Using Resolution Information to Remove Artifacts from GPS Inversions

We present a resolution analysis of an inversion of GPS data from the 2004 Mw6.0 Parkfield Earthquake. This earthquake provides observations at 13 1-Hz GPS receivers that are close to the fault, which allows for a truly co- seismic dataset that can be used to infer the static slip field. Due to the fact that the static field decays rapidly with distance from the source, we find that the resolution of our inverted slip model is very poor at depth and near the edges of our modeled fault plane, far from GPS receivers. The extreme spatial heterogeneity of the model resolution in the static field inversion leads to artifacts in poorly resolved areas of the fault plane. These artifacts look very similar in character to asperities commonly seen in the final slip models of earthquake source inversions, but in fact in this problem they are caused by a surplus of free parameters. The location of these artifacts is dependent upon the station geometry of the available data and the assumed velocity structure of the region. We demonstrate that a nonuniform gridding of model parameters on the fault can remove these artifacts from the inversion. We generate a nonuniform grid whose grid spacing matches the local resolution length on the fault, and show that it outperforms small uniform grids (which generate spurious structure in poorly resolved regions), and large uniform grids (which lose recoverable information in well-resolved areas of the fault). With a synthetic test, we show that our nonuniform grid correctly averages out small-scale structure in poorly resolved areas of the fault while recovering small-scale structure near the surface. Finally, we present an inversion of the Parkfield GPS dataset on the nonuniform grid. The final model in this inversion gives the final slip on the fault plane, which is finely parameterized near the surface and coarsely parameterized at depth.