Four-dimensional geodesy: time dependent inversion for earthquake and volcanic sources

Abstract

The past five years has witnessed a tremendous expansion in the number of permanent Global Positioning System (GPS) receivers. There are now GPS networks in Japan, California, and Hawaii that provide crustal deformation data that are dense in both space and time. These data, combined with tilt and bore hole strain measurements, can be used to invert for spatial and temporal variations in fault slip and magma chamber dilation. Previously, space-time inversions had been hampered by poor signal to noise in the data, contaminating non-tectonic motions near the instrument (benchmark wobble), and our lack of knowledge of the temporal character of aseismic motions. The recently introduced Network Inversion Filter (Segall and Matthews., 1997) yields estimates of quasi-static fault slip as a function of space and time using data from dense continuous geodetic networks. The NIF employs time domain, Kalman filtering, and allows for non-parametric descriptions of slip velocity, local benchmark motion, and measurement ’error. A state-space model for the full geodetic network is adopted, so that all data from a given epoch are analyzed together. This allows the filter to distinguish between non-steady fault slip and local surficial effects like benchmark wobble.

We have used the Network Inversion Filter to analyze the time-dependence of post-seismic slip following the 1989 Loma Prieta earthquake, (Segall and others, 1999) to image rift-zone deformation opening and aseismic fault slip following the January 30, 1997 eruption at Kilauea volcano, Hawaii, and to image a propagating dike off the Izu Peninsula in Japan (Aoki and others, 1999). In situations where the geometry of the causative geologic structures is unknown it is advantageous to use filtering techniques to image the strain-rate fields in space and time.