Correlation and Joint Distribution of Spectral Accelerations of Vertical Ground Motions

ABSTRACT

This paper estimates a correlation model and joint distribution model of spectral accelerations of vertical ground motions based on the NGA-West2 ground motion database. The correlation model calculated via BC16 vertical GMPE in this study is compared with those published models via other vertical NGA-West2 GMPEs. It is verified that the calculated residuals of vertical ground motions at multiple periods follow the multivariate normal distributions via both a qualitative validation method and a set of quantitative validation methods. The correlation model and the joint distribution model of vertical spectral accelerations are the theoretical basis for research on the joint occurrence of spectral accelerations of vertical ground motions, and an example of applied research on joint occurrence of spectral accelerations of vertical ground motions is studied: the conditional mean spectrum of vertical ground motions. Finally, the effects of different vertical correlation models and ground motion prediction equations on vertical conditional spectra are investigated for wide application of the correlation model and the joint distribution model of spectral accelerations of vertical ground motions.

KEYWORDS:

• Vertical ground motion
• spectral acceleration
• correlation coefficient
• multivariate normal distribution
• conditional mean spectrum

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was supported in part by the National Science Foundation of China [under Grant Number 51908379] and Basic Scientific Research Project of Liaoning Provincial Department of Education [LJKMZ20220943].