Numerical technique for computing the wide-angle acoustic field in an ocean with range-dependent velocity profiles

Abstract

A numerical technique for the propagation of sound in the ocean where velocity is a function of both range and depth has been developed. The technique is not restricted to the narrow-angle (parabolic) approximation and it reduces to an exact solution for a homogeneous media. The given field is transformed into a sum of plane waves via an FFT. This transformed field is propagated without approximation through a homogeneous space represented by an average wave number for that space. Updating the average wave number provides for Snell’s law bending in range. The variations from the average velocity are accounted for by summing deviations from the nominal phase to develop a group of direction-sensitive phase correction masks. A weighted group of plane waves centered about each direction are inverse transformed for multiplication by the phase mask with the results summed. The choice of overlapping weights in the transformed space provides an approximate continuous phase correction mask for all directions. The functional relationship of range-step size to frequency, angular spectrum, and velocity profiles are developed. Several results for a 1500-m channel are shown.

Extending the Utility of the Parabolic Approximation in Medical Ultrasound Using Wide-Angle Diffraction Modeling

“…The so-called wide angle parabolic equation (WAPE) was first developed as an intermediate between standard parabolic models and the more general Helmholtz equation in geophysics [11], [12] and underwater acoustics [13], [14]. The equation has also been applied to therapeutic ultrasound to model hyperthermia using a linear array [15], was compared against other models in the context of time-domain analysis of shock propagation in heterogenous media [16], and was used to model nonlinear ultrasound fields in air [17].…”

“…The equation has also been applied to therapeutic ultrasound to model hyperthermia using a linear array [15], was compared against other models in the context of time-domain analysis of shock propagation in heterogenous media [16], and was used to model nonlinear ultrasound fields in air [17]. WAPE models employ high-order approximations of the diffraction operator by retaining more terms in its Taylor expansion [13], approximation by rational function [11], [12], [14], [15], or more advanced methods [18]. In this paper the frequency-domain representation of the Westervelt equation is simplified to account for forward-wave propagation only, and the resulting pseudo-differential operator is approximated using rational functions (Padé approximations) to model continuous-wave finite-amplitude beams when backscatter and reflection are negligible.…”

Acoustic pulse propagation in a fluctuating ocean with range-dependent sound-speed profile

“…11 Recent developments in the analysis of weakly range-dependent guiding channels, using the spectral approach, have led to the development of a global spectral Green's function for range-dependent waveguides. Kamel and Felsen 12 generalized the method of characteristic Green's function for a two-dimensional ocean waveguide to accommodate weak range dependence.…”

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

“…For m any propagation problem s, the narrow -angle P E is not sufficiently accu rate. A wide-angle P E [44] can be obtained if th e quadratic term of the polynom ial is also included in the approxim ation to the square-root opera tor. This is E quation 2.13 allow propagation up to elevation angles of ab o u t 40°.…”

“…a profuse num ber of developm ents have been carried out to improve the accuracy and efficiency of the approxim ation [2,[44][45][46][47][48][49][50][51][52][53], and to expand i t 's applicability to more realistic conditions [54][55][56][57][58][59][60][61]. T he parabolic equation was originally lim ited to narrow -angle propagation; th e energy outside the angle of propagation is neglected.…”