A null-field T-matrix formalism is developed for scattering a pressure wave from a stationary elastic shell immersed in a homogeneous and isotropic fluid half-space and in proximity to a rough fluid–elastic interface. Helmholtz–Kirchhoff integral representations of the various scattered pressure and displacement fields are constructed. The surface fields are required to satisfy the elastic tensor boundary conditions and the scattered fields are required to satisfy the extended boundary condition. Spherical basis functions are used to construct a free-field T-matrix for the elastic shell and rectangular vector basis functions are used to construct a representation of the free-field T- matrix for the rough fluid–elastic interface. The free-field T-matrices are introduced into the Helmholtz–Kirchhoff and the null-field equations for the shell-interface system and a general system of equations for the spectral amplitudes of the various fields is obtained. The general system of equations is specialized to scattering from periodic surface roughness and an exact solution for the scattered pressure field in the fluid is obtained. Then the general system of equations is specialized to scattering from small-amplitude arbitrary roughness profiles and a perturbative solution is obtained. It is shown that the formalism contains multiple scattering effects on the rough surface and between the rough surface and the shell.

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Measured under-ice acoustic profile data and several large-scale geometric parameters of ice keels are used to construct and partition an ensemble of large-scale relief features into two subsets: a subset of keel-like features (e.g., ice keels) and a subset of nonkeel-like features. The draft data of each feature are regarded as a realization of a nonstationary random process while the draft increment data are regarded as a realization of a stationary zero mean random process. A maximum likelihood estimator technique (MLE) and a technique based on the variance function are used to calculate fractal dimensions for keel-like and nonkeel-like features. It is shown that for the same feature, the MLE technique and the variance function based technique yield similar values for the fractal dimension (D) and that for keel-like features 1.2 < D < 1.7 while for nonkeel-like features 1.2 < D < 1.6. The use of D in feature classification is also indicated. Fractional BrownJan motion: A maximum likelihood estimator and its application to image texture, IEEE Trans.

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The T-matrix formalism is used to calculate scattering of a plane wave from a doubly infinite fluid–solid interface with doubly periodic surface roughness. The Helmholtz–Kirchhoff integral equations are used to represent the scattered pressure field in the fluid and the displacement field in the solid. The boundary conditions are applied and a system of four coupled integral equations is obtained. The incident and scattered pressure fields in the fluid, as well as the surface pressure field, are represented by infinite series of scalar Floquet plane waves, while the scattered displacement field in the solid and the surface displacement field are represented by infinite series of rectangular vector basis functions constructed from Floquet plane waves. This process discretizes the integral equations and transforms them into a system of four coupled doubly infinite linear equations. The extended boundary condition is applied and the T matrix that relates the spectral amplitudes of the incident field to the spectral amplitudes of the scattered fields is constructed. An exact analytic solution and numerical results are obtained for plane wave scattering from doubly periodic sinusoidal and triangular surface roughness.