AccScience Publishing / JSE / Online First / DOI: 10.36922/JSE026070028
ARTICLE

Passive-source localization using contrast-source time-reversal imaging with the 2D acoustic wave equation

Shuying Wei1 Guangtan Huang2* Xilin Shi2 Zhennan Yu2
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1 State Key Laboratory of Geodesy and Earth’s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan, Hubei, China
2 State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei, China
Received: 11 February 2026 | Revised: 24 April 2026 | Accepted: 2 May 2026 | Published online: 10 June 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
Abstract

Accurate localization of weak seismic sources remains challenging in complex media, and conventional reverse time imaging is often sensitive to noise and wavefield interference. To address these issues, we propose a two-dimensional time-domain contrast-source reverse time imaging method based on scattering theory. Using a smoothed background model as a reference, the medium perturbations were reformulated as equivalent contrast-source terms. This formulation established an explicit physical link between the scattered wavefield and medium heterogeneity, enabling efficient simulation of scattering responses. Conventional cross-correlation imaging conditions are frequently dominated by high-energy channels and amplitude imbalance among receivers. We therefore developed a grouped cross-correlation imaging condition with energy normalization. This strategy suppresses the dominance of strong-energy channels and enhances coherent stacking across different receiver azimuths, leading to improved focusing and more stable source localization. Numerical experiments were conducted on a simple scatterer model and the Marmousi velocity model. The proposed method was compared with conventional finite-difference reverse time imaging under different noise levels and multi-source scenarios. Results demonstrate that the contrast-source-based approach provided clear advantages in characterizing weak scattering signals, noise robustness, and energy focusing. The proposed grouped energy-normalized imaging condition further improved imaging resolution and source detectability. These results indicate that the proposed method is stable and adaptable in complex media, offering a promising imaging framework for microseismic and other passive-source localization. The method also shows potential for extension to three-dimensional elastic wave equations and real field data.

Keywords
Reverse time imaging
Source localization
Scattering theory
Imaging condition
Wave equation
Funding
This work was supported in part by the National Key R&D Program of China (2024YFB4007100), the National Major Science and Technology Projects of China (2024ZD1004300), the National Natural Science Foundation of China (42304133 and 42574175), and the Key project from the Hubei Research Center for Basic Disciplines of Earth Sciences (HRCES-202401).
Conflict of interest
The authors declare no conflicts of interest.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing