In this work, we propose a full-waveform technique for the spatial reconstruction and characterization of (micro-) seismic events via joint source location and moment tensor inversion. The approach is formulated in the frequency domain, and it allows for the simultaneous inversion of multiple point-like events. In the core of the proposed methodology is a grid search for the source locations that encapsulates the optimality condition on the respective moment tensors. The developments cater for compactly supported elastic bodies in R2; however our framework is directly extendable to inverse (seismic) source problems in R3 involving both bounded and unbounded elastic domains. A set of numerical results, targeting laboratory applications, is included to illustrate the performance of the inverse solution in situations involving: (i) reconstruction of multiple events, (ii) sparse (pointwise) boundary measurements, (iii) “off-grid” location of the micro-seismic events, and (iv) inexact knowledge of the medium's elastic properties.
Bibliographical noteFunding Information:
This research was partly supported by CNPq (Brazilian Research Council), CAPES (Brazilian Higher Education Staff Training Agency) and FAPERJ (Research Foundation of the State of Rio de Janeiro). The support is gratefully acknowledged. The first author gratefully acknowledges the financial support received from the EPSRC in the form of grant P/R002134/1. The third author kindly acknowledges the support provided by the endowed Shimizu Professorship and the U.S. National Science Foundation (CMMI Grant #1536110) during the course of this investigation.
- Acoustic emission
- Inverse source problem
- Multiple sources
- Seismic moment tensor
- Waveform inversion