The magnitude–frequency distribution (MFD) of many earthquake catalogs is well described by the Gutenberg–Richter (GR) law or its tapered version (TGR). This distribution is usually extrapolated to any subsets of the space–time window covered by the catalog. However, some empirical observations and logical thoughts may raise doubts about the validity of this extrapolation. For example, according to the elastic rebound theory, we may assert that the probability of a strong shock nucleating within a short‐time interval in a small area A just ruptured by another strong event should be lower than that expected by GR (or TGR): a lot of energy has already been released, and it takes time to recover to the previous state. Here, we put forward a space–time modification of the TGR, named energy‐dependent TGR (TGRE) in which the corner seismic moment becomes a time‐varying energy function depending on (1) the conceivable strongest shock that may nucleate in A⁠; (2) the time elapsed since the last strong earthquake that reset the elastic energy in A to a residual value; and (3) the rate of the energy recovery, linked to the recurrence time of the fault(s) involved. The model also verifies an invariance condition: for large space–time windows, the occurrence of a strong shock does not affect significantly the whole elastic energy available, that is, the TGRE becomes the TGR. The model is simple and rooted in clearly stated assumptions. To evaluate its reliability and applicability, we apply it to the 1992 Landers sequence. As expected by TGRE, we find that the MFD close to the fault system interested by the mainshock (⁠Mw 7.3) differs from that of earthquakes off‐fault, showing a lower corner magnitude. We speculate that TGRE may be profitably used in operational earthquake forecasting and that it explains the empirical observation that the strongest aftershocks nucleate always outside the mainshock fault.

中文翻译：

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能量相关的地震矩-频率分布

古登堡-里希特（GR）律或其渐进式（TGR）很好地描述了许多地震目录的震级频率分布（MFD）。通常将这种分布外推到目录涵盖的时空窗口的任何子集。但是，一些经验观察和逻辑思想可能会引起人们对该推论有效性的怀疑。例如，根据弹性回弹理论，我们可以断言，刚好在另一个短时间间隔内，在一个小区域A内一次强震击成核的可能性刚好被另一个强事件破坏了，这应该比GR（或TGR）期望的要低。 ：已经释放了很多能量，要恢复到以前的状态需要时间。在这里，我们提出了TGR的时空修改，命名为能量相关的TGR（TGRE），其中角地震矩变为随时间变化的能量函数，取决于（1）可能在A⁠中成核的最强烈的冲击；（2）自上次强地震以来将A中的弹性能重置为残差值所经过的时间；（3）能量回收率，与所涉及故障的重现时间相关。该模型还验证了不变性条件：对于较大的时空窗口，强烈冲击的发生不会显着影响可用的全部弹性能，即TGRE变为TGR。该模型很简单，并以明确陈述的假设为基础。为了评估其可靠性和适用性，我们将其应用于1992年Landers序列。正如TGRE所预期的那样，我们发现MFD接近主震所感兴趣的故障系统（Mw 7。3）与断层地震不同，其拐角幅度较小。我们推测，TGRE可能可用于运营地震预报中，并且可以解释经验性观察，即最强余震总是在主震断层之外形成核。