Harmonic wavelet analysis of surface waves at complex geotechnical sites
Authors:   , Khan Mohammed 
Published: December 2023

The use of stress wave-based geophysical methods in geotechnical engineering has continued to grow and is now a routine component of many geotechnical site investigation programs. Surface wave methods, in particular, are now widely used in a variety of applications. Since their introduction in the 1980's, surface wave methods have evolved from the two-channel Spectral-Analysis-of-Surface-Waves (SASW) method to multi-channel, full waveform inversion methods that require hundreds of time records collected using extensive receiver spreads. With these changes, the capabilities of these methods has certainly improved, however, it has come at the cost of greater equipment requirements, increased space requirements, increased data acquisition time, and more complex data processing and interpretation. In contrast, the SASW method only requires two geophones and a laptop with a data acquisition card. However, there is a need to improve the SASW methodology, as it is both time and labor intensive and has been shown to be ineffective for some geotechnical site conditions. Surprisingly, there has been very little research effort applied to improving simpler surface wave methods. One of the few novel two-channel techniques proposed is the Harmonic-Wavelet-Analysis-of-Surface-Wave (HWAW) method. However, the literature on this method is limited and the method has not been widely adopted. The goal of this project is to improve the application of surface wave methods in geotechnical practice by evaluating the effectiveness of the HWAW method at complex geotechnical sites and developing guidelines for implementing this method generally. It is hypothesized that the HWAW method can overcome issues associated with applying the SASW method at complex geotechnical sites. Simulated surface wave measurements and experimental verification studies were performed to test this hypothesis. Simulated surface wave data were used to perform a parametric study of data collection and data processing variables used in the HWAW method. The results from this study showed that using a sufficiently narrow bandwidth was the most important variable for determining an accurate dispersion curve from HWAW processing. The sampling frequency was found to have only a small effect on the accuracy of the dispersion curves. Interestingly, receiver spacing and source offset had no effect on the effectiveness of the HWAW processing for the profiles considered in this study. It was found that data collected using the typical SASW testing arrangement of equal source offset and receiver spacing could be effectively processed with the HWAW method. Simulation results also showed that changing Poisson's ratio of the material (i.e. saturation conditions) did not adversely affect the HWAW results. However, large fluctuations in the dispersion curve were observed for sites with high values of Poisson's ratio when small receiver spacings were used. This was also confirmed from experimental results. Simulations of surface wave measurements at complex sites, including soft-over-stiff sites, sites with shallow velocity gradients, and sites with velocity inversions due to embedded soft and stiff layers also demonstrated that the HWAW method could effectively recover the dispersion curve for a variety of source and receiver configurations. Of particular note are soft-over-stiff sites with large impedance contrasts where an abrupt mode transition makes conventional SASW interpretation untenable. For these cases, HWAW processing of the SASW data effectively dealt with the mode transition and recovered the correct dispersion curve. This important finding was validated with experimental measurements. This research only focused on assessing the consistency between theoretical and HWAW-processed dispersion curves and did not address the inversion of these dispersion curves to determine shear wave velocity (VS) profiles. Future work should focus on assessing the reliability of VS profiles determined from the inversion of dispersion curves collected with small source offsets and short receiver spacings, as are used in published HWAW measurements. However, based on the findings from this research it is recommended that the current phase unwrapping approach used in the SASW methodology should be replaced with the automated HWAW processing method using the guidelines presented in this dissertation.