Frequency-moment distribution of deep earthquakes; Implications for the seismogenic zone at the bottom of slabs

We present a systematic investigation of the variation with depth of the frequency of earthquake occurrence vs. seismic moment based on 16 years of Harvard Centroid Moment Tensor (CMT) solutions. We analyze depth variations of earthquake size distribution in terms of variations in the absolute value of the slope of the regression of the logarithm of the population vs. seismic moment, a quantity known as the β parameter. The shallowest earthquakes (0–50 km depth) exhibit a well-defined and robust size distribution regime characterized by a discontinuous increase in β with increasing moment. Others have shown that this increase probably represents the effects of a physical limit in the dimensions of the area of seismogenic slip of shallow earthquake sources. The population of deep earthquakes in the depth interval 500–600 km shows two markedly different distributions. The deep earthquakes in the Tonga region feature an initially high β value (0.92) at small moments and a lower β value (0.41) at high moments. In contrast, the size distribution of non-Tonga deep events shows the reverse of those changes (β = 0.41 at low moment and β = 1.17 at higher moment). To help explain these observations, we propose a model of deep seismogenesis that assumes three-dimensional earthquake source regions that vary principally in their transverse dimensions. The two-β segment behavior in the Tonga region and other subduction zones is thought to represent, in part, constraints owing to the threshold of completeness of the CMT catalog and to its short time interval of sampling. We interpret the differences between Tonga and other deep Wadati-Benioff zones as being a consequence of Tonga's markedly higher subduction rate and, hence, its colder thermal structure and presumably thicker region of seismogenesis. We interpret the critical moments at which β values change in terms of variations in the transverse thickness of deep seismogenic zones and estimate that it is about 11 km for the Tonga region and about 3 km for other zones at depths of 500–600 km. These results are generally consistent with deep earthquakes being restricted to wedge-shaped regions of peridotite persisting metastably to as deep as 700 km in old, rapidly descending and hence cold slabs. Failure is thought to occur in metastable peridotite by transformational faulting. Great deep earthquakes present special challenges to any theory of deep earthquakes based on slab thermal structure. For example, a continuing question is how such large events can fit in a thermally controlled seismogenic zone that is diminishing in its transverse dimensions with increasing depth. The very concept of a scale-invariant earthquake size distribution may be inappropriate for these rare events and the unusual settings in which they are found.