High precision microseismic source mechanism determined by iterative relative moment tensor inversion

There is a growing interest in source mechanisms of microearthquakes particularly for induced microseismic events in oil, gas, and geothermal fields. However, their reliable estimate is a difficult task due to low S/N ratio and poor knowledge of the underground structure. Dahm (1996) develop a relative moment tensor inversion (RMTI) method for earthquake source clusters, in which relative body-wave amplitudes for two earthquakes recorded at a common station are used to eliminate the effect of propagation paths. If the source mechanism of one of those earthquakes is known a priori, the other source mechanisms can be determined without a computation of Green's function. A difficulty in this method is that errors in the mechanism of reference events may lead to biased solutions for other events. In order to avoid this problem, we propose a method that iteratively applies the RMTI to source clusters improving each moment tensor. The procedure is as follows: (1) Sample co-located multiple earthquakes. At this time, their source mechanisms are not always accurately determined. (2) Apply the RMTI to estimate the source mechanism of each event relative to those of the other events. (3) Repeat the step 2 for the modified source mechanisms until the total residual becomes almost constant. We conducted numerical tests on synthetic data, where amplitudes were computed assuming double-couple sources, amplifying by factor between 0.3 and 5 as site effects, and adding 10% random noise. Initial solutions were given by adding 20-degree-wide random noises to strike, dip, and rake angles of input mechanisms. In a test with eight sources at 12 stations, the total residual rapidly drops during the first few iterations and settles down afterwards. After the three iterations, the solutions almost reach the input mechanisms. In contrast, both of the original RMTI (i.e., without iteration) and a general MTI (i.e., single-source, absolute MTI) could not reproduce the input mechanisms, where large spurious non-double couple components were appeared, showing the superiority of the proposed method. We will also report the application of the method to real data, focusing on the existence of non-double couple component in microearthquakes.