The recent expansion of permanent Global Positioning System (GPS) networks 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 attention has been given to detecting and estimating transient deformation signals. We introduce here a Network Inversion Filter for estimating the distribution of fault slip in space and time using data from such dense, frequently sampled geodetic networks. Fault slip is expanded in a spatial basis set k(x) in which the coefficients are time varying, s(x,t)=∑k=1Mck(t)k(x). The temporal variation in fault slip is estimated nonparametrically 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 the full geodetic network is formulated, and Kalman filtering methods are used for estimation. Variance parameters, including measurement errors, local benchmark motions, and temporal and spatial smoothing parameters, are estimated by maximum likelihood, which is computed by recursive filtering. Numerical simulations demonstrate that the Network Inversion Filter is capable of imaging fault slip transients, including propagating slip events. The Network Inversion Filter leads naturally to automated methods for detecting anomalous departures from steady state deformation.¿ 1997 American Geophysical Union