Calendar Time Local Earthquake Forecasts from Earthquake Nowcasts: A Do-It-Yourself (DIY) Ensemble Method

Abstract

This paper presents a new technical 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, together with the Gutenberg-Richter (GR) magnitude-frequency relation. The GR relation states that for every large target earthquake of magnitude greater than MT , there are on average NGR small earthquakes of magnitude MT > M >= MS. The only assumption is that the GR statistics of the local area are the same as in the larger surrounding regions. This assumption is used to construct an ensemble of earthquakes in larger surrounding regions to be used in computing the forecast. 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. There is no need to assume a probability model, as the probability is instead 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.