Array Measurements Sample Clauses

Array Measurements. This technique consists in recording ambient vibration ground motion by means of an array of sensors (geophones) distributed at the surface of the subsoil to be explored (see, e.g., Okada, 2003). Relevant information concerning phase velocities of waves propagating across the array is obtained from average cross-spectral matrixes relative to sensor pairs. In the present analysis, plane waves propagating across the array were considered only. Since vertical sensors were used only, these waves are interpreted as plane Rayleigh waves in their fundamental and higher propagation modes. Determination of Rayleigh wave phase velocities VR as a function of frequency (dispersion curve) from cross-spectral matrixes can be carried on in several ways. In the present analysis, the Extended Spatial Auto Correlation (ESAC) technique (▇▇▇▇▇ et al., 2002; ▇▇▇▇▇, 2003) was applied. The basic element of this analysis is the cross-correlation spectrum deduced by the analysis of ambient vibrations measured at a couple of sensors ϕ (f,r) where f is frequency and r is the distance between the relevant sensors . To this purpose, registrations relative to each sensor are partitioned in a number of non overlapping time windows of fixed duration (20 sec). Time windows characterised by energy bursts were removed from the analysis. To this purpose, a time segment is considered in the analysis if standard deviation of all the traces of that time window does not exceed the threshold fixed in advance for each trace. In general, this threshold was fixed to be 2 times the standard deviation computed over the whole registration for the relevant trace. In each accepted time window, the time series was detrended, padded and tapered (5% cosine windows). For each time window and couple of sensors, the cross spectrum was computed. The average cross spectrum was then computed for each couple of sensors by considering all the relevant time series. The resulting average cross-spectrum was thus smoothed in the frequency domain by a moving triangular window having a half-width proportional to the central value (usually 10%) and normalized to the relevant auto spectra. In the assumption that ambient vibration wave field can be represented as a linear combination of statistically independent plane waves propagating with negligible attenuation in a horizontal plane in different directions with different powers, but with the same phase velocity for a given frequency, the normalized cross-spectrum ϕij(f,r)...