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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
-200
-100
0
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Time
Am
plit
ude
0 5 10 15 20 25 30 35 40-300
-200
-100
0
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Time
Am
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
-0.8
-0.6
-0.4
-0.2
0
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1
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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0
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Time seconds
Am
plitu
de
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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0
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Time seconds
Am
plitu
de
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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0
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Time seconds
Am
plitu
de
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
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Time seconds
Am
plit
ude
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.8
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Time seconds
Am
plit
ude
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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
101
102
103
-100
-90
-80
-70
-60
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-40
-30
-20
-10
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