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 Extracting Physical Properties from the Shot Record and The Two Layer Refraction Problem

2. Tom Wilson, Department of Geology and Geography

4. 1) label all plotted curves, 2) label all relevant points and 3) Note (comment on) basic relationships between events observed in the time-distance plots (see following)

5. Tom Wilson, Department of Geology and Geography Do Exercise II and III using Excel. In exercise II comment on the origins of the differences in the two reflection hyperbola? What is their relationship to corresponding direct arrivals.

6. Tom Wilson, Department of Geology and Geography For Exercise III, explain the differences observed in the arrival times of the reflection and diffraction observed in the shot record. Why does the diffraction event drop below the reflection?

7. Tom Wilson, Department of Geology and Geography For the Barrel Interpreter The following references will be provided on a sign out basis Brown AAPG Memoir 42, 1986 3D Interp Brown, 2004, more recent volume on 3D interp (6 th ed) Neidel, 1979, strat modeling Yilmaz, 2001, seismic data analysis, volumes 1 and 2 Lines and Newrick, 2004, fundamentals of seismic interp. Biondi, 2007, Concepts and apps in 3D imaging … We can be more focused once we know where the project area is … For now the basics … You will first want to research the AAPG bulletin and Journal Geophysics for publications related to the project area

8. Tom Wilson, Department of Geology and Geography SOFAR Channel – sound fixing and ranging channel

9. Tom Wilson, Department of Geology and Geography Absorption When we set a spring in motion, the spring oscillations gradually diminish over time. In the same manner, we expect that as a seismic wave propagates through the subsurface, energy will be consumed through the process of friction and there will be conversion of mechanical energy to heat energy. We guess the following - there will be a certain loss of amplitude dA as the wave travels a distance dr and that loss will be proportional to the initial amplitude A. i.e.

10. Tom Wilson, Department of Geology and Geography In order to solve for A as a function of distance traveled (r) we will have to integrate this expression -  is a constant referred to as the attenuation factor In the following discussion,let

11. Tom Wilson, Department of Geology and Geography

12. Mathematical Relationship Graphical Representation

13. Tom Wilson, Department of Geology and Geography  - the attenuation factor is also a function of additional terms - is wavelength, and Q is the absorption constant 1/Q is the amount of energy dissipated in one wavelength ( ) - that is the amount of mechanical energy lost to friction or heat. The physical significance of 

14. Tom Wilson, Department of Geology and Geography is also a function of interval velocity, period and frequency

15. Tom Wilson, Department of Geology and Geography  is just the reciprocal of the frequency so we can also write this relationship as

16. Tom Wilson, Department of Geology and Geography Smaller Q translates into higher energy loss or amplitude decay.

17. Tom Wilson, Department of Geology and Geography Higher frequencies are attenuated to a much greater degree than are lower frequencies. increase f and decrease A

18. Tom Wilson, Department of Geology and Geography When we combine divergence and absorption we get the following amplitude decay relationship The combined effect is rapid amplitude decay as the seismic wavefront propagates into the surrounding medium. We begin to appreciate the requirement for high source amplitude and good source-ground coupling to successfully image distant reflective intervals.

19. Tom Wilson, Department of Geology and Geography But we are not through - energy continues to be dissipated through partitioning - i.e. only some of the energy (or amplitude) incident on a reflecting surface will be reflected back to the surface, the rest of it continues downward is search of other reflectors. The fraction of the incident amplitude of the seismic waves that is reflected back to the surface from any given interface is defined by the reflection coefficient (R) across the boundary between layers of differing velocity and density.

20. Tom Wilson, Department of Geology and Geography Z 1 and Z 2 are the impedances of the bounding layers.

21. Tom Wilson, Department of Geology and Geography The transmitted wave amplitude T is

22. Tom Wilson, Department of Geology and Geography At a distance of 100 m from a source, the amplitude of a P-wave is 0.1000 mm, and at a distance of 150 m the amplitude diminishes to 0.0665 mm. What is the absorption coefficient of the rock through which the wave is traveling? (From Robinson and Coruh, 1988)

23. Tom Wilson, Department of Geology and Geography Set up the equation that needs to be solved in the foregoing problem. Write it down on a piece of paper and hand in. Write down the Excel equation you would use to solve for the diffraction time-distance relationship as portrayed in ray trace exercise II

24. Tom Wilson, Department of Geology and Geography The critical distance and the crossover distance. To determine the crossover distance set the direct arrival time equal to the critical refraction arrival time and solve for X cross

25. Tom Wilson, Department of Geology and Geography This is a new one, but pretty simple – see 3.2.4

26. Tom Wilson, Department of Geology and Geography We now have several equations which contain quantities that we can measure directly from the shot record and use to determine layer thickness - h 1. h1h1 ?

27. Tom Wilson, Department of Geology and Geography Reflection time intercept Refraction time-intercept Crossover distance Critical Distance

28. Tom Wilson, Department of Geology and Geography The two-layer refraction problem (see 3.3.1)

29. Tom Wilson, Department of Geology and Geography Time =distance traveled/velocity

30. Tom Wilson, Department of Geology and Geography For the details see 3.3.1

31. Tom Wilson, Department of Geology and Geography

35. CC Snell’s law for multiple layers

36. Tom Wilson, Department of Geology and Geography The velocity triangle

37. Tom Wilson, Department of Geology and Geography Expressing trig functions in terms of velocities

38. Tom Wilson, Department of Geology and Geography The end result, whereand …

39. Tom Wilson, Department of Geology and Geography What is the critical distance What is the relationship of the reflection from the base of layer 2 to the critical refraction from the top of layer 2

40. Tom Wilson, Department of Geology and Geography As x gets larger and larger the reflection from the base of layer 2 and the refraction across the top converge

41. Tom Wilson, Department of Geology and Geography

42. In the three layer problem the number of possible terms that could potentially be measured directly from the shot record includes - V 1, V 2 and V 3 two reflection time intercepts two refraction time intercepts one crossover distance, and two critical distances

43. Tom Wilson, Department of Geology and Geography How would you determine the thickness of layer 2 (h 2 )? From reflection arrivals From refraction events?

44. Tom Wilson, Department of Geology and Geography What variables can be determined from an analysis of the shot record V 1, V 2, V 3, t i1, & t i2, where the t i ’s refer to the reflection time intercepts

45. Tom Wilson, Department of Geology and Geography What variables can be determined from an analysis of the shot record V 1, V 2, V 3, t i1, & t i2, where the t i ’s refer to the refraction time intercepts

46. Tom Wilson, Department of Geology and Geography 1) We have assumed that our layers have successively higher and higher velocity. What happens if we have a velocity inversion - let’s say V 2 is less than V 1 and V 3 ? 2) Another assumption we have made here is that the refraction from the top of the third layer, for example, will actually show itself, and not get buried somewhere beneath the earlier refraction and reflections. This can happen if the 2 nd layer is too thin.

47. Tom Wilson, Department of Geology and Geography  Please read through Chapter 3, pages 95 to top of 114.  Chapter 4, pages 149 to 164 (as assigned previously.  Today turn in problem 2.6, 2.7 and 2.12 Continue working Exercises I-III and bring questions to class next Monday (due next Wednesday) Also consider the attenuation problem and be prepared to discuss further on Monday (due next Wednesday).