Attenuation of ambient noise in thin-plate structures due to ice accretion: A theoretical explanation

It has been observed experimentally that flow-induced ambient noise propagated in an icy thin-plate structure decays quickly. The attenuation rate is sensitive to the ice thickness and is thus potentially an important feature for passive ice detection. The main goal of the present paper is to develop a theoretical model to explain this damping behavior qualitatively and quantitatively. The wave propagation medium is assumed to be an elastic plate and a viscoelastic ice layer sandwiched by two fluid half-space layers. The Kelvin–Voigt model is employed to quantify the viscoelastic behavior of ice which results in complex-valued shear modulus, Lamé constant, and wave velocity. The classical guided wave characteristic equation is simplified by combining the transfer matrix (for the plate-ice interface) and the global matrix (for the fluid–solid interfaces) methods, by which a precise and fast computation of the complex wavenumbers of guided wave modes is realized via the logarithmic residue quadrature method. The attenuation rate, i.e., the imaginary part of a mode wavenumber, is proportional to the ice thickness and wave frequency, which is consistent with the experimental results of both direct and coda wave decay extracted from the cross-correlation of ambient noise.