Loss Functions for Temporal and Spatial Optimizing of Earthquake Prediction and Disaster Preparedness

The purpose of using loss functions for earthquake prediction and disaster preparedness is to minimize expected costs when destructive earthquakes occur. This study focuses on developing a greater understanding of the interrelation between earthquake prediction characteristics and economic parameters. Equations for estimating economic losses and optimizing both earthquake prediction and disaster preparedness are presented in different dimensional forms to improve the understanding of parametric relationships between prediction and preparedness. The equations expand upon previously presented loss functions by explicitly considering loss as a function of both time and space and the cost parameters are clearly described to allow for practical application. Derivations reveal the close relationship between the loss function in terms of earthquake prediction characteristics and the benefit-cost analysis commonly used for disaster preparedness. An optimal preparedness scheme is presented based on a concept of unpreventable damage in extreme events and is shown to be a function of the level of damage prevented by taking action in response to an earthquake prediction. The formulations show that alarm durations are optimal relative to the type and time to implement different actions and the alarm area is optimal relative to the potential earthquake size and related geohazards. The presentation shows that earthquake prediction need not be constrained at a point in space to be useful for disaster preparedness and that mitigation activity is more economically feasible the smaller the area of prediction is with respect to the potential earthquake source size. Examples are used to show how loss functions can be utilized to determine if an algorithm may be useful to implement into practice and how earthquake prediction strategies can be implemented in coordination with other risk reduction strategies to make cost effective mitigations. Optimized earthquake prediction algorithms will greatly aid disaster managers and decision makers in their preparations once a prediction is made. The loss functions help to develop a greater understanding between earthquake prediction research and disaster preparedness implementation, allowing for future improvements in earthquake disaster prevention.