Analyses of Short-period Array Data Using a Full-wave Green's Function

Abstract

We studied the effect of body waves on short period vertical ground motion based on both a numerical simulation and field array observations. The vertical components generated by the vertical point force within a close distance are targeted throughout the study. Firstly, we carried out a numerical simulation and confirmed that the effect of body waves on the full-wave field was generally limited to a close distance from the source with frequency dependence. In a frequency range lower than 5 Hz and at around the 1st predominant frequency (5.8 Hz), the effect appears beyond a far distance; in a range of about 6 to 10 Hz, it still remains up to 10 m or more; in a range higher than 10 Hz, it almost vanishes. Secondly, we analyzed the observed array data excited by a 30-kg sandbag falling 10, 20, and 40 m from the array center. The array configuration was a circle, 1 m in radius, consisting of seven sensors placed in the center and around the circumference at equal intervals. To obtain a better understanding of the results of the array analyses, simulated array data, based on the Green's functions for the full-wave field and for the Rayleigh wave, was produced and analyzed in the same manner as the observed field array data. The phase velocity results were calculated with three different methods, namely, the spatial autocorrelation (SPAC) method, a method based on the spatial 1st Fourier coeffcients in the azimuthal direction with respect to the cross spectral amplitude between the center and one of circumferential stations, and a technique which combined these two methods. In the case of an offset of 10 m (Case 1), the detected phase velocities from the observed data and the simulated data on the full-wave field were much lower than the theoretical phase velocity or that from the Rayleigh wave array data in a frequency range of 5 to 10 Hz, suggesting the strong effect of body waves. In the case of an offset of 20 m (Case 2), the estimated phase velocities from the observed data and the two other simulated array data coincided with the theoretical phase velocity, suggesting the weak effect of body waves. We conclude that in order to properly estimate an underground structure from the array measurement data at a close distance from the source, the analytical technique based on the full-wave Green's function should be applied. Taking a look at the choice of analytical methods for the array data, it can be pointed out that for our interest the two methods which use the spatial 1st Fourier coeffcients produce higher accuracy compared with the SPAC method in a relatively low frequency range. In addition, the phase velocity results were estimated from the CCA (centerless circular array) method by Cho et al. (2004). The CCA method provided similar accuracy compared with the above two methods based on the spatial 1st Fourier coeffcients. The CCA method seems to be applicable to highly directional wave fields located nearby the source.