Thin rubber layers with air-filled cavities can be used as anechoic submarine coatings. Normally incident sonar energy is redistributed in the lateral direction and absorbed. In this paper, the anechoic effect is studied theoretically and numerically by adapting techniques used in electron scattering and band-gap computations for photonic and phononic crystals. Reflection and transmission matrices are computed recursively, from basic ones for layers containing periodic arrays of spherical cavities. A method to locate zeroes of analytical functions is applied to prove the existence of, and to specify, thin coatings with vanishing reflectance at isolated frequencies. Coatings much thinner than quarter-wavelength ones are found. Most of the absorption loss takes place close to the cavities and scattering of compressional spherically symmetric waves is important. The viscoelastic shear-wave properties of the rubber are crucial for generating this loss. The requirements for vanishing reflectance are specified using a simplified model with normal plane waves and spherically symmetric waves, that includes effects of multiple scattering among the cavities. An energy relation is derived, relating the anelastic loss in the rubber coating to loss by monopole resonance scattering from isolated cavities. The noticeable effects of multiple scattering are incorporated by a modulating factor.

Thin rubber coatings with cavities in a doubly periodic lattice are able to reduce reflections of underwater sound by redistributing normally incident energy such that absorption in the surrounding rubber is enhanced. For spherical scatterers, the anechoic effect can be studied numerically by the layer-multiple-scattering (LMS) method. In comparison to more flexible but also more computer intensive methods, such as finite-element method modeling, there are two important advantages. An improved physical understanding of the anechoic effect can be achieved by simplified semianalytical analysis, and the high computational speed allows modern global optimization techniques to be applied for coating design. In this paper, the flexibility of the LMS method is improved by combination with an efficient algorithm for numerical computation of transition matrices for superellipsoidal scatterers. (A superellipsoid is a generalization of an ellipsoid, allowing more box-filling shapes, for example.) Extensions to mixtures of nonspherical scatterers of different types are also considered, in order to enhance the broadband performance. Symmetry properties are used to reduce the size of the pertinent equation systems. Examples of numerical coating design for underwater acoustic applications are presented, using differential evolution algorithms for the optimization.

This paper deals with the problem of seismic velocity estimation from first‐arrival traveltimes in a two‐dimensional (2-D) cross‐hole geometry where explosions are detonated in one borehole while recordings are made in another borehole and on the surface. Standard tomographic procedures are based on decomposition of the cross‐hole area into a number of cells and a simplifying assumption of straight raypaths. In the presence of significant low‐velocity zones, the resulting images may be contaminated. Different ways of performing tomographic inversion are tested on a number of synthetic examples. Images obtained by direct, unrestricted least‐squares inversion are often seriously distorted. However, methods using more cells and some kind of damping often give more satisfactory results. Because the risk of distorted images is always present in inversion procedures, comparison with synthetic data (forward modeling) is a valuable tool in the interpretation process. With a reasonably good initial solution, improvements can often be achieved by using iterative procedures to take account of ray‐bending affects as proposed in Bois et al.(1971). An alternative way of performing these calculations is described.

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Coupled-mode methods have been used in underwater acoustics to compute three-dimensional sound propagation and scattering. Significant computational simplifications are possible for media with a lateral variation restricted to cylindrically symmetric anomalies, such as seamounts, and also for media which are invariant in one of the horizontal directions. Typically, the upper and lower depth boundaries of the medium have then been horizontal and flat. This paper generalizes the discrete coupled-mode method with a reflection- (or scattering-) matrix formulation to media with irregular and locally reacting boundaries. Horizontal and vertical segments thereby approximate a sloping boundary. Incorporation of the boundary conditions in a correct way necessitates modifications of the basic equation systems. Additional coupling matrices appear, involving integration of normal-mode products over the depth increments for adjacent regions of the medium. The paper includes three computational examples. One is from underwater acoustics with an island that rises above the sea level. The other two are from atmospheric acoustics with sound propagation over a locally reacting irregular ground surface. Using nonlinear optimization, it is possible to select a suitable artificial absorbing medium termination for a mode representation of the field.