o n s i g n a l s

by t h e h i g h a m p l i t u d e e v e n t s . . F i r s t - a r r i v a l c o r r e c t e d ,

dynami te s o u r c e p r o f i l i n g r e c o r d s from McKenzie Road where


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Time (ms) 180,000 Y

Vrms = 4144

Vrms = 4463 Ft/se

Vrms ?= 4376 F t/sec

Vrms = 4376 F t/sec

Distance1" (fee t)360,000 950,000

F i g u r e 42 . Time S q u a r e d - D i s t a n c e Squared Graph o f High Ampl i tude Events From M a r c e l l u s Road P r o f i l i n g Seism ogram s.

ooU1

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F i g u r e 43. Dynamite Source P r o f i l i n g Seism ogram s From M a r c e l l u s Road Time C o r r e c t e d t o F i r s t A r r i v a l s .

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t h e s o u r c e o f f s e t was r e d u c e d t o 415 f e e t ( F i g u r e 47)

s t i l l e x h i b i t t h e low RMS v e l o c i t y , h i gh a m p l i t u d e e v e n t s .

U n p r o c e s s e d s e i s m i c r e c o r d s f rom n o r t h e r n M i c h i g a n

done by H os k i n g G e o p h y s i c a l o f Mt. P l e a s a n t , M i c h i g a n

( F i gu r e 48), e x h i b i t h i g h - a m p l i t u d e , l o w - v e l o c i t y e v e n t s

m i m i c k i n g t h e s h a p e o f t h e r e f r a c t e d a r r i v a l s i n t h e f a r

o f f s e t d a t a m o s t l y b e t w ee n 400 and 1000 m i l l i s e c o n d s .

Mann (1986) s t a t e d t h a t t h e s e e v e n t s a r e f a i r l y common i n

r e c o r d s s h o t i n M i c h i g a n , and p r o b a b l y o r i g i n a t e f rom

w i t h i n t h e d r i f t , p o s s i b l y a t t h e b e d r o c k - t i l l i n t e r f a c e .

Mann (1986) does not s p e c u l a t e on t h e a c t u a l mechanics o f

t h e i r o r i g i n .

A p p a r e n t l y th e s e e v e n t s ( F i g u r e 48) a r e t h e same t ype

as o b s e r v e d on r e c o r d s in t h e s t u d y a r e a , and a t e n t a t i v e

c o n c l u s i o n i s t h a t t h e y a r e r e l a t e d t o s p e c i f i c and l o c a l

g e o l o g i c c o n d i t i o n s t h a t a r e common w i t h i n t h e g l a c i a l

d r i f t i n Michigan .

Summary o f V e l o c i t y Ana l ys es

Root mean s q u a r e v e l o c i t i e s o f t h e h i g h - a m p l i t u d e

e v e n t s a r e s l o w e r t h a n e x p e c t e d f o r r e f l e c t i o n s f rom

w i t h i n t h e b e d r o c k . T-X p l o t s o f t h e a r r i v a l t i m e s do n o t

e x h i b i t normal moveout c u r v a t u r e , and t h e v e l o c i t i e s do n o t

i n c r e a s e w i t h t i m e a s e x p e c t e d f o r r e f l e c t e d a r r i v a l s .

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iii'iiilii ifcw n M n i nfci ’ i r i i i i f c y ' i i n m m T r i ~ i ~ r i T i Ji l m r r i n m if iiii 'B i’T i ^* wnMn iin M Jppjp!

F i g u r e 47. Dynamite Sour ce P r o f i l i n g Seismograms FromMckenzie Road ( s o u r c e o f f s e t = 415 f t . ) Time C o r r e c t e d t o F i r s t A r r i v a l s .


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92

The h i g h - a m p l i t u d e c o u p l e d w i t h t h e T-X v e l o c i t i e s o f

t h e s e e v e n t s c l o s e l y r e s e m b l e t h o s e o f t h e r e f r a c t e d

a r r i v a l s f rom t h e c l a y l a y e r i n t h e d r i f t , o r t h e b e d r o c k .

T h e s e f a c t s l e a d t o t h e c o n c l u s i o n t h a t t h e s e e v e n t s

o r i g i n a t e w i t h i n , or because of , c o n d i t i o n s i n t h e g l a c i a l

d r i f t . I n t e r f e r e n c e f rom t h e s e s e i s m i c e v e n t s makes

a p p l i c a t i o n o f t h i s r e f l e c t i o n p r o f i l i n g t e c h n i q u e

i n a d e q u a t e f o r m ap p i n g r e f l e c t i o n s o f f t h e T r a v e r s e

Li mes t one i n t h e s t u d y a r e a .

