Numerical Models of Crustal Deformation

Citation

Kosloff, Dan Douglas (1978) Numerical Models of Crustal Deformation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/vdzd-sz11. https://resolver.caltech.edu/CaltechTHESIS:08162024-195509226

Abstract

Several tectonic features in Southern California cannot be directly explained by the plate tectonic interpretation for the region. In particular, both the existence of the Transverse Ranges and the geometry of the San Andreas fault imply a stress pattern deviating from the simple horizontal shear, which parallels the spreading between the Pacific and North American plates. A number of possible mechanisms responsible for this anomalous stress field, are examined quantitatively in the light of seismicity and other tectonic observations, and in particular to the Palmdale uplift which was reported to have occurred between the years 1960-1965.

The subsidence in the Wilmington oil field in Long Beach has long been a source of concern, as its economic consequences were disastrous. An area of approximately 20 mi has been affected by the subsidence, which in 1965 reached a value of 29 ft in the center of a bowl shaped pattern. The subsidence was accompanied by horizontal displacements of up to 12 feet. A series of shallow earthquakes, with hypocentral depths between 500 to 600 meters took place in the years 1947, 1949, 1952, 1955, and 1961. The slip planes were within a thin shale layer above the producing zones of the Wilmington field. It is now agreed upon that the subsidence was caused by the pore fluid pressure reduction resulting from oil production in the field. Indeed, after a repressurization program had been initiated, the subsidence was virtually stopped in all areas of the field. The subsidence, and subsequent rebound are simulated with the aid of the Finite Element calculation method. Pressure data compiled from records of individual oil wells are converted to input data for the numerical calculation. The simulations reproduce synthetically the field observations of vertical movements, horizontal movements, and collar count survey data. For the material rheology of the formations of the Wilmington field, first a layered linearly elastic approximation is used. However, it is found that not all observations can be reproduced with this material model, and in particular, the size of the subsidence pattern is overestimated by the linear models. Therefore, a more complete elastic-plastic cap model is incorporated into the simulations. With the aid of the nonlinear material characterization, the field observations can be reproduced in a satisfactory manner. It is demonstrated that the stress, prior to the onset of oil production in the Wilmington field, can have a dominant influence on the size and shape of the subsidence pattern. Accordingly, the final, and most successful, simulation includes a horizontal extensional stress component which is added to the overburden stresses at points lying in the vicinity of the center of subsidence.

The lithosphere in the vicinity of island arcs and seamounts can be modeled as a plate which overlies an invicid fluid of asthenosphere material. It has been recognized that bathymetry profiles in such areas resemble the mathematical solutions of certain plate bending problems. This study attempts to improve on previous models by incorporating a lithosphere rheology based on rock deformation data for Dunn-Mountain Dunite. The material behavior is approximated to be as strain rate dependent elastic-plastic. The rheological approximation is converted into a moment-curvature relation for the lithosphere, which in turn is incorporated into a Finite Element algorithm for solving von Karman's plate bending equations. The complete formulation is tested in matching gravity and bathymetry in a profile in the vicinity of the island of Molukai of the Hawaiian-Emperor seamount chain. It is shown that the model can match the observations, while avoiding the excessive fibre stresses which have been produced in previous models.

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