Logistic Regression Applied to Seismic Discrimination

The usefulness of logistic discrimination was examined in an effort to learn how it performs in a regional seismic setting. Logistic discrimination provides an easily understood method, works with user-defined models and few assumptions about the population distributions, and handles both continuous and discrete data. Seismic event measurements from a data set compiled by Los Alamos National Laboratory (LANL) of Chinese events recorded at station WMQ were used in this demonstration study. PNNL applied logistic regression techniques to the data. All possible combinations of the Lg and Pg measurements were tried, and a best-fit logistic model was created. The best combination of Lg and Pg frequencies for predicting the source of a seismic event (earthquake or explosion) used Lg{sub 3.0-6.0} and Pg{sub 3.0-6.0} as the predictor variables. A cross-validation test was run, which showed that this model was able to correctly predict 99.7% earthquakes and 98.0% explosions for this given data set. Two other models were identified that used Pg and Lg measurements from the 1.5 to 3.0 Hz frequency range. Although these other models did a good job of correctly predicting the earthquakes, they were not as effective at predicting the explosions. Two possible biases were discovered which affect the predicted probabilities for each outcome. The first bias was due to this being a case-controlled study. The sampling fractions caused a bias in the probabilities that were calculated using the models. The second bias is caused by a change in the proportions for each event. If at a later date the proportions (a priori probabilities) of explosions versus earthquakes change, this would cause a bias in the predicted probability for an event. When using logistic regression, the user needs to be aware of the possible biases and what affect they will have on the predicted probabilities