PyWaveProp

https://wave-propagation.readthedocs.io/en/latest/
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PyWaveProp is a Python library for modeling radio wave propagation over irregular terrain,...
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### Import PyWaveProp Modules

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_shallow_water.html

Load necessary classes for source definition, environment setup, computation, and visualization.

```python
from uwa.source import GaussSource
from uwa.environment import UnderwaterEnvironment, Bathymetry
from uwa.sspade import UWASSpadeComputationalParams, uwa_ss_pade
from uwa.vis import AcousticPressureFieldVisualiser2d
```

--------------------------------

### Initialize Environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_shallow_water.html

Set up the working directory and suppress warnings.

```python
import os
os.chdir('../../../')
import warnings
warnings.filterwarnings('ignore')
```

--------------------------------

### Initialize environment and imports

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_deep_water.html

Set up the working directory and import necessary PyWaveProp modules for underwater acoustic simulation.

```python
import os
os.chdir('../../../')
import warnings
warnings.filterwarnings('ignore')
```

```python
from uwa.source import GaussSource
from uwa.environment import UnderwaterEnvironment, Bathymetry, munk_profile
from uwa.sspade import UWASSpadeComputationalParams, uwa_ss_pade
from uwa.vis import AcousticPressureFieldVisualiser2d
import math as fm
```

--------------------------------

### Initialize environment and imports

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Sets up the working directory and imports necessary modules for the RWP simulation.

```python
import os
os.chdir('../../../')
from rwp.environment import *
from rwp.sspade import *
from rwp.tworay import *
from rwp.vis import *
```

--------------------------------

### Initialize environment and imports

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/irregular_terrain.html

Sets up the working directory and imports necessary modules for the simulation.

```python
import os
os.chdir('../../../')
from rwp.antennas import GaussAntenna
from rwp.environment import *
from rwp.sspade import *
from rwp.vis import *
```

--------------------------------

### Initialize simulation environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/knife_edge_in_elevated_duct.html

Sets up the working directory and imports necessary modules for the RWP simulation.

```python
import os
os.chdir('../../../')
from rwp.sspade import *
from rwp.environment import *
from rwp.vis import *
```

--------------------------------

### Initialize environment and imports

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/std_atmosphere.html

Sets up the working directory and imports necessary modules for environment, computation, and visualization.

```python
import os
os.chdir('../../../')
from rwp.environment import *
from rwp.sspade import *
from rwp.vis import *
```

--------------------------------

### Initialize field visualizers

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Creates visualizer objects for both the Pade propagator and the two-ray model results.

```python
pade_vis = FieldVisualiser(pade_field, env=environment, trans_func=lambda v: 10 * cm.log10(1e-16 + abs(v)), label='Pade + nonlocal BC', x_mult=1)
trm_vis = FieldVisualiser(trm_field, env=environment, trans_func=lambda v: 10 * cm.log10(1e-16 + abs(v))-7, label='Two-ray model')
```

--------------------------------

### Set up Padé propagator

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/knife_edge_in_elevated_duct.html

Configures the Helmholtz propagator using Padé approximation parameters for high-order accuracy.

```python
computational_params78 = HelmholtzPropagatorComputationalParams(exp_pade_order=(7, 8),
                                                                z_order=4,
                                                                dx_wl=400,
                                                                dz_wl=1,
                                                                x_output_filter=1,
                                                                z_output_filter=1,
                                                                two_way=True,
                                                                max_propagation_angle=10)
pade78_task = TroposphericRadioWaveSSPadePropagator(antenna=antenna,
                                                    env=environment,
                                                    max_range_m=max_range,
                                                    comp_params=computational_params78)
```

--------------------------------

### Importing required modules

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/five_knife_edges.html

Initializes the environment by changing the working directory and importing necessary classes from the rwp package.

```python
import os
os.chdir('../../')
from rwp.kediffraction import *
from rwp.antennas import *
from rwp.environment import *
from rwp.vis import *
```

--------------------------------

### Importing required modules

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/one_knife_edge.html

Initializes the working directory and imports necessary classes for knife-edge diffraction modeling.

```python
import os
os.chdir('../../../')
from rwp.kediffraction import *
from rwp.antennas import *
from rwp.environment import *
from rwp.vis import *
```

--------------------------------

### Set up Crank-Nicolson propagator

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/knife_edge_in_elevated_duct.html

