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Modeling Broadscale Deformation From Plate Motions and Elastic Strain Accumulation

Mark Murray


In Murray and Segall (2001), we present a first-order method for modeling broadscale deformation consistent with both plate tectonic motions and elastic strain accumulation on plate boundary faults. This method assumes interseismic deformation is a superposition of long-term rigid-body motions between faults, defined by angular velocities of spherical plates, and backslip on shallow locked portions of faults in an elastic half-space. Unlike deep-slip fault models, which poorly describe deformation in the far-field, motions far from plate boundary faults are consistent with those predicted by Euler poles, while elastic strains due to shallow back-slip remain localized to the crust adjacent to the faults and to the fault ends at triple junctions. This method can accommodate complex, strike-slip, thrust, and normal fault systems, and incorporate additional constraints from plate tectonic models and geologic observations.

We define station velocity at geocentric position r as

{\bf v}({\bf r}) = {\bf\Omega(r)} \times {\bf r}
- \sum^F_{f=1} {\bf G} \cdot {\bf s}_f
\end{displaymath} (13.1)

where ${\bf\Omega}$ is the angular velocity vector, and the effect of interseismic strain accumulation is given by an elastic Green's function ${\bf G}$ response to backslip distribution ${\bf s}$ on each of $F$ faults. In general, the model can accommodate zones of distributed horizontal deformation if ${\bf\Omega(r)}$ varies within the zones, and the latter terms can account both for the Earth's sphericity and viscoelastic response of the lower crust and upper mantle. For the northern California and Nevada study, we make several assumptions, such as rigid plate behavior and elastic dislocations to approximate strain accumulation, that reduce the model to a simple analytical function suitable for optimization. For example, assuming strain accumulation occurs on only 3 San Andreas system faults that lie along small circles about a fixed Euler pole location, allows the second term in Eq. 13.1 to rewritten in terms of angular velocities and angular distances $\phi$ from the Euler pole:
- \frac{a}{\pi} \sum^F_{f=1}
\Delta\omega_f \sin\phi_f \tan^{-1} \frac{d_f}{a(\phi - \phi_f)}
\end{displaymath} (13.2)

where $a$ is the Earth radius, and the distance from each fault located at $\phi_f$ is $a(\phi - \phi_f)$. Each fault has deep-slip rate $s_f = a
\Delta\omega_f \sin\phi_f$, where $\Delta\omega_f$ is the difference in angular velocity rates on either side of the fault.

We applied this method to continuous GPS measurements collected during 1993-2000 at 35 sites in a profile from the San Francisco Bay area, northern California to eastern Nevada. We use continuous GPS data from the Bay Area Regional Deformation (BARD) network in northern California (Murray et al., 1998), the northern Basin and Range (NBAR) network in Nevada and eastern California, the International GPS Service (IGS), and other agencies.

Deformation is consistent within the 1 mm yr$^{-1}$ uncertainties of the observations with a simple 10-parameter model using 6 rigid plates and 3 locked San Andreas system faults. Predicted relative motions across the plate boundaries suggest that deformation across the Basin and Range province can be partitioned into 2.5 mm yr$^{-1}$ east-west extension across the Intermountain Seismic Belt, including the east-west extending Wasatch fault in Utah, 2.3 mm yr$^{-1}$ east-west extension across the Central Nevada Seismic Zone, and 3.6 mm yr$^{-1}$ primarily right-lateral strike-slip on the northern Walker Lane Belt. These results are in reasonable agreement with other GPS studies, although our observations lack sufficient precision and spatial resolution to estimate strain accumulation or detect possible zones of distributed deformation in the Basin and Range, as suggested by some of these studies.

The Sierran-Great Valley microplate moves obliquely to the San Andreas system, causing $\sim $2.4$\pm$0.4 mm yr$^{-1}$ fault-normal convergence that may be accommodated over a fairly narrow ($<$15 km) zone, possibly contributing to uplift of the Coast Ranges. The predicted deep-slip rates on the San Andreas system agree with geologic estimates. The total deep-slip rate across the San Andreas system ($\sim $37.2$\pm$1.0 mm yr$^{-1}$) is consistent with geologic estimates based on the most active Holocene faults.

Additional details are available in the July 1999-June 2000 BSL Annual Report and in Murray and Segall (2001). We are currently enhancing this study to better define the reference frame for plate motion estimation, including more continuous and survey-mode GPS observations to better resolve the spatial extent and distribution of deformation and strain accumulation effects, and developing 3D plate boundary models that will better approximate the complex fault geometry of the San Andreas system in the San Francisco Bay area and along the Cascadia subduction zone. We report on a few of these developments below.

Figure 13.1: Station velocities with 95% confidence regions relative to a "stable" North America reference frame. The reference frame is defined by minimizing the horizontal velocities of 16 stations shown. Also included are a representative set of northern California and Nevada stations showing the gradient in deformation across the Pacific-North America plate boundary. The 3 labeled stations define the velocity reference frame in Murray and Segall (2001).
\epsfig{, width=13cm}\end{center}\end{figure*}

Reference Frame Definition

In Murray and Segall (2001), we found the estimated Pacific plate angular rate about the assumed NUVEL-1A Euler pole (0.774$\pm$0.020$^{\circ }$ Ma$^{-1}$) was significantly higher than the 3.16 Ma-average NUVEL-1A rate (0.749$\pm$0.012$^{\circ }$ Ma$^{-1}$), in agreement with other recent GPS-derived estimates (DeMets and Dixon, 1999). However, our estimated Sierran-Great Valley euler pole location, as well as the assumed NUVEL-1A Pacific-North America plate Euler pole, significantly disagree with other GPS-derived estimates. We suspect that these differences may be due to the relatively weak reference frame realization we used to define the "stable" North America plate.

