Contents

• Introduction
• Ray tracing theory
  • The acoustic wave equation
  • Solving the Eikonal equation
    • Lagrangian's formalism and Fermat's principle
    • Sound slowness
    • Cilindrical symmetry (two-dimensional case)
  • Solving the transport equation
  • Transmission loss
  • Particle velocity
  
  
• Gaussian beams
  • The Gaussian beam approximation
  • Initial conditions on $\mbox{$\mathbf{P}$}$ and $\mbox{$\mathbf{Q}$}$
    • Point source
    • Line source
  • Reduction to the 2.5D case
  • Reduction to the 2D case
  
  
• Attenuation
  • Boundary reflections
  • Volume attenuation
  
  
• Numerical issues
  • Geometric beams
  • Updating $p$ and $q$ after reflections
  • Solving the Eikonal equations
  • Solving the dynamic equations
  • Calculation of derivatives
  • Calculation of normals
  • Refraction correction
  • Ray reflection at a boundary
  • Orientation of boundary normals
  • Ray-boundary intersection
  • Calculation of particle velocity
  • Eigenray search
  • Calculation of amplitudes and arrivals
  
  
• Model description
  • General strategy of calculations
  • Installation
  • The input file
  
  
• Examples and comparisons
  • Examples
    • Deep water
    • Shallow water
  • Model accuracy
    • Comparison with KRAKEN
    • Comparison with UAN models
  
  
• Conclusions and future work
• Additional topics
  • Vector form of Eikonal equations
  • Eikonal equations including wavenumber
  • Wavenumber 2D Eikonal equations
  • Ray slope 2D Eikonal equations
  • Earth 2D Eikonal equations
  • Including ocean currents
  • Hamiltonian formalism
  
  
• Bibliography