Abstract
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 (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.
Highlights
Non-ergodic hazard analyses typically require adjustments to be made to published ergodic ground-motion models in order to make them more appropriate for the target region and site location (Bommer and Stafford 2020)
For the host region, the Fourier spectral parameters are either adopted from similar empirical inversions for a region assumed equivalent to that represented by the ergodic ground-motion model(s), or the parameters are obtained from direct inversion of the ergodic ground-motion model predictions
The rupture distance is recommended for use within the stochastic ground-motion method (Boore 2003), when combined with an appropriate finite-fault factor (Boore and Thompson 2015), as seen earlier in Eq 1
Summary
Non-ergodic hazard analyses typically require adjustments to be made to published ergodic ground-motion models in order to make them more appropriate for the target region and site location (Bommer and Stafford 2020). Near-source saturation models have recently received heightened attention in the context of small-magnitude events (Atkinson et al 2016) When these models are extended to very large magnitudes, their interaction with other components of the stochastic method can lead to over-saturation of earthquake ground motions, where predicted amplitudes for very large events are lower than those from smaller magnitude events. The purpose of this short article is to define the conditions for which over-saturation occurs so that model developers can impose these constraints if they deem over-saturation to be an undesirable feature. When using the Hybrid Empirical Method of Campbell (2003), one needs to invert empirical data in the target region and a ground-motion model from the host region in order to derive the final ground-motion model for the target region
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