Gambling scores in earthquake prediction analysis

The number of successes 'n' and the normalized measure of space-time alarm 'tau' are commonly used to characterize the strength of an earthquake prediction method and the significance of prediction results. To evaluate better the forecaster's skill, it has been recently suggested to use a new characteristic, the gambling score R, which incorporates the difficulty of guessing each target event by using different weights for different alarms. We expand the class of R-characteristics and apply these to the analysis of results of the M8 prediction algorithm. We show that the level of significance 'alfa' strongly depends (1) on the choice of weighting alarm parameters, (2) on the partitioning of the entire alarm volume into component parts, and (3) on the accuracy of the spatial rate of target events, m(dg). These tools are at the disposal of the researcher and can affect the significance estimate in either direction. All the R-statistics discussed here corroborate that the prediction of 8.0<=M<8.5 events by the M8 method is nontrivial. However, conclusions based on traditional characteristics (n,tau) are more reliable owing to two circumstances: 'tau' is stable since it is based on relative values of m(.), and the 'n' statistic enables constructing an upper estimate of 'alfa' taking into account the uncertainty of m(.).Comment: 17 pages, 3 fugure

On Operational Earthquake Forecast and Prediction Problems.

In his SSA presidential address (Jordan, 2014), and later in a more extended publication with coauthors (Jordan et al., 2014), Jordan presents a vision of forecast and prediction problems of earthquake system science. As experienced practitioners and in full appreciation of scientific studies on earthquake forecasting, we find it necessary to share a complementary viewpoint

Predictability in the ETAS Model of Interacting Triggered Seismicity

As part of an effort to develop a systematic methodology for earthquake forecasting, we use a simple model of seismicity based on interacting events which may trigger a cascade of earthquakes, known as the Epidemic-Type Aftershock Sequence model (ETAS). The ETAS model is constructed on a bare (unrenormalized) Omori law, the Gutenberg-Richter law and the idea that large events trigger more numerous aftershocks. For simplicity, we do not use the information on the spatial location of earthquakes and work only in the time domain. We offer an analytical approach to account for the yet unobserved triggered seismicity adapted to the problem of forecasting future seismic rates at varying horizons from the present. Tests presented on synthetic catalogs validate strongly the importance of taking into account all the cascades of still unobserved triggered events in order to predict correctly the future level of seismicity beyond a few minutes. We find a strong predictability if one accepts to predict only a small fraction of the large-magnitude targets. However, the probability gains degrade fast when one attempts to predict a larger fraction of the targets. This is because a significant fraction of events remain uncorrelated from past seismicity. This delineates the fundamental limits underlying forecasting skills, stemming from an intrinsic stochastic component in these interacting triggered seismicity models.Comment: Latex file of 20 pages + 15 eps figures + 2 tables, in press in J. Geophys. Re

Predictability of Volcano Eruption: lessons from a basaltic effusive volcano

Volcano eruption forecast remains a challenging and controversial problem despite the fact that data from volcano monitoring significantly increased in quantity and quality during the last decades.This study uses pattern recognition techniques to quantify the predictability of the 15 Piton de la Fournaise (PdlF) eruptions in the 1988-2001 period using increase of the daily seismicity rate as a precursor. Lead time of this prediction is a few days to weeks. Using the daily seismicity rate, we formulate a simple prediction rule, use it for retrospective prediction of the 15 eruptions,and test the prediction quality with error diagrams. The best prediction performance corresponds to averaging the daily seismicity rate over 5 days and issuing a prediction alarm for 5 days. 65% of the eruptions are predicted for an alarm duration less than 20% of the time considered. Even though this result is concomitant of a large number of false alarms, it is obtained with a crude counting of daily events that are available from most volcano observatoriesComment: 4 pages, 4 figure

On the tilt of the Earth's polar axis (climat): Some 'impressionist' remarks

In this lengthy letter, we wanted to discuss the concept of climate based on definitions established for over a century and direct observations that we have been collecting for more than a century as well. To do this, we present and discuss the remarkably stable maps over time of the various physical parameters that make up the climate corpus: solar temperature, atmospheric pressure, winds, precipitation, temperature anomalies. This impressionistic tableau that we are gradually sketching as our reflection unfolds leads us to the following proposition: What if, as Laplace first proposed in 1799 and later Milankovi\{'}c in 1920, ground temperature were merely a consequence of climate and not a separate parameter of climate in its own right?Comment: 24 pages, 11 Figure

Reverse Detection of Short-Term Earthquake Precursors

We introduce a new approach to short-term earthquake prediction based on the concept of selforganization of seismically active fault networks. That approach is named "Reverse Detection of Precursors" (RDP), since it considers precursors in reverse order of their appearance. This makes it possible to detect precursors undetectable by direct analysis. Possible mechanisms underlying RDP are outlined. RDP is described with a concrete example: we consider as short-term precursors the newly introduced chains of earthquakes reflecting the rise of an earthquake correlation range; and detect (retrospectively) such chains a few months before two prominent Californian earthquakes - Landers, 1992, M = 7.6, and Hector Mine, 1999, M = 7.3, with one false alarm. Similar results (described elsewhere) are obtained by RDP for 21 more strong earthquakes in California (M >= 6.4), Japan (M >= 7.0) and the Eastern Mediterranean (M >= 6.5). Validation of the RDP approach requires, as always, prediction in advance for which this study sets up a base. We have the first case of advance prediction; it was reported before Tokachi-oki earthquake (near Hokkaido island, Japan), Sept. 25, 2003, M = 8.1. RDP has potentially important applications to other precursors and to prediction of other critical phenomena besides earthquakes. In particular, it might vindicate some short-term precursors, previously rejected as giving too many false alarms.Comment: 17 pages, 5 figure

On self-similarity of premonitory patterns in the regions of natural and induced seismicity

Anticipating the scale invariance of rock fracturing processes, we applied Keilis-Borok's algorithm M8, originally designed for identifying times of increased probability (TIPS) of occurrence of strong earthquakes (M &lt; 8.0), retrospectively to Koyna earthquakes which occurred in the region after the impoundment of the Shivaji Sagar reservoir in 1962. The algorithm which enables diagnosis of TIPS from the 7th year onwards after the commencement of the earliest available data set showed that the 5.3 magnitude earthquake of 20 September 1980 indeed occurred within a time of increased probability. This result, apart from its potential application to recognizing future TIPS in the region, points to selfsimilarity between the premonitory patterns of natural and induced earthquakes and to scale-invariant nature of their processes. Further, a typical precursory rise in seismicity followed by a relative quiescence was also found to precede all the three larger earthquakes of the sequence