Block row recursive least squares migration

TL;DR

This paper introduces a recursive least squares migration method using sliding windows and rank updates, enabling efficient, real-time geophysical imaging for both stationary and dynamic processes.

Contribution

It presents a novel recursive algorithm for wave equation least squares migration that improves computational efficiency and convergence in geophysical applications.

Findings

Method converges superlinearly for stationary processes.

Effective for both dynamic and stationary wave migration.

Numerical experiments demonstrate practical efficiency.

Abstract

Recursive estimates of large systems of equations in the context of least squares fitting is a common practice in different fields of study. For example, recursive adaptive filtering is extensively used in signal processing and control applications. The necessity of solving least squares problem via recursive algorithms comes from the need of fast real-time signal processing strategies. Computational cost of using least squares algorithm could also limits the applicability of this technique in geophysical problems. In this paper, we consider recursive least squares solution for wave equation least squares migration with sliding windows involving several rank K downdating and updating computations. This technique can be applied for dynamic and stationary processes. One can show that in the case of stationary processes, the spectrum of the preconditioned system is clustered around one and the method will converge superlinearly with probability one, if we use enough data in each windowed setup. Numerical experiments are reported in order to illustrate the effectiveness of the technique for least squares migration.