Refinement of the modified time-to-failure method for intermediate-term earthquake prediction

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The modified time-to-failure method for intermediate-term earthquake prediction utilizes empirical relationships to reduce the number of unknown parameters providing a stable and unique solution set. The only unknown parameters in the modified time-to-failure method are the time and size of the impending main shock. The modified time-to-failure equation is used to model the precursory events and a prediction contour diagram is constructed with the magnitude and time-of-failure as the axes of the diagram. The root-mean-square (rms) is calculated for each set of time and magnitude on the prediction diagram representing the difference between the model (calculated) acceleration and the actual accelerated energy release of the precursory events. A small region, corresponding to the low rms region on the diagram, defines the prediction. The prediction has been shown to consistently under-estimate the magnitude and over-estimate the time-of-failure. These shortcomings are caused by an underestimation in energy release of the modified time-to-failure equation at the very end of the sequence. An empirical correction can be applied to the predicted results to minimize this problem.

A main shock location search technique has been developed for use with the modified time-to-failure method. The location technique is used to systematically search an earthquake catalog and identify locations corresponding to precursory sequences that display accelerated energy releases. It has shown good results when applied in ‘retrospective predictions‘, and is essential for the practical application of the modified time-to-failure method. In addition, an observed linear characteristic in long-term energy release can be used to minimize false predictions.

The refined empirical relationships that eliminate or constrain unknown constants used in the modified time-to-failure method and the main shock location search technique are used in a practical application in the New Madrid Seismic Zone (NMSZ). The NMSZ, which is ‘over due’ for a magnitude 6 event according to recurrence rates (Johnston and Nava, 1985), makes this region ideal for testing the method. One location was identified in the NMSZ as a ‘high risk’ area for an event in the magnitude 4.5 range. The prediction, if accurate, is of scientific interest only because of the relatively small size of the main shock.

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