Sensitivity analysis of anisotropic parameter inversion simultaneously with microseismic source location in layered VTI media

The hypocenters of microseismic events induced by hydraulic fracturing are conventionally located with an initial model established from well logs or perforation shots. In most geological settings, the arrival times are insufficiently explained without accounting for the velocity changes introduced by the reservoir stimulation process. The model parameters and source locations should be inverted simultaneously with arrival time information. Therefore, the joint inversion of event locations and velocity model requires the information of anisotropy parameters, which leads to the problem of the selection of degree of symmetry of anisotropic media in the inversion process. Since it is not possible to retrieve all elastic moduli from limited passive seismic data, the joint inversion is constrained to layered vertical transversely isotropic (VTI) media. Various methods have been proposed to invert the velocity model and source locations from the arrival times in anisotropic media, but the number of retrievable parameters in different parametrization types and acquisition scenarios have not been decisively discussed. We analyze the sensitivities for event locations and anisotropic parameters by the singular value decomposition (SVD) of the Fréchet derivatives in a layered anisotropic medium with vertical axis of symmetry. The singular values and eigenvectors obtained from SVD can be used to predict which unknown parameters are better constrained by the available traveltimes. The comparison of different parametrizations and monitoring array configurations allows to design a better inversion strategy to provide microseismic event locations and anisotropic parameters.