Eruptions in basaltic volcanoes are often preceded by increasing seismicity and surface deformation, which progressively damage and weaken the volcanic edifice. We show how damage and crack interaction produce the inverse Omori-Utsu law for earthquakes during pre-eruptive periods. Rock mass continuity, representing damage, is shown to decrease exponentially with the earthquake number; we interpret it as a general form of the Omori-Utsu law. Pre-eruptive earthquake time series are shown to be controlled by heterogeneity distribution, finite-size effect and crack interaction, and by the feeding system characteristic time. Magma-edifice coupling is described by state variables that depend on the continuity and the feeding system characteristic time. Pre-eruptive seismicity of the 2004–2017 24 summit/proximal eruptions of Piton de la Fournaise volcano was well modeled by an inverse Omori-Utsu law. It allowed identifying two cases: (a) strong crack interaction and earthquake number acceleration, when failure in strong intact rock and finite-size effects dominate the brittle fracture process; in that case the magma-edifice interaction power exhibits a maximum before the eruption; (b) weak crack interaction, generating an almost constant earthquake rate and corresponding to a brittle fracture process at constant strain in a weak, fractured rock mass. In this latter case eruptions occurred when the continuity reached a critical value, close to 0.25. Specific times are identified, from the time variations of the state variables; they define estimators that provide values of the eruption time within 10% of the true value in 60%–75% of the cases studied, from the complete time series.

中文翻译：

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Piton De La Fournaise 火山喷发前的损害、削弱和岩浆-建筑物耦合

玄武岩火山喷发之前通常会出现地震活动增加和地表变形，从而逐渐损坏和削弱火山结构。我们展示了损伤和裂纹相互作用如何产生爆发前地震的大森宇津反定律。代表破坏的岩体连续性随着地震次数呈指数下降；我们将其解释为大森宇津法的一般形式。研究表明，爆发前的地震时间序列受非均匀性分布、有限尺寸效应和裂缝相互作用以及馈电系统特征时间的控制。岩浆-建筑物耦合由取决于连续性和供给系统特征时间的状态变量来描述。 Piton de la Fournaise 火山 2004 年至 2017 年 24 次顶峰/近端喷发的喷发前地震活动可以通过逆 Omori-Utsu 定律很好地模拟。它可以识别两种情况：(a) 强裂纹相互作用和地震次数加速，此时坚固完整岩石的破坏和有限尺寸效应主导脆性断裂过程；在这种情况下，岩浆-建筑物相互作用力在喷发前表现出最大值； (b) 弱裂纹相互作用，产生几乎恒定的地震速率，对应于弱裂隙岩体中恒定应变下的脆性断裂过程。在后一种情况下，当连续性达到接近 0.25 的临界值时，就会发生喷发。根据状态变量的时间变化确定特定时间；他们定义了估计器，在完整的时间序列中，在 60%–75% 的研究案例中，提供的喷发时间值与真实值的 10% 以内。