F u t u r e work i n i m p l e m e n t i n g t h i s r e f l e c t i o n s u r v e y

met hod w o u l d b e n e f i t g r e a t l y f rom an u n d e r s t a n d i n g o f

t h e s e h i g h - a m p l i t u d e , l o w - v e l o c i t y e v e n t s . The o r i g i n

w i l l be c o n s i d e r e d i n l i g h t of a m p l i t u d e and t r a v e l t i m e s

f o r v a r i o u s p o s s i b l e e v e n t s g i v e n t h e v e l o c i t y

d i s t r i b u t i o n i n t h e g l a c i a l d r i f t a s d e t e r m i n e d by

r e f r a c t i o n a n a l y s i s ( F i gu r e 20) .

Ampl i tude A n a l y s i s

Ampl i tude mode l i ng s e r v e s t o d i s t i n g u i s h t h e s e i s m i c

e v e n t s t h a t c o u l d p o s s i b l y be r e s p o n s i b l e f o r t h e l a r g e

a m p l i t u d e s e i s m i c e v e n t s r e c o r d e d . A s i m p l e model (F igu r e

49) i s a p l o t o f t h e r e l a t i v e a m p l i t u d e ( Ao/Ai ) o f s e i s m i c

e v e n t s v e r s u s the a n g l e o f i n c i d e n c e ( 0 i ) , where Ao i s t h e

i n i t i a l a m p l i t u d e and Ai i s t h e r e f l e c t e d o r r e f r a c t e d

a m p l i t u d e . Ampl i tude c u r v e s were c a l c u l a t e d by McCamy, e t


93

P - P R E F L E C T E D P - P REFRACTED

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Oi (degrees)

F i g u r e 49. R e l a t i v e Ampl i tude (Ao/Ai) Ver sus Angle o f I n c i d e n c e ( 0 i ) For t h e Model Case o f V1/V2 = . 522 , D e n s i t y R a t i o o f .757» C r i t i c a l Angle o f 31.5 Degrees (From McCamy e t a l . , 1962) .


94

a l . , ( 1962) f o r a mo de l c a s e o f : V1/V2 = . 522 , a d e n s i t y

r a t i o o f . 7 5 7 , and a c r i t i c a l a n g l e o f 31 . 50 d e g r e e s .

Ampl i t udes were c a l c u l a t e d by n u m e r i c a l methods s o l v i n g

t h e s i m u l t a n e o u s l i n e a r Z o e p p r i t z e q u a t i o n s which d e f i n e

t h e p a r t i t i o n i n g o f t h e a m p l i t u d e o f an i n c i d e n t wave

f r o n t a t an i n t e r f a c e ( A p p e n d i x A). The g e n e r a l

a p p l i c a b i l i t y o f t h e s e a m p l i t u d e c u r v e s by v e l o c i t y

c o n t r a s t a l o n e i s d e m o n s t r a b l e f r o m s t u d i e s o f t h e

v e l o c i t y v s . d e n s i t y r e l a t i o n (Ta lwani e t a l . , 1959).

From r e f r a c t i o n a n a l y s i s , v e l o c i t y r a t i o s o f .572 fo r

t h e d r i f t - c l a y l a y e r i n t e r f a c e and .532 f o r t h e d r i f t -

bed ro ck i n t e r f a c e were c o n s i d e r e d i n ch oo s in g t h i s s e t of

c u r v e s t o mode l t h e a m p l i t u d e r e s p o n s e o f t h e g l a c i a l

d r i f t i n t e r f a c e s i n t h e s t u d y a r e a . A n a l y s i s o f t h e s e

c u r v e s show t h a t t h e a m p l i t u d e o f t he r e f r a c t e d P-wave i s

g r e a t e r t h a n any o t h e r e v e n t up t o t h e c r i t i c a l a n g l e .

From t h e c r i t i c a l a n g l e t o 35 d e g r e e s i n c i d e n c e t h e P-wave

r e f l e c t e d e v e n t e x h i b i t s an a m p l i t u d e g r e a t e r t h a n t h e

r e f r a c t e d wave i n t h e zone p r e c e d i n g i t s a p p r o a c h t o t h e

c r i t i c a l a n g l e . The r e f l e c t e d s h e a r wave produced by an

i n c i d e n t P-wave i s o f t e n r e f e r r e d t o as a " c o n v e r t e d wave"

and h a s b e e n n o t e d by Dohr and J a n i e (1980) a s a d i s t i n c t

a r r i v a l in c o n d i t i o n s of a h i g h v e l o c i t y c o n t r a s t , such as

a d r i f t - b e d r o c k i n t e r f a c e . Dohr and J a n i e (1980) s t a t e d

V------------- ~~ : .....i


95

t h a t t h e a m p l i t u d e o f a c o n v e r t e d wave i s s t r o n g o n l y a t

l a r g e s o u r c e o f f s e t s , i . e . , l a r g e a n g l e s o f i n c i d e n c e . In

t h e w i d e - a n g l e zone between 35-55 d e g r e e s i n c i d e n c e t h e S-

r e f l e c t e d ( c o n v e r t e d ) wave has an a m p l i t u d e g r e a t e r t h an

t h e a m p l i t u d e of the r e f l e c t e d P-wave.

