NM_CT_readme, Jul. 5, 2020, Houwang Tu, National University of Defense Technology

The program NM_CT.m computes the range-independent modal acoustic field in Fig.1 using the Chebyshev-Tau spectral method (NM_CT). The method is described in the article (H. Tu, Y. Wang, Q. Lan et al., A Chebyshev-Tau spectral method for normal modes of underwater sound propagation with a layered marine environment, https://doi.org/10.1016/j.jsv.2020.115784). We have developed program in Fortran version (NM_CT.f90) and Matlab version (NM_CT.m), respectively. Both versions of the program use the same input file "input.txt", 'ReadEnvParameter' function/subroutine is used to read "input.txt" file. User can make changes to "input.txt" for the desired calculation. It is worth mentioning that the Fortran version of the program calls the subroutine 'zgeev()' in the Lapack (a numerical library) to solve the eigenvalues of the complex matrix. Both the Matlab and Fortran versions of the program will eventually generate the same format of the binary sound field file "tl.bin", and the plot_binary_tl.m program can be used to read the sound field binary data and plot.

The initial version of the program was only able to solve for sound propagation in a two-layer marine environment with an ideal seafloor. It then underwent two major extensions, the first allowing it to solve the ocean floor at half-space boundaries, and the second allowing it to solve horizontally layered media with any number of layers.

The "input.txt" file contains the parameters defining the modal calculation. See the following example:

Example8                          ! casename
2                                 ! Layers (number of layers)
20                                ! N1 (truncation order of the first layer)
20                                ! N2 (truncation order of the second layer)
3500.0                            ! cpmax (maximum phase speed limit)
50.0                              ! freq (frequency of source)
36.0                              ! zs (depth of source)
10.0                              ! zr (depth of special receiver)
3500.0                            ! rmax (receiver ranges(m))
1                                 ! dr (discrete step in horizontal direction)
50.0                              ! interface1 (depth of the first layer)
100.0                             ! interface2 (depth of the second layer)
0.1                               ! dz (discrete step in depth direction)
40                                ! tlmin (minimum value of TL in colorbar)
70                                ! tlmax (maximum value of TL in colorbar)
2                                 ! n1 (profiles' points in the first layer)
2                                 ! n2 (profiles' points in the last layer)
    0.0 1500.0  1.0   0.0         ! dep1 c1 rho1 alpha1
   50.0 1500.0  1.0   0.0
   50.0 1800.0  1.5   1.5         ! dep2 c2 rho2 alpha2
  100.0 1800.0  1.5   1.5
A                                 ! Lowerboundary (rigid/free/halfspace lower boundary condition)
2000.0  2.0   2.0                 ! sound speed, density and attenuation of semi-infinite space

The "input.txt" file include:

• casename is the name of current example,

• Layers is the number of layers,

• N1 (the number to truncated order of water column),

• N2 (the number to truncated order of bottom sediment).

  N1 and N2 may be equal or unequal. Generally speaking, the more complicated the shape of the sound speed profile, the more N1 and N2 are needed to accurately fit. Layers is how many N there are.

• cpmax is the maximum phase speed limit, which used to determine how many modes are accumulated in the final synthesized sound field, generally set by the user according to experience (m/s).

• freq (frequency of sound source, Hz),

• zs (the depth of source, m),

• zr (depth of a special receiver, user used to specify to draw the transmission loss curve of arbitrary depth, m),

• rmax (the maximum range of horizontal direction, m),

• dr (horizontal discrete step, m),

• interface1 (depth of the first layer, m),

• interface2 (depth of the second layer, m), Layers is how many interface there are,

• dz (discrete step size in depth direction, m),

• tlmin and tlmax are the minmum and maximum value transmission loss, respectively, which used to determine the color range of the output transmission loss graph, tlmin must less than tlmax.

• n1 and n2 are the amount of environmental profile data in media. There are Layers tables of environmental parameter, their units are depth(m), speed(m/s), density(g/cm$^3$) and attenuation (dB/wavelength), with n1 and n2 points in each. It is necessary that dep1(n1)=dep2(1) where the density usually has a discontinuity. The first entry dep1(1)=0 is the free surface. The last entry dep2(n2)=H determines the total thickness of the waveguide.

• Lowerboundary (User used to specify whether the seabottom boundary condition is perfectly free 'V', perfectly rigid 'R' or half-space 'A'), The last line is the parameters for the half-space.

Note that when using the half-space boundary condition, the attenuation coefficient needs to be set to a positive value for the program to run stably.

Figure 1. Layered marine environment.

The plots resulting of example 2 are as follows:

Figure 2. Complex horizontal wavenumbers.

Figure 3. Mode number 2 versus depth.

Figure 4. Transmission loss versus range for a receiver at a depth of 100 meters.

Figure 5. A colorful plot of transmission loss, range versus depth.