Microseismic event detection in large heterogeneous velocity models using Bayesian multimodal nested sampling

Abstract In passive seismic and microseismic monitoring, identifying and characterizing events in a strong noisy background is a challenging task. Most of the established methods for geophysical inversion are likely to yield many false event detections. The most advanced of these schemes require thousands of computationally demanding forward elastic-wave propagation simulations. Here we train and use an ensemble of Gaussian process surrogate meta-models, or proxy emulators, to accelerate the generation of accurate template seismograms from random microseismic event locations. In the presence of multiple microseismic events occurring at different spatial locations with arbitrary amplitude and origin time, and in the presence of noise, an inference algorithm needs to navigate an objective function or likelihood landscape of highly complex shape, perhaps with multiple modes and narrow curving degeneracies. This is a challenging computational task even for state-of-the-art Bayesian sampling algorithms. In this paper, we propose a novel method for detecting multiple microseismic events in a strong noise background using Bayesian inference, in particular, the Multimodal Nested Sampling (MultiNest) algorithm. The method not only provides the posterior samples for the 5D spatio-temporal-amplitude inference for the real microseismic events, by inverting the seismic traces in multiple surface receivers, but also computes the Bayesian evidence or the marginal likelihood that permits hypothesis testing for discriminating true vs. false event detection. Impact Statement Bayesian evidence-based reasoning is helpful in identifying real microseismic events as opposed to the environmental noise. The geophysical challenge here is the high-computational burden for simulating noiseless template seismic responses for explosive type events and combining them together having different amplitudes and origin times. We use Gaussian process based surrogate models as proxy for multi-receiver seismic responses to be used for the Bayesian detection of microseismic events in a heterogeneous marine velocity model. We used the MultiNest sampler for Bayesian inference since in the presence of multiple events, the likelihood surface becomes multimodal. From the sampled points, a density-based clustering algorithm is employed to filter out each microseismic event for improved mode separation and obtain the posterior distribution of each event in a joint 5D space of amplitude, origin time, and three spatial co-ordinates. Choice of the resolution parameter in MultiNest sampler (Nlive) is also crucial to obtain accurate inference within reasonable computational time and resources and have been compared for two different scenarios (Nlive = 300, 500). A data analytics pipeline is proposed in this paper, starting from GPU based simulation of microseismic events to training a surrogate model for cheaper likelihood calculation, followed by 5D posterior inference for simultaneous detection of multiple events.