Microseismic Waveform Modeling and Inversion using Finite-Difference and Global Optimization

Abstract

Estimating microseismic source parameters is an essential part of a microseismic monitoring project. Typically the microseismic source position and origin time are estimated utilizing kinematic methods, while the moment tensor components are found from linear inversion of P-and S-wave amplitudes. The signal-to-noise ratio (SNR) is generally low in microseismic data. Therefore, methods based on travel time picking are prone to cause errors. Microseismic waveform inversion (WI) is a powerful alternative and has the potential to do a joint inversion of microseismic source location (spatial and temporal) and moment tensor components as the full wavefield is utilized. First, a staggered finite-difference scheme is implemented to simulate P-SV waves in 2-dimensional isotropic media. A moment tensor source description is included to simulate microseismic events. A microseismic event is simulated for a homogeneous velocity model, layered velocity model and a complex velocity model. The results highlight the importance of accounting for elasticity, as most of the energy comes from the S-wave. Microseismic WI is implemented to estimate the source position, moment tensor components and origin time of microseismic events. Microseismic WI for the source parameters is a highly non-linear problem with many local minima. Local optimization methods are, therefore prone to get stuck before reaching a global minimum. Global optimization, on the other hand, searches the whole model parameter space and is, therefore, much less likely to get stuck in local minima. In this context, the global optimization method of very fast simulated annealing (VFSA) was chosen as it has been proven effective in multiple other studies. The results indicate that microseismic WI, by use of VFSA, can accurately estimate the source parameters if a sufficiently good velocity model is used. Specifically, the source parameters can be simultaneously estimated for a complex velocity model, even with low SNR. However, the precision of the source position and origin time decreases with errors in the velocity model.