Contents

• Introduction
• Mathematical Formulation
  • Derivation
  • The Isovelocity Problem
  • A Generalized Derivation
    • Derivation of the Normalization Formula
  • A Deep Water Problem: the Munk Profile
  • Elastic Media
  • Boundary and Interface Conditions
    • Perfectly Free Boundary (Dirichlet BC)
    • Perfectly Rigid Boundary (Neumann BC)
    • Acoustic Half-space Conditions (Robin BC)
    • Elastic Half-space Conditions
    • Tabulated Reflection Coefficients
  • Loss Mechanisms
    • Material Absorption
      • in nepers/m
      • in dB/meter
      • in dB/wavelength
      • in dB/(km Hz)
      • Q
    • Twersky Scatter Theory
    • Kirchhoff Scatter Theory
    • Interfacial Roughness
    • Perturbational Treatment of Loss Mechanisms
  • Normal Modes for Range-Dependent Environments
    • Coupled Modes
    • One-way Coupled Modes
    • The Adiabatic Approximation
    • Example: A Warm-Core Eddy
  • Normal Modes for 3-D Varying Environments
    • Horizontal Refraction Equations
• Numerical Solution of the Modal Equation
  • Finite-Difference Discretization
  • Treatment of Interfaces
  • Mode Normalization
  • Solving the Discretized Problem
    • Method I: Sturm Sequences
    • Method II: Deflation
  • Elastic Media
  • Richardson Extrapolation
• Running the Program
  • Structure of the KRAKEN model
  • The Main Program
    • notes.hlp
    • kraken.hlp
  • Acoustic Field Calculations
    • field.hlp
    • field3d.hlp
  • Plotting routines
    • plotfield.hlp
    • plotgrn.hlp
    • plotmode.hlp
    • plotslice.hlp
    • plotssp.hlp
    • plottld.hlp
    • plottlr.hlp
    • plottri.hlp
  • The BELLHOP ray/beam model
    • bellhop.hlp
    • plotray.hlp
  • The SCOOTER FFP model
    • scooter.hlp
    • fields.hlp
  • The SPARC pulse model
    • sparc.hlp
    • plotts.hlp
  • The BOUNCE reflection coefficient model
    • bounce.hlp
    • plotrth.hlp
• Test Problems
  • PEKERIS
  • TWERSKY
  • DOUBLE
  • SCHOLTE
  • FLUSED
  • ELSED
  • ATTEN
  • NORMAL
  • ICE
• References
• About this document ...