Configures the Helmholtz propagator using Crank-Nicolson parameters for the simulation task.

```python
computational_params_cn = HelmholtzPropagatorComputationalParams(exp_pade_order=(1, 1),
                                                                 two_way=True,
                                                                 z_order=2,
                                                                 dx_wl=80,
                                                                 x_output_filter=5,
                                                                 dz_wl=1,
                                                                 z_output_filter=1,
                                                                 max_propagation_angle=10)
crank_nicolson_task = TroposphericRadioWaveSSPadePropagator(antenna=antenna,
                                                            env=environment,
                                                            max_range_m=max_range,
                                                            comp_params=computational_params_cn)
```

--------------------------------

### Configure transmitting antenna

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/elevated_duct.html

Sets up a Gaussian antenna with specific wavelength, height, beam width, and polarization.

```python
antenna = GaussAntenna(wavelength=0.1, height=30, beam_width=2, elevation_angle=0, polarz='H')
```

--------------------------------

### Defining the environment and antenna

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/one_knife_edge.html

Sets up a flat troposphere environment with a single knife-edge obstacle and a source antenna.

```python
env = Troposphere(flat=True)
env.z_max = 150
env.knife_edges = [KnifeEdge(range=500, height=50)]
antenna = Source(wavelength=1, height_m=50)
```

--------------------------------

### Visualize Results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_shallow_water.html

Generate 2D plots of the acoustic pressure field amplitude.

```python
vis = AcousticPressureFieldVisualiser2d(field=field, env=env)
vis.plot2d(min_val=-50, max_val=-5, grid=True, show_terrain=True).show()
```

```python
vis = AcousticPressureFieldVisualiser2d(field=field, env=env)
vis.plot2d(-50, -5, grid=True, show_terrain=True).show()
```

```python
vis = AcousticPressureFieldVisualiser2d(field=field, env=env)
plt = vis.plot2d(-50, -5, grid=True, show_terrain=True)
plt.show()
```

--------------------------------

### Simulate with irregular bottom

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_deep_water.html

Define an environment with a variable bottom profile and re-run the simulation.

```python
env = UnderwaterEnvironment(
    sound_speed_profile_m_s=lambda x, z: munk_profile(z),
    bottom_profile=Bathymetry(func=lambda z: 5000 - fm.exp((-(z-100E3)**2)/1E9)*3000, max_depth=5000),
    bottom_sound_speed_m_s = 1700,
    bottom_density_g_cm = 1.5,
    bottom_attenuation_dm_lambda = 0.5
)
```

```python
field = uwa_ss_pade(
    src=src,
    env=env,
    params=params
)
```

```python
vis = AcousticPressureFieldVisualiser2d(field=field, env=env)
vis.plot2d(min_val=-80, max_val=0, grid=True, show_terrain=True).show()
```

--------------------------------

### Calculating knife-edge diffraction

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/two_knife_edges.html

Initializes the calculator with the antenna and environment, then computes the field.

```python
kdc = KnifeEdgeDiffractionCalculator(src=antenna, env=env, max_range_m=1000)
field = kdc.calculate()
```

--------------------------------

### Visualize acoustic results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_deep_water.html

Visualize the sound speed profile and the resulting 2D acoustic pressure field.

```python
vis = AcousticPressureFieldVisualiser2d(field=field, env=env)
```

```python
vis.sound_speed_profile().show()
```

```python
vis.plot2d(min_val=-80, max_val=0, grid=True, show_terrain=True).show()
```

--------------------------------

### Configuring environment and antenna

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/five_knife_edges.html

Defines the tropospheric environment with five specific knife-edges and sets up a Gaussian antenna source.

```python
env = Troposphere(flat=True)
env.z_max = 150
env.knife_edges = [KnifeEdge(range=100, height=25),
                   KnifeEdge(range=200, height=50),
                   KnifeEdge(range=300, height=75),
                   KnifeEdge(range=600, height=50),
                   KnifeEdge(range=800, height=125)]
antenna = GaussAntenna(freq_hz=300e6,
                       height=50,
                       beam_width=15,
                       elevation_angle=0,
                       polarz='H')
```

--------------------------------

### Visualize field results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/elevated_duct.html

Initializes the field visualizer with a logarithmic transformation function.

```python
vis = FieldVisualiser(field, env=environment, trans_func=lambda v: 10 * cm.log10(1e-16 + abs(v)), label='Pade + Transparent BC', x_mult=1E-3)
```

--------------------------------

### Visualize acoustic results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_ultrasound.html

Visualizes the sound speed profile and the 2D acoustic pressure field amplitude.

```python
vis = AcousticPressureFieldVisualiser2d(field=field, env=env)
vis.sound_speed_profile().show()
vis.plot2d(min_val=-20, max_val=30, grid=True, show_terrain=True).show()
```

