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Environmental and Exploration Geophysics II. Static Anomalies and Energy Partitioning. tom.h.wilson wilson@geo.wvu.edu. Department of Geology and Geography West Virginia University Morgantown, WV. Original due dates -. and pb 4.8. Due Today, Oct. 24 th. Due Tuesday, Oct. 29 th.

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slide1

Environmental and Exploration Geophysics II

Static Anomalies and Energy Partitioning

tom.h.wilson

wilson@geo.wvu.edu

Department of Geology and Geography

West Virginia University

Morgantown, WV

slide2

Original due dates -

and pb 4.8

Due Today, Oct. 24th

Due Tuesday, Oct. 29th

Velocity Analysis Problem

slide23

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.

slide24

V

Interval Velocity

Particle Velocity

v

slide25

Pi

PR

PT

Normal Incidence Raypaths

Boundary Conditions

slide26

We can rewrite boundary condition 1 as

The subscript P indicates that pressure variations are being considered in this case

slide27

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

slide28

Our two boundary conditions become

which implies

As a matrix equation, we have

slide33

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.

slide34

V

Interval Velocity

Particle Velocity

v

slide41

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

slide42

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.

slide43

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

Stick Plot

slide44

Subsurface model

Simplified representation of the source disturbance

slide45

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.

slide46

At C? -

At D? -

slide55

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

slide56

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.

slide57

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

slide58

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

slide59

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

slide60

ACCH

Note amplitude/stratigraphic relationships

slide61

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

slide62

“True Amplitude” … with some computer glitches

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?

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Once again note the amplitude relationships

slide63

This seismic display has been “gain corrected”

Note that some of the lithology dependant amplitude differences have disappeared.

slide65

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

slide66

Truer amplitude display - amplitude averaging is undertaken over longer time windows

Gain incorporates amplitude averaging over short time windows

From Ylmez

slide67

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

slide68

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.