Simultaneous inversion of Rayleigh phase velocity and attenuation for near-surface site characterization

Surface wave tests are non-invasive seismic techniques that can be used to determine the low-strain dynamic properties of a soil deposit. In the conventional interpretation of these tests, the experimental dispersion and attenuation curves are inverted separately to determine the shear wave velocity and shear damping ratio profiles at a site. Furthermore, in the inversion procedure, the experimental dispersion and attenuation curves are matched with theoretical curves, which include only the fundamental mode of propagation. The only approach available in the literature that accounts for multi-mode wave propagation is based on the use of Green's functions where the partial derivatives of Rayleigh phase velocity with respect to the medium parameters required for the solution of the inverse problem are computed numerically, and therefore very inefficiently. This study presents a new approach to the interpretation of surface wave testing. The new approach is developed around three new ideas. First, the definition of the low-strain dynamic properties of soils and the Rayleigh wave eigenproblem are revisited and reformulated within the framework of the linear theory of viscoelasticity. Secondly, an explicit, analytical expression for the effective Rayleigh phase velocity has been derived. The effective phase velocity concept forms the basis for the development of a new surface wave inversion algorithm based on multi-mode rather than modal dispersion and attenuation curves. Closed-form expressions for the partial derivatives of the effective Rayleigh phase velocity with respect to the medium parameters have also been obtained by employing the variational principle of Rayleigh waves. Thirdly, a numerical technique for the solution of the complex-valued Rayleigh eigenproblem in viscoelastic media has been implemented. An immediate application of this solution is the development of a systematic and efficient procedure for simultaneously determining the shear wave velocity and shear damping ratio profiles of a soil deposit from the results of surface wave tests. The simultaneous inversion of surface waves data offers two major advantages over the corresponding uncoupled analysis. First, it explicitly recognizes the inherent coupling existing between the velocity of propagation of seismic waves and material damping as a consequence of material dispersion. Secondly, the simultaneous inversion is a better-posed mathematical problem (in the sense of Hadamard). The new approach to surface wave analysis is illustrated using several numerical simulations and experimental data.