(Color online) Top panels: Frequency-dependent attenuation for τσ = 1000τε with the fractional derivative orders α = 0.3 (top left), and α = 0.8 (top right). The attenuation curves displayed show α k ,Z(ω) from Eq. (16) as predicted by the fractional Zener model, and as predicted for the approximate ML-NSW model by α k, ML(ω) in Eq. (23) for a set of Ω1 and Ω2 choices as displayed in the legends. The horizontal axis represents normalized frequency. For visualization convenience, each absorption curve is normalized to α k = 1 at ωτσ = 1. Bottom panels: The corresponding normalized effective compressibilities κν ML(Ω) of the continuum of relaxation processes as a function of normalized relaxation frequency Ω·τσ for α = 0.3 (bottom left), and α = 0.8 (bottom right) of the approximate ML-NSW model with Ω limits as described in the legends.
(Color online) Frequency-dependent speed of sound for τσ = 1000τε with the fractional derivative orders α = 0.3 (left pane), and α = 0.8 (right pane). The curves display c Z(ω) from Eq. (17) as predicted by the fractional Zener model, and as predicted by c ML(ω) in Eq. (24) for a set of Ω1 and Ω2 choices as displayed in the legends. The horizontal axis represents normalized frequency.
(Color online) Comparison of resulting attenuation modeled in Ref. 7 (thick solid line), fractional Zener model (dashed line), and the approximate ML-NSW model by use of κν ML(Ω) (thin solid line) of Eq. (19) . The medium parameters are displayed in Table I . The fractional Zener and approximate ML-NSW parameters are listed in Table II .
Medium parameters for the attenuation power-law fit, similar to the Yang and Cleveland parameters in Ref. 7.
Fitted fractional Zener and ML-NSW model parameters corresponding to the Yang and Cleveland attenuation properties as reproduced in Table I. The resulting attenuation is displayed in Fig. 3.
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