## Linear and nonlinear relations between relative plate velocity and seismicity

Peter Bird, Yan Y. Kagan, David D. Jackson, Frederic P. Schoenberg, & Maximilian J. WernerPublished 2009, SCEC Contribution #1264

Relationships between relative plate velocity and seismicity differ by plate boundary class. We test for linearity of earthquake rates with velocity in each of 7 classes. A linear relationship is expected if earthquake rate is proportional to seismic moment rate, which in turn is proportional to relative plate velocity. The second condition requires that the shape of the magnitude-frequency distribution and the coupling mechanism are relatively uniform within each class. To reduce bias by aftershocks and swarms, we estimate the independence probabilities of earthquakes and use them as weights. We assign most shallow earthquakes to boundary steps and classes, then sort boundary steps within each class by velocity, and plot cumulative earthquakes against cumulative model moment rate. We use 2 measures of departure from linearity, and 104 stochastic simulations to assess significance. In subduction zones the relationship between seismicity and velocity is nonlinear with 99.9% confidence. Slower subduction at <66 mm/a (which produces 35% of tectonic moment under the null hypothesis) produces only 20% of subduction earthquakes. Continental convergent boundaries display similar nonlinearity (P < 0.001 for the null hypothesis). Ocean spreading ridges show seismicity decreasing with velocity. Oceanic transform faults and oceanic convergent boundaries show marginal nonlinearity (P < 0.01; P < 0.05). Continental rifts and continental transform faults follow the null hypothesis. Three effects may contribute to velocity-dependence in subduction: (1) The brittle/ductile transition occurs at a critical temperature, which is advected deeper by faster underthrusting; (2) subducted sediment is viscous, so lower stresses in slower boundaries discourage earthquakes; (3) pore pressures increase with velocity, encouraging frictional failure. We find that mechanism (1) has only minor effects on earthquake productivity, but mechanisms (2) and (3) could be important.

**Citation**

Bird, P., Kagan, Y. Y., Jackson, D. D., Schoenberg, F. P., & Werner, M. J. (2009). Linear and nonlinear relations between relative plate velocity and seismicity. *Bulletin of the Seismological Society of America*, 99(6), 3097-3113. doi: 10.1785/0120090082.