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Threshold systems are known to be some of the most important nonlinear self-organizing systems in nature, including networks of earthquake faults, neural networks, superconductors and semiconductors, and the World Wide Web, as well as political, social, and ecological systems. All of these systems have dynamics that are strongly correlated in space and(More)
Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation(More)
We present a RELM forecast of future earthquakes in California that is primarily based on the pattern informatics (PI) method. This method identifies regions that have systematic fluctuations in seismicity, and it has been demonstrated to be successful. A PI forecast map originally published on 19 February 2002 for southern California successfully forecast(More)
No proven method is currently available for the reliable short time prediction of earthquakes (minutes to months). However, it is possible to make probabilistic hazard assessments for earthquake risk. These are primarily based on the association of small earthquakes with future large earthquakes. In this paper we discuss a new approach to earthquake(More)
— The last five years have seen unprecedented growth in the amount and quality of geodetic data collected to characterize crustal deformation in earthquake-prone areas such as California and Japan. The installation of the Southern California Integrated Geodetic Network (SCIGN) and the Bay Area Regional Deformation (BARD) network are two examples. As part of(More)
Color images can be treated as two-dimensional quaternion functions. For analysis of quaternion images, a joint space-wavenumber localized quaternion S transform (QS) is presented in this study for a simultaneous determination of the local color image spectra. The QS transform uses a two-dimensional Gaussian localizing window that scales with wavenumbers.(More)
— A method based on random field theory and Gibbs-Markov random fields equivalency within Bayesian statistical framework is used to derive three-dimensional surface motion maps from sparse GPS measurements and Differential InSAR (DInSAR) interferogram in the southern California region. The minimization of the Gibbs energy function is performed analytically(More)
—A revised method for derivation of three-dimensional surface motions maps from sparse global positioning system (GPS) measurements and two differential interferometric synthetic aperture radar (DInSAR) interferograms based on a random field theory and Gibbs–Markov random fields equivalency within Bayesian statistical framework is proposed. It is shown that(More)
We present here a methodology that allows the combination of GPS and Differential InSAR data for the calculation of continuous three-dimensional (3D) high-resolution velocity maps with corresponding errors. It is based on analytic minimization of the Gibbs energy function, which is possible in the case when neighborhood pixels of the velocity maps are(More)