[Paper Review] Reciprocity-gap misfit functional for Distributed Acoustic Sensing, combining data from passive and active sources

Florian Faucher, Maarten V. de Hoop+1 more|arXiv (Cornell University)|Apr 9, 2020

Seismic Imaging and Inversion Techniques97 references8 citations

TL;DR

This paper introduces a novel reciprocity-gap misfit functional for elastic full waveform inversion using Distributed Acoustic Sensing (DAS) data, combining passive (e.g., regional earthquakes) and active (e.g., exploration) sources. By leveraging cross-correlations of displacement and strain between observed and simulated data, the method enables multi-resolution subsurface reconstruction without requiring prior knowledge of source locations or characteristics, significantly improving low-wavenumber model recovery and mitigating cycle-skipping issues.

ABSTRACT

Quantitative imaging of sub-surface Earth's properties in elastic media is performed from Distributed Acoustic Sensing data. A new misfit functional based upon the reciprocity-gap is designed, taking cross-correlations of displacement and strain, and these products further associate an observation with a simulation. In comparison with other misfit functionals, this one has the advantage to only require little a-priori information on the exciting sources. In particular, the misfit criterion enables the use of data from regional earthquakes (teleseismic events can be included as well), followed by exploration data to perform a multi-resolution reconstruction. The data from regional earthquakes contain the low-frequency content which is missing in the exploration ones, allowing for the recovery of the long spatial wavelength, even with very few sources. These data are used to build prior models for the subsequent reconstruction from the higher-frequency exploration data. This gives the elastic Full Reciprocity-gap Waveform Inversion method, and we demonstrate its performance with a pilot experiment for elastic isotropic reconstruction.

Motivation & Objective

• To address the challenge of cycle-skipping in full waveform inversion due to limited low-frequency content in active-source exploration data.
• To enable integration of passive-source data (e.g., regional earthquakes) with active-source DAS data for improved multi-resolution subsurface imaging.
• To develop a misfit functional that requires minimal a-priori knowledge of source locations and characteristics.
• To demonstrate the feasibility of using strain and displacement cross-correlations in a reciprocity-gap framework for elastic media.
• To lay the foundation for a new Full Reciprocity-gap Waveform Inversion (FRgWI) method applicable to real-world DAS data acquisition setups.

Proposed method

• The method introduces a reciprocity-gap misfit functional based on time-correlation of displacement and normal stress (or strain) between observed and simulated data.
• The misfit is formulated using an integral over the receiver surface, allowing application on topographically complex domains with Lipschitz boundaries.
• The functional is expressed in terms of strain, replacing normal stress, to better align with DAS measurements of strain along fiber-optic cables.
• The approach operates in the frequency domain, enabling efficient computation and reduced memory usage, though time-domain extension is feasible via frequency continuation.
• Computational sources can be placed arbitrarily, enabling shot-stacking and flexible acquisition modeling.
• The method is implemented using the hawen codebase, with results reproducible via publicly archived datasets and scripts.

Experimental results

Research questions

• RQ1 Can a reciprocity-gap misfit functional be designed to effectively combine passive and active seismic sources in elastic full waveform inversion?
• RQ2 To what extent can passive-source data (e.g., regional earthquakes) recover low-wavenumber subsurface structures when active data lack low frequencies?
• RQ3 How does the proposed misfit functional perform in the absence of prior knowledge about source locations or waveforms?
• RQ4 What is the impact of using strain measurements from DAS on the accuracy and stability of elastic parameter reconstruction?
• RQ5 Can the reciprocity-gap functional mitigate cycle-skipping issues in full waveform inversion more effectively than traditional least-squares misfit functions?

Key findings

• The proposed Full Reciprocity-gap Waveform Inversion (FRgWI) method successfully reconstructs elastic subsurface parameters using combined passive and active DAS data, even with minimal source information.
• The method enables effective multi-resolution imaging by first recovering long-wavelength structures from regional earthquake data, followed by high-wavenumber details from exploration data.
• A pilot experiment demonstrates the method’s flexibility and robustness in handling diverse acquisition geometries and source configurations.
• The reciprocity-gap misfit functional avoids reliance on source location or waveform knowledge, making it suitable for real-world DAS deployments with uncertain or unknown sources.
• The method is extendable to anisotropic and attenuating media, with straightforward incorporation of complex-valued elasticity tensors in the frequency domain.
• The implementation supports shot-stacking and can be adapted to time-domain or hybrid-domain formulations, enhancing scalability for 3D applications.