Array-derived rotational seismic motions: revisited

Rotation motions derived from measurements collected by arrays of translation accelerometers are investigated. The procedure is applicable to the rotation around any one axis, however in the paper rotations around a horizontal axis, i.e. rotations in a vertical plane, are focused. Since the early training of the arrays, the spatial distribution of the translation acceleration has been described through the cross power spectrum of accelerations at nearby stations (Harichandran in Workshop on spatial variation of earthquake ground motion 1988, structural safety, 1991; Evans et al. in Workshop on rotational ground motion, Menlo Park, 2006; Abrahamson in Estimation of seismic wave coherency and rupture velocity using the SMART 1 strong-motion array recordings, 1985). These cross spectra can be used to derive rotation components of the seismic motion (Castellani et al. in Earthq Eng Struct Dyn 41: 875-891, 2012. doi:10.1002/eqe.1163; Castellani and Zembaty in Eng Struct 18(8): 597-603, 1996). In recent times the evaluation of the rotation at a point has been attempted through apposite instruments. Rotation records concerning earthquakes observed at a single station in Taiwan, and rotations obtained from cross spectra have shown a satisfactory agreement (Castellani et al. in Earthq Eng Struct Dyn 41: 875-891, 2012. doi: 10.1002/eqe.1163), when properly normalized. In the present paper, the set of records collected at a dense array of acceleration recorders are represented through an interpolation function of the surface coordinates of the instruments. In this way rotation is measured as a function of space and time, free from any model of propagation. Propagation models hold in fact at some distance from the source, in particular at distances where the source mechanism can be represented as a point source. The proposed procedure is quite general, but the present application is limited to the sets of records available to the author: the records collected at seven stations SMART-1 in Lotung, Taiwan, one event of January 29, 1981, and another of 1986 (all elaborations here shown refer to the latter one). The seven stations are nearly aligned along a precise axis Fig. 2, and the time correlations between the records at different stations is perceptible. An apparent limit of the procedure is given by the dispersion of the acceleration amplitude at the stations. Kawakami and Sharma (Earthq Eng Struct Dyn 28: 1273- 1294, 1999) have examined the spatial variation of acceleration response spectra using the entire set of strong motion records SMART-1. This spatial dispersion is repetitively present in records of closely spaced arrays, and it is responsible itself of rotations. As a consequence, in presence of such variability, the entire set of records of the array would be suitable. The way the interpolation function is determined in function of the coordinates is dictated by two requirements: ( 1) fitting, and ( 2) smoothing. Fitting requires that at least the records collected at positions at hundred meters distance (C00, I03 and I12 in Fig. 2) shall be reproduced correctly. The smoothing is attempted by suitably truncating the series to the first terms, see Sect. 3. The power spectrum of the signal shows that the dominant frequencies for rotation are in the range of 3-11 cps. Excitation provided by rotation may thus be meaningful for chimneys, tall buildings, and bridges. Underground tubes are sensitive to excitations at quasi-static frequency.