Modification of the pattern informatics method for forecasting large earthquake events using complex eigenvectors

Recent studies have shown that real-valued principal component analysis can be applied to earthquake fault systems for forecasting and prediction. In addition, theoretical analysis indicates that earthquake stresses may obey a wave-like equation, having solutions with inverse frequencies for a given fault similar to those that characterize the time intervals between the largest events on the fault. It is therefore desirable to apply complex principal component analysis to develop earthquake forecast algorithms. In this paper we modify the Pattern Informatics method of earthquake forecasting to take advantage of the wave-like properties of seismic stresses and utilize the Hilbert transform to create complex eigenvectors out of measured time series. We show that Pattern Informatics analyses using complex eigenvectors create short-term forecast hot-spot maps that differ from hot-spot maps created using only real-valued data and suggest methods of analyzing the differences and calculating the information gain.Comment: 13 pages, 1 figure. Submitted to Tectonophysics on 30 August 200

Application of DInSAR-GPS optimization for derivation of fine-scale surface motion maps of Southern California

A method based on random field theory and Gibbs-Markov random fields equivalency within Bayesian statistical framework is used to derive 3-D surface motion maps from sparse global positioning system (GPS) measurements and differential interferometric synthetic aperture radar (DInSAR) interferogram in the southern California region. The minimization of the Gibbs energy function is performed analytically, which is possible in the case when neighboring pixels are considered independent. The problem is well posed and the solution is unique and stable and not biased by the continuity condition. The technique produces a 3-D field containing estimates of surface motion on the spatial scale of the DInSAR image, over a given time period, complete with error estimates. Significant improvement in the accuracy of the vertical component and moderate improvement in the accuracy of the horizontal components of velocity are achieved in comparison with the GPS data alone. The method can be expanded to account for other available data sets, such as additional interferograms, lidar, or leveling data, in order to achieve even higher accuracy

Earthquake forecasting and its verification

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 forecasting. This approach is based on a pattern informatics (PI) method which quantifies temporal variations in seismicity. The output is a map of areas in a seismogenic region (``hotspots'') where earthquakes are forecast to occur in a future 10-year time span. This approach has been successfully applied to California, to Japan, and on a worldwide basis. These forecasts are binary--an earthquake is forecast either to occur or to not occur. The standard approach to the evaluation of a binary forecast is the use of the relative operating characteristic (ROC) diagram, which is a more restrictive test and less subject to bias than maximum likelihood tests. To test our PI method, we made two types of retrospective forecasts for California. The first is the PI method and the second is a relative intensity (RI) forecast based on the hypothesis that future earthquakes will occur where earthquakes have occurred in the recent past. While both retrospective forecasts are for the ten year period 1 January 2000 to 31 December 2009, we performed an interim analysis 5 years into the forecast. The PI method out performs the RI method under most circumstances.Comment: 10(+1) pages, 5 figures, 2 tables. Submitted to Nonlinearl Processes in Geophysics on 5 August 200

Surface uplift and time-dependent seismic hazard due to fluid injection in eastern Texas

Observations that unequivocally link seismicity and wastewater injection are scarce. Here we show that wastewater injection in eastern Texas causes uplift, detectable in radar interferometric data up to >8 kilometers from the wells. Using measurements of uplift, reported injection data, and a poroelastic model, we computed the crustal strain and pore pressure. We infer that an increase of >1 megapascal in pore pressure in rocks with low compressibility triggers earthquakes, including the 4.8–moment magnitude event that occurred on 17 May 2012, the largest earthquake recorded in eastern Texas. Seismic activity increased even while injection rates declined, owing to diffusion of pore pressure from earlier periods with higher injection rates. Induced seismicity potential is suppressed where tight confining formations prevent pore pressure from propagating into crystalline basement rocks

An Ising model for earthquake dynamics

This paper focuses on extracting the information contained in seismic space-time patterns and their dynamics. The Greek catalog recorded from 1901 to 1999 is analyzed. An Ising Cellular Automata representation technique is developed to reconstruct the history of these patterns. We find that there is strong correlation in the region, and that small earthquakes are very important to the stress transfers. Finally, it is demonstrated that this approach is useful for seismic hazard assessment and intermediate-range earthquake forecasting

Topography and self-gravitation interaction in elastic-gravitational modeling

Changes in gravity due to volcanic loading of the crust are influenced by topography. We investigate the relative importance of topography and self-gravitation in the interpretation of gravity changes. It is shown that modeling of gravity changes can be more precise with the introduction of topographic relief, although it is neglected self-gravitation of the medium. This paper exploits this result by suggesting a mathematical simplification that could be useful in the future development of a numerical technique to accurately include topographic effects in the modeling of deformation and gravity changes. Finally, we perform an inversion of the gravity changes observed at Mayon volcano (Philippines) between December 1992 and December 1996 including topographic effects by varying the depth of the source. Failure to account for topographic influences can bias estimates of source parameters particularly when the lateral extension of the relief is of the same order of magnitude as the source depth.Peer reviewe