For each day, we estimated weakly constrained station positions using tightly constrained IGS orbits and International Earth Rotation Service parameters. Station velocities were estimated by tightly constraining 3 IGS stations (ALGO, DRAO, FAIR) to their velocities in the North America plate reference frame of Kogan et al. (2000). In this reference frame DRAO (Penticton, British Columbia) and FAIR (Fairbanks, Alaska), both located within the internally deforming western margin of the North American plate, have motions greater than 1 mm yr$^{-1}$. Although we tried to account for these effects, relying on the horizontal motions of three stations provides only marginal redundancy to define a reference frame specified by a 3-component Euler pole.

To improve the reference frame definition, we are now analyzing the GPS observations in combination with about 50 additional stations, distributed both globally for independent orbit determination and regionally within the Pacific and North America plates for robust estimation of their relative motion. We have estimated velocities from daily station positions at 32-day intervals from 1992-2001. To define a North America plate reference frame, an angular velocity vector that minimizes the horizontal velocities of 16 stations is estimated. The residual velocities of the 16 stations are generally less than 1 mm yr$^{-1}$, except for DRAO, FAIR and a few other stations (Figure 13.1). We are testing the sensitivity of the estimated reference frame to the station assignment, but preliminary results suggest that the reference frame defined by 16 stations is in better agreement with DeMets and Dixon (1999) than the Murray and Segall (2001) reference frame.

Figure 13.2: Observed (solid vectors, with 95% confidence regions) and predicted (open vectors) station velocities in Oregon and Washington relative to stable North America. Predicted velocities assume a uniform angular velocity about the pole (diamond) and 55-km wide locked thrust zone on the offshore Cascadia megathrust.
\epsfig{, width=8cm}\end{center}\end{figure}

Cascadia Subduction Zone

In Svarc et al. (2001), we report on velocities estimated over the interval 1992-2000 at 75 station collected primarily by survey-mode techniques in western Oregon and southwestern Washington. The observed velocity field is approximated by a combination of rigid rotation relative to stable North America, uniform regional strain rate, and a dislocation model representing subduction of the Juan de Fuca plate beneath North America. Subduction south of 44.5$^{\circ }$N was represented by a 40-km wide locked thrust zone and north of 44.5$^{\circ }$N by a 75-km wide thrust zone. The rotation pole is close to the pole previously found in Savage et al. (2000). The strain rate represents uniform contraction in the direction of oblique Juan de Fuca-North America convergence.

These results were derived using a method that is not consistent with plate motions in the far-field. We are currently extending the methodology of Murray and Segall (2001) to the Cascadia subduction zone by applying backslip to rectangular dislocations on the megathrust. As a first approximation, we simultaneously estimate a regional angular velocity, which is close to the Svarc et al. (2001) pole and a uniform 55-km-width locked zone on the entire megathrust (Figure 13.2). Although the velocities in southwestern Oregon are well described, the misfit in southwestern Washington is significant. Allowing the locking width to vary along the subduction zone, as suggesting by other studies (e.g., Murray and Lisowski, 2000), should provide a better fit. We are developing more complex models that better represent the curvature of the megathrust to assess the trade-offs between strain accumulation, rigid rotation, and uniform strain rates.

This study represents our preliminary effort to extend the angular velocity backslip method to the entire western U.S., encompassing both strike-slip and subduction regimes. We are in the process of adding the USGS survey-mode observations in Nevada, the Pacific Northwest, the San Francisco Bay Area to provide better spatial resolution of the deformation field, estimate locking on the other plate boundary faults, and detect zones of distributed deformation.


DeMets, C., and T. H. Dixon, New kinematic models for Pacific-North America motion from 3 ma to present, I: Evidence for steady motion and biases in the NUVEL-1A model, Geophys. Res. Lett., 26, 1921-1924, 1999.

Kogan, M. G., G. M. Steblov, R. W. King, T. A. Herring, D. I. Frolov, S. G. Erorov, V. Y. Levin, A. Lerner-Lam, and A. Jones, Geodetic constraints on the rigidity and relative motion of Eurasia and North America, Geophys. Res. Lett., 27, 2041-2044, 2000.

Murray, M. H., and Lisowski, M., Strain accumulation along the Cascadia subduction zone from Cape Mendocino, California to the Strait of Juan de Fuca, Geophys. Res. Lett., 22, 3631-3634, 2000.

Murray, M. H., and P. Segall, Continuous GPS measurement of Pacific-North America plate boundary deformation in northern California and Nevada, Geophys. Res. Lett., in press, 2001.

Murray, M. H., R. Bürgmann, W. H. Prescott, B. Romanowicz, S. Schwartz, P. Segall, and E. Silver, The Bay Area Regional Deformation (BARD) permanent GPS network in northern California, EOS Trans. AGU, 79, F206, 1998.

Svarc, J. L., J. C. Savage, W. H. Prescott, and M. H. Murray, Strain accumulation and rotation in western Oregon and southwestern Washington, J. Geophys. Res., in review, 2001.

Savage, J. C., J. L. Svarc, W. H. Prescott, and M. H. Murray, Deformation across the forearc of the Cascadia subduction zone at Cape Blanco, Oregon, J. Geophys. Res., 105, 3095-3102, 2000.

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