Envelope-Based Early Warning Algorithm Using Nested Grid Search

We present an envelope-based algorithm that implements a nested grid search. This algorithm is a direct solution that is simple to implement in parallel execution. The goal is to predict the magnitude, location, and origin time of an event using a probabilistic approach, based on Cua-Heaton ground motion prediction equations. A unique aspect of this algorithm is that it will be valuable for complex sequences, such as foreshocks and mainshocks that are closely spaced in time.

Grids in consideration are magnitude, latitude, longitude, and origin time. These grids depend highly on the information given by the first-triggered station for it is assumed to be the nearest to the epicenter. At each grid point, observed and predicted envelopes are calculated and compared in a goodness-of-fit test. The predicted envelopes we use are the Cua-Heaton ground motion envelopes. They are combinations of noise, P-, and S-wave envelopes as a function of magnitude, epicentral distance, and soil conditions. Nested within this grid search is another search of previous recorded events from the catalog. These envelopes are also considered in the goodness-of-fit test.

For each station, intensity measure, and component, likelihoods are quantified to find the parameters that give the best fitting envelopes. We look at the sensitivity of the grid search predictions to different conditions, such as station density and P/S wave discriminants. We look at different constraints that affect the envelope fittings, such as the choice of norms.