The correlation between three components of ground motion at the same point based on the variance principal axis method

Based on near-field and far-field strong motion records from 11 moderate-to-large earthquakes, the study investigates the correlation of the three translational components of seismic ground motion using the variance principal axis method. And then the correlation is examined at different scales, with the characteristics of the correlation described at both the sample level and the statistical level.

By considering the time-varying characteristics of the principal axes, the ground motion records are divided into three segments: the ascending phase, the strong ground motion phase, and the descending phase. The study investigates the direction of the minor variance principal axis in these three phases. Both at the sample level and statistical level, it is found that the minor variance principal axis during the strong ground motion and descending phases is nearly vertical. However, the principal axis in the ascending phase exhibits a more complex variation and cannot simply be assumed to be vertical. Since the earthquake intensity during the ascending phase is typically lower or the duration is shorter, it can be approximated as vertical in engineering practice by ignoring the ascending phase.

Statistical analysis of parameters based on fault distance and site conditions indicates that the major variance principal axis in the horizontal plane follows an approximately uniform distribution. The direction of the major variance principal axis exhibits significant time-dependent variability and strong randomness in the horizontal plane, far exceeding its variability in the vertical direction. Statistically, the occurrence probability of the major variance principal axis in any direction is approximately equal, following a uniform distribution.

Detailed analysis of the 1999 Chi-Chi earthquake, the 2008 Wenchuan earthquake, and the 2018 Hualien earthquake indicates that in the near-fault region, a small subset of observation points exhibits approximately time-invariant characteristics for the variance principal axes, while many other stations show strong randomness in the direction of the variance principal axes. For the stations with nearly time-invariant principal axes, the orientation may be closely related to the source mechanism. In the vicinity of reverse faults, the major variance principal axis is oriented perpendicular to the fault strike, while in the vicinity of strike-slip faults, it is parallel to the fault strike. In near-fault regions with complex source mechanisms, there exist both components parallel and perpendicular to the fault strike.