A B S T R A C TInversion for seismic impedance is an inherently complicated problem. It is ill-posed and band-limited. Thus the inversion results are non-unique and the process is unstable. Combining regularization with constraints using sonic and density log data can help to reduce these problems. To achieve this, we developed an inversion method by constructing a new objective function, including edge-preserving regularization and a soft constraint based on a Markov random field. The method includes the selection of proper initial values of the regularization parameters by a statistical method, and it adaptively adjusts the regularization parameters by the maximum likelihood method in a fast simulated-annealing procedure to improve the inversion result and the convergence speed. Moreover, the method uses two kinds of regularization parameter: a 'weighting factor' λ and a 'scaling parameter' δ. We tested the method on both synthetic and field data examples. Tests on 2D synthetic data indicate that the inversion results, especially the aspects of the discontinuity, are significantly different for different regularization functions. The initial values of the regularization parameters are either too large or too small to avoid either an unstable or an over-smoothed result, and they affect the convergence speed. When selecting the initial values of λ, the type of the regularization function should be considered. The results obtained by constant regularization parameters are smoother than those obtained by adaptively adjusting the regularization parameters. The inversion results of the field data provide more detailed information about the layers, and they match the impedance curves calculated from the well logs at the three wells, over most portions of the curves. I N T R O D U C T I O NIn seismic surveying, impedance inversion is one of the most effective methods of quantitatively interpreting seismic data. It can integrate seismic data with well-logging data and geological information. It is also essential in estimating reservoir properties. A number of impedance inversion methods were developed in the previous century, such as generalized linear inversion (Tarantola and Vallete 1982;Cooke and Schneider 1983), constrained inversion (Wang, Liu and Xie 1996) and inversion in which a feedforward neural network is combined with very fast simulated annealing (Calderón-Macías, Sen and Stoffa 1998). In recent years, non-linear inversion methods, *
Using the regularization, we can turn an ill‐posed inverse problem into a good‐posed one. Through selecting a reasonable initial value of regular parameters by the statistic method and estimating regular parameter values by the maximum likelihood (ML) in inverse procedure, the inverse result and convergent speed can be improved. Meanwhile, we combine the regularization and the fast simulated annealing algorithms to play the full role of regular parameters, then we can acquire a global optimum result and gain good applied effect.
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 anisotropic Markov 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.
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