Adaptive Multiple Subtraction Using Regularized Nonstationary Regression

TLDR: In this article, a general method of non-stationary regression is proposed to constrain the variability of nonstationary coefficients, which is called shaping regularization, and applied to the adaptive subtraction of multiple reflections.

Abstract: Stationary regression is the backbone of seismic data-processing algorithms including match filtering, which is commonly applied for adaptive multiple subtraction. However, the assumption of stationarity is not always adequate for describing seismic signals. I have developed a general method of nonstationary regression and that applies to nonstationary match filtering. The key idea is the use of shaping regularization to constrain the variability of nonstationary regression coefficients. Simple computational experiments demonstrate advantages of shaping regularization over classic Tikhonov's regularization, including a more intuitive selection of parameters and a faster iterative convergence. Using benchmark synthetic data examples, I have successfully applied this method to the problem of adaptive subtraction of multiple reflections.