# Semblance

Series | Geophysical References Series |
---|---|

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, .

## Continue reading

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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