Nonlinear attenuation and rock damage during strong seismic ground motions

Norman H. Sleep, & Paul N. Hagin

Published October 25, 2008, SCEC Contribution #1217

Strong seismic waves cause nonlinear behavior in the shallow subsurface in fractured rocks. Seismologists use low-amplitude signals from small repeating earthquakes to measure S wave velocity decrease after strong motion. The 2004 Parkfield, California, earthquake provides examples of such velocity changes in fractured sandstone with an S wave velocity of ∼300 m s−1. This nonlinear behavior occurred around the wave number depth of the incident waves, ∼30 m, for the ∼10 s−1 dominant angular frequency on a velocity seismogram. The low-amplitude S wave velocity gradually recovered with the logarithm of time. The attenuation of strong waves in general depends nonlinearly on their amplitude. High dynamic stress triggered small, very shallow earthquakes, at sites including Parkfield. The theoretical frictional behavior of a fractured medium with heterogeneous prestress relates these phenomena. Failure occurs in the highly prestressed domains causing small earthquakes and opening-mode cracks. The energy to dilate the cracks dissipates a significant fraction of the incoming seismic energy. The local high-porosity domains close with the logarithm of time, as expected from the aging law of rate and state friction, increasing the S wave velocity. The domain model indicates that nonlinear effects increase gradually over a range of dynamic Coulomb stresses as observed and as included in the widely used Masing rules. The Linker and Dieterich (1992) relationship provides the maximum sustainable dynamic coefficient of friction needed to utilize the Masing rules. This parameter is the coefficient of friction at a laboratory normal traction plus a constant ∼0.15 times the logarithm of the ratio of field normal traction to the laboratory normal traction. It is helpful to relate S wave velocity to starting frictional strength, as coefficient of friction near the quarter-wavelength depth determines nonlinear behavior. Then the dynamic coefficient of friction and equivalently the maximum sustainable acceleration at the dominant frequency depend weakly on S wave velocity. For example, the coefficient of friction at an angular frequency of 10 s−1 is less than 1.5 for rocks ranging from Parkfield sandstone to intact granite.

Sleep, N. H., & Hagin, P. N. (2008). Nonlinear attenuation and rock damage during strong seismic ground motions. Geochemistry, Geophysics, Geosystems, 9, Q10015. doi: 10.1029/2008GC002045.