Here we define and report the relationship between the maximum seismic magnitude (M) and injection volume (ΔV) through fluid-injection fault-reactivation experiments and analysis. This relationship incorporates the in situ shear modulus (G) and fault pre-stress as a fraction of the strength drop (c), expressed as M = c/(1-c) GΔV. Injection response defines a sigmoidal relation in \(M-\Delta {V}\) space with unit gradient limbs linked by an intermediate up-step. Both laboratory observations and analysis for a rigid fault with slip limited to the zone of pressurization show trajectories of cumulative \(M-\Delta {V}\) that evolve at a gradient of unity, are offset in order of increasing pre-stress and are capable of step changes in moment with shear reactivation at elevated critical-stresses – key features apparent in field observations. The model and confirmatory laboratory observations explain the occurrence of some triggered earthquakes at EGS sites significantly larger than expected relative to injection volumes and based on previous models.

在这里，我们通过注液断层再活动实验和分析定义并报告了最大地震震级（ M ）和注入量（ ΔV ）之间的关系。该关系将原位剪切模量 ( G ) 和断层预应力作为强度降 ( c ) 的一部分，表示为M = c/(1-c) GΔV 。注入响应定义了\(M-\Delta {V}\)空间中的 S 形关系，其中单位梯度肢体由中间上步链接。对仅限于加压区域的滑动刚性断层的实验室观察和分析都显示，累积的轨迹\(M-\Delta {V}\)以统一的梯度演化，并按预应力和预应力增加的顺序进行偏移。能够在临界应力升高的情况下随着剪切重新激活而瞬间发生阶跃变化——这是现场观察中显而易见的关键特征。该模型和验证性实验室观察解释了 EGS 站点发生的一些引发的地震，其相对于注入量和基于先前模型的预期明显大于预期。