Exceedance Probabilities for Large Earthquakes From DIY Local Earthquake Ensemble Nowcasting and Forecasting: Magnitude, Natural Time, and Calendar Time

This paper focuses on the problem of anticipating the local occurrence of future large earthquakes. "Local" is defined as the probability of a large earthquake occurring with a defined circle of arbitrary radius surrounding a point of interest. The main (and for that matter, the only) assumption for all these works is that the Gutenberg-Richter (GR) magnitude-frequency relation holds. Here we describe a method for computing calendar time forecasts in a local area for large earthquakes of a target magnitude MT using a count small earthquakes MS < MT in the area. Using the idea that the GR relation is valid throughout the surrounding region, we define an ensemble of earthquakes in larger surrounding regions to be used in computing the forecast. What follows is simple data mining. The method has significant skill, as defined by the Receiver Operating Characteristic (ROC) test, which improves as time since the last major earthquake increases. The probability is conditioned on the number of small earthquakes n(t) that have occurred since the last large earthquake. The probability is computed directly as the Positive Predictive Value (PPV) associated with the ROC curve. The method is validated by comparison to the UCERF3 forecasts for the UCERF3-defined geographic boxes centered on Los Angeles and San Francisco. The method is then applied to a 125-KM radius circular area around Los Angeles, California, following the January 17, 1994 magnitude M6.7 Northridge earthquake, and short term forecasts (1 year and 5 year ) are computed.