| While a variety of innovative, nonlinear analysis techniques are applied to measured data in other areas of physics, they rarely are employed in the field of solid earth geophysics. Yet a wide variety of geophysical data already exists which could be studied using these methods. The historical earthquake record, for example, while not complete, spans hundreds to thousands of years of human history. As a result, earthquakes in seismically active regions are known to be associated with a variety of spatial and temporal patterns. Examples include precursory quiescence or enhanced activity, aftershocks, characteristic earthquakes, and seismic clustering. A spatially coherent, uniformly high level of stress on a fault is a necessary precondition for the occurrence of a large earthquake. Recently, several groups have found that spatial coherence in the stress field is reflected in a similar coherence in the seismic activity. Here I employ a Karhunen-Loeve decomposition method to systematically quantify the spatial and temporal characteristics of patterns in historic seismicity in southern California based upon these underlying correlations. This Karhunen-Loeve decomposition expands the seismicity into its orthonormal eigenvectors and eigenvalues, isolating the important normal mode patterns. The demonstrated results strongly support the view that seismic activity is highly correlated across many space and time scales within large volumes of the earth's crust.; I then identify systematic space-time variations in the seismicity from southern California using a new technique. This procedure is based upon the idea that seismic activity corresponds geometrically to the rotation of a pattern state vector in the high-dimensional correlation space spanned by the eigenvectors; of a correlation operator. Using this new technique it is possible to isolate emergent regions of coherent, correlated seismicity. Analysis of data taken only up to December 31, 1991 reveals that the appearance of these correlated regions is often associated with the future occurrence of major earthquakes in the same areas. These major earthquakes include the 1992 Landers, the 1994 Northridge, and the 1999 Hector Mine events.; The space-time patterns in the seismic activity, identified by these two phase dynamical applications, directly reflect the existence of stress correlations. The success of both the Karhunen-Loeve decomposition on the historic seismicity in southern California, and the identification of anomalous seismicity or precursory quiescence prior to large earthquakes, supports recent work that suggests that correlated structure exists in the underlying stress and strain fields, a necessary precondition for the occurrence of large earthquakes. |
