**Three-Dimensional
Models
and
Benchmark (Analytic) Solutions
**

The term 'Three-Dimensional' is used here to refer to or imply
the effects of horizontal refraction, e.g., refraction in the
lat./lon. plane for a cartesian coordinate system. Although the
standard acoustic models can produce full 3D fields by
assembling slices in the range-depth plane for different bearing
angles, such models do not generally allow for refraction out of
each range-depth plane. In spherical coodinates for the globe,
we are obviously talking about propagation that deviates from
great-circle paths.

When does horizontal refraction matter? Clearly, the stronger
the horizontal gradients in the environment, the greater the
likelihood that horizontal refraction will matter. Canyons,
fjords, and seamounts are examples of bathymetric features with
stong gradients. Nonlinear internal waves with particularly
short spatial scales (e.g. 1 km) may similarly provide
oceangraphic features with strong gradients. The refractive
effects tend to accumulate with increasing range so that a
continental slope may have no significant effect at a few km in
range, but strong effects at tens of kms.

However, an equally important issue is how the signal is
observed. One tends to think about transmission loss plots, but
those plots represent a jumble of arrivals where differences in
the individual components are obscured. In contrast, if the
signal is split into parts by observing it through a beamformer,
then the horizontal refraction may become a huge effect. Similar
comments apply to a signal observed in the time domain where the
echoes are distinguished in time (rather than angle). Finally
spectrograms, that result when the signial is passed through a
sound prism, may also reveal more clearly the 3D effects.

Analytic solution for the penetrable
wedge shaped ocean and documentation based on the Modal
PE approach of Petrov and Sturm (JASA 2016).

(P. Petrov/V.I.Il'chev
Pacific Oceanological Inst. and F. Sturm/École
Centrale de Lyon)

Analytic solution for the penetrable wedge
shaped ocean based on the G. Deane and M. Buckinham paper
(JASA 1993)

(P. Petrov/V.I.Il'chev
Pacific Oceanological Inst.)

Analytic solution for the elastic
penetrable wedge shaped ocean. This is a mod of the
Petrov code above to handle elasticity.
* (2017)
(唐骏 Jun Tang,
College of Underwater Acoustic Engineering, Harbin
Engineering University)
*

BELLHOP3D ray/beam tracing code (part of the Acoustics
Toolbox) and

KRAKEN3D adiabatic normal mode code (see FIELD3D in the
Acoustics Toolbox)

Source code (in Acoustics
Toolbox) *(M. Porter)
*

HWT_3D_mm ---
Huygens Wavefront Tracing in 3D for moving media *(2013)*

(*Nikolay
Zabotin, Oleg A. Godin, and Liudmila Ye. Zabotina,
National Oceanic and Atmospheric Administration)
*

TRACEO3D: Beam tracing code for
3D *(Orlando Camargo
Rodríguez and Rogério de Moraes Calazan,
SiPLAB/LARSyS, Univ. of Algarve, Portugal)** (2018)
*

USML: Under Sea
Modeling Library with WaveQ3D beam tracing code for 3D with eigenray capability*(S. Reilly, Univ.
Rhode Island and AEgis Technologies Group)** (2015) *