1. Tom Wilson, Department of Geology and Geography Environmental and Exploration Geophysics II tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Time-distance relationships Ray-tracing Don’t forget to visit the web site for slides and other info - http://www.geo.wvu.edu/~wilson/geol554/lect3/lec3.pdf

2. Tom Wilson, Department of Geology and Geography I’m often in my office, so feel free to drop by. To be sure I’m not tied up with something send me an e-mail in advance.

3. Tom Wilson, Department of Geology and Geography Quick Review …

4. Tom Wilson, Department of Geology and Geography Data are collected in shot record form so our initial goal is to develop an understanding of the different types of events that appear in a shot record and to understand how their travel times (t) vary with source receiver offset (x).

5. Tom Wilson, Department of Geology and Geography Some shallow high res data from Marshall Co. WV

6. Tom Wilson, Department of Geology and Geography

7. Another record from the Marshall Co. site

8. Tom Wilson, Department of Geology and Geography Migrated stack display- The “geological” display

9. Tom Wilson, Department of Geology and Geography Routine logs ( , , resistivity, July, 07). Sonic Scanner for Acoustic and Mechanical Properties (March, 08) Geophysical Characterization Logging Effort

10. Tom Wilson, Department of Geology and Geography Schematic Schlumberger Sonic Scanner

11. Tom Wilson, Department of Geology and Geography Pittsburgh Coal The Poisson ratio of ~0.4 is what we would expect for a coal, but the Young’s Modulus is much too high. Geophysical Characterization Mechanical Properties

12. Tom Wilson, Department of Geology and Geography The synthetic seismogram

13. Tom Wilson, Department of Geology and Geography A shot record is a recording of ground movements produced by a single shot (mechanical disturbance created at some point on or near the earth’s surface). The recording is made at several locations ideally along a straight line extending in either or both directions away from the source. You’ll get plenty of chances to interpret data but remember that one of the class objectives is to understand the basics of reflection seismology – so …

14. Tom Wilson, Department of Geology and Geography How will the travel times of the direct arrival vary with offset? What will a direct arrival look like in a time distance plot?

15. Tom Wilson, Department of Geology and Geography Direct Arrival shot record Also need to consider the type of direct arrival...

16. Tom Wilson, Department of Geology and Geography Time Distance Plot Direct Arrival

17. Tom Wilson, Department of Geology and Geography The reflection event and its time distance relationships- The reflection law These chalk board slides are just for reference. I’ll set this up independently in class and you’ll find prettier notes in the text.

18. Tom Wilson, Department of Geology and Geography The image point

19. Tom Wilson, Department of Geology and Geography V1V1 The image point

20. Tom Wilson, Department of Geology and Geography Triangles come in quite handy in geophysics

21. Tom Wilson, Department of Geology and Geography Seismic reflections have a hyperbolic shape in their time-distance representation.

22. Tom Wilson, Department of Geology and Geography Reflection time distance curve in basic hyperbolic form

23. Tom Wilson, Department of Geology and Geography Some basic math probably worth seeing again

24. Tom Wilson, Department of Geology and Geography Location of the apex in time

25. Tom Wilson, Department of Geology and Geography As time goes by reflection events approach start to come in linearly with time. They approach the asymtotes of the hyperbola

26. Tom Wilson, Department of Geology and Geography The direct arrival has the relationship of an asymptote to the arrival times of the reflection event.

27. Tom Wilson, Department of Geology and Geography From the basic time-distance relationship When x = 0, which is the time intercept.

28. Tom Wilson, Department of Geology and Geography When x becomes very large with respect to the thickness of the reflecting layer, the x 2 /V 2 term becomes much larger than the 4h 2 /V 2 term so that

29. Tom Wilson, Department of Geology and Geography The single layer refraction time- distance relationship - but first -

30. Tom Wilson, Department of Geology and Geography The c’s cancel out and we have...

31. Tom Wilson, Department of Geology and Geography One of our assumptions - Assume V 1 < V 2 < V 3

32. Tom Wilson, Department of Geology and Geography

33. because sin(  /2) = 1

34. Tom Wilson, Department of Geology and Geography Critical Refraction

35. Tom Wilson, Department of Geology and Geography With the direct arrival and the single layer reflection we travel from point A to B with constant velocity The critical refraction problem is still a simple distance over velocity function, but the velocity changes on us.

