The general dislocation source model and its application to microseismic focal mechanism inversion

Abstract

Research on the non-double-couple (NDC) components in an earthquake is important for characterizing true source processes. The moment-tensor (MT) source model is commonly used to study NDC earthquakes. However, MT inversions are still challenging when earthquakes have small magnitudes, especially microearthquakes. The general-dislocation (GD) model specifies the focal mechanism as a shear-tensile slip on a fault plane; thus, GD inversion is better constrained than MT inversion. We focus on GD model-based waveform forward modeling and its application to microseismic source inversions. We expand the generalized reflection-transmission matrix method to synthesize waveforms based on the GD model and fully describe a GD source with five parameters: the scalar seismic moment (which defines the magnitude) and the strike, dip, rake, and slope angles (which define the fault geometry). We compare the GD, MT, and double-couple models and introduce the differences in their characterization and wave synthesis theories. We have developed a GD model-based microseismic focal mechanism inversion method that requires calculating only four angles under hybrid constraints. Two sets of solutions correspond to the same seismograms in a GD model-based inversion. These two solutions have the same scalar seismic moment and slope angle but different strike, dip, and rake angles, and we have derived formulas for mapping from one solution to the other. Synthetic and field surface microseismic data sets are used to test our GD model-based modeling and inversion methods. According to our study, the GD model is effective in microseismic focal mechanism inversion. By developing specific wave synthesis and inversion methods for the GD model, we offer a novel perspective to study this model and the NDC mechanisms for hydraulic fracturing-induced microearthquakes.