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We propose the use of statistical measures to quantify robustness, uncertainty, and significance for Markovian models of large magnitude seismic systems, and we also propose a method for choosing the best of different models by using the normalized measures in a discriminant function. We tested the proposed methods on earthquakes occurring in an area around Japan, divided into four regions; modeling the system as having four states, where each state corresponds to the region where the latest large earthquake, larger than a given threshold moment magnitude, has occurred. Our results show that for the 7.0–7.3 threshold magnitude range the seismicity of this region does occur according to a Markovian process, with optimum results for threshold magnitude 7.1, whereas for magnitudes outside this range seismicity is less Markovian.

Large earthquakes have semi-periodic behavior as a result of critically self-organized processes of stress accumulation and release in seismogenic regions. Hence, large earthquakes in a given region constitute semi-periodic sequences with recurrence times varying slightly from periodicity. In previous papers, it has been shown that it is possible to identify these sequences through Fourier analysis of the occurrence time series of large earthquakes from a given region, by realizing that not all earthquakes in the region need belong to the same sequence, since there can be more than one process of stress accumulation and release in the region. Sequence identification can be used to forecast earthquake occurrence with well determined confidence bounds. This paper presents improvements on the above mentioned sequence identification and forecasting method: the influence of earthquake size on the spectral analysis, and its importance in semi-periodic events identification are considered, which means that earthquake occurrence times are treated as a labeled point process; a revised estimation of non-randomness probability is used; a better estimation of appropriate upper limit uncertainties to use in forecasts is introduced; and the use of Bayesian analysis to evaluate the posterior forecast performance is applied. This improved method was successfully tested on synthetic data and subsequently applied to real data from some specific regions. As an example of application, we show the analysis of data from the northeastern Japan Arc region, in which one semi-periodic sequence of four earthquakes with M ≥ 8.0, having high non-randomness probability was identified. We compare the results of this analysis with those of the unlabeled point process analysis.

Ground deformation and seismicity in Mexicali Valley, Baja California, Mexico, the southern part of the Mexicali-Imperial valley, are influenced by active tectonics and human activity. In this study, data from two successive leveling surveys in 2006 and 2009/2010 are used to estimate the total deformation occurred in Mexicali Valley during 2006–2009. The leveling data span more than 3.5 years and include deformation from several natural and anthropogenic sources that acted at different temporal and spatial scales during the analyzed period. Because of its large magnitude, the aseismic anthropogenic deformation caused by fluid extraction in the Cerro Prieto geothermal field obscures the deformation caused by other mechanisms and sources. The method of differential interferograms stacking was used to estimate the aseismic (interseismic tectonic and anthropogenic) components of the observed displacement, using SAR images, taken in 2007 during a period when no significant seismicity occurred in the study area. After removing the estimated aseismic signal from the leveling data, residual vertical displacement remained, and to identify possible sources and mechanisms of this displacement, a detailed analysis of records from tiltmeters and creepmeters was performed. The results of this analysis suggest that the residual displacement is mainly caused by moderate-sized seismicity in the area of study. Modeling of the vertical ground deformation caused by the coseismic slip on source fault (primary mechanism) of the two most important earthquakes, May 24, 2006 (Mw = 5.4) and December 30, 2009 (Mw = 5.8), was performed. The modeling results, together with the analysis of geotechnical instruments data, suggests that this moderate-sized seismicity influences the deformation in the study area by coseismic slip on the source fault, triggered slip on secondary faults, and soft sediments deformation.

Among the schemes for earthquake forecasting, the search for semi-periodicity during large earthquakes in a given seismogenic region plays an important role. When considering earthquake forecasts based on semi-periodic sequence identification, the Bayesian formalism is a useful tool for: (1) assessing how well a given earthquake satisfies a previously made forecast; (2) re-evaluating the semi-periodic sequence probability; and (3) testing other prior estimations of the sequence probability. A comparison of Bayesian estimates with updated estimates of semi-periodic sequences that incorporate new data not used in the original estimates shows extremely good agreement, indicating that: (1) the probability that a semi-periodic sequence is not due to chance is an appropriate estimate for the prior sequence probability estimate; and (2) the Bayesian formalism does a very good job of estimating corrected semi-periodicity probabilities, using slightly less data than that used for updated estimates. The Bayesian approach is exemplified explicitly by its application to the Parkfield semi-periodic forecast, and results are given for its application to other forecasts in Japan and Venezuela.

