# Summary

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

Title | Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing |

Author | Enders A. Robinson and Sven Treitel |

Chapter | 9 |

DOI | http://dx.doi.org/10.1190/1.9781560801610 |

ISBN | 9781560801481 |

Store | SEG Online Store |

Let us summarize. A receiver consisting of dual geophone-hydrophone sensors measures two attributes of the wavefield: particle velocity and pressure. The dual-sensor receiver is buried below the level of the buried source. Einstein deconvolution, which requires dual-sensor data, removes all reverberations and ghosts that result from interfaces above the receiver. Einstein deconvolution also removes the unknown source signature in the same operation. The resulting deconvolved seismogram is the unit-impulse reflection response that would have been produced in the absence of any layers above the buried receiver. If desired, we can perform dynamic deconvolution on the unit-impulse reflection response that we previously have obtained with Einstein deconvolution. The output of the dynamic deconvolution process is the sequence of reflection coefficients for interfaces below the receiver. Einstein deconvolution operates under the same limitations as does predictive deconvolution. Thus, the limitations for Einstein deconvolution are similar to those for predictive deconvolution.

Both deconvolution methods have much in common; the difference is in the fundamental assumptions that determine how we obtain the deconvolution operator. The common goal of both predictive deconvolution and Einstein deconvolution is to obtain the reflection-coefficient series as the deconvolved signal. Both predictive (spiking) deconvolution and Einstein deconvolution conduct the deconvolution process on the upgoing signal. Both predictive deconvolution and Einstein deconvolution share the same deconvolution operator: the inverse of the downgoing signal. The difference between these two methods is in the fundamental assumptions that determine the way the deconvolution operator is obtained. The small white reflectivity hypothesis allows the predictive deconvolution operator to be computed by least squares from the upgoing signal. In addition, the small white reflectivity hypothesis often eliminates the need for a final dynamic deconvolution step. Predictive deconvolution has the advantage of many years of successful use. It is robust and stable in the presence of noise. Einstein deconvolution enjoys the advantage that it is not based on the small white reflectivity hypothesis. In this sense, Einstein deconvolution is more general. However, Einstein deconvolution also is more sensitive to noise. Ideally, then, the two methods should be used together to yield the best results.

## Continue reading

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Deconvolution: Einstein or predictive? | Appendix I: Exercises |

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Synthetics | Deconvolution |

## Also in this chapter

- Wavelets
- The shaping filter
- Spiking filter
- White convolutional model
- Wavelet processing
- All-pass filter
- Convolutional model
- Nonminimum-delay wavelet
- Signature deconvolution
- Vibroseis
- Dual-sensor wavelet estimation
- Deconvolution: Einstein or predictive?
- Appendix I: Exercises