--------------------------------

### Execute field calculation

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/knife_edge_in_elevated_duct.html

Runs the calculation for both the Padé and Crank-Nicolson propagation tasks.

```python
pade78_field = pade78_task.calculate()
crank_nicolson_field = crank_nicolson_task.calculate()
```

--------------------------------

### Configuring the troposphere and antenna

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/two_knife_edges.html

Defines the troposphere environment with two knife-edges and sets up a Gaussian antenna.

```python
env = Troposphere(flat=True)
env.z_max = 150
env.knife_edges = [KnifeEdge(range=200, height=50), KnifeEdge(range=800, height=50)]
antenna = GaussAntenna(freq_hz=300e6, height=50, beam_width=15, elevation_angle=0, polarz='H')
```

--------------------------------

### Define Gaussian source

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_ultrasound_pond.html

Create a Gaussian source with specific frequency, depth, and beam characteristics.

```python
src = GaussSource(
    freq_hz=31.4E3,
    depth_m=2,
    beam_width_deg=20,
    elevation_angle_deg=0,
    multiplier=0.1
)
```

--------------------------------

### Compute Acoustic Pressure Field

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_shallow_water.html

Execute the SS-Pade solver using the defined source, environment, and parameters.

```python
field = uwa_ss_pade(
    src=src,
    env=env,
    params=params
)
```

--------------------------------

### Configure underwater environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_ultrasound_pond.html

Define the pond environment parameters including sound speed, bathymetry, and bottom properties.

```python
max_range_m = 100
env = UnderwaterEnvironment(
    sound_speed_profile_m_s=lambda x, z: 1500,
    bottom_profile=Bathymetry(
        ranges_m=[0, max_range_m],
        depths_m=[4, 1]),
    bottom_sound_speed_m_s = 1700,
    bottom_density_g_cm = 1.5,
    bottom_attenuation_dm_lambda = 0.1
)
```

--------------------------------

### Set computational parameters

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Defines the Helmholtz propagator parameters for the finite-difference Pade method.

```python
pade_params = HelmholtzPropagatorComputationalParams(two_way=False,
                                                     exp_pade_order=(7, 8),
                                                     max_propagation_angle=abs(antenna.beam_width) + abs(antenna.elevation_angle) + 5,
                                                     z_order=5,
                                                     dx_wl=2,
                                                     dz_wl=0.05,
                                                     inv_z_transform_tau=10**(3 / (max_range / antenna.wavelength / 2))
                                                     )
```

--------------------------------

### Visualize simulation results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/knife_edge_in_elevated_duct.html

Generates horizontal and 2D plots to visualize the field intensity in decibels.

```python
pade78_vis = FieldVisualiser(pade78_field, env=environment, trans_func=lambda v: 10 * cm.log10(1e-16 + abs(v)),
                             label='Pade-[7/8] + NLBC', x_mult=1E-3)
crank_nicolson_vis = FieldVisualiser(crank_nicolson_field, env=environment, trans_func=lambda v: 10 * cm.log10(1e-16 + abs(v)),
                                     label='Claerbout-CN', x_mult=1E-3)
plt = crank_nicolson_vis.plot_hor(150, pade78_vis)
plt.xlabel('Range (km)')
plt.ylabel('10log|u| (dB)')
plt.tight_layout()
plt.grid(True)
plt.show()

plt = crank_nicolson_vis.plot2d(min=-70, max=0)
plt.xlabel('Range (km)')
plt.ylabel('Height (m)')
plt.tight_layout()
plt.grid(True)
plt.show()

plt = pade78_vis.plot2d(min=-70, max=0)
plt.title('10log|u|')
plt.xlabel('Range (km)')
plt.ylabel('Height (m)')
plt.tight_layout()
plt.grid(True)
plt.show()
```

--------------------------------

### Set Computational Parameters

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_shallow_water.html

Define the grid and range limits for the SS-Pade computation.

```python
params = UWASSpadeComputationalParams(
    max_range_m=max_range_m,
    max_depth_m=500,
    dx_m=1, # output grid steps affects only on the resulting field, NOT the computational grid
    dz_m=1,
)
```

--------------------------------

### Calculating the diffraction field

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/one_knife_edge.html

Initializes the diffraction calculator and computes the field over the specified range.

```python
kdc = KnifeEdgeDiffractionCalculator(src=antenna,
                                     env=env,
                                     max_range_m=1000)
field = kdc.calculate()
```

