Effects of wave propagation direction on the evaluation of torsional motion

The benefits of the determination of rotational motion in seismology and engineering are still under investigation. Four main approaches have been developed to incorporate the rotational motions in engineering and seismology: one is numerical simulation of radiation field from source mechanism. The second approach is based on theoretical formulation of spatial distribution of ground motion, The third approach is the application of recorded strong motion data from seismic arrays and the last one is using instruments to direct measurement of torsional component. Due to the slow development of instruments for direct measurement of rotational motion, dense arrays are one of the unique sources of experimental information on rotational motion estimation by the spatial derivatives. The average rotational motions can be evaluated from difference of two translational records in an array of stations on the ground. Usually the conventional spatial derivative of two accelerograms, are employing to estimate torsional ground motion in the array. In some cases this method were applied without attention to the effect of wave propagation direction on the rotational motion. In this study assuming simple plane wave propagation and variation of propagation angle, it was shown that direction of wave propagation has principal role in the evaluation of torsional motion. Results showed that based on using two or four stations and the arrangement of those stations, torsional motion has different values. This is very important issue in the evaluation of torsional motions that must be considered.