A new approach to time-dependent inversion of geodetic data using a Monte Carlo mixture Kalman filter

• Published in: Geophysical journal international Vol. 159; no. 1; pp. 17 - 39
• Main Authors: Fukuda, Jun'ichi, Higuchi, Tomoyuki, Miyazaki, Shin'ichi, Kato, Teruyuki
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01-10-2004; Blackwell Science Ltd
• Subjects: conditional dynamic linear model; fault slip; geodetic data; Monte Carlo mixture Kalman filter; time-dependent inversion; transient crustal deformation
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1111/j.1365-246X.2004.02383.x

In the last decade, continuous Global Positioning System (GPS) networks have observed transient crustal deformation associated with various types of aseismic fault-slip event in many subduction zones. It is important to precisely clarify the entire time history of these events to understand the physical process of earthquake generation. For this purpose, we have developed a new time-dependent inversion method for imaging transient fault slips from geodetic data. Segall & Matthews (1997) presented a time-dependent inversion method to infer the spatiotemporal distribution of fault slip from geodetic data. They modelled a transient crustal deformation associated with fault-slip events using a linear Gaussian state space model and employed a Kalman filter. They introduced a scaling parameter that represents the temporal smoothness of the fault slip, and assumed that the scaling parameter is constant over the observation period. Under this assumption, abrupt changes of slip have been overly smoothed, whereas estimated slips in a ‘quiet’ steady-state period have been oscillatory. To improve the method, we developed a new filtering technique, a Monte Carlo mixture Kalman filter (MCMKF), and apply it to time-dependent inversion. The MCMKF allows variations of the temporal smoothness of slips by regarding it as a stochastic variable. The MCMKF is based on a Monte Carlo method in which conditional probability density functions of the stochastic variable are estimated recursively. We examine the validity of the introduced MCMKF-based inversion scheme through numerical experiments using simulated displacement time-series. Then, the results are compared with those obtained by a conventional Kalman filter-based scheme. In all cases, MCMKF gives a significantly smaller Akaike information criterion (AIC) values than the Kalman filter. This indicates that MCMKF yields better state estimates than the Kalman filter. We also find that MCMKF is capable of imaging the initiation process of transient slip events in cases with a high signal-to-noise ratio, while the Kalman filter is not. Furthermore, MCMKF is superior to the Kalman filter in detecting small signals from noisy data sets. From all of the results above, we conclude that the new filtering approach introduced here may provide a powerful tool for imaging the time history of fault slips.