This study examined empirical correlations among several horizontal and vertical ground‐motion intensity measures (IMs), including spectral acceleration (SA), peak ground acceleration (PGA), peak ground velocity, acceleration spectrum intensity, velocity spectrum intensity, displacement spectrum intensity, spectrum intensity, effective peak acceleration (EPA), effective peak velocity (EPV), and effective peak displacement (EPD). The theoretical basis for the prediction equations of EPA, EPV, and EPD were developed based on the ground‐motion model (GMM) of SA(T). Horizontal and vertical Next Generation Attenuation (NGA)‐West2 GMMs and associated ground motions from active shallow crustal earthquakes in the NGA‐West2 database were used to calculate empirical correlations. Fisher ? transformation and nonparametric bootstrapping methods were able to accurately describe the uncertainty caused by the limited sample size. The multivariate normality of the total residuals of the horizontal and vertical ground‐motion IMs was verified. The results have shown a moderate correlation between the same IMs of horizontal and vertical ground motions. The difference in correlations between the IMs for two different combination cases (IMi,HIMj,V and IMj,HIMi,V) was not significant. The trends of ρlnIMV,lnSAH and ρlnIMH,lnSAV were almost the same, except that ρlnIMV,lnSAH was greater than ρlnIMH,lnSAV in the 0–0.3 s period, except for ρlnPGAV,lnSAH. Moreover, the median correlation coefficients were parametrically fitted to establish a correlation coefficient prediction model. Finally, an example of constructing the conditional distribution using the correlation coefficient models for horizontal and vertical ground motions IMs was given. The correlation coefficient models by this study provide the theoretical basis for the selection of horizontal and vertical ground motions using generalized conditional intensity measure.

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