As a contribution to step 3 of the ESG6 blind prediction exercise, we present an application of two different, purely empirical approaches to estimate the strong ground motion at a soft site ("KUMA") from the observed ground motion at a reference rock site ("SEVO") for the two largest shocks of the Kumamoto 2016 sequence (a foreshock with Mj=6.5, and the mainshock with Mj=7.3). The two methods estimate the non-linear transfer function between a reference rock and a sedimentary site by modifying the linear transfer function derived from weak motion recordings. The modification is based either on a machine learning tool based on a wide collection of Japanese weak and strong motion recordings and the associated site metadata (method M1), or on an estimate of a site-specific parameter related to an average non-linear site response (M2). The acceleration time series are then derived at the sedimentary site of interest using an estimation of the time delay between wave arrivals at the rock and site stations, and a minimum phase assumption for the site transfer function.
These predictions were made blindly, but after the ESG6 conference they could be compared both with the actual ground motion recorded at KUMA during the two shocks, and the average and range of all other predictions preformed for this benchmark.
The quality of predictions is quantified through various "goodness of fit" (GOF) measures. The agreement may be considered as "excellent" for the foreshock and "good" for the mainshock for usual engineering ground motion parameters (peak values, response spectra, integral parameters), but is very poor in terms of waveform details – as usual for all ground motion predictions even in the linear domain –. The performance of these two purely empirical approaches is at least comparable to those of the numerical simulation methods for the foreshock – if not better -, and slightly worse for the (largest) mainshock. This may come either from an underestimation of non-linear effects, or from the relatively large distance (8 km) between the reference and the target site which limits the reliability of the empirical transfer functions and thus the applicability of the approaches used here for such an instrumental layout.
Both of these purely empirical methods provide an honorable prediction of the Fourier spectra and acceleration time histories of the two target events, as the methods required only recordings of weak motions at the target and a referent sites and very simple description of the soil profile. The use of moderate motions to constrain the frequency shift prediction for the second method and the consideration of an alternative phase modification are possible ways to improvement.