Lengths of intermediate and deep seismic zones and temperatures in downgoing slabs of lithosphere

Summary. If intermediate and deep earthquakes occur in the coldest portions of the downgoing slabs of lithosphere, then different lengths of seismic zones represent different temperatures in the slabs. As the slab descends through the aesthenosphere, it warms primarily by conduction of heat through its upper and lower surfaces. Isotherms are advected downwards to distances approximately proportional both to the rate of subduction and to the square of the thickness of the lithosphere. Consequently, the lengths of seismic zones should be approximately proportional to the product of the rates and the squares of these thicknesses. As these thicknesses are approximately proportional to the square root of the age of the lithosphere, the lengths ought therefore to be approximately proportional to the product of the convergence rates times the ages. Although there is considerable scatter, observed lengths are approximately proportional to such products, and are not simply related to the rate, the age or the thickness alone. The data crudely fit the relationship: length = rate × age/10. Using this relationship, we infer that the Philippine sea and Pacific plates move slowly, if at all, with respect to one another and that the Farallon plate may have been too young to be subducted to a great distance beneath western North America in the Palaeogene. Calculations of temperatures at the depths of the deepest events suggest that these cut‐off temperatures increase from about 600 ± 100°C at 200 km to 830 ± 50°C at 650 km depth, but the cut‐off potential temperature is approximately constant. Assuming that the strength is a thermally activated parameter, and using the activation energy for olivine, a crude estimate of activation volume is obtained from the dependence of the cut‐off temperature on depth.