Multi-trace acoustic impedance inversion with multiplicative regularization

Abstract

Acoustic impedance (AI) inversion is one of the important workflows in petroleum seismology. Many kinds of additive regularization techniques have been proposed to obtain impedance profiles with a relatively high resolution or to take the lateral information of the model into account. However, the determination of a proper regularization parameter is time-consuming. In this paper, we introduce the weighted L2-norm anisotropic total-variation multiplicative regularization to solve the multi-trace AI inversion problem. This regularization scheme has two main characteristics: adaptive adjustment of the regularization parameter, vertical resolution enhancement and anti-noise ability. Besides, space directional difference is naturally integrated to the regularization operator, by which the lateral connection is taken into consideration. To solve the large scale non-quadratic functional efficiently, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) direction is used to update the acoustic impedance, and update step is calculated analytically in each iteration. Well log synthetic test demonstrates that the single trace multiplicative regularized AI inversion performs well. Further, a test on a classical wedge model with thin interbeds shows the superiority of the method. A complex two-dimensional test and field data application illustrate the effectiveness of the multi trace multiplicative regularized AI inversion scheme.