Frequency-wavenumber analysis of passive surface waves

The Spectral Analysis of Surface Waves (SASW) test is a non-invasive field technique which uses the dispersion properties of surface waves to determine the shear wave velocity profile at a site. Traditional SASW methods typically use an active source to generate surface (Rayleigh) waves that are measured by a linear array of geophones. The depth of investigation is usually limited by the inability of the source to produce low frequency, long wavelength surface waves. This limitation can be overcome by using passive measurements of surface waves arising from microtremors and/or cultural noise such as traffic. Surface wave dispersion relationships are determined using frequency-wavenumber analyses. Ground vibrations are recorded by a two-dimensional array of sensors deployed on the ground surface. The frequency-wavenumber spectrum is determined with Capon's Minimum Variance Distortionless Look method, which adapts the array's sensor weights to the observed signal and noise characteristics. The sensor weights produce a spatial filter that passes undistorted any monochromatic plane wave traveling at a velocity corresponding to a selected wavenumber k(0) and suppresses waves traveling at velocities corresponding to wavenumbers other than k(0) Once the dispersion curve is determined using frequency-wavenumber analysis, a non-linear, smoothed inversion algorithm is employed to determine the shear wave velocity profile. The approach is described and illustrated using measurements performed on the campus of the Georgia Institute of Technology.