Development of a Regional Ground Motion Prediction Equation for Peak Ground Acceleration Using Japanese Earthquake Data: A Least Squares Regression Approach

Abstract

Leveraging seismic data from four Japanese earthquakes, this study formulates a regional ground motion prediction equation (GMPE) for peak ground acceleration (PGA) tailored to the Japanese tectonic setting. An ordinary least squares regression framework was applied to quantify the dependence of PGA on earthquake magnitude and epicentral distance. The analysis utilized 80 observations in total derived from 20 recording stations per event with magnitudes (M) between 3.7 and 6.9 and epicentral distances (R) ranging from 20 to 163 km. The derived attenuation relationship follows the form log(A) = k₁M + k₂log(R) + k₃, where A represents PGA, M denotes earthquake magnitude, and R indicates epicentral distance. Through matrix-based least squares analysis, the constants were determined as k₁ = 0.20521, k₂ = –0.4950, and k₃ = 0.9878, yielding the final equation = log(A) = 0.20521M - 0.4950log(R) + 0.9878. The model demonstrates physically consistent behavior with positive magnitude scaling and negative distance decay, typical of seismic wave attenuation. The dataset’s PGA values range from 1.8 to 25.2 cm/s², and the derived log-linear model effectively captures ground motion variability across a broad spectrum of magnitude–distance conditions. Tailored to the Japanese seismotectonic environment, this regional GMPE provides a dependable tool for hazard quantification and resilient design with broader applicability to analogous plate-boundary earthquake regimes.