Resolving the Variability Discrepancy between Peak Ground Acceleration and Spectral Stress Drop: Insight from Double‐Corner‐Frequency Spectra

This study addresses a challenge in ground‐motion prediction, in which the observed variability of spectral stress drop $Δσfc$ estimated from corner frequencies is significantly larger than the between‐event variability of peak ground acceleration (PGA) supported by ground‐motion prediction equations. To tackle this issue, we performed spectral ratio analyses on 34 crustal earthquakes with $Mw$ 5.0–7.1 in Japan. Initially, we employed the standard spectral ratio method to estimate the corner frequencies $fc$ and the spectral stress drops $Δσfc$⁠. This method assumes the single‐corner‐frequency (SCF) spectral model. Next, we introduce a two‐stage spectral ratio method to obtain the double‐corner‐frequency (DCF) spectra. This method first estimates the corner frequency of the small events in advance using further smaller events and the standard method. Then, it computes the spectra of the target event using the spectra of the small events predicted from the SCF model with the estimated corner frequency. We fit the SCF model to the observed spectra to estimate a high‐frequency‐fitted corner frequency $fch$ and calculate the corresponding spectral stress drops $Δσfch$⁠, called the stress parameter. Our analyses reveal that the variability of $Δσfch$ aligns with the observed PGA variability, in contrast to the $Δσfc$ variability, which is significantly larger and consistent with findings in previous corner‐frequency studies. Thus, at least regarding the spectral ratio approach, the discrepancy between spectral stress drop and PGA variabilities primarily stems from the difference in the $Δσfc$ and $Δσfch$ variabilities, attributed to the diversity in source spectral shapes. This study demonstrates that although source spectra for $Mw$ 5.0 align with the SCF model on average, deviations from the SCF model become increasingly pronounced with larger magnitudes. The results emphasize the significance of implementing the DCF model for improved ground‐motion predictions.