Nonlinear Interaction of High‐Frequency Seismic Waves With Sliding Fault Planes

Slip during large crustal earthquakes continues for extended periods of time on spatially extensive fault planes. High‐frequency body waves from other parts of the fault system thus impinge on patches of the fault that are still actively sliding. Intuitively, the material within sliding fault planes does not rheologically distinguish between the low‐frequency stresses driving the gross earthquake and high‐frequency dynamic stresses from impinging body waves. Nonlinear interaction occurs, interrogating the rheology of the fault plane. High‐frequency S waves nonlinearly produce additional inelastic slip Δ S on the sliding fault. The ratio of this slip to the elastic displacement ( Δ S /Δ S E ), where Δ S E is the elastic displacement, depends on the slip‐reflection number, ( ∂V / ∂τ ) ρβ , where ∂V / ∂τ is the derivative of sliding velocity with respect to shear traction, ρ is density, and β is S ‐wave velocity. The sliding fault transmits and weakly reflects S waves for small values ≪2 of the parameter; it weakly transmits and strongly reflects for high values ≫2. It is relevant to evaluate ∂V / ∂τ at the long‐period slip velocity V 0 and shear traction τ 0 of the gross earthquake. The ratio is then Δ S /Δ S E  =  ρβV 0 Φ/ τ 0 , where Φ ≡ ( ∂V / ∂τ )( τ 0 / V 0 ) is measure of the nonlinearity the fault rheology. For example, the parameter Φ at high‐frequency impinging S waves is the ratio μ 0 / a of the coefficient of friction to the rate parameter a  ≈ 0.01 for rate and state friction. Weak sliding faults (low τ 0 and high V 0 ) strongly reflect impinging S waves. During waning slip, dynamic stresses from S waves antithetical to the gross slip direction and compressional P waves may heterogeneously lock the fault.