Surrogate regression modelling for fast seismogram generation and detection of microseismic events in heterogeneous velocity models

Given a 3D heterogeneous velocity model with a fewmillion voxels, fast generation of accurate seismic responses at specified receiver positions from known microseismic event locations is a well-known challenge in geophysics, since it typically involves numerical solution of the computationally expensive elastic wave equation. Thousands of such forward simulations are often a routine requirement for parameter estimation of microseimsic events via a suitable source inversion process. Parameter estimation based on forward modelling is often advantageous over a direct regression-based inversion approach when there are unknown number of parameters to be estimated and the seismic data have complicated noise characteristics which may not always allow a stable and unique solution in a direct inversion process. In this paper, starting from Graphics Processing Unit based synthetic simulations of a few thousand forward seismic shots due to microseismic events via pseudo-spectral solution of elastic wave equation, we develop a step-by-step process to generate a surrogate regression modelling framework, using machine learning techniques that can produce accurate seismograms at specified receiver locations. The trained surrogate models can then be used as a high-speed meta-model/emulator or proxy for the original full elastic wave propagator to generate seismic responses for other microseismic event locations also. The accuracies of the surrogate models have been evaluated using two independent sets of training and testing Latin hypercube quasi-random samples, drawn from a heterogeneous marine velocity model. The predicted seismograms have been used thereafter to calculate batch likelihood functions, with specified noise characteristics. Finally, the trained models on 23 receivers placed at the sea-bed in a marine velocity model are used to determine the maximum likelihood estimate of the event locations which can in future be used in a Bayesian analysis for microseismic event detection.