--------------------------------

### Simulate antenna inside thermocline

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_ultrasound.html

Updates source depth to 7m and re-runs the simulation to observe propagation changes.

```python
src.depth_m = 7
field2 = uwa_ss_pade(
    src=src,
    env=env,
    params=params
)
vis2 = AcousticPressureFieldVisualiser2d(field=field2, env=env)
vis2.plot2d(min_val=-20, max_val=30, grid=True, show_terrain=True).show()
```

--------------------------------

### Define acoustic source

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_deep_water.html

Configure a Gaussian source for the acoustic simulation.

```python
src = GaussSource(
    freq_hz=50,
    depth_m=100,
    beam_width_deg=3,
    elevation_angle_deg=0,
    multiplier=5
)
```

--------------------------------

### Simulate antenna below thermocline

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_ultrasound.html

Updates source depth to 10m and re-runs the simulation.

```python
src.depth_m = 10
field3 = uwa_ss_pade(
    src=src,
    env=env,
    params=params
)
vis3 = AcousticPressureFieldVisualiser2d(field=field3, env=env)
vis3.plot2d(min_val=-20, max_val=30, grid=True, show_terrain=True).show()
```

--------------------------------

### Visualize acoustic field results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_ultrasound_pond.html

Visualize the 2D field amplitude and compare different elevation angles.

```python
vis1 = AcousticPressureFieldVisualiser2d(field=field1, env=env, label="Horizontal")
```

```python
vis1.plot2d(min_val=-60, max_val=0, grid=True, show_terrain=True).show()
```

```python
src.elevation_angle_deg = -60
```

```python
field2 = uwa_ss_pade(
    src=src,
    env=env,
    params=params
)
```

```python
vis2 = AcousticPressureFieldVisualiser2d(field=field2, env=env, label="Vertical")
vis2.plot2d(min_val=-60, max_val=0, grid=True, show_terrain=True).show()
```

```python
vis1.plot_hor(0.5, [-70, -10], vis2).show()
```

```python
vis1.plot_hor(2, [-70, -10], vis2).show()
```

--------------------------------

### Calculate electromagnetic field

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/elevated_duct.html

Initializes the SSPade propagator and computes the field based on the defined antenna and environment.

```python
propagator = TroposphericRadioWaveSSPadePropagator(antenna=antenna, env=environment, max_range_m=max_range)
field = propagator.calculate()
```

--------------------------------

### Define Underwater Environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_shallow_water.html

Configure the sound speed profile and bottom bathymetry parameters.

```python
max_range_m = 3000
env = UnderwaterEnvironment(
    sound_speed_profile_m_s=lambda x, z: 1500 + z*0,
    bottom_profile=Bathymetry(
        ranges_m=[0, max_range_m],
        depths_m=[300, 300]),
    bottom_sound_speed_m_s = 1700,
    bottom_density_g_cm = 1.5,
    bottom_attenuation_dm_lambda = 0.01
)
```

```python
env = UnderwaterEnvironment(
    sound_speed_profile_m_s=lambda x, z: 1500 + z*0,
    bottom_profile=Bathymetry(
        ranges_m=[0, max_range_m],
        depths_m=[400, 0]),
    bottom_sound_speed_m_s = 1700,
    bottom_density_g_cm = 1.5,
    bottom_attenuation_dm_lambda = 0.05
)
```

--------------------------------

### Configure deep water environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_deep_water.html

Define the underwater environment with a Munk sound speed profile and flat bottom bathymetry.

```python
max_range_m = 200E3
env = UnderwaterEnvironment(
    sound_speed_profile_m_s=lambda x, z: munk_profile(z),
    bottom_profile=Bathymetry(ranges_m=[0], depths_m=[5000]),
    bottom_sound_speed_m_s = 1700,
    bottom_density_g_cm = 1.5,
    bottom_attenuation_dm_lambda = 0.5
)
```

--------------------------------

### Generate reference two-ray model

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Calculates the reference field using the two-ray model for comparison.

```python
trm = TwoRayModel(src=antenna, env=environment)
x_grid_m = np.linspace(1, max_range, 5000)
z_grid_m = np.linspace(1, environment.z_max, 500)
trm_f = trm.calculate(x_grid_m, z_grid_m)
trm_field = Field(x_grid=x_grid_m, z_grid=z_grid_m, freq_hz=antenna.freq_hz)
trm_field.field[:, :] = trm_f
```

