A primary goal of the Geodesy Group is to develop models of interseismic velocities in the LA basin that are plausible from both a geological and a con-tinuum mechanics perspective. Our previous work with viscoelastic models supports the hypothesis that, in steady state, deformation on geologic time scales equals the sum of interseismic deformation plus coseismic deformation. If the effective viscosity of the ductile lower crust is sufficiently high, the variation of crustal velocity during the interseismic period is sufficiently small that the instantaneous velocity field measured by geodesy is close to the average interseismic velocity. We can then use geodetic measurements of interseismic velocities to test prevailing geologic models of the structure of the LA basin. Our research this year focused on determining whether either "thin-skinned" or "thick-skinned" models of geologic structure, with observed fault slip rates: 1) Are internally consistent, within their errors; and 2) Can predict the SCEC GPS velocity field. There is, in general, a problem with regional geologic models (e.g., Dolan et al 1995) in that they violate St. Venant compatibility (or path-integral constraints). That is, the fault geometries and slip rates are not self-consistent; following different paths between two points often results in different accumulated displacements. We solve this problem by deriving a block model of the LA basin (Fig. 1), which automatically enforces compatibility. The motion of each finite block is described as a combination of translation and rotation; infinite blocks can only translate.
We solve for the block motions for both "thin-skinned" and "thick-skinned" models of geologic structure using observed geologic rates of fault slip as data (Fig. 2, black). For a dip-slip displacement rate vr on a ramp fault with dip d, the relative horizontal convergence between blocks for the thin-skinned model is vr, while for the thick-skinned model it is vrcos(d). Thus the resulting block velocities are different for thin- vs. thick-skinned models. The rms mismatch between observed and predicted fault slip rates for the thin-skinned model (Fig. 2, blue) is 1.4 mm/yr. For the thick-skinned model (Fig. 2, red), the rms mismatch is 1.6, marginally worse. We also use the SCEC GPS velocity field (Fig. 3a) to test these predictions of relative block motion. We assume that the interseismic
Figure 1: Geometry of the block model. Boundaries of the 14 blocks (black lines) are superimposed on a fault map of southern Caifornia (gray lines).
velocity can be obtained by subtracting the average rate of interseismic strain accumulation from the geologic rates. We use Okada's formalism to calculate interseismic strain accumulation from the 3-D network of faults forming the boundaries between the rotating and translating blocks. This required us to develop an efficient numerical technique for calculating the strain associated with nonuniform slip on rectangular and triangular fault surfaces.
Both the thin-skinned and the thick-skinned model show excellent general agreement with the observed SCEC velocity field. It is most useful to examine the residual velocities obtained by subtracting the model predictions from the observed velocities in the local reference frame of the Channel Island block. The normalized root mean square (NRMS) residual for the thin-skinned model (Fig. 3b) is 6.9. For the thick-skinned model (Fig. 3c) the NRMS = 4.9. Figure 4 shows the observed and predicted interseismic velocities along the proposed SCIGN dense profile AA'. (The location of the profile and GPS stations are shown in gray in Fig. 3c). Within the basin (distance < 80 km), the thin- and thick-skinned models are indistinguishable, but the plate-parallel velocities in the Mojave are larger for the thin-skinned model, which shows a systematic mismatch to the GPS observations.
Figure 4: Observed and predicted interseismic velocities along the proposed SCIGN dense profile AA', projected into motions parallel to (top) and perpendicular to (bottom) the Pacific-North American relative plate velocity vector. The solid line is the thin-skinned model and the dashed line is the thick-skinned model.
Discussion of results
The main difference in the velocity field for thin- vs. thick-skinned models is that, for the same ramp velocity, vr, the thin-skinned model has a higher far-field horizontal convergence rate, vr, than the thick-skinned model, , vrcos(d). The differences between the two models are largest in the far-field, where convergence on several subparallel dip-slip faults can accumulate, and more important for the GPS comparison than for the geologic comparison.
For the geologic comparison, both thin- and thick-skinned block models give reasonable predictions of fault slip rates, with rms mismatches of ~ 1.5 mm/yr, comparable to the uncertainties in determining fault slip rates. For both thin- and thick-skinned block models, the main mismatch between observed geologic fault slip rates and inferred model rates is a prediction of significant convergence across predominantly strike-slip faults (e.g., San Andreas, Garlock, San Jacinto, Elsinore). In addition the inversions for block velocities predict less strike-slip motion on the San Jacinto and Elsinore than is observed geologically. Thus, including compatibility constraints leads to the inference of more compression across the Los Angeles region than is accounted for in geologic estimates. If this compression is taken up seismically, the hazard from blind thrust faults is higher than that recognized in geologic studies.
Both thin- and thick-skinned block models fit the GPS observations within the LA basin, but both show many-sigma residuals in the far-field; the NRMS for the thin-skinned model (6.9) is 40% larger than for the thick-skinned model (4.9). The largest discrepancies are in the CR block, where there are significant residual velocities oriented along the direction of the Pacific plate motion. One likely explanation is that the CR block should be divided into two blocks, separated by a strike-slip fault. Although the CR block is far from Los Angeles, estimates of convergence within the Los Angeles basin are strongly influenced by how motion is fed into (and out of) the Los Angeles basin by strike-slip faults, so including such a structure seems important. The other region with substantial systematic mismatches is in the vicinity of the Salton trough, perhaps because the parameterization of the eastern boundary of the Mojave block (Fig. 1) is inadequate.
Publications and Products
During the current year, under partial SCEC funding, one paper was revised and published, one is nearing submission, and Souter's Ph. D. thesis is to be completed:
Fault propagation fold growth during the 1994 Northridge, California, Earthquake?, B. J. Souter and B. H. Hager, J. Geophys. Res., 102, 11,931-11,942, 1997.
Three-dimensional block models of deformation of the Los Angeles region, B. J. Souter and B. H. Hager, J. Geophys. Res., to be submitted, December, 1997.
Comparisons of geologic models to GPS observations in southern California, B. J. Souter, Ph. D. thesis, Massachusetts Institute of Technology, to be submitted, December, 1997. Hager presented these results at the September 18-19, 1997, SCEC Workshop "Uncertainty in Earthquake Source Characterization for the Los Angeles Basin." He is also on the SCIGN Coordinating Committee.
