Time-Window Effects on Monte Carlo Spectral Inversion of Translational and Rotational Ground Motion

Abstract A Monte Carlo–based spectral inversion approach was applied to obtain seismic source and propagation parameters from single-station observations of translational and rotational motions. The method is based on the Brune source model and inverts for seismic moment (\(\:{M}_{o}\)), corner frequency (\(\:{f}_{c}\)), attenuation (\(\:Q\)), and site amplification (\(\:A\)). The results showed that the Brune model adequately reproduces both translational and rotational spectra, yielding statistically stable parameter estimates across wave types and motion representations, which was confirmed by consistently high R² values and AIC scores. Translational S waves consistently presented higher \(\:Q\) values than P waves, resulting in \(\:{Q}_{P}/{Q}_{S}\) ratios below unity, consistent with enhanced fluid-related attenuation of compressional waves in shallow, partially saturated sediments. Rotational S-wave attenuation was systematically weaker than translational S-wave attenuation, indicating reduced sensitivity of rotational measurements to volumetric strain, pore-fluid effects, and scattering processes. Attenuation estimates derived from displacement spectra show strong dependence on time-window length, whereas velocity-based \(\:Q\) estimates remained stable across all window configurations. Corner-frequency values were firmly controlled by time-window selection. P-wave corner frequencies were generally higher than S-wave values, although the \(\:{f}_{c}^{P}/{f}_{c}^{S}\) ratio varies with window length. Seismic moment estimates were most stable for translational S-wave displacement spectra, whereas rotational data showed large scatter due to the suppression of long-wavelength energy. Overall, translational and rotational ground motions sample the same wavefield but emphasise different physical aspects, enabling detailed interpretation of the seismic source and propagation processes in strongly attenuating near-surface environments.