Math 2.0

Geophysics Definition

Coulomb stress transfer

Builds on Cauchy stress tensorMohr–Coulomb theory

Definition

Let Δσ\Delta\sigma be the change of the Cauchy stress tensor at a point of the crust caused by a source earthquake, with tension counted positive. Let a receiver fault through that point have unit normal nn and unit slip direction ss, with s⊥ns \perp n. The shear stress change is Δτ=s⋅(Δσ n)\Delta\tau = s \cdot (\Delta\sigma\, n), and the normal stress change is Δσn=n⋅(Δσ n)\Delta\sigma_n = n \cdot (\Delta\sigma\, n). For an effective friction coefficient μ′≥0\mu' \ge 0, the Coulomb failure stress change is ΔCFS=Δτ+μ′Δσn.\Delta \mathrm{CFS} = \Delta\tau + \mu' \Delta\sigma_n. Coulomb stress transfer is the change of CFS\mathrm{CFS} on receiver faults produced by the source earthquake; a fault with ΔCFS>0\Delta \mathrm{CFS} > 0 is brought closer to failure.

Remarks

Example: Δτ=0.1\Delta\tau = 0.1 MPa, Δσn=−0.2\Delta\sigma_n = -0.2 MPa (more compression) and μ′=0.4\mu' = 0.4 give ΔCFS=0.1−0.08=0.02\Delta \mathrm{CFS} = 0.1 - 0.08 = 0.02 MPa, a small loading. Non-example: the change of the full magnitude of the shear traction is not Δτ\Delta\tau, because only the component along the slip direction ss of the receiver fault promotes its slip. The coefficient μ′\mu' includes the effect of pore fluid pressure, which reduces the normal stress that clamps the fault. The definition is the change of the Coulomb (Mohr–Coulomb) failure function τ+μ′σn\tau + \mu' \sigma_n, so it depends on the orientation and slip direction of the receiver fault. In practice Δσ\Delta\sigma is computed from a model of the source slip in a linear elastic half-space.

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Further reading

  1. Web https://en.wikipedia.org/wiki/Coulomb_stress_transfer
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MSC86A15, 74B05
DefinesCoulomb stress transfer
UsesCauchy stress tensor, Mohr–Coulomb theory
Changed3 November 2026

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