The width beyond a static arrest point predicts which static arrests span the fault

Wenjie Lyu 

Population models treat a static arrest as the end of the rupture, although some of those arrests span the fault in a fully dynamic calculation. This paper tests whether the static crack itself shows which ones. A static stress-intensity criterion and a fully dynamic rupture were compared on 180 new random stress fields on one 120 km antiplane fault with linear slip weakening. The predictor is the subcritical width, the extra distance one crack tip must be extended, with the other tip held fixed, before the static stress intensity factor returns to its critical value. Two logistic models were fitted on 52 earlier antiplane ruptures, 10 of which span the fault. One uses the static arrest length alone and the other adds the width. Both were applied unchanged to the 158 new ruptures that the static criterion stops. Of the 158, 24 span the fault dynamically. Adding the width raises the probability that a spanning rupture ranks above an arrested one from 0.880 to 0.956, a gain of 0.076 with a 95% interval from 0.037 to 0.126. The test and the required gain were fixed before the new fields were drawn. Halving the grid spacing along strike left the outcome of all 158 ruptures unchanged. On 120 earlier ruptures on the same fault, the static criterion and the dynamic rupture disagreed 22 times, and all 22 were static arrests that spanned the fault. Population models and induced earthquake estimates that use the static balance make that error in one direction. The width read from the static crack can rank which of those static arrests should be run dynamically first, at the correlation length tested here. At a correlation length 1.78 times longer, a width threshold flags 19 of 38 spanning ruptures and a length threshold flags 34, so that ranking is not shown to carry over. The test covers antiplane rupture, one correlation length, three stress amplitudes, and linear slip weakening.