Summary. Let X = (~, t ~IR) be a stationary Gaussian process on (f2, Y, P), let H(X) be the Hilbert space of variables in L 2 (s P) which are measurable with respect to X, and let (Us, sslR) be the associated family of time-shift operators. We say Yell(X) (with E(Y)= 0) satisfies the functional central Maruyama (1976) and Breuer and Major (1983).

The philosophy behind the first method of earthquake forecasting is the assumption that the average statistical properties of the spatial and temporal occurrences of earthquakes with M ≥ 4.0 during the future forecast period are the same as the average properties of those variables over the past 70 or so years. This

This paper develops a novel method, based on hidden Markov models, to forecast earthquakes and applies the method to mainshock seismic activity in southern California and western Nevada. The forecasts are of the probability of a mainshock within one, five, and ten days in the entire study region or in specific subregions and are based on the observations available at the forecast time, namely the inter event times and locations of the previous mainshocks and the elapsed time since the most recent one. Hidden Markov models have been applied to many problems, including earthquake classification; this is the first application to earthquake forecasting

No abstract

No abstract

No abstract

No abstract

The M4+ mainshocks throughout California and western Nevada from 1932 to 2004 show non-Poissonian temporal clustering over time periods of a few days. The short-term clustering is independent of the distance between earthquake epicenters. It implies that some of the M4+ mainshocks are mutually triggered by some unknown regional cause. In southern California, more short-term clustering is found for M4+ earthquakes east of the San Andreas Fault. In central California, most M4+ mainshocks at Long Valley, CA have occurred within 10 days of M4+ mainshocks around the San Francisco Bay area. The clustering implies predictable behavior in the occurrences of M4+ mainshocks. We propose a hidden Markov model (HMM) as an earthquake forecast method for the region. Our HMM assumes a hidden sequence of interevent time states associated with observations of earthquake occurrences (times, locations, and magnitudes) with transition probabilities between states determined with the Baum-Welch algorithm and the past earthquake data. Given the seismic history up to the latest earthquake, the probability of another earthquake within the next few days is estimated. Tests of our HMM with two, three, and four temporal states show some modest success. We plan to extend the model to forecast magnitude and spatial parameters.