Never fear velocity reversals

Velocity reversals are layers within the soil/rock profile that have a velocity lower than that of the overlying strata. When performing site-response analysis, these reversals are often avoided because of the complexity they introduce. In this study, we explore the effect of a velocity reversal on the fundamental mode of the 1D linear elastic response for the case of two layers over a half-space. We define a criterion for tolerable velocity reversals, in which the amplitude change imposed by the reversal is relatively insignificant. We do so by modeling three-layer velocity profiles with different combinations of thickness and velocities. We observe that the amplitude is affected by both the impedance ratio and the thickness ratio between the upper two layers. We find that the amplitude of the linear transfer function at the fundamental frequency is, on a first order, a function of the effective impedance ratio—the impedance ratio between the half-space and a layer having the combined thickness of the upper two and their time-averaged shear-wave velocity. We suggest a model to compute the minimum allowable velocity in the reversal layer while maintaining an amplitude change smaller than 10% with respect to a nonreversal velocity profile. The reversal velocity in our model is a function of the overlaying velocity and the thickness ratio.