36. Tom Wilson, Department of Geology and Geography V1V1 V2V2 Isolating travel paths based on velocity

37. Tom Wilson, Department of Geology and Geography The slant path length

38. Tom Wilson, Department of Geology and Geography The path along the interface

39. Tom Wilson, Department of Geology and Geography Sum them together

40. Tom Wilson, Department of Geology and Geography Variables and constants

41. Tom Wilson, Department of Geology and Geography Direct Arrival 2 1 Which of the two lines have the correct relationship of the critical refraction to the direct arrival? time x – source receiver offset distance

42. Tom Wilson, Department of Geology and Geography Trig functions and velocity ratios

43. Tom Wilson, Department of Geology and Geography Snell's law gives us an easy way to look trig functions in the critical triangle

44. Tom Wilson, Department of Geology and Geography Going through the algebraic substitution the constants in our earlier expression are represented in terms of velocity instead of critical angle.

45. Tom Wilson, Department of Geology and Geography The critical or minimum distance

46. Tom Wilson, Department of Geology and Geography Determining the critical distance

47. Tom Wilson, Department of Geology and Geography Putting all these events together in the time-distance plot reveals useful information content in the shot record.

48. Tom Wilson, Department of Geology and Geography Basic time-distance relationships for the refracted wave - Single horizontal interface 1) straight line 2) Refraction and reflection arrivals coincide at one offset 3) Refraction arrivals follow a straight line with 4) slope 1/V 2, where 5) 1/V 2 is less than 1/V 1

49. Tom Wilson, Department of Geology and Geography Diffraction (point source) Events

50. Tom Wilson, Department of Geology and Geography Diffractions, like reflections are hyperbolic in a time-distance plot. They are usually symmetrical about the apex. Diffractions usually arise from point-like discontinuities and edges ( for example the truncated edges of stratigraphic horizons across a fault).

51. Tom Wilson, Department of Geology and Geography For next time give some thought to the mathematical representation of the diffraction response.

52. Tom Wilson, Department of Geology and Geography From prediction to observation

53. Tom Wilson, Department of Geology and Geography Miller et al. 1995 Can you name the events?

54. Tom Wilson, Department of Geology and Geography This is a shot record from the Granny Creek oil field in Clay Co. WV. What kinds of acoustic events can you recognize in this shot record? Where is the source?

55. Tom Wilson, Department of Geology and Geography We start off with these noisy looking field records and with some effort get a more geological look at the subsurface

56. Tom Wilson, Department of Geology and Geography Hopefully these shot data make a little more sense

57. Tom Wilson, Department of Geology and Geography

58. INTRODUCTORY RAY TRACING EXERCISES (I -VI) GENERAL INSTRUCTIONS These exercises are designed to illustrates some of the basic characteristics of wave propagation in a single layer model use ray-tracing concepts to determine the arrival times of particular events. These exercises require that you construct the time-distance plot for the given model (I - VI). In addition to constructing the time-distance plots, For next time do ray-trace exercises I, II and III

59. Tom Wilson, Department of Geology and Geography

61. Be sure to do the following 1) label all plotted curves, 2) label all relevant points, and 3) in a paragraph or so discuss the significance and origins of the interrelationships portrayed in the resultant time-distance plots

62. Tom Wilson, Department of Geology and Geography In exercise II for example, how do you account for the differences in the two reflection hyperbola? How is their appearance explained by the equations derived in class for the reflection time-distance relationship.

63. Tom Wilson, Department of Geology and Geography In Exercise III, explain the differences observed in the arrival times of the reflection and diffraction observed in the shot record.

64. Tom Wilson, Department of Geology and Geography As noted earlier - accurately portray the arrival times at different offsets or surface locations. Your plots should serve as an accurate representation of the phenomena in question. If there is time remaining in the class today we’ll spend it working on Exercises I-III.

65. Tom Wilson, Department of Geology and Geography For next time - Review Chapter 3. Consider discussions of Attenuation of Seismic Energy along Ray Paths and how you might approach problems 2 & 3 (page 42). Work on Exercises I-III and bring them to class next time along with any questions you have. **They are not due next time just be prepared to ask questions about them