Long-Period Ground Motion Prediction Equations for Relative, Pseudo-Relative and Absolute Velocity Response Spectra in Japan

Many of the empirical ground motion prediction equations (GMPE) also known as attenuation relations have been developed for absolute acceleration or pseudo relative velocity response spectra. For a small damping, pseudo and absolute acceleration response spectra are nearly identical and hence interchangeable. It is generally known that the relative and pseudo relative velocity response spectra differ considerably at very short or very long periods, and the two are often considered similar at intermediate periods. However, observations show that the period range at which the two spectra become comparable is different from site to site. Also, the relationship of the above two types of velocity response spectra with absolute velocity response spectra are not discussed well in literature. The absolute velocity response spectra are the peak values of time histories obtained by adding the ground velocities to relative velocity response time histories at individual natural periods.

There exists many tall buildings on huge and deep sedimentary basins such as the Kanto basin, and the number of such buildings is growing. Recently, Japan Meteorological Agency (JMA) has proposed four classes of long-period ground motion intensity (http://www.data.jma.go.jp/svd/eew/data/ltpgm/) based on absolute velocity response spectra, which correlate to the difficulty of movement of people in tall buildings. As the researchers are using various types of response spectra for long-period ground motions, it is important to understand the relationships between them to take appropriate measures for disaster prevention applications. In this paper, we, therefore, obtain and discuss the empirical attenuation relationships using the same functional forms for the three types of velocity response spectra computed from observed strong motion records from moderate to large earthquakes in relation to JMA magnitude, hypocentral distance, sediment depths, and AVS30 as predictor variables at periods between 1 and 10 s for 1 and 5% damping ratios. Our preliminary analyses show that the pseudo and absolute velocity response spectra scale almost identically to the predictor variables while the relative velocity response spectra scale differently. It is manifested that the difference at a site is dependent on magnitude, distance, and periods.