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We provide a new derivation of the Kramers-Kronig relations on the basis of the Sokhotski-Plemelj equation with detailed mathematical justifications. The relations hold for a causal function, whose Fourier transform is regular (holomorphic) and square-integrable. This implies analyticity in the lower complex plane and a Fourier transform that vanishes at the high-frequency limit. In viscoelasticity,...
The theories developed by White and co-workers describe the complex moduli of a medium partially saturated with spherical gas pockets and those of stratified layers composed of two heterogeneous porous media. A generalization to gas patches of arbitrary shape has been given by Johnson. These models represent the mesoscopic-loss mechanism, which is one of the most significant causes of attenuation...
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