1. Energy Loss and Partitioning
Environmental and Exploration Geophysics II
Energy Loss and Partitioning
tom.h.wilson
Department of Geology and Geography
West Virginia University
Morgantown, WV
Tom Wilson, Department of Geology and Geography

2. Objectives for the day Review time-distance plots
Discuss energy loss through divergence and absorption mechanisms
Present basic definition of reflection coefficient and how it varies with offset or incidence angle
Basic definition of transmission coefficient
Tom Wilson, Department of Geology and Geography

3. Can you name the events? Miller et al. 1995
What events can you identify in this shot record?
Miller et al. 1995
Tom Wilson, Department of Geology and Geography

4. Ground roll = noise to the exploration geophysicist
Tom Wilson, Department of Geology and Geography

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

6. Diffraction (point source) Events
Engineers may want to think in terms of ground penetrating radar - Drums will be diffractors, perhaps pipelines and underground storage tanks
Geologists may want to think of diffractors as voids or narrow meanedring channels that the seismic line might cross.
They could also be associated with the edges of layers that are truncated by faults Draw Diagram
Tom Wilson, Department of Geology and Geography

7. Diffractions, like reflections are hyperbolic in a time-distance plot
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).
Tom Wilson, Department of Geology and Geography

8. Note that the apex of the diffraction event is not located at the source location (X=0). The apex is located over the discontinuity.
Tom Wilson, Department of Geology and Geography

9. Use the image point to help you get reflection times
Ray Trace Exercise I
A direct path
Use the image point to help you get reflection times
How do you figure out Xmin & tmin for the critical refraction? What is the critical refraction time at longer offsets?
Tom Wilson, Department of Geology and Geography

10. In ray-trace exercises I-III
1) label all plotted curves,
2) label all relevant points and
3) Describe the relationships that you’ve graphed.
Tom Wilson, Department of Geology and Geography

11. Do Exercise II and III using Excel.
Ray Trace Exercise II
What to you think the influence of higher velocity will be on the moveout?
What’s the t0 for these two cases?
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.
Tom Wilson, Department of Geology and Geography

12. Although the time intercept remains the same - how do the shapes of the reflection hyperbola differ in these two cases?
Tom Wilson, Department of Geology and Geography

13. Ray Trace Exercise III Hands on Work your way along each path
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?
Tom Wilson, Department of Geology and Geography

14. In Exercises I-III
Your plots should be consistent with expected relationships discussed in class
Tom Wilson, Department of Geology and Geography

15. Questions?
Tom Wilson, Department of Geology and Geography

16. Review - Questions?
Tom Wilson, Department of Geology and Geography

17. First arrival picks and velocity
170 feet offset
Can you pick out the direct arrival?
Can you pick out the refraction arrivals?
How many critical refractions are there?
How would you determine the refraction velocity?
How would you determine the air wave or direct arrival velocity?
0.15 seconds
Tom Wilson, Department of Geology and Geography

18. Velocities > VA, VB VC, Vairwave
Tom Wilson, Department of Geology and Geography

19. Section 2.3
What happens to the seismic energy generated by the source as it propagates through the subsurface?
Basic Concepts-
Energy - The ability to do work. It comes in two forms - potential and kinetic
Work expended (W) equals the applied force times the distance over which an object is moved.
Power is the rate at which work is performed.
As a mechanical disturbance or wavefield propagates through the subsurface it moves tiny particles back and forth along it path. Particle displacements are continually changing. Hence, it is more appropriate for us to consider the power, or the rate at which energy is being consumed at any one point along the propagating wavefront.
Tom Wilson, Department of Geology and Geography

20. The rate of change of work in unit time.
One horsepower equals 550 foot-pound force /second
745 Newton meters/second
1 watt is one joule per second
This force is the force exerted by the seismic wave at specific points along the propagating wavefront.
Tom Wilson, Department of Geology and Geography

21. and since force is pressure (p) x area (A), we have
The power generated by the source is PS. This power is distributed over the total area of the wavefront A so that
We are more interested to find out what is going on in a local or small part of the wavefield.
* Note we are trying to quantify the effect of wavefront spreading at this point and are ignoring heat losses.
Tom Wilson, Department of Geology and Geography

22. Over what surface area is the energy generated by the source distributed?
Tom Wilson, Department of Geology and Geography

23. Area of a hemisphere is 2R2 - hence -
This is the power per unit area being dissipated along the wavefront at a distance R from the source. (Recall p is pressure, v is the particle velocity, PS magnitude of the pressure disturbance generated at the source and R is the radius of the wavefront at any given time.
Tom Wilson, Department of Geology and Geography

