Inversions of empirical data and ground-motion
models to find Fourier spectral parameters can result in parameter combinations that produce over-saturation of shortperiod 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 adjustmentsthat are made to published groundmotion 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 oversaturation effects, it is desirable impose constraints upon the
Fourier parameters to match the scaling of the host-region
model. The key parameters that determine whether oversaturation arises are the geometric spreading rate (γ) and the
exponential rate within near-source saturation models (hβ ).
The article presents the derivation of simple nonlinear constraints that can be imposed to prevent over-saturation when
undertaking Fourier spectral inversions.