Hypothesis testing and earthquake prediction (original) (raw)
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Earthquake prediction: the null hypothesis
Geophysical Journal International, 1997
The null hypothesis in assessing earthquake predictions is often, loosely speaking, that the successful predictions are chance coincidences. To make this more precise requires specifying a chance model for the predictions and/or the seismicity. The null hypothesis tends to be rejected not only when the predictions have merit, but also when the chance model is inappropriate. In one standard approach, the seismicity is taken to be random and the predictions are held fixed. 'Conditioning' on the predictions this way tends to reject the null hypothesis even when it is true, if the predictions depend on the seismicity history. An approach that seems less likely to yield erroneous conclusions is to compare the predictions with the predictions of a 'sensible' random prediction algorithm that uses seismicity up to time t to predict what will happen after time t. The null hypothesis is then that the predictions are no better than those of the random algorithm. Significance levels can be assigned to this test in a more satisfactory way, because the distribution of the success rate of the random predictions is under our control. Failure to reject the null hypothesis indicates that there is no evidence that any extra-seismic information the predictor uses (electrical signals for example) helps to predict earthquakes.
Testing earthquake predictions
Institute of Mathematical Statistics Collections, 2008
Statistical tests of earthquake predictions require a null hypothesis to model occasional chance successes. To define and quantify 'chance success' is knotty. Some null hypotheses ascribe chance to the Earth: Seismicity is modeled as random. The null distribution of the number of successful predictionsor any other test statistic-is taken to be its distribution when the fixed set of predictions is applied to random seismicity. Such tests tacitly assume that the predictions do not depend on the observed seismicity. Conditioning on the predictions in this way sets a low hurdle for statistical significance. Consider this scheme: When an earthquake of magnitude 5.5 or greater occurs anywhere in the world, predict that an earthquake at least as large will occur within 21 days and within an epicentral distance of 50 km. We apply this rule to the Harvard centroid-moment-tensor (CMT) catalog for 2000-2004 to generate a set of predictions. The null hypothesis is that earthquake times are exchangeable conditional on their magnitudes and locations and on the predictions-a common "nonparametric" assumption in the literature. We generate random seismicity by permuting the times of events in the CMT catalog. We consider an event successfully predicted only if (i) it is predicted and (ii) there is no larger event within 50 km in the previous 21 days. The P-value for the observed success rate is < 0.001: The method successfully predicts about 5% of earthquakes, far better than 'chance,' because the predictor exploits the clustering of earthquakes-occasional foreshocks-which the null hypothesis lacks. Rather than condition on the predictions and use a stochastic model for seismicity, it is preferable to treat the observed seismicity as fixed, and to compare the success rate of the predictions to the success rate of simple-minded predictions like those just described. If the proffered predictions do no better than a simple scheme, they have little value.
2008
Robert K. Vincent, Advisor successfully predicted 100 earthquakes in the Western Pacific Rim including China, Japan, Taiwan, and Philippine, using a temperature anomaly method. Their model is based on a predicted increase of ground temperatures in the lower atmosphere from 2 to 8 days before an earthquake of with a Richter Scale magnitude of 5 or greater. Mixed gases, such as CO 2 and CH 4 , in different ratios under the action of a transient electric field, cause the temperature of the lower atmosphere to increase up to 6 °C, while solar radiation only increases temperature by 3 °C. The authors detected the thermal anomalies using ground-based evidence and thermal infrared anomalies in METEOSAT thermal infrared image data. Despite their apparent success at predicting the earthquakes, they did not compare their prediction with the natural rate of occurrence in the area, which experiences an earthquake of Richter magnitude greater than 4 every week.
Efficient testing of earthquake forecasting models
Acta Geophysica, 2011
Computationally efficient alternatives are proposed to the likelihood-based tests employed by the Collaboratory for the Study of Earthquake Predictability for assessing the performance of earthquake likelihood models in the earthquake forecast testing centers. For the conditional L-test, which tests the consistency of the earthquake catalogue with a model, an exact test using convolutions of distributions is available when the number of earthquakes in the test period is small, and the central limit theorem provides an approximate test when the number of earthquakes is large. Similar methods are available for the R-test, which compares the likelihoods of two competing models. However, the R-test, like the N-test and L-test, is fundamentally a test of consistency of data with a model. We propose an alternative test, based on the classical paired t-test, to more directly compare the likelihoods of two models. Although approximate and predicated on a normality assumption, this new T-test is not computer-intensive, is easier to interpret than the R-test, and becomes increasingly dependable as the number of earthquakes increases.
