Adaptive multiple subtraction with wavelet-based complex unary Wiener filters

TL;DR

This paper introduces a wavelet-based complex unary Wiener filter approach for adaptive multiple subtraction, effectively reducing multiple contamination while preserving primaries by decomposing wide-band problems into narrow-band filters.

Contribution

It presents a novel single-pass adaptive subtraction method using complex unary Wiener filters in a wavelet domain, simplifying filter estimation and improving performance over traditional methods.

Findings

Effective attenuation of multiples demonstrated on field data.

Narrow-band decomposition improves filter accuracy.

Simplifies adaptive subtraction process.

Abstract

Adaptive subtraction is a key element in predictive multiple-suppression methods. It minimizes misalignments and amplitude differences between modeled and actual multiples, and thus reduces multiple contamination in the dataset after subtraction. Due to the high cross-correlation between their waveform, the main challenge resides in attenuating multiples without distorting primaries. As they overlap on a wide frequency range, we split this wide-band problem into a set of more tractable narrow-band filter designs, using a 1D complex wavelet frame. This decomposition enables a single-pass adaptive subtraction via complex, single-sample (unary) Wiener filters, consistently estimated on overlapping windows in a complex wavelet transformed domain. Each unary filter compensates amplitude differences within its frequency support, and can correct small and large misalignment errors through phase and integer delay corrections. This approach greatly simplifies the matching filter estimation and, despite its simplicity, narrows the gap between 1D and standard adaptive 2D methods on field data.