The spatiotemporal patterns of injection-induced seismicity (IIS) are commonly interpreted with the concept of a triggering front, which propagates in a diffusion-like manner with an associated diffusivity parameter. Here, we refer to this diffusivity as the “seismic diffusivity.” Several previous studies implicitly assume that seismic diffusivity is equivalent to the effective hydraulic diffusivity of the subsurface, which describes the behavior of the mean pressure field in heterogeneous porous media. Seismicity-based approaches for hydraulic characterization or simulations of IIS using domains of homogeneous equivalent porous media are implicitly based on this assumed equivalence. However, seismicity is expected to propagate with the threshold triggering pressure, and thus not be controlled by the evolution of the mean pressure field. We present numerical simulations of fluid injection to compare the seismic and effective hydraulic diffusivities in heterogeneous formations (including fractured rock). The numerical model combines uncoupled, linear pressure diffusion with the Mohr-Coulomb failure criterion to simulate IIS. We demonstrate that connected pathways of relatively high hydraulic diffusivity in heterogeneous media (particularly in fractured rock domains) allow the threshold triggering pressure to propagate more rapidly than predicted by the effective hydraulic diffusivity. As a result, the seismic diffusivity is greater than the effective hydraulic diffusivity in heterogeneous porous media, possibly by an order of magnitude or more. Additionally, we present a case study of IIS near Soultz-sous-Forêts where seismic diffusivity is found to be at least one order of magnitude larger than the effective hydraulic diffusivity.

中文翻译：

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地震扩散率和非均质性对注入诱发地震的影响

注入诱发地震活动 (IIS) 的时空模式通常用触发前沿的概念来解释，触发前沿以类似扩散的方式传播，并具有相关的扩散参数。在这里，我们将这种扩散系数称为“地震扩散系数”。先前的几项研究隐含地假设地震扩散率等于地下的有效水力扩散率，它描述了非均质多孔介质中平均压力场的行为。使用均质等效多孔介质域对 IIS 进行水力表征或模拟的基于地震学的方法隐含地基于这种假定的等效性。然而，地震活动预计会随着阈值触发压力传播，因此不受平均压力场演变的控制。我们提出了流体注入的数值模拟，以比较非均质地层（包括裂隙岩）中的地震扩散系数和有效水力扩散系数。该数值模型将非耦合线性压力扩散与 Mohr-Coulomb 失效准则相结合来模拟 IIS。我们证明了在非均质介质（特别是在裂隙岩石域）中相对较高的水力扩散率的连接路径允许阈值触发压力比有效水力扩散率预测的传播速度更快。因此，地震扩散率可能比非均质多孔介质中的有效水力扩散率大一个数量级或更多。此外，