Semblance
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Series | Geophysical References Series |
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Title | Problems in Exploration Seismology and their Solutions |
Author | Lloyd P. Geldart and Robert E. Sheriff |
Chapter | 9 |
Pages | 295 - 366 |
DOI | http://dx.doi.org/10.1190/1.9781560801733 |
ISBN | ISBN 9781560801153 |
Store | SEG Online Store |
Contents
Problem
Semblance is the ratio of the energy of a stack of traces to times the sum of the energies of the component traces, all summed over some time interval. Show that when the traces are identical.
Background
While crosscorrelation is a quantitative measure of the similarity of two traces, semblance is a measure of the similarity of a number of traces. Assuming traces, we sum (stack) the traces at time , square the sum to get the total energy, and sum the values over a time interval . The equation for is
( )
Solution
The sum of traces is and its energy is . If the traces are identical, the numerator of equation (9.10a) becomes . The denominator becomes . Since numerator and denominator are equal, .
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Digital calculations | Convolution and correlation calculations |
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Reflection field methods | Geologic interpretation of reflection data |
Also in this chapter
- Fourier series
- Space-domain convolution and vibroseis acquisition
- Fourier transforms of the unit impulse and boxcar
- Extension of the sampling theorem
- Alias filters
- The convolutional model
- Water reverberation filter
- Calculating crosscorrelation and autocorrelation
- Digital calculations
- Semblance
- Convolution and correlation calculations
- Properties of minimum-phase wavelets
- Phase of composite wavelets
- Tuning and waveshape
- Making a wavelet minimum-phase
- Zero-phase filtering of a minimum-phase wavelet
- Deconvolution methods
- Calculation of inverse filters
- Inverse filter to remove ghosting and recursive filtering
- Ghosting as a notch filter
- Autocorrelation
- Wiener (least-squares) inverse filters
- Interpreting stacking velocity
- Effect of local high-velocity body
- Apparent-velocity filtering
- Complex-trace analysis
- Kirchhoff migration
- Using an upward-traveling coordinate system
- Finite-difference migration
- Effect of migration on fault interpretation
- Derivative and integral operators
- Effects of normal-moveout (NMO) removal
- Weighted least-squares