Environmental and Exploration Geophysics II

Environmental and Exploration Geophysics II

[email protected]

Department of Geology and GeographyWest Virginia University

Morgantown, WV

Static Anomalies Static Anomalies and Energy and Energy PartitioningPartitioning

Due Tuesday, Oct. 29th

Due Today, Oct. 24th

Original due dates -

Recall Energy partitioning

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.

Interval Velocity

Particle Velocity

Pi

PT

PR

R

i

PR

P

T

i

PT

P

Normal Incidence Raypaths

I. Pressure

II. Velocityi R T

i R T

P P P

v v v

1

1

i R T

R T

i i

P P

P P P

P P

P P

R T

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

We can rewrite boundary condition 1 as

From the wave equation, we have that or

P Vv

P Zv

This allows us to rewrite boundary condition II i R Tv v v

in terms of the pressures, as -

1 1 2

i R TP P P

Z Z Z

By convention, up is negative, thus

1

RR

Pv

Z

Our two boundary conditions become

1 1 2

I. 1

1II.

Z

P P

P P

R T

R T

Z Z

which implies

1 2 1

I. 1

1II.

Z

P P

P P

R T

R T

Z Z

As a matrix equation, we have

12

1 2 1

1 1

1 1 1P

P

aR

TZ Z Z

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.

Interval Velocity

Particle Velocity

Note that Pv =Vv2

Thus Ev2

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

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

Density, velocity and impedance plots are usually represented in step-plot form.

Step Plot

1.0

1.5

2.0

2.5

3.0D

ensi

ty

0.5 1.0 1.5 2.0 2.5

Two-way Travel Times

The values as listed are constant through an interval and marked by abrupt discontinuity

across layer boundaries.

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

-1.0 -0.5 0.0 0.5 1.0

Reflection Coefficient

0.0

0.5

1.0

1.5

2.0

2.5

Tw

o-w

ay tr

avel

tim

e

Subsurface model

Simplified representation of the source disturbance

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.

AppC PTRP 1223At C? -

ApppD PTTRP 211223At D? -

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

…. Solve for the Ps and vs and then plot

AppC PTRP 1223

ApppD PTTRP 211223

ApB PTP 1211V

Pv AA

AvB vTv 12

.etc

The plot portrays the amplitude of the wavelet at subsurface points A, B, C and D.

Input wavelet

1AP

5.1BP

?CPC

Provide a general representation of wavelet amplitudes measured at points A - D. Do for both the pressure and velocity measurements

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.

rsr e

r

AA

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.

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.

020log AA A

Recall that on the decibel scale the relationship between two amplitudes is expressed as

where A is in decibels

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 rs

r er

ATA

rsr e

r

ATA

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

Rer

ATA rs

r

RAr

The geologist would like to have

Note amplitude/stratigraphic relationships

Accurate portrayal of reflection coefficients is important in stratigraphic interpretations of seismic data.

10,000

14,000

18,500

19,500

16,500

14,500 21,00

0

18,500

“True Amplitude” … with some computer glitches

Once again note the amplitude relationships

This seismic display has been “gain corrected”

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

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

From Ylmez

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

Gain incorporates amplitude averaging over short time windows

The basic synthetics exercises handed out today will be due next Friday. Look over them and bring questions to class this Thursday.

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.