Developing ground motion prediction equations: an alternate methodology and its implementation with a subset of NGA-West2 database

Ground-motion-prediction-equations (GMPEs) play a critical role in seismic hazard analysis. However, the conventional methods for developing GMPEs, which rely on functional forms and assumptions like homoscedasticity, can introduce biases. The Consistent Spectral Shape (CSS) approach introduces a novel framework for GMPE construction, which extends the widely adopted maximum likelihood approach while remaining independent of the homoscedasticity assumption. This approach decouples the logarithmic mean spectrum into two components: logarithmic spectral shape and logarithmic mean peak ground acceleration (normalizing factor). This decoupling enables a specific study of the spectral shape, allowing for an investigation of how it varies across different sets of independent variables and different definitions of intensity measures. An alternate perspective of decoupling is also explored in line with the conventional representation of the median/design spectrum. Additionally, the paper also describes methods to account for aleatory variability by the construction of logarithmic variance spectra in three cases depending on the existence of systematic trend against magnitude-distance (M-R), given a soil category: (A) systematic trend against M-R; (B) no systematic trend against M-R; and (C) nearly invariant with M-R. The CSS framework is demonstrated through its application to the NGA-West2 database for five spectral acceleration definitions: (a) RotD50; (b) RotD100; (c) Geo-mean; (d) GMRotD50; and (e) GMRotD100. The proposed framework, followed by the constructed CSS-GMPEs, is anticipated to serve as a crucial input for performing seismic hazard analysis.