Scale-model and numerical simulations of near-fault seismic directivity

Steven M. Day, Sarah H. Gonzalez, Abdolrasool Anooshehpoor, & James N. Brune

Published 2008, SCEC Contribution #1111

Foam rubber earthquake experiments provide a means to explore the sensitivity of near-fault ground motions to fault and rupture geometry. Cross-validation of foam rubber models with spontaneous-rupture numerical models can reduce uncertainties in both modeling methodologies. We analyze waveforms generated by foam rubber experiments simulating unilaterally propagating strike-slip earthquakes and compare them with 3D numerical simulations of the same experiments. Subsurface accelerometers on the fault plane show rupture propagation that, within experimental uncertainty, approaches a limiting velocity close to the Rayleigh velocity of the foam rubber. The slip-velocity waveform at depth is crack-like, in the sense that slip duration at a point is of the order of the narrower fault dimension W divided by the S wavespeed . Free-surface accelerometers record near-fault ground motion enhanced along strike by rupture-induced directivity. Most features of the foam-model waveforms, such as the initiation time, shape, duration and absolute amplitude of the main acceleration pulses, are successfully reproduced by the numerical model. An exception is displacement amplitude, which is under-predicted in the numerical simulations as a consequence of artificial boundary constraints in the latter. The acceleration pulses in the physical and numerical models show similar decay with distance away from the fault, and the fault-normal components in both models show similar, large amplitude growth with increasing distance along fault strike. This forward directivity effect is also evident in response spectra: the fault-normal spectral response peak (at period ~ ) increases approximately 6-fold along strike, on average, in the experiments, with similar increase (~5-fold) in the corresponding numerical simulation. A comparison of the physical and numerical model response spectra with an empirical directivity model for earthquake strong motion spectra reveals good agreement at long periods (periods near ~ ). Both foam and numerical models over-predict shorter-period directivity effects, with the amount of over-prediction increasing systematically with diminishing period. We speculate that this period-dependent difference is attributable to fault-zone heterogeneities in stress, frictional resistance, and elastic properties. These complexities, present in the earth but absent or minimal in the foam model (and in our numerical simulations of the foam model), can be expected to reduce rupture- and wave-front coherence, likely leading to reduced short-period directivity relative to the current scale-model events.

Day, S. M., Gonzalez, S. H., Anooshehpoor, A., & Brune, J. N. (2008). Scale-model and numerical simulations of near-fault seismic directivity. Bulletin of the Seismological Society of America, 98, 1186-1206. doi: 10.1785/0120070190.