Wavefield migration plus monte carlo imaging of 3d prestack seismic data

Prestack wave-equation migration has proven to be a very accurate shot-by-shot imaging tool. However, 3D imaging with this technique of a large field acquisition, especially one with hundreds of thousands of shots, is prohibitively costly. Naively adapting the technique to migrate many superposed shot-gathers simultaneously would render 3D wavefield prestack migration cost-effective but introduces uncontrolled non-physical interference among shot-gathers, making useless the final image. However, it has been observed that multi-shot signal interference can be kept under some control by averaging over many such images, if each multi-shot migration is modified by a random phase encoding of the frequency spectra of the seismic traces. In this article we analyze this technique, giving a theoretical basis for its observed behavior: that the error of the image produced by averaging over small $M$ phase encoded migrations decreases as small $M^-1$. Furthermore, we expand the technique and define a general class of Monte Carlo encoding methods for which the noise variance of the average imaging condition decreases as small $M^-1$; these methods thus all converge asymptotically to the correct reflectivity map - without exhibiting prohibitive costs. The theoretical asymptotic behavior is illustrated for three such methods on a 2D test case. Then numerical verification in 3D is presented for one such method implemented with a 3D PSPI extrapolation kernel for two test cases: the SEG-EAGE salt model and a real test constructed from field data.

@Article{BBCZ06a,
  author       = {Bonomi, E. and Brieger, L. and Cazzola, L. and Zanoletti, F.},
  title        = {Wavefield migration plus monte carlo imaging of 3d prestack seismic data},
  journal      = {Geophysical Prospecting},
  volume       = {54},
  pages        = {505--514},
  year         = {2006},
  keywords     = {Wavefield extrapolation, prestack depth migration, random phase encoding, Monte Carlo methods},
  url          = {https://publications.crs4.it/pubdocs/2006/BBCZ06a},
}