Notes on Spatial Correlation for Average Spectral Acceleration: Direct and Indirect Approaches

When seismic risk assessments are performed on a regional scale, simulating representative ground motion fields (GMFs) at several locations over the area of interest is a key step. This is in terms of the intensity of shaking at each single site location with respect to the considered earthquake rupture scenario and also the coherence of the simulated shaking intensity values between each site location. For this, spatial correlation models are crucial and have received much attention in recent years. They have been developed mainly for well‐known intensity measures (IMs) such as peak ground acceleration and spectral acceleration, . For next‐generation IMs, such as average spectral acceleration, , there are no spatial correlation models specifically developed for this IM, inhibiting its application in practical regional applications. A recent proposal has developed an indirect formulation for this correlation model, capitalising on the fundamental definition of and the availability of other models that can be used to infer it. In this study, we compare the indirect approach with a recently developed direct spatial correlation model for . Results show that both methods exhibit very similar trends, with the indirect approach closely matching the direct formulation. Analysis of total and within‐event residuals indicates that total‐residual correlations approach an asymptotic value of around 0.2, while lack of care when generating GMFs using an indirect method can overestimate the IM by up to two orders of magnitude compared to the observed values. These findings highlight the need for care when modelling spatial correlation of , as well as potential unintended pitfalls in routine applications when applying an indirect modelling approach.