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.

Assessing Search and Unsupervised Clustering Algorithms in Nested Sampling

“…Density-based spatial clustering for applications with noise (DBSCAN) [20] was recently implemented as a post-processing step to recluster points sampled by MultiNest [3] since the clustering methods used in the program (X-means and k-means) were not adapted to a specific problem (microseismic events) [21]. DBSCAN requires two input parameters that are chosen by the user: a radius ϵ and a minimal number of neighbors m. Using these parameters, the points are divided into three categories:…”

Bayesian Noise Modelling for State Estimation of the Spread of COVID-19 in Saudi Arabia with Extended Kalman Filters

“…Among these methods, we used the nested sampling algorithm proposed in [ 2 ] due to its simplicity and efficiency in approximating the marginal likelihood for even large-scale Bayesian inference problems, as shown by [ 31 ], in comparison to other methods. The nested sampling and efficient Bayesian inference algorithms have been successfully applied in various fields, including cosmology [ 32 , 33 ], epidemiology [ 1 , 34 ], spatio-temporal inference problems in geophysics [ 35 ], material science [ 36 ] and other such fields where Bayesian inferences are traditionally applied to fit data with mechanistic models.…”