Earthquake Prediction and its Optimization

George Molchan, & Yan Y. Kagan

Published 1992, SCEC Contribution #4

This paper continues the work by Molchan (1990, 1991b), who has considered earthquake prediction as a problem of the optimization of a certain loss function γ. Function γ is defined by specific social, economic, and geophysical goals. This problem can be fully solved for the loss function γ dependent on only two parameters: fraction of alarm time, τ, and fraction of failures to predict, ν. For such a loss function the tasks of geophysicists and decision makers are clearly denned and can be separated; the requirements of the prediction algorithm can be completely formulated in terms of hazard function. We also consider a more complex model of the loss function, introducing a finite number of various alarms. For each of these alarms, γ depends on three parameters; in addition to τ and ν1 we take into account the total number of alarms, λ. For this model we find strategies which optimize the losses for each time unit (locally optimal). Contrary to the simple case of γ(τ, ν), such strategies may not be optimal globally (for the entire time interval). We determine the conditions under which the locally optimal strategy becomes globally optimal. We illustrate our results using the model of a short-term earthquake prediction for central California. We emphasize that for this complex case, the tasks of geophysicists and decision makers in prediction are intertwined. Prediction and mitigation of many other natural disasters may benefit from the alert strategies discussed here.

Key Words
United States, California, theoretical studies, prediction, seismology, geologic hazards, Central California, earthquakes, data processing, optimization, mathematical models, algorithms

Molchan, G., & Kagan, Y. Y. (1992). Earthquake Prediction and its Optimization. Journal of Geophysical Research, 97(B4), 4823-4838.