Passive-source localization using contrast-source time-reversal imaging with the 2D acoustic wave equation
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.
- Maxwell SC, Chorney D, Goodfellow SD. Microseismic geomechanics of hydraulic-fracture networks: Insights into mechanisms of microseismic sources. Leading Edge. 2015;34(8):904-910. doi: 10.1190/TLE34080904.1
- Eyre TS, Eaton DW, Zecevic M, et al. Microseismicity reveals fault activation before Mw 4.1 hydraulic-fracturing induced earthquake. Geophys J Int. 2019;218(1):534-546. doi: 10.1093/gji/ggz168
- Geiger L. Probability method for the determination of earthquake epicentres from the arrival time only. Bull St Louis Univ. 1912;8:60-71.
- Waldhauser F, Ellsworth WL. A double-difference earthquake location algorithm: Method and application to the northern Hayward fault, California. Bull Seismol Soc Am. 2000;90(6):1353-1368. doi: 10.1785/0120000006
- Keranen KM, Weingarten M, Abers GA, et al. Sharp increase in central Oklahoma seismicity since 2008 induced by massive wastewater injection. Science. 2014;345(6195):448- 451. doi: 10.1126/science.1255802
- Sheng M, Chu R, Ni S, et al. Source parameters of three moderate size earthquakes in Weiyuan, China, and their relations to shale gas hydraulic fracturing. J Geophys Res Solid Earth. 2020;125(10). doi: 10.1029/2020JB019932
- Chu R, Sheng M. Stress features inferred from induced earthquakes in the Weiyuan shale gas block in southwestern China. J Geophys Res Solid Earth. 2023;128(2). doi: 10.1029/2022JB025344
- Gajewski D, Tessmer E. Reverse modelling for seismic event characterization. Geophys J Int. 2005;163(1):276-284. doi: 10.1111/j.1365-246X.2005.02732.x
- Fink M. Time reversed acoustics. In: Wapenaar K, Draganov D, Robertsson JOA, Pelissier MA, eds. Seismic Interferometry: History and Present Status. Vol 26. Tulsa, OK: Society of Exploration Geophysicists; 2008. doi: 10.1190/1.9781560801924
- Lin Y, Zhang H. Imaging hydraulic fractures by microseismic migration for downhole monitoring system. In: SEG Technical Program Expanded Abstracts 2016. Society of Exploration Geophysicists; 2016. doi: 10.1190/segam2016-13973310.1
- Li L, Tan J, Schwarz B, et al. Recent advances and challenges of waveform‐based seismic location methods at multiple scales. Rev Geophys. 2020;58(1):e2019RG000667. doi: 10.1029/2019RG000667
- Miao SY, Zhang HJ, Tan YY, et al. Development of a new high resolution waveform migration location method and its applications to induced seismicity. Earth Planet Phys. 2021;5(6):520-531. doi: 10.26464/epp2021056
- Artman B, Podladtchikov I, Witten B. Source location using time‐reverse imaging. Geophys Prospect. 2010;58(5):861- 873. doi: 10.1111/j.1365-2478.2010.00911.x
- Douma J, Snieder R. Focusing of elastic waves for microseismic imaging. Geophys J Int. 2014;200(1):390-401. doi: 10.1093/gji/ggu398
- Wu S, Wang Y, Zheng Y, et al. Microseismic source locations with deconvolution migration. Geophys J Int. 2018;212(3):2088-2115. doi: 10.1093/gji/ggx518
- Eaton DW. Weak elastic-wave scattering from massive sulfide orebodies. Geophysics. 1999;64(1):289-299. doi: 10.1190/1.1444525
- Huang L, Fehler MC, Roberts PM, et al. Extended local Rytov Fourier migration method. Geophysics. 1999;64(5):1535- 1545. doi: 10.1190/1.1444657
- Li X. Scattering of seismic waves in arbitrarily heterogeneous and acoustic media: A general solution and simulations. Geophys Res Lett. 2001;28(15):3003-3006. doi: 10.1029/2000GL012658
- Lam CH, Bakrac S, van den Berg PM, et al. On the background model for non‐linear inversion of seismic data. In: SEG Technical Program Expanded Abstracts 2006. Texas, TX: Society of Exploration Geophysicists; 2006:2012-2016. doi: 10.1190/1.2369931
- Jakobsen M. T-matrix approach to seismic forward modelling in the acoustic approximation. Stud Geophys Geod. 2012;56(1):1-20. doi: 10.1007/s11200-010-9081-2
- Osnabrugge G, Leedumrongwatthanakun S, Vellekoop IM. A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media. J Comput Phys. 2016;322:113-124. doi: 10.1016/j.jcp.2016.06.034
- Huang L, Fehler M, Zheng Y, et al. Seismic-Wave Scattering, Imaging, and Inversion. Commun Comput Phys. 2020;28(1):1-40. doi: 10.4208/cicp.2020.swsii.review
- Abubakar A, Hu W, Habashy TM, et al. Application of the finite-difference contrast-source inversion algorithm to seismic full-waveform data. Geophysics. 2009;74(6):WCC47- WCC58. doi: 10.1190/1.3250203
- Abubakar A, Pan G, Li M, et al. Three‐dimensional seismic full‐waveform inversion using the finite‐difference contrast source inversion method. Geophys Prospect. 2011;59:874- 888. doi: 10.1111/j.1365-2478.2011.00953.x
- Han B, He Q, Chen Y, et al. Seismic waveform inversion using the finite‐difference contrast source inversion method. J Appl Math. 2014;2014(1):532159. doi: 10.1155/2014/532159
- He Q, Han B, Chen Y, et al. Application of the finite-difference contrast source inversion method to multiparameter reconstruction using seismic full-waveform data. J Appl Geophys. 2016;124:4-16. doi: 10.1016/j.jappgeo.2015.10.011
- Abubakar A, Hu W, van Den Berg PM, et al. A finite-difference contrast source inversion method. Inverse Probl. 2008;24(6):065004. doi: 10.1088/0266-5611/24/6/065004
- Salucci M, Poli L, Lusa S, et al. Recent Advances in Multiscale- Multiphysics Inverse Scattering. In: 2024 18th European Conference on Antennas and Propagation (EuCAP). IEEE; 2024:1-4. doi: 10.23919/EuCAP60739.2024.10501373
- Tan Y, He C, Mao Z. Microseismic velocity model inversion and source location: The use of neighborhood algorithm and master station method. Geophysics. 2018;83(4):KS49-KS63. doi: 10.1190/geo2017-0308.1
