Earthquake catalogs most commonly represent events as point sources, specified by a moment tensor and a centroid (location and time), which are the zeroth and first degree polynomial moments of the earthquake's source distribution respectively. We have begun cataloging the 2nd degree moments of the source distributions of earthquakes between M_W=7.0 and M_W=8.2 occurring since 1994. We invert frequency dependent measurements of amplitude and arrival time anomalies for fundamental mode Rayleigh waves and P-waves recorded at global stations for the 0th, 1st, and 2nd degree moments of an earthquake. The inversion procedure enforces the non-linear, physical constraint that the source region have non-negative volume. The 2nd moments describe the spatial and temporal extent of a rupture, as well as its average propagation velocity. They can be interpreted in terms of a characteristic rupture length, L_c, and a characteristic rupture duration, tau_c, whose ratio gives the apparent rupture velocity, v_c = L_c / tau_c. Because the 2nd spatial moment describes the extent and orientation of the source, it can be used to resolve the fault-plane ambiquity associated with an event's moment-tensor. The mixed moment between space and time represents the average velocity of the instantaneous centroid during rupture, v₀.
One of the initial results to come out of cataloging 2nd moments is an apparent statistical preference for unilateral rather than bilateral rupture. For a perfectly symmetric bi-lateral rupture, v₀= 0, whereas for uniform-slip unilateral ruptures, v₀=v_c. Thus by comparing v₀ and v_c we can infer the nature of rupture propagation during an event. Approximately 85% of the events in our catalog have v₀ = 0.5*v_c indicating a dominately unilateral rupture. This predominance of unilateral propagation as the mode of rupture appears to hold for both strike-slip and subduction zone thrust-fault events. We will discuss several potential explanations for the predominance of unilateral ruptures in large earthquakes, including fault interface waves and the control of rupture nucleation by features such as asperities or fault segment boundaries.