Fast spatial structure constrained 3D prestack inversion based on the Sylvester equation

Abstract

Structurally constrained inversion (SCI) is a multitrace processing technology that can effectively reduce the complexity of prestack seismic inversion caused by complex geology such as faults and steeply dipping structures. Nevertheless, several factors limit its wide application in 3D prestack inversion, the most significant of which is the high computational cost. In addition, the existing SCI is mostly applied in 2D profiles, which can only consider structural features in one direction, making it challenging to ensure spatial continuity. We have developed a fast spatial structure constrained inversion for 3D prestack seismic data. First, based on the conventional SCI, we develop a new way to describe the spatial structural characteristics of the stratum by estimating the dip angles along two perpendicular directions. Second, we introduce the spatial structure constraints through the Hadamard product operator and construct a computationally well-behaved objective function with spatial structural constrained. Using our matrix operators, which are symbols representing the multiplication of 2D and 3D matrices, the minimization of the objective function can be simplified to solve a specific Sylvester equation. Moreover, we justify the rationality of our operator symbols and derive a fast algorithm for solving 3D problems with the Sylvester equation. Finally, the stability and computational efficiency of our method are compared with the 2D SCI algorithm on the 3D overthrust model and field prestack seismic data.