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

2. Velocity Analysis Problem
Original due dates -
and pb 4.8
Due Today, Oct. 24th
Due Tuesday, Oct. 29th
Velocity Analysis Problem

22. Recall Energy partitioning

23. Geophone output is often designed to be proportional to pressure, particle velocity, acceleration or displacement. Land geophone output is typically proportional to particle velocity, while marine geophones record pressure variations.

24. V
Interval Velocity
Particle Velocity v

25. Normal Incidence RaypathsPi PT PR
Boundary Conditions

26. We can rewrite boundary condition 1 as
The subscript P indicates that pressure variations are being considered in this case

27. From the wave equation, we have that
This allows us to rewrite boundary condition II
in terms of the pressures, as -
By convention, up is negative, thus

28. Our two boundary conditions become
which implies
As a matrix equation, we have

33. Part II
Geophone output is often designed to be proportional to pressure, particle velocity, acceleration or displacement. Land geophone output is typically proportional to particle velocity, while marine geophones record pressure variations.

34. V
Interval Velocity
Particle Velocity v

38. Note that Pv =Vv2
Thus Ev2

40. We have, as expected, a decrease of energy across the interface
We have, as expected, a decrease of energy across the interface. Energy is conserved!

41. Compute and plot two-way interval transit times, two-way total reflection time, layer impedance and boundary reflection coefficients

42. Density, velocity and impedance plots are usually represented in step-plot form.
The values as listed are constant through an interval and marked by abrupt discontinuity across layer boundaries.

43. Reflection coefficients exist only at boundaries across which velocity and density change, hence their value is everywhere 0 except at these boundaries.
Stick Plot

44. Simplified representation of the source disturbance
Subsurface model
Simplified representation of the source disturbance

45. Follow the wavefront through the subsurface and consider how its amplitude changes as a function only of energy partitioning.
A. What is the amplitude of the disturbance at point A?
B. At point B we have transmission through the interface separating media 1 and 2.
At C?
We consider only transmission and reflection losses. Geometrical divergence and absorption losses are ignored. Hence PA = 1psi.
- hence the amplitude of the wavefront at B is Tp 12 PA.

46. At C? -
At D? -

47. Consider for a moment- the general n-layer case.

54. …. Solve for the Ps and vs and then plot

55. The plot portrays the amplitude of the wavelet at subsurface points A, B, C and D.
Input wavelet
Provide a general representation of wavelet amplitudes measured at points A - D. Do for both the pressure and velocity measurements

56. Total loss - incorporating divergence, absorption and reflection/transmission effects.
We have considered the above factors individually. All of them act to attenuate seismic waves as they propagate through the earth.
Recall that divergence and absorption losses were combined into the following equation
Each mechanism acts as a factor that scales the amplitude of the propagating wavefield. So the net effect on amplitude determined by taking the product of all effects on source amplitude AS.

57. Energy partitioning is a step-like function
Energy partitioning is a step-like function. Wave amplitudes will take a jump to higher or lower amplitude across individual interfaces, however, we can consider the effect of transmission through a series of layers having various average values of reflection and transmission coefficient as shown below.
Recall that on the decibel scale the relationship between two amplitudes is expressed as
where A is in decibels

58. Total amplitude decay at distance r
If average reflection coefficient is not too high (for example 0.05 or 0.1) then the effect is relatively constant over a large range of depths and we can represent transmission reductions by a single scale factor - say T.
Total amplitude decay at distance r

59. These amplitude effects are non-geological in a sense
These amplitude effects are non-geological in a sense. Geologists are interested to have accurate information about the reflection coefficients - not only their position, but their value. The above equation indicates that the amplitude of a reflection from a particular reflector will equal
The geologist would like to have

60. ACCH
Note amplitude/stratigraphic relationships

61. Accurate portrayal of reflection coefficients is important in stratigraphic interpretations of seismic data.
10,000
18,500
14,000
19,500
18,500
16,500
14,500
21,000

62. ? ? ? ? “True Amplitude” … with some computer glitches
Once again note the amplitude relationships

63. This seismic display has been “gain corrected”
Note that some of the lithology dependant amplitude differences have disappeared.

65. Note that the amplitudes in the gain corrected trace at right do not accurately portray relative differences in the value of reflection coefficients

66. Gain incorporates amplitude averaging over short time windows
Truer amplitude display - amplitude averaging is undertaken over longer time windows
Gain incorporates amplitude averaging over short time windows
From Ylmez

67. Also due next Friday, Nov. 8th
Additional Homework -
The basic synthetics exercises handed out today will be due next Friday. Look over them and bring questions to class this Thursday.
Problem 4.14, Chapter 4
Also due next Friday, Nov. 8th

68. Background reading
Read over the paper I handed out to you last Thursday by Sheriff. A proper understanding of resolution issues is critical to stratigraphic interpretations and also to structural interpretations where the identification of subtle structures, such as faults with small offset may be important.
We’ll be studying resolution in forthcoming computer labs and relating resolution limits to your exploration data set.