An analytic, Fourier domain description of shear wave propagation in a viscoelastic medium using asymmetric Gaussian sources.

Recent measurements of shear wave propagation in viscoelastic materials have been analyzed by constructing the two-dimensional Fourier transform (2D-FT) of the spatial-temporal shear wave signal and using an analysis procedure derived under the assumption the wave is described as a plane wave, or as the asymptotic form of a wave expanding radially from a cylindrically symmetric source. This study presents an exact, analytic expression for the 2D-FT description of shear wave propagation in viscoelastic materials following asymmetric Gaussian excitations and uses this expression to evaluate the bias in 2D-FT measurements obtained using the plane or cylindrical wave assumptions. A wide range of biases are observed depending on specific values of frequency, aspect ratio R of the source asymmetry, and material properties. These biases can be reduced significantly by weighting the shear wave signal in the spatial domain to correct for the geometric spreading of the shear wavefront using a factor of x(p). The optimal weighting power p is found to be near the theoretical value of 0.5 for the case of a cylindrical source with R = 1, and decreases for asymmetric sources with R > 1.