THE EFFECTS OF MULTI-SCALE HETEROGENEITIES ON WAVE-EQUATION MIGRATION

摘要

Velocity models used for wavefield-based seismic imaging represent approximations of the velocity characterizing the area under investigation. We can conceptually decompose the real velocity model into a background component which can be inferred using conventional velocity analysis techniques, and into another component encapsulating the model heterogeneities. This unknown component is responsible for mispositioning of reflection energy which usually takes the form of imaging artifacts. Model heterogeneity can be described stochastically using, for example, correlated Gaussian random distributions or fractal distributions. Data simulated for the various distributions are characterized by spectra with different shapes when analyzed in the log-log domain. For example, Gaussian distributions are characterized by exponential functions and fractal distributions are characterized by linear functions with fractional slopes. These properties hold for both data and migrated images after deconvolution of the source wavelet. On the other hand, the image heterogeneities induced by model heterogeneities can be considered as noise to be removed by an image filtering operation. Among many possibilities, filtering with the seislet transform (a wavelet transform technique) and Gabor-Wigner distribution (a time-frequency analysis technique) are effective at suppressing noise, although both techniques affect the signal corresponding to the major geologic structure. Such filtering can be applied at different stages of wave-equation imaging, for example on data, on the reconstructed wavefields, or on the migrated image. Of all possibilities, filtering of the reconstructed wavefields is most effective.