Ya-Ting Lee

Negative correlation between frequency-magnitude power-law exponent and Hurst coefficient in the Long-Range Connective Sandpile model for earthquakes and for real seismicity

The Long-Range Connective Sandpile (LRCS) model was applied to the Italian seismicity. The Hurst exponent and the power-law slope of the frequency-size distributions for the avalanches in the LRCS model and for earthquakes in Italy are investigated. This study shows the transition of the correlation coefficient between b and H values with different calculation window length. The result shows similar behaviors in the LRCS model and the Italy catalogue. The negative correlation between b and H values can be clearly seen when an appropriate window length is employed for various time series. We suggest that the negative relationship is caused by the increasing correlation length as the system accumulates enough energy. Also the calculation window length is an important index to display the intensity of the negative correlation between these two exponents. The appropriate window length can be related to the period time for the avalanches with various sandpile and seismicity time series.

Evaluating the RELM Test Results

We consider implications of the Regional Earthquake Likelihood Models (RELM) test results with regard to earthquake forecasting. Prospective forecasts were solicited for earthquakes in California during the period 2006–2010. During this period 31 earthquakes occurred in the test region with . We consider five forecasts that were submitted for the test. We compare the forecasts utilizing forecast verification methodology developed in the atmospheric sciences, specifically for tornadoes. We utilize a “skill score” based on the forecast scores of occurrence of the test earthquakes. A perfect forecast would have , and a random (no skill) forecast would have . The best forecasts (largest value of ) for the 31 earthquakes had values of to . The best mean forecast for all earthquakes was . The best forecasts are about an order of magnitude better than random forecasts. We discuss the earthquakes, the forecasts, and alternative methods of evaluation of the performance of RELM forecasts. We also discuss the relative merits of alarm-based versus probability-based forecasts.

A statistical damage model with implications for precursory seismicity

Acoustic emissions prior to rupture indicate precursory damage. Laboratory studies of frictional sliding on model faults feature accelerating rates of acoustic emissions prior to rupture. Precursory seismic emissions are not generally observed prior to earthquakes. To address the problem of precursory damage, we consider failure in a fiber-bundle model. We observe a clearly defined nucleation phase followed by a catastrophic rupture. The fibers are hypothesized to represent asperities on a fault. Two limiting behaviors are the equal load sharing p = 0 (stress from a failed fiber is transferred equally to all surviving fibers) and the local load sharing p = 1 (stress from a failed fiber is transferred to adjacent fibers). We show that precursory damage in the nucleation phase is greatly reduced in the local-load sharing limit. The local transfer of stress from an asperity concentrates nucleation, restricting precursory acoustic emissions (seismic activity).