First Results of the Regional Earthquake Likelihood Models Experiment
Pure and Applied Geophysics, 2010
The ability to successfully predict the future behavior of a system is a strong indication that the system is well understood. Certainly many details of the earthquake system remain obscure, but several hypotheses related to earthquake occurrence and seismic hazard have been proffered, and predicting earthquake behavior is a worthy goal and demanded by society. Along these lines, one of the primary objectives of the Regional Earthquake Likelihood Models (RELM) working group was to formalize earthquake occurrence hypotheses in the form of prospective earthquake rate forecasts in California. RELM members, working in small research groups, developed more than a dozen 5-year forecasts; they also outlined a performance evaluation method and provided a conceptual description of a Testing Center in which to perform predictability experiments. Subsequently, researchers working within the Collaboratory for the Study of Earthquake Predictability (CSEP) have begun implementing Testing Centers in different locations worldwide, and the RELM predictability experiment-a truly prospective earthquake prediction effort-is underway within the U.S. branch of CSEP. The experiment, designed to compare time-invariant 5-year earthquake rate forecasts, is now approximately halfway to its completion. In this paper, we describe the models under evaluation and present, for the first time, preliminary results of this unique experiment. While these results are preliminary-the forecasts were meant for an application of 5 years-we find interesting results: most of the models are consistent with the observation and one model forecasts the distribution of earthquakes best. We discuss the observed sample of target earthquakes in the context of historical seismicity within the testing region, highlight potential pitfalls of the current tests, and suggest plans for future revisions to experiments such as this one.
Basic principles for evaluating an earthquake prediction method
Geophysical Research Letters, 1996
A three year continuous sample of earthquake predictions based on the observation of Seismic Electric Signals in Greece was published by Varotsos and Lazaridou [1991]. Four independent studies analyzed this sample and concluded that the success rate of the predictions is far beyond chance. On the other hand, Mulargia and Gasperini [1992] (hereafter cited as MG) claim that these predictions can be ascribed to chance. In the present paper we examine the origin of this disagreement. Several serious problems in the study of MG are pointed out, such as: 1. The probability of a prediction's being successful by chance should be approximately considered as the product of three probabilities, Pv, PE and PM, i.e., the probabilities with respect to time, epicenter and magnitude. In spite of their major importance, P•. and PM were ignored by MG. The incorporation of P•. decreases the probability for chancy success by more than a factor of 10 (when P•. is taken into account it can be shown that the VAN predictions cannot be ascribed to chance). 2. MG grossly overestimated the number of earthquakes that should have been predicted, by taking different thresholds for earthquakes and predictions. With such an overestimation, MG' s procedure can "reject" even an ideally perfect earthquake prediction method. 3. MG's procedure did not take into account that the predictions were based on three different types of electrical precursors with different lead-times. 4. MG applied a Poisson distribution to the time series of earthquakes but included a large number of aftershocks. 5. The backward time correlation between predictions and earthquakes claimed by MG is due to misinterpretation of the text of some predictions and an incorrect use of aftershocks. Although even the discussion of the first problem alone is enough to invalidate the claims of MG, we also discuss the other four problems because MG violated some basic principles even in the time domain alone. The results derived in this paper are of general use when examining whether a correlation between earthquakes and various geophysical phenomena is beyond chance or not.
