Seismic Full-waveform Inversion Using a Source-receiver Compression Scheme
2012
In seismic full-waveform inversion (FWI), one usually deals with a large size data set. This is one of the major bottlenecks for inversion, particularly if a significant part of this data set is lacking sensitivity (redundant) to the unknown model parameters. Such redundancy is usually the result of collecting data employing a non-optimally designed survey. A large number of sources in the survey contributes to a large computational cost in running the forward simulator a number of times corresponding to the number of these sources. On the other hand, a large number of receivers contributes to the computational cost of constructing the Jacobian matrix (the derivative of the simulated data with respect to the unknown parameters), as well as in inverting the Hessian matrix in a Newton-type inversion approach. To deal with these issues, the simultaneous-source encoded FWI approach was proposed to reduce the number of sources used in the inversion, see Krebs et al. (2009). In this approach, a large number of physical sources are converted into one simultaneous source or several simultaneous sources by summing the individual physical sources using a phase-encoding technique. Another approach to reduce the computational time and memory usage of an inversion algorithm is the so-called source-receiver compression scheme, see Habashy et al. (2010). This approach constructs compressed simultaneous source and receiver arrays that have minimum redundancy and maximum sensitivity to the unknown model parameters. The synthesized simultaneous source array has a reduced number of sources that decreases the number of forward model simulations required to carry out the inversion. In addition, the synthesized simultaneous receiver array has a reduced number of receivers that further decreases the size of the Jacobian matrix. Hence, this compression approach significantly reduces the computational time and memory usage of any inversion method. Moreover, because this approach removes the small eigenvalues in the data, the effects of noise are also suppressed. In this paper, we apply the source-receiver compression approach for solving three-dimensional (3D) acoustic FWI for obtaining the compressional (P-wave) velocity. The forward problem is formulated using a frequency-domain finite-difference (FDFD) approach with fourth-order accuracy. For the inversion method, we employ the Gauss-Newton framework described in Habashy and Abubakar (2004) combined with the multiplicative-regularization technique described in van den Berg and Abubakar (2001). As a demonstration, we show inversion results of 3D SEG/EAGE salt model.
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