The spectral velocity (SV) is necessary information in the seismic design of structures with supplemental velocity‐dependent dampers, and it is conventionally approximated by the pseudospectral velocity (PSV), which is available in seismic codes. Because of the significant approximation error, it is important to clarify the relationship between the two spectra to establish a suitable formulation to relate SV to PSV. Recent studies have point out that this relationship is influenced not only by the oscillator period and damping ratio but also by earthquake characteristics (Papagiannopoulos et al., 2013; Samdaria and Gupta, 2018). To clarify the seismological effects, in this study, an approach to relate SV to PSV based on the random vibration theory is proposed, and it is verified by comparing its results with those of traditional time‐series analysis. The effects of earthquake magnitude and distance as well as site conditions on the relationship between the two spectra are explored based on the proposed approach as well as statistical analysis of recorded seismic motions. It is found that the SV approaches the PSV with increasing magnitudes at long oscillator periods but performs oppositely at short oscillator periods. The demarcation range beyond which the opposite trend is observed varies from (0.07–0.24) to (0.12–0.87) s using the proposed approach and considering the regions of central and eastern North America. The range varies from (0.1–0.15) to (0.3–0.7) s based on the results obtained by the statistical analysis of seismic records in Japan. The observed phenomena were theoretically explained, and the seismological effects were found to be governed by the ground‐motion frequency content.

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