We explore fractal properties of two observed seismicity distributions prior to the 2003 M w 7.4 Colima, Mexico and 1992 M w 7.3 Landers, USA earthquakes, together with several mathematical fractal distributions and two non-fractal ones, in order to estimate minimum reliable sample sizes, determine whether fractality for observed seismicity is essentially different from random uniform distributions, and explore the possibility of extracting premonitory information from fractal characteristics of seismicity before large earthquakes. Sample sizes above 800 events for whole catalogs appear to be sufficient to maintain ordered multifractality and to yield dimension estimates that vary smoothly and reliably. Fractal estimates appear to be best for whole catalogs that include aftershocks. The fractal characteristics of spatial distributions of seismicity are essentially different from those of the uniform random distribution, which is the null hypothesis of a non-fractal distribution with minimum information. The fractal dimensions and afractality measures of seismicity distributions change with time and show distinctive behaviors associated with foreshocks and main events, although these behaviors are different for each example. Results suggest the possibility of a priori identification of foreshocks to large earthquakes. A combination of fractal dimension and afractality measures over time may be helpful in large earthquake premonitory studies.

Previous works have shown that ground deformation and seismicity in the Cerro Prieto geothermal field (CPGF) are due to both tectonics and field exploitation. Here, we use information about current tectonics and data from precision leveling surveys, to model tectonic and anthropogenic subsidence. Our results show that tectonic subsidence constitutes only ∼4% of the measured subsidence. Anthropogenic subsidence was evaluated using a model of rectangular tensional cracks, based on the hydrological model of the field, together with the Coulomb 2.0 program. From the resulting values of the fissure parameters and from extraction and injection data, we calculate that the volume changes caused by closure of the geothermal and cold water reservoirs account for only ∼3% and ∼7%, respectively, of the volume change which should occur due to extraction. Since 18% of the extracted fluids are reinjected, external recharge must compensate for about 72% of the expected volume reduction. An analysis of the changes in Coulomb stress caused by exploitation of the geothermal field suggest that even though the anthropogenic stresses account for only a fraction of tectonic stresses, they are large enough to trigger seismicity.

Seismogenic regions within some geographic area are interrelated through tectonics and seismic history, although this relation is usually complex, so that seismicity in a given region cannot be predicted in a straightforward manner from the activity in other region(s). We present a new statistical method for seismic hazard evaluation based on modeling the transition probabilities of seismicity patterns in the regions of a geographic area during a time interval, as a Markov chain. Application of the method to the Japan area renders good results, considering the occurrence of a high probability transition as a successful forecast. For magnitudes M≥5.5 and time intervals Δ t=0.10 year, the method yields a 78% aftcast (forecast of data already used to evaluate the hazard) success rate for the entire catalog, and an indicative 80% forecast success rate for the last 10 transitions in the catalog. A byproduct of the method, regional occurrence probabilities determined from the transition probabilities, also provides good results; aftcasts of regional activity have a 98% success rate, and those of activity in the highest probability region about 80.5% success rate. All results are superior to those from the null hypotheses (a memory-less Poissonian, fixed-rate, or uniform system) and have vanishingly small probabilities of resulting from purely random guessing.

—Crackmeter data from the southern tip of the Imperial fault in the Mexicali-Imperial Valley in northern Baja California, Mexico, show slip events that tend to group in episodes, or suites, that last over a few days, with months of quiescence between them. The events in these suites are apparently triggered and stopped by ground strain related to temperature changes. A characteristic decrease in peak extension velocities during the slip event suites indicates the presence of viscoelastic afterworking which contributes the strain necessary for succeeding events with diminishing driving stresses, and which can be roughly modeled as a series of Kelvin-Voigt viscoelastic solids. Occurrence of very small events towards the end of the suites plus gaps between suites indicate that for the sediments significant fault healing requires a minimum of several days without slip.