Earthquake statistics at Parkfield: 2. Probabilistic forecasting and testing
Journal of Geophysical Research, 2004
1] In paper 1 we showed that the spatial b value (of the Gutenberg-Richter relation) distribution at the Parkfield segment of the San Andreas fault remained stationary for the past 35 years. In this paper (paper 2) we extend those results, construct two probabilistic forecasts (H 1 with a spatially varying b value and H 2 with a uniform b value), and test these hypotheses against each other. Both hypotheses use a spatially varying seismicity level (a value) determined from past seismicity. We used a range of sampling parameters (magnitude threshold, cell size, etc.) to assure robust results. We found that in most of the tests, hypothesis H 1 showed a higher likelihood than H 2 , although both are a poor approximation to the seismicity data. The most positive results for H 1 are obtained for testing magnitude ranges down to M = 1.5 and with sampling radii as defined in paper 1 as appropriate for Parkfield. The superior performance of H 1 suggests that spatially varying b values should be considered in earthquake forecasts.
Bulletin of the Seismological Society of America, 2013
Among scoring methods employed to determine the performance of probability predictions, the log-likelihood method is the most common and useful. Although the log-likelihood score evaluates the comprehensive power of forecasts, we need to further evaluate the topical predictive powers of respective factors of seismicity, such as total numbers, occurrence times, locations, and magnitudes. For this purpose, we used the conditional-or marginal-likelihood function based on the observed events. Such topical scores reveal both strengths and weaknesses of a forecasting model and suggest the necessary improvements. We applied these scores to the probability forecasts during the devastating period of March 2011, during which the M w 9.0 Off the Pacific Coast of Tohoku-Oki earthquake struck. However, the evaluations did not suggest that any of the prospective forecast models were consistently satisfactory. Hence, we undertook two additional types of retrospective forecasting experiments to investigate the reasons, including the possibility that the seismicity rate pattern has changed after the M 9 mega-earthquake. In addition, our experiments revealed a technical difficulty in the one-day forecasting protocol adopted by the Collaboratory for the Study of Earthquake Predictability (CSEP). Results of further experiments lead us to recommend specific modifications to the CSEP protocols, leading to real-time forecasts and their evaluations.
Bulletin of the Seismological Society of America, 2003
The moment magnitude M 7.8 earthquake in 1906 profoundly changed the rate of seismic activity over much of northern California. The low rate of seismic activity in the San Francisco Bay region (SFBR) since 1906, relative to that of the preceding 55 yr, is often explained as a stress-shadow effect of the 1906 earthquake. However, existing elastic and visco-elastic models of stress change fail to fully account for the duration of the lowered rate of earthquake activity. We use variations in the rate of earthquakes as a basis for a simple empirical model for estimating the probability of M Ն6.7 earthquakes in the SFBR. The model preserves the relative magnitude distribution of sources predicted by the Working Group on California Earthquake Probabilities' (WGCEP, 1999; WGCEP, 2002) model of characterized ruptures on SFBR faults and is consistent with the occurrence of the four M Ն6.7 earthquakes in the region since 1838. When the empirical model is extrapolated 30 yr forward from 2002, it gives a probability of 0.42 for one or more M Ն6.7 in the SFBR. This result is lower than the probability of 0.5 estimated by WGCEP (1988), lower than the 30-yr Poisson probability of 0.60 obtained by WGCEP (1999) and WGCEP (2002), and lower than the 30-yr time-dependent probabilities of 0.67, 0.70, and 0.63 obtained by WGCEP (1990), WGCEP (1999), and WGCEP (2002), respectively, for the occurrence of one or more large earthquakes. This lower probability is consistent with the lack of adequate accounting for the 1906 stress-shadow in these earlier reports. The empirical model represents one possible approach toward accounting for the stress-shadow effect of the 1906 earthquake. However, the discrepancy between our result and those obtained with other modeling methods underscores the fact that the physics controlling the timing of earthquakes is not well understood. Hence, we advise against using the empirical model alone (or any other single probability model) for estimating the earthquake hazard and endorse the use of all credible earthquake probability models for the region, including the empirical model, with appropriate weighting, as was done in WGCEP (2002).
Evaluating the statistical validity beyond chance of ‘VAN’ earthquake precursors
Geophysical Journal International, 1992
November 30 recently published by Varotsos & Lazaridou (1991) using any possible combination of the 'rules of the game' that they consider. We find that the apparent success of V A N predictions can be confidently ascribed t o chance; conversely, we find that the occurrence of earthquakes with M ,~5. 8 is followed by V A N predictions (with identical epicentre a n d magnitude) with a probability too large to be ascribed t o chance.