Abstract
For the correct interpretation of data gathered in the seismic prospecting of complex heterogeneous structures, elastic effects must often be taken into consideration. The use of the elastic wave equations to model the seismic response of an hypothesized geological structure is a valuable tool for relating observed seismic data to the earth’s inhomogeneities and verify an interpretation. Several methods may be used to integrate numerically the partial differential equations describing elastic wave propagation. Pseudospectral (Fourier) methods represent the leading numerical integration technique. Their main advantage is high accuracy and suitability to vector and parallel computer architectures, while their main drawback is high computational cost. However, for a given accuracy, the required grid size with pseudospectral methods is smaller than that required by finite‐difference schemes, thus balancing the computational cost. We describe a two‐dimensional pseudospectral elastic model implemented on the vector multiprocessor IBM 3090 VF. The algorithm has been suitably adapted to fully exploit the computer architecture and thereby maximize the performance. The elastic model has been validated in a variety of problems in geophysics and, in particular, in the amplitude‐versus‐offset analysis which has proved to be an effective technique to extract additional information from the recorded (prestack) data. With proper conditioning and processing of seismic data, and separating amplitude variations due to changes in reflectivity from variations due to other effects, the resulting offset signatures have been successfully used, for instance, to distinguish true bright spots due to gas‐bearing sands, from false ones associated with lithological changes. To interpret the observed amplitude‐versus‐offset signatures, it is necessary to know the reflection coefficients as a function of angle and frequency for planar interfaces, as well as for other structures of geological interest. The modelling is first validated by computing the reflection coefficients for planar interfaces, and then used to analyse the reflection signatures of thin beds, corrugated interfaces and multilayers. Their implications, as well as impact on amplitude‐versus‐offset analysis, are discussed. We conclude that elastic modelling is an effective and valuable tool to further our understanding of the amplitude anomalies observed in field data. Copyright © 1989, Wiley Blackwell. All rights reserved
