Full waveform inversion (FWI) using the adjoint-state method is a technique well established in controlled-source seismic exploration for recovering the velocity structure of the subsurface. FWI of microseismic data presents additional challenges as the source parameters (location and moment tensor) are also unknown. However, recent synthetic studies have demonstrated that the technique has the potential to provide higher-resolution velocity models and better event locations for microseismic data. In this abstract we provide a pedagogical overview of the adjoint-state method in the context of waveform modelling of microseismic data recorded in an anisotropic medium. Using examples relevant to the microseismic community, we demonstrate how the interaction of forward and adjoint wavefield simulations can be used to efficiently find the misfit gradient for the source model parameters and sensitivity kernels for the velocity model parameters. We also identify potential pitfalls associated with the choice of model parameterisations, which may lead to trade-offs between particular parameters for a given array geometry. These gradient calculations provide the basis for joint full-waveform inversion for the velocity model and source parameters from elastic three-component microseismic data.


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