Post-seismic stress evolution.
Liz Hearn has been studying the various transient behaviors excited by an earthquake. In general, this evolution takes the coseismic stress (the half-space solution) toward the layer solution, which involves a transfer of load to the elastic upper layer (which is, essentially, seismogenic layer) as the underlying visco-elastic material relaxes. This process has been modeled analytically under various idealized conditions (e.g., Li and Rice, 1987) and modeled numerically in some simple cases (e.g., Lyzenga et al., 1991). Motivated by a desire to model the actual data produced by the post-seismic stress and strain response of actual earthquakes, our goal is a development of methods to model these more complicated situations. Towards this end, we are developing finite element code that incorporates capabilities to handle: finite, arbitrarily shaped faults; body forces (important in dip-slip ruptures); sub-seismogenic creeping faults; and laterally variable rheological properties (described either statistically or deterministically). Two examples of our results are shown in Figure 1. In part (a) we compare the effects of two relaxation processes: lower crustal visco-elastic relaxation and lower crustal creep on the downward extension of the upper crustal dislocation. These initial results are encouraging in that the predicted geodetic responses are considerably different, suggesting an ability to differentiate between these mechanisms of relaxation (recall that for an infinite fault, Savage (1990) found that little difference may exist between these two cases). In part (b) we show initial results for the Landers-Big Bear earthquake pair, modeled with the creeping deep fault assumption. This work is being presented at the AGU (Hearn and Humphreys, 1997a).
Southern California kinematics and dynamics.
Liz Hearn has modeled the kinematics of the southern Walker Lane Belt (the northern extension of the eastern California shear zone) using the finite element technique of Saucier and Humphreys (1993). This work was submitted to JGR in September (Hearn and Humphreys, 1997b). The focus on this region was to resolve major kinematic contradictions that result from estimates derived from geologic (fault slip rate and orientation) and geodetic data sets. Figure 2 shows some of these results.
From the standpoint of SCEC's mission, resolution of Sierra Nevada-Great Valley block motion is the most important result: since the San Andreas system lies between the rigid Pacific plate and the Sierra Nevada-Great Valley block, knowledge the motion of the bounding rigid bodies provides strong constraint on the strain (and clues on the stress behavior) in the vicinity of the San Andreas in central California. Prior estimations of the Sierra Nevada relied on the motion of VLBI site OVRO (Figure 2); the result has the Sierra Nevada rotating counter clockwise at ~0.6 degrees/m.y. (Argus and Gordon, 1990) which, among other things, would result in right-lateral slip on the Garlock fault. New, high-resolution VLBA (very long baseline array) data indicate that OVRO is moving significantly more westerly than deduced from VLBI data, and the new data result in Sierra Nevada motion that occurs without significant rotation. In particular, this admits up to 6 mm/yr of left-lateral slip on the Garlock fault; in general, it is consistent with the geologic data. The new Sierra Nevada velocity also results in more contraction normal to the San Andreas fault (from ~2.5 mm/yr near Gorman to zero near Cape Mendocino).
Randy Palmer has been working on southern California kinematics and dynamics. Because of a nine-month leave from this project, current results are not significantly beyond where they were at this time last year. However, Randy currently is working exclusively on this project, and every effort will be made to achieve our proposed goals and get the resulting papers submitted prior to the end of this year's funding cycle. With little progress to show, I simply review the goals of this project. The main purpose of this project is to understand in southern California the importance of plate interaction and locally-created forces derived from southern California's density structure. The former is transform in nature, and therefore purely passive; the latter is purely active. One important goal is to quantify the strength of the San Andreas fault, averaged over depth and earthquake cycles (i.e., the "tectonic" strength of the San Andreas). We addresses this as follows. The Pacific plate moves past North America with no regard to the tectonics of southern California, and the resulting forces are controlled by the local rheology (e.g., fault strength). Southern California tectonics are significantly perturbed from that which is possible solely with transform tectonics: motion of the Salton and Perris blocks away from the Salton Trough and toward the Transverse Ranges (Kosloff, 1977) requires the action of locally derived forces (Bird and Baumgardner, 1984; Humphreys and Hager, 1990). The force responsible for this behavior is understood to be mantle downwelling beneath the Transverse Ranges (Bird and Rosenstock, 1984; Humphreys and Clayton, 1990). Moho and surface topography also contributes to the locally-created forces (and these forces resist the motion of the Salton and Perris blocks). Because the local forces can be estimated (from their inferred densities), and the transform-derived forces are related to the (know) plate velocity through the rheology, a balancing of forces results in an estimate of the controlling rheologies (especially the tectonic strength of major faults).
The western U.S. tectonic system.
On a more general level, I'm coming to understand the importance of viewing the western U.S. as an integrated tectonic system, and that interactions among the various tectonic domains are important to the local behavior in any region. On the time scale of earthquake cycles, stress interactions are limited in space by length scales commensurate with the coseismic rupture, and by visco-elastic stress diffusion. These interactions are controlled by the coseismic elastic stress changes (e.g., Stein, 1994), and the interseismic stress relaxation described above (Liz Hearn's work). Secular stress accumulation can simply be summed with the these earthquake-induced fields. But important in controlling the long-term state of stress (the "DC" state at the time scales of earthquake cycles) are the regional tectonic interactions, and these can be far reaching. An example, important to the San Andreas fault in south-central California, is the origin of the normal stress acting on this fault. The southern Sierra Nevada-Great Valley block is bounded on its east side by a zone of positive dilation (the transtensional Walker Lane Belt), and on its west side by a zone of contraction (the transpressional zone that includes the San Andreas fault and an active fold and thrust belt (Mount and Suppe, 1987)). By simple force balance, a force is acting on the Sierra Nevada-Great Valley block that is directed WSW, normal to the San Andreas. Hence, the observation that the maximum compressive stress is oriented nearly normal to the San Andreas does not mean that this fault is weak (or strong).
We currently are developing a capability to model western U.S. dynamics quantitatively, so as to estimate stresses and strengths everywhere. Central to this effort is the development of (what I envision to be) a master-model approach to attacking complex, data-intensive problems that involve many data types. [This effort is being done as a part of a rapidly growing collaboration between the University of Oregon Departments of Geological Sciences and Computer Science.] A highly structured approach is required to manage these kinds of problems. The key elements are data, code that relate data ("filters"), and basic utility programs. Coordination among these elements is crucial. As an example, our finite element code can be viewed as a linear filter that weights and sums "inputs" (such as the density structure and boundary velocities) to produce "outputs" (such as stress and deformation rates). Outputs like deformation rate (i.e., model predictions) can then be compared to relevant observations (e.g., fault slip rate and geodetic data). All output is considered potential input to other routines. In this example, density structure is itself the output of a filter for which data like topography, gravity and seismic structure are inputs.
References
Bird, P., & J. Baumgardner, 1984, JGR.
Bird, P., & R. Rosenstock, 1984, GSA Bull.
Humphreys, E., & R. Clayton, 1990, JGR.
Hearn, E. & E. Humphreys, 1997a, EOS (abs.).
Hearn, E. & E. Humphreys, 1997b, Kinematics of the southern Walker Lane Belt and motion of the Sierra Nevada block, submitted in Sept. to JGR.
Humphreys, E., & B. Hager, 1990, JGR.
Humphreys, E., & R. Weldon, 1994, JGR.
Kosloff, D., 1977, Geophys. J. R. astr. Soc.
Mount, V. & J. Suppe, 1987, Geology.
Saucier F., & E. Humphreys, 1993, in AGU Geodyn. Series, vol. 23, Crustal Dynamics: Space Geodynamics v. 23, AGU.