24. In the acoustic wave equation a quantity Z which is called the acoustic impedance. Z = V, where  is the density of the medium and V is the interval velocity or velocity of the seismic wave in that medium.
Z is a fundamental quantity that describes reflective properties of the medium.
We also find that the pressure exerted at a point along the wavefront equals Zv or Vv, where v is the particle velocity - the velocity that individual particles in the disturbed medium move back and forth about their equilibrium position.
Tom Wilson, Department of Geology and Geography

25. Particle velocity versus interval velocity
Tom Wilson, Department of Geology and Geography

26. Combining some of these ideas, we find that v, the particle displacements vary inversely with the distance traveled by the wavefield R.
Tom Wilson, Department of Geology and Geography

27. We are interested in the particle velocity variation with distance since the response of the geophone is proportional to particle (or in this case) ground displacement. So we have basically characterized how the geophone response will vary as a function of distance from the source.
The energy created by the source is distributed over an ever expanding wavefront, so that the amount of energy available at any one point continually decreases with distance traveled.
This effect is referred to as spherical divergence. But in fact, the divergence is geometrical rather than spherical since the wavefront will be refracted along its path and its overall geometry at great distances will not be spherical in shape.
Tom Wilson, Department of Geology and Geography

28. The effect can differ with wave type
The effect can differ with wave type. For example, a refracted wave will be confined largely to a cylindrical volume as the energy spreads out in all directions along the interface between two intervals. z R
The surface area along the leading edge of the wavefront is just 2Rz.
Tom Wilson, Department of Geology and Geography

29. Hence (see earlier discussion for the hemisphere) the rate at which source energy is being expended (power) per unit area on the wavefront is
Remember Zv2 is just
Following similar lines of reasoning as before, we see that particle velocity
Tom Wilson, Department of Geology and Geography

30. The dissipation of energy in the wavefront decreases much less rapidly with distance traveled than does the hemispherical wavefront.
This effect is relevant to the propagation of waves in coal seams and other relatively low-velocity intervals where the waves are trapped or confined. This effect also helps answer the question of why whales are able to communicate over such large distances using trapped waves in the ocean SOFAR channel.
Visit for some info on the SOFAR channel.
Tom Wilson, Department of Geology and Geography

31. Sound Surveillance System
Detected a 1 pound TNT explosion 2000 miles away (Bahmas to Africa).
See also -
Tom Wilson, Department of Geology and Geography

32. Divergence losses decrease particle velocity or the amplitude of a seismic wave recorded by the geophone - i.e. the amplitude of one of the wiggles observed in our seismic records.
Unless we correct for this effect – turn up the volume – the signal will become too weak for us to hear.
Tom Wilson, Department of Geology and Geography

33. Geophone Output
Since amplitude (geophone response) is proportional to the square root of the pressure, we can rewrite our divergence expression as
Thus the amplitude at distance r from the source (Ar) equals the amplitude at the source (AS) divided by the distance traveled (r).
This is not the only process that acts to decrease the amplitude of the seismic wave.
Tom Wilson, Department of Geology and Geography

34. How many of you remember how to solve such an equation?
Absorption
When we set a spring in motion, the spring oscillations gradually diminish over time and the weight will cease to move. In the same manner, we expect that as s 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.
How many of you remember how to solve such an equation?
Tom Wilson, Department of Geology and Geography

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

36. Tom Wilson, Department of Geology and Geography

37. Mathematical Relationship
Graphical Representation
Tom Wilson, Department of Geology and Geography

38.  - 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.
Tom Wilson, Department of Geology and Geography

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

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

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

42. increase f and decrease A
Run through brief discussion of db scale note that logato the x = x log a in this case a is e and log base 10 of e is approximately 0.43 and 20 (0.43) = 8.68
Higher frequencies are attenuated to a much greater degree than are lower frequencies.
Tom Wilson, Department of Geology and Geography

43. 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.
Tom Wilson, Department of Geology and Geography

44. 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.
Tom Wilson, Department of Geology and Geography

45. Z1 and Z2 are the impedances of the bounding layers.
Tom Wilson, Department of Geology and Geography

46. http://www. crewes. org/ResearchLinks/ExplorerPrograms/ReflEx/REcrewes
Tom Wilson, Department of Geology and Geography

47. You can also have a look at AVO.xls linked on the class site
Tom Wilson, Department of Geology and Geography

48. AVA response predicted for shallow strata in the Central Appalachians, Marshall Co., WV
Tom Wilson, Department of Geology and Geography

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

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

51. Assignments
Please read through Chapter 3, pages 65 through 95; Chapter 4, pages 149 to 164.
Hand in problems 2.3 and 2.6 (Today)
Questions about problems 2.7 and 2.12? Hand those in on Wednesday.
Start working Exercises I-III and bring questions to class on Wednesday.
Any questions about the attenuation problem? We’ll probably end up discussing this some more in class on Wednesday. This will be due next Monday.
Tom Wilson, Department of Geology and Geography