Cubic moment-duration relationship of low-frequency earthquakes

Low-frequency earthquakes (LFEs) are seismic phenomena with the shortest timescale among various slow earthquakes observed on broad-band timescales. To understand the nature of such a broad-band slow phenomenon, it is important to investigate the rupture evolution process of individual slow events, such as LFEs. Here, we investigated the moment-duration relationship of LFEs at plate interfaces and volcanic regions, and showed that the moment-duration relationship of both tectonic and volcanic LFEs is characterized by a moment proportional to the cubic duration, similar to that in ordinary earthquakes. The difference between our obtained moment-duration relationship and the broad-band scaling suggests that the evolution process of LFEs may not be controlled, but only triggered by the slow earthquakes with longer durations, such as slow slip events driven by aseismic diffusion. The seismic moments of the LFEs are approximately three orders of magnitude smaller than those of ordinary earthquakes with similar durations. This result indicates that LFEs have rupture growth similar to that of ordinary earthquakes, although the rupture velocity and/or stress drop are much smaller. Considering the hypocentre spread of LFEs, the estimated rupture velocity and stress drop were approximately 100 m /s-1 km /s and 2 kPa-1 MPa, respectively. Additionally, the estimated moment magnitudes are much larger than the local magnitudes determined based on the maximum amplitudes, which is due to the longer durations and resultant smaller amplitudes of LFEs than those of ordinary earthquakes.