A constrained-based optimization approach for seismic data recovery problems

TL;DR

This paper presents a convex optimization framework for seismic data recovery that effectively separates primary signals from structured noise using adaptive filtering and constraints, improving data interpretation.

Contribution

It introduces a novel convex optimization approach incorporating hard constraints and adaptive filtering for seismic data denoising, enhancing separation of signals from structured noise.

Findings

Effective separation of primaries from structured noise.

Improved seismic data quality with constrained optimization.

Enhanced performance using hyperplane-based constraints.

Abstract

Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation is obtained through time-varying filtering, compensating inaccuracies in given approximate templates. The under-determined problem can then be formulated as a convex optimization one, providing estimates of both filters and primaries. Within this framework, the criterion to be minimized mainly consists of two parts: a data fidelity term and hard constraints modeling a priori information. This formulation may avoid, or at least facilitate, some parameter determination tasks, usually difficult to perform in inverse problems. Not only classical constraints, such as sparsity, are considered here, but also constraints expressed through hyperplanes, onto which the projection is easy to compute. The latter constraints lead to improved performance by further constraining the space of geophysically sound solutions.