An Approximate Analytical Three-Dimensional Time-Domain Green’s Function for Shear Wave Attenuation with Power Law Exponent y = 1/2

Time-domain Green’s functions are effective for modeling shear waves. However, existing Green’s functions for shear waves are inconsistent with the power law attenuation observed in soft tissue. To address this problem, the shear term of an analytical time-domain Green’s function is derived for power law attenuation with exponent y=1/2. This new solution is obtained by replacing the expression within the shear term that is responsible for attenuation in the viscoelastic time-domain Green’s function derived by Bercoff et al. with the corresponding component of the solution to the Power Law wave equation evaluated at y=1/2. The resulting expression has a ‘heavy tail,’ which is an established characteristic of power law and fractional calculus solutions.