Constraints on near-source saturation models for avoiding over-saturation of response spectral ordinates in RVT-based stochastic ground-motion simulations

Inversions of empirical data and ground-motion models to find Fourier spectral parameters can result in parameter combinations that produce over-saturation of short-period response spectral ordinates. While some evidence for over-saturation in empirical data exists, most ground-motion modellers do not permit this scaling within their models. Host-to-target adjustments that are made to published ground-motion models for use in site-specific seismic hazard analyses frequently require the identification of an equivalent set of Fourier spectral parameters. In this context, when inverting response spectral models that do not exhibit over-saturation effects, it is desirable to impose constraints upon the Fourier parameters to match the scaling of the host-region model. The key parameters that determine whether over-saturation arises are the geometric spreading rate (gamma) and the exponential rate within near-source saturation models (h(beta)). The article presents the derivation of simple nonlinear constraints that can be imposed to prevent over-saturation when undertaking Fourier spectral inversions.