Using Eigenpattern Analysis to Constrain Seasonal Signals in Southern California

Abstract

— Earthquake fault systems are now thought to be an example of a complex nonlinear system (Bak, et al., 1987; Rundle and Klein, 1995). The spatial and temporal complexity of this system translates into a similar complexity in the surface expression of the underlying physics, including deformation and seismicity. Here we show that a new pattern dynamic methodology can be used to define a unique, finite set of deformation patterns for the Southern California Integrated GPS Network (SCIGN). Similar in nature to the empirical orthogonal functions historically employed in the analysis of atmospheric and oceanographic phenomena (Preisendorfer, 1988), the method derives the eigenvalues and eigenstates from the diagonalization of the correlation matrix using a Karhunen-Loeve expansion (KLE) (Fukunaga, 1970; Rundle et al., 2000; Tiampo et al., 2002). This KLE technique may be used to determine the important modes in both time and space for the southern California GPS data, modes that potentially include such time-dependent signals as plate velocities, viscoelasticity, and seasonal effects. Here we attempt to characterize several of the seasonal vertical signals on various spatial scales. These, in turn, can be used to better model geophysical signals of interest such as coseismic deformation, viscoelastic effects, and creep, as well as provide data assimilation and model verification for large-scale numerical simulations of southern California.