A m p l i t u d e m o d e l i n g s u g g e s t s t h a t a P-wave i n c i d e n t

b e t w e e n 30 and 35 d e g r e e s on t h e c l a y l a y e r or b e d r o c k

i n t e r f a c e s c o u l d be r e s p o n s i b l e f o r a P-P r e f l e c t i o n

a r r i v a l comparab l e i n a m p l i t u d e t o the r e f r a c t e d P-wave.

Al so , a P-wave i n c i d e n t between 35 and 55 d e g r e es c o u l d be

r e s p o n s i b l e f o r a P-S r e f l e c t i o n a r r i v a l c o m p a r a b l e i n

a m p l i t u d e t o t h e r e f r a c t e d P-wave.

Raypath Model ing

The v e l o c i t y d i s t r i b u t i o n model f o r t h e g l a c i a l d r i f t

as i n t e r p r e t e d from r e f r a c t i o n a n a l y s i s ( F i gu r e 50) shows

r a y p a t h s o f r e f l e c t e d P-waves wi th a n g l e s of i n c i d e n c e of

30 and 35 d e g r e e s . T h i s mode l s u g g e s t s t h a t P-wave

r e f l e c t i o n s o f f t h e c l a y l a y e r and b e d r o c k i n t e r f a c e s

be tween t h e s e a n g l e s o f i n c i d e n c e c o u l d n o t be r e s p o n s i b l e

f o r t h e e v e n t s r e c o r d e d a t a s o u r c e o f f s e t o f 612 f e e t .

I f r e s p o n s i b l e , t h ey would e x h i b i t normal moveout and a T-

X v e l o c i t y of r o u g h l y M000 f t / s e c , which i s a bo ut 1/2 t h e

T-X v e l o c i t y of t h e q u e s t i o n e d e v e n t s .

A r a y p a t h mode l o f c o n v e r t e d w av es p r o d u c e d by P-

_ . _ - - -

k ■Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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612 feet

V = 1265 f t / sec

V = 4791 f t / sec 100—

150 -

V = KM? f t . /spc ■20tT

V = 4791 f t / sec250

300—V = 9000 f t / sec

350 “1" = 100U.S.

F i g u r e 50 . V e l o c i t y D i s t r i b u t i o n Model o f G l a c i a l D r i f t i n t h e Study Area With Raypa ths o f P-Waves I n c i d e n t a t 30 and 35 Degr ees .

612 fe e tV = 1265 f t / s ec

V = 4791 f t / s ec100

150

■ m

V = 4791 f t / s ec250

300V = 9000 f t / sec

350V.S. 1" = 100

F i g u r e 51. V e l o c i t y D i s t r i b u t i o n Model o f G l a c i a l D r i f t i n t h e S tudy Area With Raypa ths o f Conver t ed Waves i n c i d e n t a t 35 and 55 Degrees .

98

w a v e s i n c i d e n t b e t w e e n 3 5 - 5 5 d e g r e e s ( F i g u r e 51) i s

c a l c u l a t e d f o r a P-wave v e l o c i t y / S - w a v e v e l o c i t y r a t i o o f

1.85. Th i s v a l u e i s t a k e n f rom t a b u l a t e d v a l u e s o f P and

S- wave v e l o c i t i e s in a g l a c i a l m o r r a i n e by P a r a s n i s

( 1972) . Not e t h a t a c o n v e r t e d wave r e f l e c t i o n o f f t h e

b e d r o c k d o e s n o t o c c u r f o r i n c i d e n t a n g l e s g r e a t e r t h a n

the c r i t i c a l a n g l e a s s o c i a t e d w i t h t h e c l a y l a y e r . Thi s

model d e m o n s t r a t e s t h a t i t i s i m p o s s i b l e f o r a c o n v e r t e d

wa v e , p r o d u c e d by a P- wave i n c i d e n t be twe en 35 and 55

d e g r e e s , t o be r e s p o n s i b l e f o r t h e h i g h a m p l i t u d e e v e n t on

t h e p r o f i l i n g r e c o r d s , whe r e t h e s o u r c e o f f s e t i s 612

f e e t .

