Introduction

This document describes the first (distribution-ready) release of TRACEO, a ray tracing model written in Fortran 77 but tested with the GNU gfortran compiler, and available under a Creative Commons license. The current version of the model replaces the models previously known as TRACE (a standard ray tracing model) and TRACEO (an adaptation of TRACE, which allowed to consider the presence of a single object, located between the acoustic source and the array of receivers). Not only the former TRACE and TRACEO were merged into what is now TRACEO, as the original code was carefully rewritten, in order to allow the optional inclusion of one or more objects, to allow upper and lower boundaries with range-dependent properties (including compressional and shear velocities and attenuations), to allow eigenray calculations at the positions specified by array coordinates, and to output the results (rays, arrivals, amplitudes, acoustic pressure and particle velocity components) as Matlab MAT files^1.1. TRACEO can handle a particular set of analytical sound speed profiles, or general tabulated sound speed profiles or fields. The receiver array can be horizontal, vertical, rectangular, or it can have an arbitrary curvilinear shape; the hydrophones are not required to be equidistant. Rays can be partially or totally reflected on any boundary of the waveguide, or be completely absorbed. TRACEO was developed in order to model acoustic propagation in environments, which available models were not able to handle (like wavy surfaces, complex bathymetries, depth and range variations of sound speed, etc.), and for applications in the areas of geoacoustics, vector sensor arrays, underwater communications and acoustic barriers.

TRACEO strongly benefited from the availability of the Bellhop ray tracing model[1], one of the components of the Acoustic Toolbox[2]; Bellhop is developed (and constantly updated) by Michael Porter from HLS research. TRACEO borrows many methods from Bellhop, but goes beyond Bellhop's capabilities by allowing calculations in the following cases:

• using a set of analytical profiles;
• positioning targets between the source and the array of receivers;
• considering boundaries with range-dependent properties (which also account for shear velocity and attenuation);
• considering boundaries, which besides being partially or totally reflective can be completely absorbent.

The present document was not written with the intention of being just TRACEO's manual. Ray tracing and Gaussian beams are so compelling subjects, that the presentation of TRACEO was not considered to be complete without a detailed discussion of Ray tracing and Gaussian beams in independent chapters. Researchers with more interest in applications can skip directly to the chapters describing the model (installation, the general structure of the input file, etc.), and to the discussion of relevant model numerical issues, particular examples and comparisons with other models. The final chapter presents some conclusions and future directions of potential development. An appendix contains additional topics covering ray tracing modeling in more complex cases (accounting for ocean currents and earth's curvature) and within the context of the Hamiltonian formalism.

Before proceeding a final word of acknowledgement should be addressed to those, which one way or another made possible the development of TRACEO. First of all is Michael Porter, Bellhop's author, whose constantly updated code was a valuable guide to understand and test most the methods implemented in TRACEO. Michael Porter is also a co-author of COMPUTATIONAL OCEAN ACOUSTICS [3], a central reference for underwater acoustic modeling. Second in the list goes Mikhail Mikhailovich Popov, whose excellent RAY THEORY AND GAUSSIAN BEAM METHOD FOR GEOPHYSICISTS (available in the internet) provides an excellent discussion of Gaussian beam theory. Finally, a word of gratitude should be addressed to Vlastislav Cerveny, Ludek Klimes and Petr Bulant, members of the consortium research project Seismic waves in complex 3-D structures (SW3D), which maintain an online library of valuable papers, related to Gaussian beams; the consortium provides also an extensive set of ray tracing codes, oriented to seismic applications, which share a lot of methodologies used in acoustic underwater ray models. To all of them I would like to present my deepest gratitude.