Simultaneous Bayesian inversion for effective anisotropy parameters and source locations: a physical modelling study

Estimating microseismic event locations is important for applications of geophysical monitoring, including hydraulic fracturing and carbon-capture and storage. Field sites for these applications are typically located in sedimentary basins that include finely stratified sediments, particularly around the target depth of the application. The fine stratification causes vertical transverse isotropy (VTI) for seismic wave propagation. In addition, such sediments often exhibit a vertically fractured rock mass that can cause horizontal transverse isotropy (HTI). Therefore, geophysical monitoring can be strongly affected by the occurrence of anisotropy caused by sets of aligned vertical fractures in finely horizontally layered media. While both HTI and VTI theories exist, a more efficient approximation to include both effects is by effective orthorhombic (ORT) models. To account for such anisotropy in microseismic monitoring, we simultaneously estimate ORT parameters, perforation shot locations, and microseismic event locations with Bayesian methods based on direct P-wave arrival times. A comparison to a HTI parametrization is carried out to examine anisotropy-model choice. The quasi-P-wave group velocities in HTI and ORT media are approximated by linearization. Anisotropy parameters are estimated with Markov chain Monte Carlo sampling that includes parallel tempering and principal-component diminishing adaptation to ensure efficient sampling of the parameter space. In contrast to deterministic inversion, our probabilistic non-linear approach includes uncertainty quantification by approximating the posterior probability density with an ensemble of model-parameter sets for effective anisotropy parameters, microseismic event locations, and horizontal locations of perforation shots. The noise standard deviation of P-arrival times is also treated as unknown. The inversion is carried out for simulated data, and for data from a physical laboratory model. In the latter case, an anisotropic layer is represented by a phenolic canvas electric material, and a star-shaped surface-receiver configuration is used to record microseismic signals. Results show that obtaining unbiased event locations requires an appropriate choice of anisotropy model and the ability to resolve anisotropy parameters. The resolution of anisotropy parameters requires significantly more data information from microseismic acquisition than required for isotropic models. Therefore, we study several acquisition scenarios for simulated and laboratory data. Assuming an HTI model in the inversion when data originate from an ORT medium causes systematic errors in event locations. However, appropriate resolution of ORT parameters requires a large acquisition aperture, an accurate perforation-shot timing, and the combination of surface acquisition with a vertical downhole array. These scenarios provide new knowledge about field requirements to produce sufficient information for the resolution of microseismic event locations in the presence of ORT effects in the data.