Assuming t h e q u e s t i o n e d e v e n t i s n o t a r e f l e c t i o n ,

b u t i s a r e f r a c t e d a r r i v a l t r a v e l l i n g a t a v e l o c i t y

s i m i l a r t o t h e c l a y l a y e r and b e d r o c k v e l o c i t i e s , an

e x p l a n a t i o n of i t s o r i g i n i s l i m i t e d t o m u l t i p l e phenomena

s e r v i n g t o d e l a y r e f r a c t e d a r r i v a l s f rom t h e c l a y l a y e r o r

b e d r o c k i n t e r f a c e s . A r a y p a t h m o d e l o f p o s s i b l e n e a r

s u r f a c e and i n t e r f o r m a t i o n a 1 m u l t i p l e s ( F i g u r e 52) i s

c a l c u l a t e d f o r a n g l e s o f i n c i d e n c e l e s s t h an t h e c r i t i c a l

a n g l e a s s o c i a t e d w i t h t h e c l a y l a y e r . Any, an d

c omb in a t i on s o f a l l of t h e s e m u l t i p l e s can c o n t r i b u t e t o

d e l a y s i n r e f r a c t e d wave a r r i v a l s . However, t h e r e g u l a r

p e r i o d of abou t 40 m i l l i s e c o n d s e x h i b i t e d by t he e v e n t s on

t he s e i s m i c r e c o r d s s u g g e s t s a c y c l i c o r r e g u l a r d e l a y i n


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i

612 feetV = 1265 f t / s ecR=.38

V = 4791 f t / s ec100

150 "R=.13

V = H37Z f t / s e c 7 m

V = 4791 f t / s ec250

R=.18300 —

V = 9000 f t / s ec350—

= 100V.S.

F i g u r e 52 . V e l o c i t y D i s t r i b u t i o n Model o f G l a c i a l D r i f t i n t h e Study Area With Raypa ths o f P o s s i b l e N e a r - S u r f a c e and I n t e r f o r m a t i o n a l M u l t i p l e s I n c i d e n t a t 35 Degrees .

100

t h e r e f r a c t e d a r r i v a l s .

R a y p a t h m o d e l i n g ( F i g u r e 52) s u g g e s t s two s i m p l e

m e c h a n i s m s o f m u l t i p l e e v e n t s c a p a b l e o f p r o d u c i n g a

c y c l i c d e l a y g i ve n t h e assumed v e l o c i t y d i s t r i b u t i o n : a

s e r i e s o f n e a r - s u r f a c e m u l t i p l e s d e l a y i n g t h e s e i s m i c

s i g n a l b e f o r e o r a f t e r r e f r a c t i o n , o r a s e r i e s o f

i n t e r f o r m a t i o n a l m u l t i p l e s i n t h e low v e l o c i t y z one

b e t w e e n t h e c l a y l a y e r and b e d r o c k d e l a y i n g t h e b e d r o c k

r e f r a c t i o n . In each c a s e t h e d e l a y s p roduced a r e e q u a l t o

t h e t r a v e l t i m e f o r one m u l t i p l e . S u c c e s s i v e m u l t i p l e s

c o u l d produce r e f r a c t e d a r r i v a l s wi th an a p p a r e n t p e r i o d

e q u a l t o t h e t r a v e l t ime o f t he m u l t i p l e .

Near S u r f ac e M u l t i p l e s

Assuming a v e l o c i t y i n t h e u n s a t u r a t e d n e a r - s u r f a c e

d r i f t o f 1265 f t / s e c and i n t h e s a t u r a t e d d r i f t o f 4791

f t / s e c a l o n g w i t h a v e r a g e d e n s i t i e s o f 1.6 g / cm^ and 1.8

g / cm^ t a k e n f rom T e l f o r d e t a l . ( 1 9 7 6 ) , t h e c a l c u l a t e d

r e f l e c t i o n c o e f f i c i e n t (R) o f .38 f o r t h e w a t e r t a b l e i s

q u i t e h i g h and s u p p o r t s p o s s i b i l i t i e s o f n e a r - s u r f a c e

m u l t i p l e s . The n e a r - s u r f a c e m u l t i p l e mechan i sm may be

s i g n i f i c a n t i n c e r t a i n c a s e s , b u t i t does n o t e x p l a i n t he

a b s e n c e of t h e s e t y p e s o f a r r i v a l s i n g l a c i a l t e r r a n e

where t h e wa t er t a b l e i s n o t a t t h e s u r f a c e . Based on t h e

r andom o c c u r r e n c e o f t h e s e t y p e s o f e v e n t s i n w i d e l y

I .


s c a t t e r e d s e i s m i c s t u d i e s t h r o u g h o u t M i c h i g a n by Mann

( 1 9 8 6 ) , t h i s m echan i sm i s p r o b a b l y n o t an a c c e p t a b l e

e x p l a n a t i o n o f t h e o r i g i n o f t h e q u e s t i o n e d s e i s m i c e v e n t s .

