A source time reversal method for seismicity induced by mining

Rodrigo I Brevis,Jaime H Ortega,David Pardo

doi:10.3934/ipi.2017002

Abstract

In this work, we present a modified Time-Reversal Mirror (TRM) Method, called Source Time Reversal (STR), to find the spatial distribution of a seismic source induced by mining activity. This methodology is based on a known full description of the temporal dependence of the source, the Duhamel's principle, and the time-reverse property of the wave equation. We also provide an error estimate of the reconstruction when the measurements are acquired over the entire boundary, and we show experimentally the influence of measuring on a subdomain of the boundary. Numerical results indicate that the methodology is able to recover continuous and discontinuous sources, and it remains stable for partial boundary measurements.

Highlights

As mining is a very important activity around the world and one of the principal economic activities in several countries such as Chile, Peru, South Africa, and China, it is expected to continue for a long time
Fink point of view; we show an error estimate for our problem following the ideas of [17], and we provide a three dimensional example of how the time-reversal mirror method works in an exact case
We introduce a new approach of a time-reversal method called Source Time Reversal (STR)

Summary

Introduction

As mining is a very important activity around the world and one of the principal economic activities in several countries such as Chile, Peru, South Africa, and China, it is expected to continue for a long time. Geiger [15] developed one of the most classical methods for locating sources in mining, based on an accurate propagation velocity map of the mine structure and a least-square technique This method is able to estimate the hypocenter location using the arrival time to measurement stations. [14]) to obtain stability conditions and to reconstruct the spatial dependence of the source This approach has been used for medical imaging, see, e.g., chapter 12 of [3], where authors summarize time-reversal methods applied to tomography techniques by considering Dirac delta functions as source. Works as [26] attempt to find an accurate representation of the amplitude of a seismic wave using Ricker wavelet, and if we include any method to estimate the origin time t0 as [15,30], it is possible to obtain a complete characterization of the temporal source term g(t).

Model assumptions and the time-reversal method

Numerical results

Findings

Conclusions