Dalcio K. Dacol

A wide angle and high Mach number parabolic equation

Various parabolic equations for advected acoustic waves have been derived based on the assumptions of small Mach number and narrow propagation angles, which are of limited validity in atmospheric acoustics. A parabolic equation solution that does not require these assumptions is derived in the weak shear limit, which is appropriate for frequencies of about 0.1 Hz and above for atmospheric acoustics. When the variables are scaled appropriately in this limit, terms involving derivatives of the sound speed, density, and wind speed are small but can have significant cumulative effects. To obtain a solution that is valid at large distances from the source, it is necessary to account for linear terms in the first derivatives of these quantities [A. D. Pierce, J. Acoust. Soc. Am. 87, 2292-2299 (1990)]. This approach is used to obtain a scalar wave equation for advected waves. Since this equation contains two depth operators that do not commute with each other, it does not readily factor into outgoing and incoming solutions. An approximate factorization is obtained that is correct to first order in the commutator of the depth operators.

A mapping approach for handling sloping interfaces

A mapping approach for handling sloping interfaces in parabolic equation solutions is developed and tested. At each range, the medium is rigidly translated vertically so that a sloping interface becomes horizontal. To simplify the approach, the slope is assumed to be small and the extra terms that arise in the wave equation under the mapping are neglected. The effects of these terms can be approximately accounted for by applying a leading-order correction to the phase. The mapping introduces variations in topography, which are relatively easy to handle for the case of a pressure-release boundary condition. The accuracy of the approach is demonstrated for problems involving fluid sediments. The approach should also be accurate for problems involving elastic sediments and should be useful for solving three-dimensional problems involving variable topography.

Manifestly reciprocal scattering amplitudes for rough interface scattering

A new exact expression for scattering amplitudes for rough interface scattering is presented. This expression is explicitly reciprocal and it is shown to hold for a variety of boundary conditions: Dirichlet (pressure release), Neumann (rigid surface), impedance, fluid‐fluid, and fluid‐solid interfaces. This expression is shown to be a convenient starting point for deriving approximations that also respect reciprocity. Examples include a small‐slope approximation, a reciprocal phase perturbation approximation, and a reciprocal smoothing approximation. [Work supported by ONR.]

Geoacoustic inversion using a rotated coordinate system and simulated annealing

An efficient method for geoacoustic inversions in a range-dependent ocean waveguide is implemented and tested with synthetic data. This method combines a simulated annealing search with an optimal coordinate rotation that increases the efficiency of navigating parameter landscapes for which parameter coupling is important. The coordinate rotation associated with the parameter couplings also provides information about which parameters are resolvable for a particular inversion frequency and array geometry. Using this information, results from several single-frequency inversions can be combined to obtain an estimate for the sediment parameters.

A higher-order on-surface radiation condition derived from an analytic representation of a Dirichlet-to-Neumann map

On-surface radiation conditions are useful for obtaining approximate solutions to scattering problems involving compact obstacles. An analytic representation of the Dirichlet-to-Neumann map for a circle is derived and used to construct a higher-order on-surface radiation condition for a generally convex perfectly conducting body in two dimensions. This approach is based on a Hankel function in which a tangential operator appears in the index. In the high-frequency limit, this analytic representation approaches the square root of a differential operator which commonly arises in the application of parabolic equation techniques to propagation problems. Treating the scattered field propagation angle relative to the surface normal and the surface curvature as independent parameters, the representation is fit to a rational function to provide an accurate and efficient on-surface radiation condition that is tested for various examples.

Acoustical scattering by arrays of cylinders in waveguides

Multiple scattering of acoustic waves in a planar horizontal waveguide by finite-length cylinders is considered. Cylinder height equals the waveguide depth, and both are vertically constrained by the pressure-release boundaries. An analytically exact solution is obtained via normal mode expansion method in conjunction with the concept of the T matrix. The problem is decomposed into an infinite number of two-dimensional multiple scattering problems, modulated by waveguide mode shapes. Examples are presented for an isovelocity waveguide in which the medium is uniform and the waveguide depth is constant. It is found that, in numerical computations, including one or two evanescent modes captures the essence of the evanescent modes. Multiple scattering in the waveguide is compared with the corresponding two-dimensional case. It is concluded that, in low frequencies, the wave patterns in the two cases are very similar, with a shift in the frequency. The similarity diminishes when there are multiple propagating modes. Despite the mode mixing, some key features in the scattering as observed in the two-dimensional problem remain observable in the waveguide case.

The Kirchhoff approximation for acoustic scattering from a rough fluid–elastic solid interface

The Kirchhoff approximation for wave scattering from a penetrable surface is applied to the case of acoustic scattering from a rough fluid–elastic solid interface. An approximation to a surface integral yields a simpler expression for the scattering amplitude. It turns out to be similar to an approximation previously introduced by Hagfors [J. Geophys. Res. 69, 3779 (1964); J. Geophys. Res. 71, 379 (1966)] to study radar backscattering from the moon. This simpler version produces results that compare favorably with exact numerical results for the case of periodic fluid–solid interfaces. This approximation is well suited to describe acoustic scattering from a randomly rough fluid–solid interface. To illustrate this point, the coherent field reflection coefficient as a function of angle of incidence and the incoherent scattering coefficient as a function of scattering angle were computed and plotted for the case of a model randomly rough fluid–solid interface with acoustical parameters of a water–granite int...

An efficient parabolic equation solution based on the method of undetermined coefficients

An implementation of the self-starter based on the method of undetermined coefficients is described and tested. For many problems, this parabolic equation technique for solving short range propagation problems provides an efficiency gain of an order of magnitude or more over the finite difference solution. With this forward model, it is possible to solve geoacoustic inverse problems in seconds on the current generation of desktop computers. The approach can be implemented for the inverse problem so that efficiency is essentially independent of the depth of the water column.

Consistency and reliability of geoacoustic inversions with a horizontal line array

Geoacoustic inversions with a towed horizontal array are of interest for rapidly characterizing sediment properties over changing regions. To be of practical value, inversions must yield consistent and reliable results for consecutive or neighboring data. A method of determining inversion reliability a priori is delineated using an empirical approach and confirmed with inversion results in terms of consistency. Geoacoustic parameter hierarchy and resolvability are empirically analyzed using two different methods: one requires knowledge of the source function and the other does not. Inversion results using the two methods are compared using both synthetic data and experimental data from MAPEX2000. The inversions employ a global optimization technique which navigates the parameter space in directions aligned with valleys of the cost function, increasing inversion algorithm efficiency and disclosing parameter correlations and hierarchy.

Wave scattering in waveguides

The scattering of scalar waves by objects located inside a waveguide or a cavity is discussed using the method of pseudopotentials. Pseudopotentials were introduced to simulate short-range potentials in quantum mechanics and proved useful in many-body problems and in problems involving multicentered potentials. In this work it is shown that this approach can also be used to describe the scattering of classical scalar waves by objects confined to the interior of a waveguide or a cavity in terms of the scattering amplitudes of those objects in an extended medium.