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Multi-trace post-stack seismic data sparse inversion with nuclear norm constraint

Dai Ronghuo, Zhang Fanchang, Yin Cheng, Hu Ying

Acta Geophysica

2021

Vol. 69, no. 1

53--64

Among many seismic inversion methods, the sparse spike inversion for post-stack seismic data uses the migrated and stacked seismic data which is regarded as zero ofset refection seismic data in the case of normal incidence to extract refectivity and impedance of underground rocks. The seismic refectivity and impedance can refect underground rocks’ lithology, petrophysical property, oil–gas possibility, and so forth. However, the common used post-stack seismic inversion adopts single trace in the process of inversion and completes the whole data cube’s inversion through trace by trace. It cannot use lateral regularization. Hence, the lateral continuity of single trace inversion result is poor. It is difcult to represent the lat eral variation features of underground rocks. Based on the conventional sparse spike inversion, the nuclear norm of matrix in the matrix completion theory is introduced in the process of post-stack seismic inversion. At the same time, the strategy of multi-trace seismic data simultaneous inversion is used to carry out lateral regularization constraint. Numerical tests on 2D model indicate that the inversion results obtained from the proposed method can clearly represent not only the vertical variation features but also the lateral variation features of underground rocks. At last, the inversion results of real seismic data further show the feasibility and superiority of the proposed method in practical application.

Sharp and laterally constrained multitrace impedance inversion based on blocky coordinate descent

Wang Y., Lin W., Cheng S., She B., Hu G., Liu W.

Acta Geophysica

2018

Vol. 66, no. 4

623--631

Seismic impedance inversion is a well-known method used to obtain the image of subsurface geological structures. Utilizing the spatial coherence among seismic traces, the laterally constrained multitrace impedance inversion (LCI) is superior to trace-by-trace inversion and can produce a more realistic image of the subsurface structures. However, when the traces are numerous, it will take great computational cost and a lot of memory to solve the large-scale matrix in the multitrace inversion, which restricts the efficiency and applicability of the existing multitrace inversion algorithm. In addition, the multitrace inversion methods are not only needed to consider the lateral correlation but also should take the constraints in temporal dimension into account. As usual, these vertical constraints represent the stratigraphic characteristics of the reservoir. For instance, total-variation regularization is adopted to obtain the blocky structure. However, it still limits the magnitude of model parameter variation and therefore somewhat distorts the real image. In this paper, we propose two schemes to solve these issues. Firstly, we introduce a fast algorithm called blocky coordinate descent (BCD) to derive a new framework of laterally constrained multitrace impedance inversion. This new BCD-based inversion approach is fast and spends fewer memories. Next, we introduce a minimum gradient support regularization into the BCD-based laterally constrained inversion. This new approach can adapt to sharp layer boundaries and keep the spatial coherence. The feasibility of the proposed method is illustrated by numerical tests for both synthetic data and field seismic data.