I n t e r f o r m a t i o n a l M u l t i p l e s

Assuming a d r i f t v e l o c i t y o f 4791 f t / s e c b e l o w t h e

c l a y l a y e 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 f o r t h e d r i f t -

bedrock and c l a y l a y e r - d r i f t i n t e r f a c e s o f .18 and .13 a r e

s i g n i f i c a n t , a l t h o u g h n o t as l a r g e a s t h e r e f l e c t i o n

c o e f f i c i e n t a t t h e w a t e r t a b l e . Based on t h i s v e l o c i t y ,

t h e m u l t i p l e r a y p a t h ( F i g u r e 52) a s s o c i a t e d w i t h t h i s

v e l o c i t y l a y e r can o n l y bounce once b e f o r e t r a v e l l i n g as a

c r i t i c a l l y r e f r a c t e d wave a l o n g t h e b e d r o c k i n t e r f a c e .

T h a t i s , o n l y one m u l t i p l e e v e n t , i n s t e a d o f a s e r i e s o f

e v e n t s , would a r r i v e a t a l l t w e l v e geophones o f f s e t from

t h e s ou rc e 612 f e e t .

P r e v i o u s T2-X2 a n a l y s i s ( F i gu r e 33) o f t h e r e f l e c t i o n

as i n t e r p r e t e d on dynami te walk away r e c o r d s gaye a d ep t h

o f o r i g i n o f 1000 f e e t and an RMS v e l o c i t y o f 6200 f t / s e c .

T h i s v e l o c i t y i s o v e r 1000 f t / s e c s l o w e r t h a n t h e RMS

v e l o c i t y o f 7372 f t / s e c p r e d i c t e d f o r t h e T r a v e r s e

Limes tone r e f l e c t i o n . The s y n t h e t i c model from which t h i s

p r e d i c t i o n came i s p a r t l y b a s e d on t h e p r e v i o u s , and

p o s s i b l y e r r o n e o u s , a s s u m p t i o n t h a t t h e v e l o c i t y o f t h e

d r i f t s e p a r a t e d by t h e c l a y l a y e r i s t h e same on b o t h

1 .


102

s i d e s . A s y n t h e t i c seismogram wi th a d r i f t v e l o c i t y be low

t h e c l a y l a y e r o f 3000 f t / s e c g i v e s an RMS v e l o c i t y f o r

t h e T r a v e r s e r e f l e c t i o n o f 6900 f t / s e c .

U s i n g t h e v e l o c i t y o f 3000 f t / s e c i n t h e r a y p a t h

model ( F igur e 53) r e f l e c t i o n c o e f f i c i e n t s o f the c l a y and

b e d r oc k i n t e r f a c e s become .30 and .36, r e s p e c t i v e l y . The

c r i t i c a l a n g l e i s r edu ced to 20 d e g r e e s a l l o w i n g s e v e r a l

b o u n c e s a t t h e c r i t i c a l a n g l e c a p a b l e o f p r o d u c i n g

m u l t i p l y - d e l a y e d , r e f r a c t e d a r r i v a l s w i t h a r e g u l a r p e r i o d

e q u a l t o t h e bounce t ime in t h e low v e l o c i t y l a y e r .

Thi s mechanism of m u l t i p l e s i n t h e low v e l o c i t y zone

above t h e bedrock p r o v i d e s a f a i r l y s i mp l e e x p l a n a t i o n of

t h e r e g u l a r p e r i o d , a p p a r e n t v e l o c i t y , l a c k o f n o r m a l

moveout , and r e l a t i v e l y high a m p l i t u d e of t h e q u e s t i o n e d

e v e n t s . T h i s mechan is m i s d e p e n d e n t on an i n t e r p r e t e d ,

s p e c i f i c and l o c a l g e o l o g i c c o n d i t i o n i n t h e g l a c i a l

d r i f t , namely t h e p r e s e n c e o f a c o n t i n u o u s , h i gh v e l o c i t y

c l a y l a y e r u n d e r l a i n by lower v e l o c i t y g l a c i a l m a t e r i a l

t o b e d r o c k . C o n d i t i o n s s i m i l a r t o t h e s e a r e p r o b a b l y

common, b u t not p e r v a s i v e , t h r o u g h o u t t h e g l a c i a l d r i f t i n

Mich igan .


Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

Depth ( f t )612 feetV = 1265 f t / sec

V = 4791 f t / sec100—

150 -

V = 8372 f l / SETT 2 WR=.30

V = 3000 f t / sec 250—

R=.36

V = 9000 f t / s ec

350V.S. 1" = 100'

F i g u r e 53 . V e l o c i t y D i s t r i b u t i o n Model o f G l a c i a l D r i f t i n t h e Study Area With Raypaths o f P o s s i b l e M u l t i p l e I n c i d e n t a t 20 Degr ees .

103

104

REMOVING THE MULTIPLES

C o n v e n t i o n a l means o f d e a l i n g w i t h h i g h - a m p l i t u d e ,

l o w - v e l o c i t y s e i s m i c m u l t i p l e s a r e c o m m o n - d e p t h - p o i n t

(CDP) p r o c e s s i n g c o u p l e d w i t h F/K ( v e l o c i t y ) f i l t e r i n g .

G r o u n d r o l l i s s u p p r e s s e d by a c o m b i n a t i o n o f l o w - c u t

f r e q u e n c y f i l t e r i n g and w a v e - n u m b e r f i l t e r i n g , which i s

s i m p l y t h e t y p e o f d i s c r i m i n a t i o n a c c o m p l i s h e d by CDP

s t a c k i n g .

F r e q u e n c y / R e c i p r o c a l o f W a v e l e n g t h ( F / K ) f i l t e r s a r e

v e l o c i t y f i l t e r s f o r removing c o h e r e n t n o i s e on r e f l e c t i o n

r e c o r d s t h a t has a d i f f e r e n t a p p a r e n t moveout o r a p p a r e n t

v e l o c i t y t h a n t h e d e s i r e d r e f l e c t i o n e v e n t s . The t i m e

d i f f e r e n t i a l f o r a p a r t i c u l a r e v e n t b e t w e e n a d j a c e n t

t r a c e s i s the c r i t e r i o n on which t h e f i l t e r i n g o p e r a t i o n

i s based . F/K f i l t e r s a r e based on p l o t s o f wave numbers

( r e c i p r o c a l of wave le ng t h - K) v e r s u s f r e q u e n c y (F) which i s

e f f e c t i v e l y a c o n v e n t i o n a l t i m e - d i s t a n c e p l o t r o t a t e d by

90 d e g r e e s . Th i s i s c a l l e d an F/K p l o t and t h e s l o p e s o f

t h e l i n e s are p r o p o r t i o n a l t o t h e a p p a r e n t v e l o c i t i e s o f

t h e e v e n t s , r a t h e r t h a n t h e r e c i p r o c a l o f t h e a p p a r e n t

v e l o c i t i e s , as on a T-X p l o t (Dobrin, 1976). R e f l e c t i o n s

n o r m a l l y h a v e a s m a l l m o v e o u t a c r o s s a r e c o r d , and f a l l

w i t h i n a narrow wedge c e n t e r e d on t h e v e r t i c a l a x i s o f t h e

F/K p l o t . High v e l o c i t y n o i s e g e n e r a l l y f a l l s w i t h i n a

i ■.


wedge o f i n t e r m e d i a t e s l o p e ( F i g u r e 54) . F/K v e l o c i t y

f i l t e r s p r o v i d e a means o f s u p p r e s s i n g h i g h a p p a r e n t

v e l o c i t y n o i s e w i t h o u t d e t r i m e n t t o r e f l e c t i o n s i g n a l

q u a l i t y . Thus , c o n v e n t i o n a l s e i s m i c p r o c e s s i n g o f CDP

d a t a a u t o m a t i c a l l y removes t h e e f f e c t s of t h e s e t y p e s o f

m u l t i p l e e v e n t s .

B a r r i n g use of CDP p r o f i l i n g and v e l o c i t y f i l t e r i n g ,

an a l t e r n a t i v e f o r t h e e n g i n e e r i n g g e o p h y s i c i s t i s t o

r e m o v e t h e e f f e c t s o f t h e g r o u n d r o l l . Removing t h e

g r o u n d r o l l opens t h e t i m e zone w i t h i n the l o w - a n g l e zone

o f i n c i d e n c e f o r r e f l e c t i o n s , a l l o w i n g r e c o r d i n g o f

r e f l e c t i o n s w i t h o u t i n t e r f e r e n c e from t h e m u l t i p l y - d e l a y e d

r e f r a c t e d wave o r i g i n a t i n g f rom t h e b e d r o c k i n t e r f a c e .

