Figure 3.

Validation of the numerical integration procedure by comparison of the analytic results (black lines) calculated using (27) with results from the numerical calculations (dashed red lines) for the real (top row) and imaginary (bottom row) parts of the $G_{11}^{SH}$($\overrightarrow{r}$, ω), $G_{12}^{SH}$($\overrightarrow{r}$, ω), and $G_{22}^{SH}$($\overrightarrow{r}$, ω) components of the Green’s tensor for the SH propagation mode. The signals have MKS units of mN⁻¹ or Pa⁻¹ m⁻¹. Results are shown for a material with μ_L = 25 kPa and μ_T = 9 kPa for the specific position r = 10 mm and angle θ_r = 45°. Near perfect agreement is observed for the $G_{11}^{SH}$($\overrightarrow{r}$, ω) and $G_{22}^{SH}$($\overrightarrow{r}$, ω) components. For the $G_{12}^{SH}$($\overrightarrow{r}$, ω) component, the analytic value is zero, and any nonzero signal from the numerical calculation is the result of numerical inaccuracies from the use of finite step sizes in the numerical integrations (35) and (36), or from roundoff errors.