A nonlinear method for multiparameter inversion of pre-stack seismic data based on anisotropic Markov random field
H. Zhang, Q. Guo, L. Liang, C. Cao and Z. Shang
Journal name: Geophysical Prospecting
Issue: Vol 66, No 3, March 2018 pp. 461 - 477
Info: Article, PDF ( 23.12Mb )
Multiparameter inversion for pre-stack seismic data plays a significant role in quantitative estimation of subsurface petrophysical properties. However, it remains a complicated problem due to the non-unique results and unstable nature of the processing; the pre-stack seismic inversion problem is ill-posed and band-limited. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularisation can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function that includes edge-preserving regularisation and soft constraints based on anisotropic Markov random fields and is intended especially for layered formations. We applied a fast simulated annealing algorithm to solve the nonlinear optimisation problem. The method directly obtains reflectivity RPP values using the full Zoeppritz equation instead of its approximations and effectively controls the stability of the multiparameter inversion by assuming a sectionally constant S- and P-wave velocity ratio and using the generalised Gardner equation. We substituted the inverted parameters, i.e., the P-wave velocity, the fitting deviation of S-wave velocity, and the density were inverted instead of the P-wave velocity, the S-wave velocity, and the density, and the generalised Gardner equation was applied as a constraint. Test results on two-dimensional synthetic data indicated that our substitution obtained improved results for multiparameter inversion. The inverted results could be improved by utilising high-order anisotropic Markov random field neighbourhoods at early stages and low-order anisotropicMarkov random field neighbourhoods in the later stages. Moreover, for layered formations, using a large horizontal weighting coefficient can preserve the lateral continuity of layers, and using a small vertical weighting coefficient allows for large longitudinal gradients of the interlayers. The inverted results of the field data revealed more detailed information about the layers and matched the logging curves at the wells acceptably over most parts of the curves.