Modeling of Tectonic Processes Associated with Earthquakes

Citation

Jungels, Pierre Henri (1973) Modeling of Tectonic Processes Associated with Earthquakes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5R3G-8281. https://resolver.caltech.edu/CaltechETD:etd-09202005-112510

Abstract

A finite element variational method is described and applied to the analysis of zero frequency seismic data. This technique presents a suitable tool for the analysis of permanent displacements, tilts and strains caused by seismic events, since it can model variable fault offsets in heterogeneous media.

The accuracy of the technique is demonstrated by detailed static field computations for vertical and dipping dislocations acting in plane strain, corresponding to an infinite-length fault in a homogeneous half space, by comparison with closed form analytic solutions. A parametric study of material inhomogeneities and variable fault offsets reveals that order of magnitude changes in the solutions can occur for both near and far field displacements and strains.

The technique was applied to the San Fernando earthquake using a two-dimensional (plane strain) model. The best solution was obtained by separating the fault into two distinct parts, both having offsets near the surface a factor of five larger than the average slip. Both stress drop and displacements vary by more than an order of magnitude along the fault plane, the maximum occurring at 1 km depth. Several solutions are investigated for the hypocentral region, one of them giving as much as 5 m offset.

The Alaskan earthquake of 1964 is also studied in plane strain, and the observed vertical movements are inverted numerically to yield a "best fit" offset on the fault surface. This solution gives good results for the observed horizontal movement. It is characterized by large variations of the slip with a maximum of 33 m below Montague Island.

Then, a relationship is derived, giving energy released as a function of prestress, fault area, change in the local gravitational potential energy and fault offset, neglecting nonlinear behavior outside the fault zone. The finite element method is shown to allow direct calculation of the terms of the resulting equation from static consideration of failure in a prestress medium.

This is applied to the last solution for the San Fernando earthquake, the best fit offset of the Alaska earthquake and a simple model of the Montana earthquake, 1959. In all three cases, the results indicate that a spatially variable prestress field gives the best representation of the tectonic processes involved. The force of gravity is found to be a significant factor in the energy balance of each event, increasing the estimate of prestress for the thrust faults and the apparent stress drop for the Montana normal fault.

For the San Fernando earthquake, the prestress field in the hypocentral region is shown to exceed critical stress levels corresponding to granite strength as measured in the laboratory, while the average stress drop for the entire fault is below 200 bars. This is a possible answer to the apparent discrepancy between laboratory and average field measurements.

The Wilmington oil field subsidence is modeled by using a finite element code which solves numerically Biot's consolidation theory. The best fit is obtained for a very small interaction constant. The models result in significant stress concentrations which could have triggered the small magnitude events known as the Long Beach subsidence earthquakes.

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