Slicing up the San Francisco Bay Area: Block Kinematics from GPS-derived Surface Velocities

Matthew A. d'Alessio, Ingrid A. Johanson, Roland Bürgmann, David A. Schmidt, and Mark H. Murray

The Berkeley Seismological Laboratory has collected and compiled interseismic velocities at over 200 Bay Area stations. This data set, the Bay Area Velocity Unification (BAVU, pronounced ``Bay View") is the most comprehensive picture of crustal deformation in the region compiled to date. We use a block modeling approach to interpret these velocities at an unprecedented range of spatial scales. In this approach, we solve for the motion of fault bounded blocks that is most consistent with the observed surface velocities.

Figure 19.1: Calculated poles of rotation and 95% confidence limits for blocks in the Bay Area. Other than the Pacific-SNGV pole, all poles are relative to North America (NA). The diamond near Hudson Bay indicates the PA-NA from a two plate model that excludes stations near the plate boundary.
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The Global Picture

Using the block model, we constrain the motion of blocks in the Bay Area relative to adjacent global plates (North America and Pacific), as well as the SNGV microplate. Individual blocks within the Bay Area do not move about identical poles of rotation of any of these major blocks as a ``perfect transform" system, but instead have poles at intermediate locations. The poles transition systematically from west to east (Fig. 19.1). This systematic pattern may have implications for the development of the fault system.

Slip Rates on Bay Area Faults

We show a comparison between data and model velocities in (Fig. 19.2). Looking at the Bay Area region itself, we focus on quantifying the slip rates of individual faults. We use precise relocations of earthquakes to determine the maximum depth of seismicity as a proxy for the local seismic/aseismic transition. We find slip rates that are typically within the uncertainty of geologic estimates (Table 19.1). We also document substantial slip on segments that have not been emphasized in previous studies. Models that include up to 4 $mm \cdot yr^{-1}$ of strike-slip on the West Napa fault north of San Pablo Bay provide almost identical model fit to those that exclude this fault. In our preferred model, we favor this geometry because it is consistent with geologic evidence showing that the some slip from the Calaveras fault is transferred westward, eventually connecting to the West Napa fault system. Adding a fault along the eastern margin of the Coast Range in our preferred model produces lower misfit and a geologically reasonable slip sense (right-lateral) on the Greenville - a notable improvement over models that exclude this ``Valley Margin" deformation zone. This fault, running parallel to the San Andreas through central California carries $\sim5$ $mm \cdot yr^{-1}$ of right-lateral slip and 3 $mm \cdot yr^{-1}$ of fault-normal convergence. Poor data coverage near the model fault segment prevent us from determining if the deformation is accommodated by a single structure or a broad zone with many structures as might be implied by the distribution of moderate thrust earthquakes within the Diablo and Coast Ranges. We find that a similar magnitude of convergence is preferred along the entire eastern front of the Coast Range, but that an equal and opposite extension is observed west of the Bay in our models. Our block modeling approach provides the first strong geodetic constraints on the slip rates of several other faults because we include global GPS data from the Pacific plate and the physical constraint of coherent block motion. These faults include the San Gregorio fault ($2.4 \pm 0.5$ $mm \cdot yr^{-1}$ right-lateral slip rate) and the Mount Diablo thrust ($3.9 \pm 0.5$ $mm \cdot yr^{-1}$ reverse slip and an almost equal magnitude of right-lateral strike-slip). Overall, we find that the slip rates we determine fit GPS data substantially better than the slip rates defined in Working Group on California Earthquake Probabilities.

Figure 19.2: Observations (wider vectors with error ellipses) compared with model results (narrow, darker vectors) for our preferred model. Dotted grey lines represent the simplified geometry of faults in our model. Numbers indicate strike-slip and tensile-slip rates and 95% ($2\sigma$) uncertainties for select fault segments. Positive strike-slip indicates right-lateral slip. Positive tensile-slip indicates contraction while negative tensile-slip indicates extension.
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Fault Connectivity

Locally, block modeling allows us to test the connectivity of faults. Faults that are connected can transfer slip, so these connections have implications for slip rates and seismic hazard assssment. We show that shallow creep on Paicines fault is important, but that deep slip is best modeled when the Calaveras fault is directly connected to both the Paicines and San Andreas faults. East of the Bay, we explore the possibility that the northern Calaveras fault transfers its slip east to the Concord/Green Valley fault, west to the West Napa fault system, or a combination of the two. The data slightly favor the eastern step over the western step alone, but we prefer models where both connections are included because they most closely reproduce the geologically inferred slip rate on the Green Valley fault and the lowest total model misfit.

In block modeling, three-dimensional fault geometry and connectivity have a very strong impact on the interpretation of surface deformation. While we systematically explored an extremely wide range of model geometries in this work, we look forward to further geologic constraints on fault geometry in 3-D to improve the reliability of block models. The ability to iteratively explore these different block geometries and test their consistency with geodetic data make the block modeling approach an excellent tool for understanding fault kinematics in the Bay Area.


Table 19.1: Comparison of strike-slip rates for geologic estimates (Working Group on California Earthquake Probabilities, WG03) and this study. Fault system names from top row: SG, San Gregorio; SA, San Andreas; RC, Rodgers Creek; H, Hayward; C, Calaveras; GV, Green Valley; Gr, Greenville. Fault segments from second row: N, North; C, Central; S, South; Mr, Marin; SF, San Francisco; SCM, Santa Cruz Mountains; RC, Rodgers Creek; H, Hayward; WN, West Napa; Cn, Concord; Gr, Greenville. Total for the northern section includes the sum of SA-Mrn + RC + WN + GV. Southern total is sum of SG-S + SA-SCM + C-C + Gr. We show 95% confidence bounds ($\pm 2 \sigma$) for the three main models. Bounds for other models are similar in magnitude.
Study SG SA RC/H C GV/Gr Total    
  N S Mr SF SCM RC H WN N C S GV Cn Gr N S    
WG03 7 3 24 17 17 9 9 - 6 15 15 5 4 2 38 37    
This Study 2.4 3.0 20.2 17.1 16.4 6.6 6.5 4.0 6.2 12.9 12.7 7.0 6.7 5.4 37.8 37.7    
$\pm$ 1.0 0.8 1.4 1.4 1.0 2.4 1.4 3.0 0.8 0.6 0.4 1.8 1.4 0.6 4.5 1.5    

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