Joint multi-mode dispersion extraction in Fourier and space time domains

TL;DR

This paper introduces a new broadband method for extracting multiple overlapping dispersion curves in borehole acoustic data by combining Fourier and space-time domain analysis, improving accuracy over existing methods.

Contribution

It presents a joint Fourier and space-time domain approach that effectively handles multiple overlapping signals, with improved group slowness estimation using a linear least squares method.

Findings

Successfully applied to real borehole data

Outperforms existing space-time methods in overlapping scenarios

Provides more accurate group slowness estimates

Abstract

In this paper we present a novel broadband approach for the extraction of dispersion curves of multiple time frequency overlapped dispersive modes such as in borehole acoustic data. The new approach works jointly in the Fourier and space time domains and, in contrast to existing space time approaches that mainly work for time frequency separated signals, efficiently handles multiple signals with significant time frequency overlap. The proposed method begins by exploiting the slowness (phase and group) and time location estimates based on frequency-wavenumber (f-k) domain sparsity penalized broadband dispersion extraction method as presented in \cite{AeronTSP2011}. In this context we first present a Cramer Rao Bound (CRB) analysis for slowness estimation in the (f-k) domain and show that for the f-k domain broadband processing, group slowness estimates have more variance than the phase slowness estimates and time location estimates. In order to improve the group slowness estimates we exploit the time compactness property of the modes to effectively represent the data as a linear superposition of time compact space time propagators parameterized by the phase and group slowness. A linear least squares estimation algorithm in the space time domain is then used to obtain improved group slowness estimates. The performance of the method is demonstrated on real borehole acoustic data sets.