Seismic Event Due to Fluid Injection or Withdrawal - Induced Seismicity Potential in Energy Technologies - page 200

FIGURE G.2 The normal and shear stress, σ and τ , acting across the fault depends on the vertical and
horizontal stresses, σ n and σ h , and the fault inclination β . The fault is infiltrated by fluid at pressure ρ .

The normal and shear stress on the fault can actually be expressed in terms of the in
situ vertical and horizontal stresses, σ v and σ h , through a relation that depends on the fault
inclination β (Figure G.2). The above Coulomb criterion can then be expressed as a limiting
condition in terms of the effective vertical and horizontal stresses σ′ v = σ v - ρ and σ′ h = σ h - ρ
or equivalently in terms of their half-sum and half-difference, P ′ and S . Figure G.3 provides
a graphical representation of the Coulomb criterion in terms of these two quantities.
The fault is stable if the point representative of the (effective) in situ stress state is below
the slip criterion. A perturbation (ΔΡ′, ΔS), induced by fluid injection or withdrawal, to an
existing state (Ρ′ o , S o ) that moves the point (Ρ′ o + ΔΡ′, S o + ΔS) to be on the Coulomb line will
cause slip and trigger a seismic event. However, only some perturbations are destabilizing
in nature (i.e., they move the representative stress point [Ρ′, S] closer to the critical condi- closer to the critical condi-

tions). For example, the destabilizing perturbation shown in Figure G.3 is characterized
by a slope m = ΔS/ΔΡ′ smaller than m o and a “direction” corresponding to both ΔΡ′ and ΔS
being negative. A perturbation characterized by the same slope m , but positive variations
ΔΡ′ and ΔS, would be stabilizing.