GEOPHYS 6001 MUST Geophysical Data Analysis Worksheet Assignment 9; 10 points Known Wt=[1,2,3,2,1] Calculate (you can use Matlab) and graph St=Wt*RC for t

GEOPHYS 6001 MUST Geophysical Data Analysis Worksheet Assignment 9; 10 points

Known Wt=[1,2,3,2,1]
Calculate (you can use Matlab) and graph St=Wt*RC for the following three situations.

RC1t = [1/2,0,0,0]
RC2t = [1/2,0,0,0,0,0,0,-1/2] RC3t = [1/2,0,-1/2].

How many interfaces (peaks with the wave shape similar to Wt) you can see from each of the graphs? Explain your results.

Note:

 Study Lecture 21
 conv –convolution in Matlab Geophys 6001: Advanced Geophysical Data Analysis
Assignment 9; 10 points
Known Wt=[1,2,3,2,1]
Calculate (you can use Matlab) and graph St=Wt*RC for the following three
situations.
RC1t = [1/2,0,0,0]
RC2t = [1/2,0,0,0,0,0,0,-1/2]
RC3t = [1/2,0,-1/2].
How many interfaces (peaks with the wave shape similar to Wt) you can see
from each of the graphs? Explain your results.
Note:
 Study Lecture 21
 conv –convolution in Matlab
GEOPHYS 6001
Advanced Geophysical Data Analysis
Contents
 Resolution
 Resolution vs. bandwidth
 Resolution vs. bandwidth ratio
Lecture 21
Kelly Liu
References: Lillie, “Whole Earth Geophysics”
Fowler, “The Solid Earth”
Yilmaz, “Seismic Data Analysis”
Liu’s Geophys 6001, Summer 2020
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Resolution
Resolution means the
minimum separation
between two features,
so we can tell that
there are two features
rather than only one.
Liu’s Geophys 6001, Summer 2020
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Lillie, “Whole Earth Geophysics”
Resolution
Rayleigh Criterion: The seismic “measure” is a wavelength.
In order for two nearby reflective interfaces to be distinguished well, they
have to be about 1/4 wavelength in thickness.
For thicknesses larger than 1/4 wavelength, we can use the wave shape
to judge the bed thickness.
Liu’s Geophys 6001, Summer 2020
3
Resolution
For a fault to be detected,
the vertical distance h
must be larger than λ/4.
A quarter of wavelength (λ/4)
Example: V=2000 m/s, f=50 Hz, λ=?, vertical resolution?
Wavelength=40 m; Resolution: 10 m.
Liu’s Geophys 6001, Summer 2020
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Fowler, “The Solid Earth”
Resolution
Better resolution
Liu’s Geophys 6001, Summer 2020
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Resolution
 Same frequency bandwidth
 Bandwidth ratio: high cut/low-cut frequency
a. High ratio
b. Low ratio
Centered
@ 15 Hz
a
Liu’s Geophys 6001, Summer 2020
b
Centered
@ 35 Hz
6
Yilmaz, “Seismic Data Analysis”
Resolution
The greater ring of
the second operator
is the results from its
low bandwidth ratio,
i.e., the ratio of the
high-cut to the lowcut frequency.
Centered
@ 35 Hz
Centered
@ 15 Hz
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Yilmaz, “Seismic Data Analysis”
Resolution
What happens to a wavelet if its amplitude spectrum is changed?
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Yilmaz, “Seismic Data Analysis”
Resolution
The wavelet in the frequency domain is compressed as the frequency
bandwidth is increased. Liu’s Geophys 6001, Summer 2020
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Yilmaz, “Seismic Data Analysis”
Resolution
Liu’s Geophys 6001, Summer 2020
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Yilmaz, “Seismic Data Analysis”
Resolution
The broader the bandwidth, the more compressed the filter operator; the fundamental
property of frequency filters.
The time span of a time series is inversely proportional to the spectral bandwidth.
Liu’s Geophys 6001, Summer 2020
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Resolution
The broader the bandwidth, the more compressed the filter operator.
The time span of a time series is inversely proportional to its spectral bandwidth.
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Yilmaz, “Seismic Data Analysis”
Resolution
Reflection from Several Interfaces
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Lillie, Whole Earth Geophysics
Resolution
The input wavelets have the same
bandwidth 10 Hz but centered at
different frequencies.
48-
24-
12-ms
Liu’s Geophys 6001, Summer 2020
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Yilmaz, “Seismic Data Analysis”
Resolution
48-
24-
12-ms
The low frequency is foxed at 10 Hz.
The frequency bandwidth is increased.
48-
24-
12-ms
Liu’s Geophys 6001, Summer 2020
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Yilmaz, “Seismic Data Analysis”
Summary
 Resolution
Liu’s Geophys 6001, Summer 2020
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