Estimation of microseismic source parameters by anisotropic waveform inversion

Abstract

In microseismic data processing, source locations and origin times are usually obtained using kinematic techniques, whereas moment-tensor estimates are typically based on linear inversion of P- and S-wave amplitudes. Waveform inversion (WI), which has been used primarily for high-resolution velocity analysis, has the potential to provide more accurate source parameters along with an improved velocity model by incorporating both phase and amplitude information. The first issue addressed in the thesis is efficient calculation of the gradient of the WI objective function with respect to the model parameters. Application of the adjoint-state method helps obtain closed-form expressions for the gradient with respect to the source location, origin time, and moment tensor. Computation of the forward and adjoint wavefields is performed with a finite-difference algorithm that handles elastic VTI (transversely isotropic with a vertical symmetry axis) models. Numerical examples illustrate the properties of the gradient for multicomponent data recorded by a vertical receiver array placed in homogeneous and horizontally layered VTI media. Then WI is implemented to estimate the location, origin time, and seismic moment tensor of microseismic sources embedded in 2D VTI media. Both a constant and variable step-length computed by line-search followed by the nonlinear conjugate method (NCG) are used for model updating. Although in the current algorithm the interval VTI parameters are assumed to be known, they can be included in WI at almost no additional cost. Velocity estimation, however, is likely to make the objective function more complicated and increase ambiguity of the inversion. Synthetic tests for data recorded by vertical receiver arrays show that it is possible to tightly constrain all source parameters, if a sufficiently accurate initial model is available. In particular, the source location in layered VTI media can be estimated simultaneously with the moment tensor. The resolution of event location, however, somewhat decreases when the origin time is unknown or there is an error in one of the VTI parameters.