Scaling of ground motion parameters, state of stress, and focal depth

Abstract

The ground motion parametersRv and ρRa, where R is hypocentral distance, v is peak velocity, ρ is density, and a is peak acceleration, are found observationally to be strong functions of stress state and linearly related to focal depth z. If the stress state and focal depth are properly taken into account, then the ground motion parameters depend on the seismic moment M0, as expected from basic scaling principles. That is, Rv ∝ M01/3, and ρRa is independent of earthquake size. Regression lines fitted to observations, covering broad ranges in seismic moment and focal depth, indicate that for extensional and compressional tectonic regimes, corresponding to normal and thrust or reverse faulting earthquakes, respectively, peak acceleration is given by ρRa = ‐ 1.08 MPa + 3.06 (MPa/km)z (normal) and ρRa = 5.65 MPa + 8.76 (MPa/km)z (thrust), and for peak velocity, Rv/M01/3 = 10−4(m2/s) (N m)−1/3 [3.00+0.69 (km−1)z] (normal) and Rv/M01/3 = 10−4(m2/s) (N m)−1/3 [4.63+1.82 (km−1)z] (thrust). For strike‐slip earthquakes the data currently are insufficient to define regression fits, but such lines would definitely lie between those for the normal and thrust stress regimes. These equations are appropriate for ground motion at small hypocentral distance as recorded in a whole space. It follows that for comparable hypocentral depth, peak acceleration in a compressional tectonic regime, for example, much of the eastern United States, is a factor of about 3 greater than in an extensional regime, such as Nevada, and for peak velocity a similar comparison yields a factor of 2 difference. The similarity in behavior of the peak acceleration parameter to crustal strength, estimated from Byerlee's law of friction, with respect to depth and stress state, indicates that crustal strength is probably the factor governing the seismic source processes that give rise to the high‐frequency peak ground motion. Analysis of the peak acceleration data in the context of crustal strength suggests bounds on this ground motion parameter, as recorded at a typical surface site, that depend on stress state, specifically, a (normal) ≲0.5 g and a (thrust) ≲1.9 g. Thus the state of stress as well as the focal depth clearly is an important factor to be taken into account in the prediction of seismic ground motion.