Improving the uniqueness of surface wave inversion using multiple-mode dispersion data

The use of multiple-mode dispersion data in surface wave inversion to derive shear-wave velocity (vs) profiles has increased in the past decade as the inclusion of higher mode data can improve the accuracy of the inversion results. However, the error associated with nonuniqueness in the multiple-mode inversion has not been clarified and quantified. This research focuses on the attempt to improve the accuracy of multiple-mode surface wave inversion result by optimizing the use of multiple-mode dispersion data to reduce the error associated with the nonuniqueness in inversion. In this research, an alternative approach was used where inversion of surface wave dispersion data was performed using three distinct modes. Four different vs profiles, representing regular and irregular cases, were used, and multiple-mode dispersion data were synthesized from these profiles using the dynamic stiffness matrix method as the theoretical model. The dispersion data were then inverted using the Levenberg-Marquardt method. The results demonstrated that, as expected, inclusion of higher modes did not improve the accuracy of the inversion results for the regular profiles. However, inclusion of higher modes significantly improved the uniqueness of the inversions for the irregular profiles. The results also demonstrate that regardless of the nature of the profile, the accuracy of the inversion improves when the starting profile more closely matches the true profile. Of all the inversion approaches investigated, the best approach was one where three successive inversions, using one, two, and three modes, respectively, was used, where the inverted profile from one inversion was used as a starting model for a subsequent inversion that used one additional mode.