A physical model for earthquakes: 2. Application to southern California

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Abstract
The purpose of this paper is to apply ideas developed in a previous paper to the construction of a detailed model for earthquake dynamics in southern California. The basis upon which the approach is formulated is that earthquakes are perturbations on, or more specifically fluctuations about, the long‐term motions of the plates. This concept is made mathematically precise by means of a “fluctuation hypothesis,” which states that all physical quantities associated with earthquakes can be expressed as integral expansions in a fluctuating quantity called the “offset phase.” While in general, the frictional stick‐slip properties of the complex, interacting faults should properly come out of the underlying physics, a simplification is made here, and a simple, spatially varying friction law is assumed. Together with the complex geometry of the major active faults, an assumed, spatially varying Earth rheology, the average rates of long‐term offsets on all the major faults, and the friction coefficients, one can generate synthetic earthquake histories for comparison to the real data. The result is a set of slip‐time histories for all of the major faults which are similar to data obtained by geologic trenching studies. However, the patterns of earthquake occurrence are evidently chaotic (in the technical sense), meaning that although there is an element of periodicity to the events, the patterns shift, change, and evolve with time. Time scales for pattern evolution seem to be of the order of a thousand years for average recurrance intervals of a hundred years or so. In the synthetic slip histories for the model faults a series of events on the Big Bend is identified which resembles the pattern of events leading up to the 1857 Fort Tejon earthquake. One of the events is similar enough to the 1857 event that it is taken as a model of that earthquake. The horizontal surface deformation 130 years after the model event is calculated for comparison to the data observed by various methods during the past decade in southern California. For example, horizontal surface rates of strain and velocities are calculated and compared to U.S. Geological Survey trilateration data, to very long baseline interferometry line length changes, and to laser ranging data on the San Andreas fault experiment baseline. With a few exceptions, agreement is good.