# Seismic deconvolution

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

Author | Enders A. Robinson and Sven Treitel |

Chapter | 10 |

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

ISBN | 9781560801481 |

Store | SEG Online Store |

*Seismic deconvolution* is a general term for deconvolution methods designed to remove effects that tend to mask the primary reflected events on a seismogram. Such masking effects can be produced by the earth itself — in the form of absorption, reverberation (multiple reflections), and ghosting — whereas other masking effects result from the seismic source and receiver. To deconvolve seismic data, first we must supply certain required parameters. Then we can design and apply deconvolution filters. Basic to the understanding of deconvolution in the processing of reflection seismic data is development of a model of the layered earth.

An oil well drilled in a sedimentary basin will reveal the layering of sediments. When a wave of unit energy strikes an interface between two layers, some of the energy is reflected, and the remainder of the energy is transmitted. The amount of reflected energy depends on the reflection coefficient of the interface. If we plot the reflection coefficients of all these interfaces as a function of two-way traveltime, we obtain the so-called reflectivity function. This reflectivity gives vital information about the geologic structure. In the ideal case of distinct, well-defined layers, this reflectivity function would consist of a pip at each interface. The size of such a pip would be equal to the value of the reflection coefficient at that interface. The magnitudes of most reflection coefficients encountered in petroleum exploration are small, generally much smaller than one. For the simplified case of no multiples and no transmission losses, a powerful model of the reflection seismogram can be obtained by attaching the source wavelet to each pip on the reflectivity function.

In Chapter 9, in our discussion of equations **28** and **29** of that chapter, we examined the convolutional model , where *s* is the seismic source (or signature), *a* is the intrinsic seismic absorption operator, *m* is the multiple-reflection response, *i* is the instrument response, and is the reflectivity. (Note that in this book, we use the symbol *a* in two ways: as the inverse of the minimum-delay wavelet *b* and as the absorption operator. The meaning is made clear by the context in which the symbol appears.) The signature and the instrument response are more subject to our control, so usually they can be measured or estimated. In such cases, these responses are removable with signature deconvolution methods, as described in Chapter 9.

On the other hand, the earth controls the nature of both intrinsic seismic absorption and the multiple-reflection response, so these are not handled as easily. In Chapter 14, we deal with seismic absorption, so we will neglect it here. As a result, we are left with a further simplified convolutional model given by the signature-free trace . Seismic deconvolution is based on this simple convolutional model. We can think of the reflectivity as the filter input, the wavelet *m* as the impulse response of the filter, and the signature-free trace *z* as the filter output. In this model, we assume that the reflectivity series is white and that the multiple-reflection response *m* is a minimum-phase wavelet. The purpose of deconvolution in the present model is to remove the multiples from the observed seismogram, thus yielding the ideal seismogram (i.e., the reflectivity function). To describe how deconvolution works in practice, we must justify our model. We will do so by considering the earth as a stack of sedimentary layers.

Many great oil fields discovered in the early days of seismic prospecting were in areas that produced textbook-type seismograms. Such seismograms showed beautiful primary reflections that accurately represented the sedimentary structure, because in those areas, the sedimentary layers were characterized by interfaces with small and uncorrelated reflection coefficients (i.e., interfaces without major reflectivity magnitudes). In other words, such favorable seismic areas contained no major interfaces that would give rise to strong multiple reflections in the depth range of interest. Because of the smallness and randomness of the reflectivity in these sedimentary columns, the multiples tended to interact destructively with each other, with the net effect that no strong multiples tended to appear.

On land, the situation became quite different in areas where major multiples originated from near-surface limestone layers. At sea, the situation was different as well — the water layer introduced strong multiple energy in the form of so-called multiple reverberations. At that time, seismograms containing such water-layer-induced reverberations were known as “ringing” or “singing” records.

When one or more strongly reflecting interfaces exist in the sedimentary column, multiples from these reflectors start to build up and tend to mask the primary events. For example, in marine exploration, the water layer represents a nonattenuating medium bounded by two strongly reflecting interfaces, so it represents an energy trap. A seismic pulse generated in this energy trap will be reflected successively between the two interfaces. Those water reverberations will obscure reflections arriving from deeper horizons below the water layer. On land, a deep limestone layer bounded by strongly reflecting interfaces also can produce multiple reflections, which then interfere with primary reflections.

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Wavelet Processing | Fine Points |

## Also in this chapter

- Model used for deconvolution
- Least-squares prediction and smoothing
- The prediction-error filter
- Spiking deconvolution
- Gap deconvolution
- Tail shaping and head shaping
- Piecemeal convolutional model
- Time-varying convolutional model
- Random-reflection-coefficient model
- Implementing deconvolution
- Canonical representation
- Appendix J: Exercises