The focus of this study is an analytical and computational platform for shallow seismic profiling via the dispersion and attenuation analysis of Love surface waves. Although the Rayleigh waves are now commonly used as an engineering tool for nonintrusive identification of shallow subsurface stratigraphy, little attention has been paid so far to utilizing their horizontally polarized, Love-wave counterpart. The proposed methodology revolves around a causal viscoelastic model for the wave motion in a layered half-space caused by action of a surficial, torsionally vibrating disc. It is shown that the use of Love waves as a sounding tool reduces the number of material parameters relevant to viscoelastic site characterization by precluding the effect of Poisson's ratio and of the compressional-wave quality factor of each subterranean layer. For practical purposes, solution to the inverse problem is reduced to the minimization of a spectral misfit between experimental observations and theoretical predictions of the horizontally polarized surface ground motion. To maintain the rigor and computational effectiveness of the inverse solution, sensitivities of the viscoelastodynamic model with respect to relevant layer parameters are determined analytically. The Love-wave testing methodology for which this article establishes a necessary theoretical framework may be used either in a stand-alone fashion or as a complement to the (well-established) spectral analysis of Rayleigh waves. The proposed technique may be especially useful for (1) shallow surveying applications in which material dissipation is important and (2) accurate characterization of saturated layers in which vertically polarized waves find limited use owing to their sensitivity to the pore fluid.