流体注入引起的自相似断层滑动
Self-similar fault slip in response to fluid injection
AI总结：
本文通过建立弹性半空间界面断层在恒压线源流体注入下的积分-微分方程模型，利用自相似解和匹配渐近展开方法揭示了滑动扩展规律，并提供了高精度数值基准。
摘要：
科学界和工业界对理解地质断层如何响应瞬态流体源有着浓厚兴趣。自然和人工来源可以升高断层摩擦界面上的孔隙流体压力，从而可能诱发滑动。我们考虑一个简单的边值问题，以提供该物理过程的基本模型，并为数值求解程序提供基准。我们研究作为两个弹性半空间界面的断层的滑动。注入被建模为恒定压力下的线源，并假设流体压力沿界面扩散。由此产生的问题是一个控制断层滑动的积分-微分方程，该方程具有一个单一的无量纲参数。滑动的扩展是自相似的，破裂前沿以扩散长度尺度$\sqrt{αt}$的因子$λ$传播。我们确定了对应于$λ$较小或较大的两种渐近状态，并在每种极限下进行摄动展开。对于较大的$λ$，在所谓的临界应力断层状态下，在扩散长度尺度上出现一个边界层，该边界层远远落后于破裂前沿。我们展示了积分-微分方程的高阶匹配渐近方法，并在此过程中推导出一个多极展开，以捕捉相对于裂纹尺寸较小的驱动力对外部断层滑动问题的逐阶影响。渐近展开与完整问题的精确数值解进行了比较，这些数值解被高精度地列成表格。
英文摘要：
There is scientific and industrial interest in understanding how geologic faults respond to transient sources of fluid. Natural and artificial sources can elevate pore fluid pressure on the fault frictional interface, which may induce slip. We consider a simple boundary value problem to provide an elementary model of the physical process and to provide a benchmark for numerical solution procedures. We examine the slip of a fault that is an interface of two elastic half-spaces. Injection is modeled as a line source at constant pressure and fluid pressure is assumed to diffuse along the interface. The resulting problem is an integro-differential equation governing fault slip, which has a single dimensionless parameter. The expansion of slip is self-similar and the rupture front propagates at a factor $λ$ of the diffusive lengthscale $\sqrt{αt}$. We identify two asymptotic regimes corresponding to $λ$ being small or large and perform a perturbation expansion in each limit. For large $λ$, in the regime of a so-called critically stressed fault, a boundary layer emerges on the diffusive lengthscale, which lags far behind the rupture front. We demonstrate higher-order matched asymptotics for the integro-differential equation, and in doing so, we derive a multipole expansion to capture successive orders of influence on the outer problem for fault slip for a driving force that is small relative to the crack dimensions. Asymptotic expansions are compared to accurate numerical solutions to the full problem, which are tabulated to high precision.
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