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/lect2/lec2.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 Grading 25% on computer labs, 30% problem sets, 10% mid term exam, 20% Expl project/term report and class presentation, 15% final exam. Questions about class content and grading? The exploration project? Have you tried using your class accounts? Go ahead and give that a try now if you already haven’t.

4. Tom Wilson, Department of Geology and Geography Different kinds of waves … Body Waves

5. Tom Wilson, Department of Geology and Geography Surface Waves

6. Tom Wilson, Department of Geology and Geography Body vs. “Surface” Waves

7. Tom Wilson, Department of Geology and Geography In general V R <V L <V S <V P But this is not strictly true. The Love wave is a surface wave and its velocity will be equal to the shear wave velocity in the upper medium. The Love wave like the Rayleigh wave is also a dispersive wave. That means that deeper Love wave motion usually propagates more rapidly since velocity increases with depth. Shear waves beneath the surface layers are generally much faster than those in the surface, so in application, the shear waves that we are concerned with generally have higher velocity than the Love waves.

8. Tom Wilson, Department of Geology and Geography Love waves tend not to be recorded in the conventional seismic survey where the interest is primarily in the recording of P-waves. The geophones used in such surveys respond to vertical ground motion and thus do not respond to the side-to-side vibrations produced by Love waves. Rayleigh waves produce large vertical displacements and are a significant source of “noise” in the conventional P-wave reflection seismic survey. Single component vertical motion detectors

9. Tom Wilson, Department of Geology and Geography Breaking seismic disturbances down into their component parts Some nomenclature

10. Tom Wilson, Department of Geology and Geography time and frequency

11. Tom Wilson, Department of Geology and Geography wavelength and wavenumber

12. Tom Wilson, Department of Geology and Geography Sinusoid arguments Temporal form Spatial form

13. Tom Wilson, Department of Geology and Geography Some examples of the seismic source

14. Tom Wilson, Department of Geology and Geography The seismic wavelet

15. Tom Wilson, Department of Geology and Geography The wavelet or pulse is a transient disturbance – it comes and goes

16. Tom Wilson, Department of Geology and Geography Spatial view

17. Tom Wilson, Department of Geology and Geography A Wave Packet or Wavelet Time domain and frequency domain a different way of viewing the time series

18. Tom Wilson, Department of Geology and Geography Creating a wavelet using a sum of sinusoids See http://www.geo.wvu.edu/~wilson/geol554/SumofCosines.xls

19. Tom Wilson, Department of Geology and Geography The wavelet Any time series can be represented as a sum of sinusoids

20. Tom Wilson, Department of Geology and Geography How do mechanical waves get from point A to B

21. Tom Wilson, Department of Geology and Geography You can go straight there or …

22. Tom Wilson, Department of Geology and Geography The reflection events we see in a seismic section don’t start off looking like this The geologist usually immediately starts to see layers, stratigraphy, depositional history, structure… Fruitland coals- San Juan Basin, NM The migrated stack

23. Tom Wilson, Department of Geology and Geography When we bang on the ground, the reflection events are mixed together with a variety of other events This time-distance record shows everything coming in with different shapes, sometimes almost at the same time and sometimes earlier, sometimes later. A real mess!

24. Tom Wilson, Department of Geology and Geography Our initial goal is to develop an understanding of the different types of events that appear in a shot record and how to extract information from these observations and to understand how their travel times (t) vary with source receiver offset (x).

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

26. Tom Wilson, Department of Geology and Geography

27. Another record from the Marshall Co. site

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

29. 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

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

31. Tom Wilson, Department of Geology and Geography Pittsburgh Coal Geophysical Characterization Mechanical Properties

32. Tom Wilson, Department of Geology and Geography For the seismic work we take information from sonic and density logs and create a synthetic seismogram

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

34. 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.

35. 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?

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

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

38. 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.

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

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

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

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

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

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

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

46. 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

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

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

49. 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

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

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

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

53. Tom Wilson, Department of Geology and Geography

54. because sin(  /2) = 1

55. Tom Wilson, Department of Geology and Geography For next time Hand in problems 2.1 and 2.2 Continue your reading of Chapter 2 Review background on the refraction time- distance relationship Look over problems 2.3 and 2.6 for next Monday. These problems will be due next Wednesday, January 20 th.