Monte Carlo Mixture Kalman Filter and Its Application to Space-time Inversion

It is important to precisely know the whole time history of various types of fault slip events to understand the physics of earthquake generation. We develop a new time dependent inversion method for imaging transient fault slips from geodetic data. Past studies employed a linear Gaussian state space model and applied Kalman filter. The Kalman filter based methods, however, do not allow any variation to the temporal smoothness (or roughness) of fault slips. In the present study, we develop/apply a new filtering scheme, Monte Carlo mixture Kalman filter (MCMKF), to the time dependent inversion. MCMKF allows variation to the temporal smoothing of slips in the following scheme; (1) we prepare a finite number of competing state space models, each of which follows a different state space model, (2) we introduce a switching structure among these competing models.