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Figure 1. Depicted is a 15-km 3-D simulation of a 1,100-Hz harmonic sound emitted from a source at 50 m depth (y = −150 m; x = 0 [*]) in a 95-m deep volume (z-axis upward). At y = 0 lies a tilted warm/cold water boundary (subsurface front). The Woods Hole Oceanographic Institution three-dimensional (3-D) parabolic equation solver was used. To the left (y > 0), a surface layer of warm water (fast sound speed) extends deeper than it does at the right (y < 0), indicated by the transparent surface. At the x = 15,000-m plane, the darker colors (high intensity) indicate that the sound has refracted away from the feature. The bottom colors show a column average of sound energy in the water above, with intense refraction and focus evident. The black lines are drawn for perspective.
Major reasons that sound fields in water are so frequently numerically computed are that the sound speed in the gov- erning wave equation has a four-dimensionally varying nature with large spectral and dynamic ranges of variability, and the boundary conditions are applied at a shaped sea- floor. The possible states of the sound field are thus endless.
A few situations like water of uniform temperature over a flat seafloor can be solved analytically with fair accuracy, but to move forward, two-dimensional (2-D) and three-dimen- sional (3-D) numerical solutions have proven essential.
Simulation as a Tool
Faced with the vastness of the ocean and the richness of its features and physical processes, oceanographers use what- ever tools or methodologies are available. These tools can be divided into three categories: observation, theory, and simulation. Many discoveries are made using a combina- tion of these.
In ocean acoustics, the third of these, simulation, argu- ably began with the discovery in the 1940s of the ocean sound channel (sound fixing and ranging [SOFAR] chan- nel) that allows sound to efficiently travel a long distance
in nonpolar seas, away from the ocean surface and bottom. At that time, mathematical ray tracing, computed using some
clever approximations, was used to predict sound propaga- tion behavior. The ray trajectories undulate vertically in the channel, with sound speed gradients controlling the refrac- tion. The predictions were rudimentary by today’s standards but were simulations nonetheless. Simulated propagation has changed in the last 40 years to be dominated by computational simulations that allow full-wave physics, moving on from the ray model of wave propagation (geometric model) dating back to Newton and transforming how oceanography involving acoustics is tackled.
Computations foster progress in at least two ways: stimulat- ing discoveries and enabling better outcomes of data-based research. One example of the importance of simulation is that the Ocean Acoustics Library website (oalib-acoustics.org), which was conceived by the US Office of Naval Research in the 1990s and then developed and hosted for many years by Dr. Michael Porter, prominently features computational acoustic codes in its collection. Researchers from around the world use those codes, and others, with regularity.
Stimulation of Reason by Observation or Simulation
The role of propagation simulation in wave-based remote sensing is clear to most. An early application of this was the use of seismic wave modeling to locate earthquakes from recorded ground motion. This advanced, eventually yielding joint solutions for earth structure, fault locations, shapes, and motions. Joint data/model analyses like this may form the majority of computational acoustics appli- cations to ocean science, but something else can come from computer simulations: pure discovery. The stimu- lation of reason (theory) by observations is an ancient practice, often leading to discovery, and the interconnec- tion between observational evidence and theory has been subjected to some critical thinking (Bogen, 2017). This includes considering the question of whether high-fidelity simulations of physical systems based on theories and rules constitute observations in their own right, although the predominant community answer is probably “no” at this time. (Bogen states: “...scientists continue to find ways to produce data that can’t be called observational without stretching the term to the point of vagueness.”) Neverthe- less, we have found analysis of simulated ocean acoustic fields to stimulate many research directions as hypotheses; some are explored in the field.
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