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.

中文翻译：

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日本地震矩的深度变化和重复间隔

在特定的水平区域内重复地震事件序列时，矩量通常与递归间隔成比例。除了两个水平维度，垂直维度在影响缩放定律方面也起一定作用。但是，深度的变化是否以及如何影响缩放定律仍然是个谜。根据日本近几十年来大量具有高分辨率震中位置的地震记录，我们着重于3D地震矩和地震间隔之间的比较，该地震矩将垂直尺寸与水平距离识别为相同尺寸。结果表明：（1）地震矩尺度定律适用于多参数3-D模型，通过访问在15年内收集的180万个事件；（2）深度的垂直维度在Mo-SI关系以及3-D地震矩-间隔幅度的方差中起着重要作用；（3）板块收敛速度引起的地震矩速率随面积和深度的变化而影响区域地震的复发频率。