Frequency-Wavenumber Analysis Of Passive Surface Waves

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