A l t h o u g h , t h e same m u l t i p l e s p r o d u c i n g t h e m u l t i p l y

d e l a y e d r e f r a c t e d wave may t h e n be r e c o r d e d a s m u l t i p l e

r e f l e c t i o n s . R e m o v i n g t h e g r o u n d r o l l c a n n o t be

a c c o m p l i s h e d by l o w - c u t f i l t e r s a l o n e , due s im pl y t o t h e

magni tude o f t he g r o u n d r o l l . The summing o f a t l e a s t two

geophone r e s p o n s e s i s r e q u i r e d t o c a n c e l g r o u n d r o l l .

Knapp a nd S t e e p l e s ( 1 9 8 6 a ) h a s h a d s u c c e s s i n

r e m o v i n g t h e g r o u n d r o l l by " g e o p h o n e d i f f e r e n c i n g . "

Geophone d i f f e r e n c i n g i n v o l v e s t a k i n g t h e d i f f e r e n c e o f

t h e o u t p u t r e s p o n s e o f two g e o ph o ne e l e m e n t s t h a t a r e

v e r t i c a l l y s e p a r a t e d by a s m a l l d i s t a n c e . This t e c h n i q u e

a t t e n u a t e s h o r i z o n t a l l y p r o p a g a t i n g e ne r gy ( g r o u n d r o l l ) as


Reproduced

with perm

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i

\ \ SIGNAL RANGE / X\

Cu \ \ *°

\ % *e . \ \ \ V / V /o / / * /\ V A \ \ 4

\ > \ \ * *

\ jt \ \ o \ ^ V \ \ p

° / / ^ / V / .? /

* / / > Xt / / > /

♦ / / ^ /

* 7 / * /t / / /

K—

F i g u r e 5M. R e c i p r o c a l o f Wavelength (K) Versus Frequency (F) C a l l e d an F/K P l o t (From Do br in , 1976) .

oo \

107

i t i s r e c e i v e d by t h e two g e o p h o n e s i n - p h a s e and i s

s u b t r a c t e d ou t . V e r t i c a l l y p r o p a g a t i n g e n e r g y , however ,

i s s l i g h t l y phase s h i f t e d due t o t h e geophone s e p a r a t i o n ,

and d i f f e r e n c i n g o f t h e r e f l e c t i o n s i g n a l r a t h e r t h a n

c a n c e l l a t i o n r e s u l t s ( K n a p p an d S t e e p l e s , 1 9 8 6 d ) .

E x p e r i m e n t a l r e s u l t s (Knapp and S t e e p l e s , 1986) s u g g e s t

t h a t a b u r i a l d e p t h o f 3 f e e t i s d e e p enough t o p r e v e n t

d i f f e r e n c i n g from i n t e r f e r i n g wi th t h e r e f l e c t i o n s i g n a l .

Geophone d i f f e r e n c i n g a t t e n u a t e s the g r o u n d r o l l and has a

g e n t l e h i g h - p a s s f i l t e r i n g e f f e c t on P-waves.

The a p p l i c a t i o n o f t h i s m e t h o d f o r r e f l e c t i o n

p r o f i l i n g wi th l i m i t e d s e i s m i c c a p a b i l i t y sys tems as used

i n t h i s s t u d y w o u l d r e q u i r e t h e u s e o f a s m a l l and v e r y

m ob i l e d r i l l r i g f o r d r i l l i n g t h e s m a l l d i a m e t e r s h a l l o w

h o l e s n e c e s s a r y t o b u r y a g e o ph on e a t d e p t h . A s p e c i a l

s e t o f geophone t u b e s would a l s o be needed f o r t h e b u r y i n g

of one geophone a t d e p t h .

ir ■ " ■ '' ■ “ * - - - ■ ...........................................r •I-:it


CONCLUSIONS

S l ed ge hammer, b u f f a l o gun and b l a s t i n g cap s o u rc e s

p r o d u c e a s e i s m i c p u l s e r i c h i n h i g h f r e q u e n c i e s o f 100

h e r t z and above. However, i n s e i s m i c p r o f i l i n g t o l o c a t e

an i n t r a - b e d r o c k r e f l e c t o r ( T r a v e r s e L i m e s t o n e ) t h r o u g h

r e l a t i v e l y t h i c k g l a c i a l d r i f t (<500 f t ) , t h e o v e r a l l

e n e r g y p r o d u c e d by t h e s e s o u r c e s i s n o t g r e a t en ou g h t o

n e g a t e a t t e n u a t i o n o f t h e s i g n a l by t h e d r i f t i n t h e s t u d y

a r e a .

