Seismic inversion based on proximal objective function optimization algorithm

Abstract

Seismic impedance inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is its low computational efficiency, especially in 3D. To improve the computational efficiency, we have developed an inversion method derived from the proximal objective function optimization algorithm. Our inversion method calculates each unknown parameter in the model vector, one by one during iteration. Compared with routine gradient-dependent inversion algorithms, such as the iteratively reweighted least-squares (IRLS) algorithm, our inversion method has lower computational complexity as well as higher efficiency. In addition, to obtain a sparse reflectivity series, a long-tailed Cauchy distribution is used as the a priori constraint. The weak nonlinear problem owing to the introduction of Cauchy sparse constraint is addressed by taking advantage of reweighting strategy. Results of synthetic and real data tests illustrate that the proposed inversion method has higher computational efficiency than IRLS algorithm, and its inversion accuracy remains the same.

Seismic deconvolution and inversion with erratic data

“…In this paper, as an alternative to L1‐norm, we use the Cauchy regularization term (Sacchi ; Youzwishen ; Downton ; Zhang et al . ; Dai, Zhang and Liu ) as sparse constraint. Therefore, the objective function takes the following form where λ is the regularization parameter of Cauchy sparse regularization constraint as well, σ is the Cauchy derivation parameter, represents the i th element of r , n is the dimension of vectors.…”

“…monotone fast iterative shrinkage‐thresholding algorithm proposed by Beck and Teboulle (,b), are very effective. Recently, Dai, Zhang and Liu () extended the proximal point algorithm to resolve the inverse problem constrained by Cauchy regularization. Hence, the algorithm proposed by Dai, Zhang and Liu () is chosen to solve equation .…”

“…So, a priori model regularization constraint (Dai et al . ; Zhang, Dai and Liu ; Dai, Zhang and Liu , ; Gholami ; Yin et al . ) is used to enhance the inversion stability, to make the low‐frequency information contained in inversion results more consistent with actual work area and to improve the lateral continuity of inversion results.…”

“…In order to get a sparse reflectivity series, a sparse regularization constraint should be used (Sacchi ; Youzwishen ; Zhang et al . ; Dai, Zhang and Liu ).…”

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