Real-time seismic signal enhancement utilizing a hybrid Rao-Blackwellized particle filter and hidden Markov model filter

This letter outlines a novel and robust algorithm for identifying seismic events within low signal-to-noise ratio (SNR) passive seismic data in real time. Since the event detection problem is a continuous, real-time process which has nonlinear mathematical representations, a Rao-Blackwellized particle filter (RBPF) is utilized. In this algorithm, a jump Markov linear Gaussian system (JMLGS) is defined where changes (i.e., jumps) in the state-space system and measurement equations are due to the occurrences and losses of events within the measurement noise. The RBPF obtains optimal estimates of the possible seismic events by individually weighting and subsequently summing a bank of Kalman filters (KFs). These KFs are specified and updated by samples drawn from a Markov chain distribution which defines the probability of the individual dynamical systems which compose the JMLGS. In addition, a hidden Markov model filter is utilized within the RBPF filter formulation so that real-time estimates of the phase of the seismic event can be obtained. The filter is demonstrated to provide up to an 80-fold improvement in the SNR when processing simulated seismic data with Gauss-Markov measurement noise.