A s c a l e d down c h a r g e s i z e o f d y n a m i t e c o n t a i n s

s u f f i c i e n t e n e r g y and i s s i g n i f i c a n t i n i n c r e a s i n g t h e

h i g h f r e q u e n c y compon en t o f t h e s e i s m i c p u l s e , a l l o w i n g

t h e p o s s i b i l i t y of b e t t e r r e s o l u t i o n .

The a p p l i c a t i o n o f t h e opt imum window t e c h n i q u e o f

r e f l e c t i o n p r o f i l i n g was n o t s u c c e s s f u l in l o c a t i n g i n t r a

b e d r o c k r e f l e c t i o n s i n t h e s t u d y a r e a . The m e t h o d

p r o b a b l y f a i l e d due t o l o c a l c o n d i t i o n s i n t h e g l a c i a l

d r i f t c r e a t i n g a l ow RMS v e l o c i t y , h i g h - a m p l i t u d e e v e n t

masking r e f l e c t i o n a r r i v a l s i n t he optimum window zone .

The l o c a l c o n d i t i o n in t h e d r i f t i s i n t e r p r e t e d from

r e f r a c t i o n a n a l y s i s t o be a v e l o c i t y i n v e r s i o n caused by a

r e l a t i v e l y t h i n , c o n t i n u o u s , dense c l a y l a y e r w i t h i n t h e

d r i f t , t h e l o w v e l o c i t y zone b e l o w t h e c l a y l a y e r and

a b o v e t h e b e d r o c k i s t h e g e n e r a t o r o f i n t e r f o r m a t i o n a l

108


m u l t i p l e s s e r v i n g t o d e l a y s u c c e s s i v e r e f r a c t i o n s from th e

bed r ock i n t e r f a c e . The m u l t i p l y - d e l a y e d r e f r a c t i o n s a r e

i n t e r p r e t e d as t h e h i g h a m p l i t u d e evfents which f i l l up the

optimum window zone.

S i m i l a r c o n d i t i o n s in t h e g l a c i a l d r i f t a r e c e r t a i n l y

common t h r o u g h o u t Michigan , and c o u l d s i g n i f i c a n t l y d e t e r

a t t e m p t s at r e f l e c t i o n p r o f i l i n g u s i n g t h e optimum window

method.

S o l v i n g t he p r ob lem o f t h e h i g h - a m p l i t u d e m u l t i p l e s

w o u l d r e q u i r e a b a n d o n i n g t h e opt imum window p r o f i l i n g

met hod and w o r k i n g i n t h e low i n c i d e n t a n g l e g r o u n d r o l l

z o n e . A method f o r c a n c e l l i n g g r o u n d r o l l by Knapp and

S t e e p l e s ( 1 9 8 6d) may be e f f e c t i v e . U t i l i z a t i o n o f t h i s

me thod w o u l d r e q u i r e t h e a d d i t i o n o f m o b i l e d r i l l i n g

e q u i p m e n t a n d p o s s i b l y a new g e o p h o n e s e t u p t o t h e

s t a n d a r d se i smograph equipment .


Appendix

Z o e e p r i t z Ampl i tude E q u a t i o n s

110

r : ~ " .Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

111

The equations were taken after Richter (1958).

for incident P,

(A — C) sin a + D cos 6 — K sin e + F cos/ = 0

(A + C) cos a + 1) sin b — E cos c — / ’sin / = 0

- ( .4 + C) sin 2 a + 2 ) ^ cos 2b + EK ]J-‘sin 2e - FK ( j £ j cos2 / = 0

- ( A - C) cos 2b + D p sin 2b + EK cos 2/ + FK sin 2f = 0t 1 r l I i

and for incident SF,

(B + D) sin b + (' cos a — E cos e — F sin/ = 0

(B — D) cos b + C sin a + E sin e — F cos/ = 0

(B + D) cos 26 - e iy i sin 2a + EK , sin 2e - FK cos 2/ = 0 Vi iiV-2 Ui J

— (B — D) sin 26 + C Yl cos 26 + A’A' £ cos 2 / + FA sin 2/ = 0.k i Ci Ci

Where .4 and B arc the amplitudes of P and AT, incident at angles a and 6 respectively and C, D, E, F, are the amplitudes of the resultant rays, reflected P, reflected AT, refracted P and refracted AT, at angles a, 6, e, and /. V i , t ' i , Vi and l \ are the P and AT velocities in the first and second layers respectively. K is the ratio of the density of the second layer to the density of the first. The angles a, 6, e, / are related by Snell’s Law:

sin a _ sin 6 _ sin e _ sin /T i 0 7 ’~~V, (77 ■


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112


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