Earthquake Forecast based on Probability

Abstract

A new probability process model for earthquake forecast is presented based on Bayesian treatment. The prior probability at the beginning of this process is estimated from long-term data from earthquake history and active fault activities in a target area. The posterior probability is deduced from Bayes' theorem in terms of the prior probability and two conditional probabilities: “alarm rate” and “null alarm rate”. The former is defined to be the probability that a precursory anomaly is detected on condition that an earthquake is accompanied, and the latter to be that on condition that no earthquake is accompanied. These probabilities are estimated mainly by statistical tests of previously accumulated observation data. The test consists of trials of detecting anomaly during each assigned detecting period and of registering earthquake events during the corresponding hypothetical forecasting period. Regarding the estimated posterior probability as the prior probability for the next step of the Bayesian process, we will obtain a new posterior probability when data from another anomaly event is input into the process. Successive application of this procedure continues to renew the posterior probability until a dicision is made to issue an earthquake warning. The final posterior probability p_N for N independent anomaly observations with alarm rate q_i and null alarm rate s_i for i=1, 2, …N is given by
P_N=x₁x₂…x_N/x₁x₂…x_N+a₁-p₀x₁x₂…x_N,
where p₀ is the first prior probability, a₁=(1-p₀)/p₀, x_i=q_i/s_i and the approximation (-) is valid if p_N<<1. The well known terms, “secular probability” and “success rate” are interpreted in the above framework to be a prior probability and the induced posterior probability, respectively. The ratio of alarm rate to null alarm rate, i. e., x_i in the above formula, for each precursory anomaly observation is a key factor for reliability on earthquake prediction. The probability gain, i. e., the ratio of the posterior probability to the prior probability, is approximated to be the product of the above ratios.