The unidentified object problem in a shallow ocean

Abstract

This work addresses the inverse problem of the identification of a passive three-dimensional impenetrable object in a shallow-water environment. The latter is assumed to have flat perfectly reflecting ͑sound-soft top and sound-hard bottom͒ boundaries and therefore acts as a guide for acoustic waves. These waves are employed to interrogate the object and the scattered acoustic wavefield is measured on the surface of a ͑virtual͒ vertically oriented cylinder ͑of finite or infinite radius, corresponding to near-or far-field measurements͒ fully enclosing the object. The direct scattering problem is resolved in approximate manner by employing, in a local manner, the known separated-variable solution for a scattering by a vertically oriented cylinder in a perfect waveguide. The inverse problem is resolved in the same manner ͑i.e., with the same approximate field ansatz͒ by least-squares matching of theoretical fields ͑for trial objects͒ to the measured field. Examples are given of successful shape reconstructions for two types of immersed objects. This manner of solving approximately both the forward and inverse problems is generalized to the case of a body of shallow water with an elastic seabed.

Cylindrical vibration of an elastic cusped plate under the action of an incompressible fluid in case ofN = 0 approximation of I. Vekuas hierarchical models

“…After substituting the last expession into (12), in case of harmonic vibration with the oscillational frequency !, we get…”

“…Various authors dedicated their work to the solid-fluid contact problems (see e.g., [8][9][10][11][12][13][14][15][16][17][18][19][20][21]). …”

“…In case of the harmonic vibration of the plate with a cusped edge under the action of an incompressible ideal fluid (i.e., equations (1), (2), (8),(15) and(16), under the transmission conditions (11),(12) and(17), under the conditions at infinity…”

Identification of objects in an acoustic wave guide inversion II: Robin–Dirichlet conditions

“…Another variant consists in ÿnding this local radius by minimizing the L 2 cost functional of the aforementioned 17 discrepancy. Gilbert et al [7,8] extended these ideas to considering the ICBA in a wave guide; however, 19 they used a cylinder as the canonical body, which led to inaccuracies on the upper-and lower-most portions of the body. See also the later works using ICBA by these authors 21…”

“…The detailed analytical computations have been relegated to the Appendix to make the paper more accessible. 7 The ICBA method assumes that the amplitudes in the partial wave representation of the scattered ÿeld are nearly those of a canonical body, for example, a circular cylinder in the 9 two-dimensional problem. This is true locally for each observation angle, the canonical body having the same local radius at this angle as that of the real body.…”