Theoretical approaches to earthquake instabilities propose shear-dominated source mechanisms. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of thermo-hydro-mechano-chemical reaction–diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion or quasi-soliton waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a stationary wave focus from large to small scale. We show that the rich solution space of the reaction–cross-diffusion approach to earthquake instabilities can recover classical Turing instabilities (periodic in space instabilities), Hopf bifurcations (spring-slider-like earthquake models), and a new class of quasi-soliton waves. Only the quasi-soliton waves can lead to extreme focussing of the wave energy into short-wavelength instabilities of short duration. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of “rogue waves” and high energy pulses of light in photonics. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike. This spike is likely to cause unstable slip on a pre-existing (near-critically stressed) fault acting as a trigger for the ultimate (shear) seismic moment release.

中文翻译：

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多尺度、多物理场不稳定性引起的交叉扩散波：在地震中的应用

地震不稳定性的理论方法提出了剪切主导的震源机制。在这里，我们重新审视了剪切不稳定之前可能的体积不稳定性的作用。我们使用 THMC 扩散矩阵中的热-水-机械-化学反应-扩散方程的耦合来研究可能导致地震不稳定性的现象。我们表明，非对角交叉扩散率可以产生一类新的波，称为交叉扩散或准孤子波。它们的独特之处在于，在临界条件下，交叉扩散波可以将波能量从大尺度到小尺度汇集到驻波焦点中。我们表明，地震不稳定性的反应-交叉扩散方法的丰富解空间可以恢复经典的图灵不稳定性（空间不稳定性的周期性），Hopf 分岔（类似弹簧滑块的地震模型）和一类新的准孤子波。只有准孤子波才能导致波能极度集中成短时间的短波长不稳定性。海浪和光纤中的等效极端事件导致光子学中“流氓波”和高能光脉冲的出现。在流体机械耦合的背景下，流氓波将表现为突然的流体压力峰值。这个尖峰很可能在预先存在的（接近临界应力）断层上引起不稳定滑动，作为最终（剪切）地震矩释放的触发器。只有准孤子波才能导致波能极度集中成短时间的短波长不稳定性。海浪和光纤中的等效极端事件导致光子学中“流氓波”和高能光脉冲的出现。在流体机械耦合的背景下，流氓波将表现为突然的流体压力峰值。这个尖峰很可能在预先存在的（接近临界应力）断层上引起不稳定滑动，作为最终（剪切）地震矩释放的触发器。只有准孤子波才能导致波能极度集中成短时间的短波长不稳定性。海浪和光纤中的等效极端事件导致光子学中“流氓波”和高能光脉冲的出现。在流体机械耦合的背景下，流氓波将表现为突然的流体压力峰值。这个尖峰很可能在预先存在的（接近临界应力）断层上引起不稳定滑动，作为最终（剪切）地震矩释放的触发器。