In repeating seismic event sequences within a specialized horizontal area, the moment magnitude is usually scaled with the recurrence interval. In addition to two horizontal dimensions, the vertical dimension plays a certain role in affecting the scaling law. However, whether and how the changing depth influences the scaling law remain enigmatic. Based on a large number of earthquake records with high-resolution epicenter locations in recent decades in Japan, we focus on a comparison between the 3-D seismic moment and seismic interval, which recognize the vertical dimension as the same dimension as the horizontal distances. The results show that (1) the seismic moment scaling law is applicable in the multiparameter 3-D models by visiting the 1.8 million events collected during a period of 15?years; (2) the vertical dimension of depth plays an important role in the Mo–SI relationship as well as in the variance in the 3-D seismic moment–interval magnitudes; and (3) the seismic moment rate, attributable to the plate convergence rate, varies with area and depth in influencing the regional earthquake recurrence frequency.
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