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

Abstract

International audienceThe 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 non-double-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-Forêts 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

Assessment of focal mechanisms of microseismic events computed from two three‐component receivers: application to the Arkema‐Vauvert field (France)

“…We applied the method developed by Godano et al (2009) to compute double‐couple focal mechanisms on a brine production field that is seismically very active. This method, which is based on a non‐linear inversion of the P, Sv and Sh amplitudes of the recorded seismograms enables, in theory, the estimation of the focal mechanisms from a few sensors.…”

“…In this paper we use the method proposed by Godano et al (2009). This method enables determining the fault plane solution parameters, (the strike (ϕ), the dip (δ) and the rake (λ)), related to the P, Sv and Sh amplitudes of the direct wave, by a non‐linear functional G as follows: where are the amplitudes and are the parameters ϕ, δ and λ.…”

“…In this latter case, it has been demonstrated (Godano et al 2009) that a fault plane solution is not accurately determined.…”

“…We applied the method developed by Godano et al (2009) to compute double-couple focal mechanisms on a brine production field that is seismically very active. This method, which is Figure 11 Comparison of the moment magnitude obtained from the first arrival amplitude best fit for inversion #1 (x-axis) and for inversion #2 (y-axis).…”

“…Moreover, in networks with few sensors, the calculation of conventional source parameter attributes such as magnitude, the stress drop and the source radius are biased due to the lack of information on the focal mechanism. In this paper we apply, on a real case, the focal mechanism determination method recently proposed by Godano et al (2009). This method allows full determination of the focal mechanism and, consequently, source parameter updates in networks with only a microseismic events (e.g., Bohnhoff, Baisch and Harjes 2004;Charlety et al 2007).…”