We invert geodetic measurements of coseismic deformation from the 1989 M(S)7.1 Loma Prieta earthquake to determine the geometry of the fault and the distribution of slip on the fault plane. The data include electronic distance measurements, Global Positioning System and very long baseline interferometry vectors, and elevation changes derived from spirit leveling. The fault is modeled as a rectangular dislocation surface in a homogeneous, elastic half-space. First, we assume that the slip on the fault is uniform and estimate the position, orientation, and size of the fault plane using a nonlinear, quasi-Newton algorithm. The best fitting dislocation strikes N48 degrees +/- 4 degrees W and dips 76 degrees +/- 9 degrees SW, consistent with the trend of the aftershock zone and moment tenser solutions. Bootstrap resampling of the data is used to graphically illustrate the uncertainty in the location of the rupture plane. The 95% confidence envelope overlaps the aftershock zone, arguing that there is not a significant discrepancy between the geodetic data and the aftershock locations. Second, we estimate the slip distribution using the best fitting uniform slip fault orientation but increase the fault length to 40 km and the downdip width to 18 km. The fault is divided into 162 subfaults, 18 along strike and 9 along dip. Each subfault is allowed to have constant right-lateral and reverse components of slip. We then solve for the slip on each subfault that minimizes a linear combination of the norm of the weighted data residual and the roughness of the slip distribution. The smoothing parameter, which determines the relative weight put on fitting the data versus smoothing the slip distribution, is chosen by cross validation. Simulations indicate that cross-validation estimates of the smoothing parameter are nearly optimal. The preferred slip distribution is very heterogeneous, with maximum strike slip and dip slip of about 5 and 8 m, respectively, located roughly 10 km north of the hypocenter. There is insignificant dip slip in the southeastern most part of the fault, causing the rake to vary from nearly pure right-lateral in the southeast to oblique right-reverse in the northwest. The change in rake is consistent with a uniform stress field if the fault dip increases by about 10 degrees toward the southeast, as indicated by the aftershock locations. There was little slip above 4 km depth, consistent with the observation that there was little, if any, surface rupture.
