1Geophysics 438Introductory Lecture

2Introduction

Overview of Class What are we going to do?

What is data? Data Conditioning

Gains Frequency Content Filtering

3Seismic Profiles

41 km

EastWest

Seismic Section J. Ahmad

1 km

5Seismic Profile

6GPR Turtle Mountain

7GPR Profile

Basson, U., 2000. Imaging of active fault zone in the Dead Sea Rift: Evrona Fault Zone as a case study. Thesis submitted for the degree of Ph.D., Tel-Aviv University, Raymond & Beverly Sackler, Faculty of Exact Sciences, Department of Geophysics & Planetary

Sciences, 196 p.

8GPR Hyperbola

Scattered from buried tank nice image from www.naevageophysics.com/gpr.html

9A look ahead Data Processing

Start

AcquireData

DataAcceptable?

NO

PreprocessingEdit, mute, filter

Deconvolve, gain, field statics,Geometries, etc. etc.

CMP sorting

Velocity Analysis

Dynamic Correction

Residual Static

CorrectionCorrection

Acceptable?

CMP Stack

AdditionalCorrectionse.g. Migration

Output forinterpretation

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What is data???

Analog Digital Data: Sampling:

Time sampling Amplitude sampling dynamic range, clipping What are bits??

How is data stored in computer? Integers Floating Point ASCII (???) - strings

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Time Sampling

0 5 10 15 20 25 30 35 40-300

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plit

ude

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plit

ude

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

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Time secondsA

mpl

itude

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

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Methods of Sampling

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Attenuation of Seismic Waves

How can attenuation be measured? What physical mechanisms are important? Global flow (Biot, de la Cruz Spanos) Local flow (squirt flow) Either? Both? Dislocations Scattering Friction

( )( )rArA o = exp)(2

2

1

112

)(

++=

Q

QVo

oo

oo

o

o

o

o

oo V

fV

VV

Q

=

=

21

2)( 2

22

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Theoretical Background

Amplitude can be modeled as:

Q is the quality factor. The higher the Q,the less a wave is attenuated.

For sedimentary rocks it varies from 20 to 150.

(1) Qvf frequency

wave velocityQuality factor

5

Attenuation Estimates Thanks to Gabe Solano

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Amplitude

Intensity = energy/m^2For sound dB = 10log10(I/Io)

Amplitude = particle displacement, particle velocity, particle acceleration, pressure, stress.

dB = 20log10(A/Ao)

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Decay)(

1

2.

1

.

212 RR

n

eRRyy

=

10-1

100

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103

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0

Source-Receiver Offst Distance (m)

Rel

ativ

e A

mpl

itude

s dB Body Wave Decay

Surface Wave Decay

10

100

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Gains Define Energy E and

Intensity F vs Amplitude A (particle displacement)

Correct for amplitude decay with time Geometrical Spreading:

Intensity 1/r2

Amplitude 1/r Attenuation (intrinsic +

scattering)

2

22 oAE =

22

2222 ZAVAF oPo ==

E is the average over one wavelength of the total energy conveyedper unit wavefront (in units that reduce to J/m3 and as such is analogous to an energy density)

F has units of kg/s3 which is dimensionally the same as the intensity: the power per unit area in Watts/m2

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Empirical Approaches

Scale by tn Scale by exp(Bt) Automatic Gain Control

N

aA

N

ii

== 12

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Another Way to Look at Time Series

There are two ways we can describe a seismic trace. Normal Way - s(t): time domain Another Way - S(f): frequency domain

Why bother?? - Many advantages when looking for noise. Often the seismic signal will have a very different frequency than the noise.

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Frequency Content

Examples Seismic Reflections - often 10-100 Hz Ground Roll Noise - 3 - 20 Hz Air Wave Noise - 100-400 Hz Electrical Noise - 60 Hz & 50 Hz

Frequency filtering can help to separate these leaving the desired information.

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Fouriers idea

..\..\G326\Lectures\Fourier\add_cosines.m

..\..\G326\Lectures\Fourier\make_boxcars.m

..\..\G326\Lectures\Fourier\make_triangles.m

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Fourier Transform Pair

Generally S() is a complex function

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Useful Properties of the Fourier Transform Pair

1. Addition x(t) + y(t) X(f) + Y(f)2. Multiplication x(t)y(t) X(f) * Y(f)3. Convolution x(t)*y(t) X(f)Y(f)4. Autocorrelation x(t)*x(-t) |X(f)2|5. Derivative dx(t)/dt iX()

Other consideration: A broad function in one domain corresponds to a narrow function in the other domain. Implication for deconvolution, data acquisition, resolution want to maximize the bandwidth as much as possible

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Considerations

Bandpass filter should not be too sharp this causes problematic ringing (Gibbs phenomena) that can obscure data.

For trapezoidal filter, rule of thumb is slope should be equal to of an octave.

Unfortunately there is no clean separation of data and noise, a bandpass filter must be designed to try to minimize the loss of crucial information.

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Mechanics of FFT

Geophysics 438Introductory LectureIntroductionSeismic ProfilesSeismic ProfileGPR Turtle MountainGPR ProfileGPR HyperbolaA look ahead Data ProcessingWhat is data???Time SamplingMethods of SamplingAttenuation of Seismic WavesAmplitudeDecayGainsEmpirical ApproachesFrequency ContentFouriers ideaMechanics of FFT