The rational approximation to the acoustic wave equation with bottom interaction

The rational-linear approximation to the wave equation is a full-wave approach to modeling range-dependent ocean acoustic propagation with bottom interaction. It is a one-way wave equation which gives an accurate treatment of high-angle propagation to angles of about 40° with respect to the horizontal. Reflection from sound speed and density discontinuities is treated using the natural wave equation matching conditions. Bathymetry is allowed to vary in range. A tridiagonal implicit finite-difference solution of this equation has been implemented. It has several advantages over the tridiagonal Crank–Nicholson solution of the parabolic equation. It more accurately models high angles of propagation, treats attenuation as a function of path length rather than range, and models range-dependent bathymetry in a way that suits the form of the one-way wave equation. The numerical methods are fourth-order accurate in depth. The resulting implicit range step is still in the simple tridiagonal form.