TIME-DEPENDENT INVERSION OF GEODETIC DATA

The recent expansion of permanent Global Positioning System(GPS) netwo rks provides crustal deformation data that are dense in both space and time. While considerable effort has been directed toward using these data for the determination of average crustal velocities, little atten tion has been given to detecting and estimating transient deformation signals. We introduce here a Network Inversion Filter for estimating t he distribution of fault slip in space and time using data from such d ense, frequently sampled geodetic networks. Fault, slip is expanded in a spatial basis set B-k(X) in which the coefficients are time varying , s(x,t) = Sigma (M)(k=1) C-k(t)B-k(X). The temporal variation in faul t slip is estimated nonparameterically by taking slip accelerations to be random Gaussian increments, so that fault slip is a sum of steady state and integrated random walk components. A state space model for t he full geodetic network is formulated, and Kalman filtering methods a re used for estimation. Variance parameters, including measurement err ors, local benchmark motions, and temporal and spatial smoothing param eters, are estimated by maximum likelihood, which is computed by recur sive filtering. Numerical simulations demonstrate that the Network Inv ersion Filter is capable of imaging fault slip transients, including p ropagating slip events. The Network Inversion Filter leads naturally t o automated methods for detecting anomalous departures from steady sta te deformation.