Acoustic scattering analysis for remote sensing of manganese nodules

The theory of the scattering of plane waves in a fluid medium by an isotropic elastic sphere representing a manganese nodule is developed. Scattering cross sections were computed using the theory and the results are presented graphically. The scattering cross section and the reflectivity factor govern the characteristic acoustic signature of the Pacific where manganese nodules are present.

Preliminary experimental data for the compressional and shear wave speeds in nodule material is given. This data was used in the scattering computations. Limiting cases of Rayleigh scattering and scattering from fixed rigid and fluid spheres are also shown for comparison. It is shown that the rigidity of the nodules dominates the high frequency response.

The problem of the multiple scattering of acoustic waves by randomly distributed nodules on the flat ocean bottom is investigated analytically. The statistical description of nodule deposits is given. The concept of the configurational average is introduced in order to obtain the average scattered response. The size averaging is found to be able to smooth the acoustic response in the high frequency region.

The plane wave analysis for the multiple scattering problem is justified by the narrow beam investigation. It shows that the beam effect on the average backscattered field can be neglected in the remote sensing.

For a planar distribution of nodules, the average scattered field excited by a normally incident plane wave is verified to be plane waves characterized by coherent reflection and transmission coefficients. The multiple scattering effect is found to be a higher order correction to the average scattered field. For a sparse distribution of nodules, the average scattered field can be well evaluated using the single scattering theory in which the scattering process is also shown to be energy conserved.

For a dense distribution of nodules, the radial distribution function is used in the Foldy-Lax hierarchy. The result shows that the pair correlation affects the phase of the second order correction term in the expression for the average scattered field when the higher order statistics are truncated using the quasi crystalline approximation.