THE 1989 LOMA-PRIETA EARTHQUAKE IMAGED FROM INVERSION OF GEODETIC DATA

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 ele ctronic distance measurements, Global Positioning System and very long baseline interferometry vectors, and elevation changes derived from s pirit leveling. The fault is modeled as a rectangular dislocation surf ace in a homogeneous, elastic half-space. First, we assume that the sl ip on the fault is uniform and estimate the position, orientation, and size of the fault plane using a nonlinear, quasi-Newton algorithm. Th e best fitting dislocation strikes N48 degrees +/- 4 degrees W and dip s 76 degrees +/- 9 degrees SW, consistent with the trend of the afters hock zone and moment tenser solutions. Bootstrap resampling of the dat a is used to graphically illustrate the uncertainty in the location of the rupture plane. The 95% confidence envelope overlaps the aftershoc k zone, arguing that there is not a significant discrepancy between th e geodetic data and the aftershock locations. Second, we estimate the slip distribution using the best fitting uniform slip fault orientatio n but increase the fault length to 40 km and the downdip width to 18 k m. The fault is divided into 162 subfaults, 18 along strike and 9 alon g dip. Each subfault is allowed to have constant right-lateral and rev erse components of slip. We then solve for the slip on each subfault t hat minimizes a linear combination of the norm of the weighted data re sidual and the roughness of the slip distribution. The smoothing param eter, which determines the relative weight put on fitting the data ver sus smoothing the slip distribution, is chosen by cross validation. Si mulations indicate that cross-validation estimates of the smoothing pa rameter are nearly optimal. The preferred slip distribution is very he terogeneous, 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, ca using the rake to vary from nearly pure right-lateral in the southeast to oblique right-reverse in the northwest. The change in rake is cons istent with a uniform stress field if the fault dip increases by about 10 degrees toward the southeast, as indicated by the aftershock locat ions. There was little slip above 4 km depth, consistent with the obse rvation that there was little, if any, surface rupture.