A NEW APPROACH TO TIME-DEPENDENT INVERSION OF GEODETIC DATA USING A MONTE CARLO MIXTURE KALMAN FILTER

Abstract

It is important to precisely clarify time history of transient fault slip or magma intrusion (hereafter we simply call them fault slip) from surface deformation measurements to understand the physical processes of earthquake generation and volcano eruption. We have developed a new time dependent inversion method for imaging detailed time history of fault slip from geodetic data. We employed a stochastic model that enables non-parametric description of fault slip evolution. In this framework, temporal smoothness of slip is determined by a scaling parameter (temporal smoothing parameter). In order to reconstruct detailed time history of fault slip, we assumed that the temporal smoothing parameter is variable in space and time. In this case, Kalman filter that has been used in past studies cannot be used because spatio-temporal distribution of the temporal smoothing parameter is unknown. In order to estimate slip history under this condition, we have developed a new filtering technique, Monte Carlo mixture Kalman filter (MCMKF), and applied it to the time dependent inversion. The validity of the MCMKF based inversion scheme is investigated through numerical experiments. In the numerical experiments, the MCMKF based inversion scheme is applied to the simulated displacement time series generated by 4 sources: 1 Mogi source, 2 tensile faults, and 1 shear fault. In a source, the temporal smoothing parameter and the slip are assumed to be temporally variable and spatially uniform, and the temporal evolutions of the temporal smoothing parameter and the slip are allowed to take different values in respective sources. Then results are compared with those obtained by the conventional Kalman filter based scheme. The results show that the MCMKF based method is capable of imaging spatio-temporal variation of fault slip together with the temporal smoothing parameter that is variable in space and time. We also find that the MCMKF is able to image whole time history of transient slip events more precisely than Kalman filter. Especially, the MCMKF is superior to Kalman filter in precisely reproducing slip rate changes and propagating slip. Furthermore, the MCMKF gives significantly smaller AIC (Akaike information criterion) values than Kalman filter. These results indicate that the MCMKF yields better slip estimates than Kalman filter.