Focal Mechanisms from Sparse Observations by Nonlinear Inversion of Amplitudes: Method and Tests on Synthetic and Real Data

The purpose of this article is to address the problem of the focal mechanism determination using few seismological records acquired by a sparse network of 3-component sensors. Such cases are frequently encountered in reservoir contexts for the monitoring of the fluid-induced microseismicity. Focal mechanisms of fluid-induced earthquakes are characterized by a nondouble-couple part. However, we show and discuss that the double-couple moment tensor approximation is valid as a source model. Then, we propose a nonlinear inversion method of the direct P-, SV- and SH-wave amplitudes, based on a simulated annealing algorithm to determine double-couple focal mechanisms. Simultaneously, we determine the associated uncertainty. We take into account three sources of uncertainty related to the convergence process of the inversion to the amplitude picking uncertainty caused by the noise level and to the uncertainty of the event location. First, we test our method on synthetic data. Second, we apply the method on four events induced in the Soultz-sous-Forets geothermal field whose focal mechanisms were already determined by Charlety et al. (2007). We obtain focal mechanisms with uncertainties containing the solutions previously determined. Finally, we evaluate the required minimum number of sensors and their geometrical configuration to obtain a focal mechanism. The direction of the nodal planes and the type of mechanism are retrieved for data sets as small as three 3-component stations. The tests also reveal that the reliability of the fault plane solution depends on the configuration the stations used. It also seems that the coverage of the focal sphere by the stations, that is, the opening angle of the network and the coverage of several quadrants, has an influence on the reliability of the fault plane solution retrieval. The use of only one 3-component sensor allows retrieval of the type of focal mechanism in most of the cases studied.