--------------------------------

### Visualizing field results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/five_knife_edges.html

Generates 2D intensity plots and vertical amplitude profiles at specific ranges using the FieldVisualiser.

```python
vis = FieldVisualiser(field, env=env, trans_func=lambda v: 10 * cm.log10(1e-16 + abs(v)), label='ke')
plt = vis.plot2d(min=-40, max=0)
plt.title('The intensity of the field component 10log10|u|')
plt.xlabel('Range (m)')
plt.ylabel('Height (m)')
plt.show()

plt = vis.plot_ver(175)
plt.title('x = 175 m')
plt.xlabel('Amplitude, dB')
plt.ylabel('Height, m')
plt.show()

plt = vis.plot_ver(700)
plt.title('x = 700 m')
plt.xlabel('Amplitude, dB')
plt.ylabel('Height, m')
plt.show()
```

--------------------------------

### Configure antenna parameters

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/std_atmosphere.html

Defines the transmitting antenna characteristics for a given frequency.

```python
antenna = GaussAntenna(freq_hz=300E6,
                       height=30,
                       beam_width=2,
                       elevation_angle=0,
                       polarz='H')
```

```python
antenna = GaussAntenna(freq_hz=3E9,
                       height=30,
                       beam_width=2,
                       elevation_angle=0,
                       polarz='H')
```

--------------------------------

### Visualizing diffraction results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/one_knife_edge.html

Generates 2D field intensity plots and horizontal cross-section plots for the calculated diffraction field.

```python
vis = FieldVisualiser(field, env=env, trans_func=lambda v: 10 * cm.log10(1e-16 + abs(v)), label='ke')
plt = vis.plot2d(min=-40, max=0)
plt.title('The intensity of the field component 10log10|u|')
plt.xlabel('Range (m)')
plt.ylabel('Height (m)')
plt.show()

plt = vis.plot_hor(50)
plt.title('The intensity of the field component 10log10|u| at the height 50 m')
plt.xlabel('Range (m)')
plt.ylabel('10log|u| (dB)')
plt.show()
```

--------------------------------

### Visualizing diffraction results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/two_knife_edges.html

Generates 2D field intensity plots and horizontal intensity plots at a specific height.

```python
vis = FieldVisualiser(field, env=env, trans_func=lambda v: 10 * cm.log10(1e-16 + abs(v)), label='ke')
plt = vis.plot2d(min=-40, max=0)
plt.title('The intensity of the field component 10log10|u|')
plt.xlabel('Range (m)')
plt.ylabel('Height (m)')
plt.show()

plt = vis.plot_hor(51)
plt.title('The intensity of the field component 10log10|u| at the height 51 m')
plt.xlabel('Range (m)')
plt.ylabel('10log|u| (dB)')
plt.show()
```

--------------------------------

### Configure Transmitting Antenna

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_shallow_water.html

Define the Gaussian source properties including frequency, depth, and beam characteristics.

```python
src = GaussSource(
    freq_hz=1000,
    depth_m=100,
    beam_width_deg=1,
    elevation_angle_deg=-30,
    multiplier=5
)
```

```python
src = GaussSource(
    freq_hz=200,
    depth_m=150,
    beam_width_deg=10,
    elevation_angle_deg=10,
    multiplier=5
)
```

--------------------------------

### Simulate propagation without thermocline

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/uwa/uwa_ultrasound.html

Resets the sound speed profile to a constant value and visualizes the resulting field.

```python
env.sound_speed_profile_m_s = lambda x, z: 1500+z*0
field4 = uwa_ss_pade(
    src=src,
    env=env,
    params=params
)
vis4 = AcousticPressureFieldVisualiser2d(field=field4, env=env)
vis4.plot2d(min_val=-20, max_val=30, grid=True, show_terrain=True).show()
```

--------------------------------

### Configure troposphere environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/irregular_terrain.html

Defines the terrain elevation, ground material, M-profile, and vegetation impediments.

```python
environment = Troposphere()
environment.terrain = Terrain(
    elevation=gauss_hill_func(
        height_m=125,
        length_m=40E3,
        x0_m=50E3
    ),
    ground_material=WetGround()
)
elevated_duct = interp1d(
    x=[0, 100, 150, 300],
    y=[0, 32, 10, 45],
    fill_value="extrapolate")
environment.M_profile = lambda x, z: elevated_duct(z)
environment.vegetation = [Impediment(
    left_m=30E3,
    right_m=70E3,
    height_m=25,
    material=CustomMaterial(eps=1.004, sigma=180e-6)
)]
```

--------------------------------

### Define tropospheric environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/knife_edge_in_elevated_duct.html

Configures the refractive index profile, terrain, and knife-edge obstacle for the simulation.

```python
elevated_duct = interp1d(x=[0, 100, 150, 300], y=[0, 32, 10, 50], fill_value="extrapolate")
environment = Troposphere()
environment.terrain = Terrain(ground_material=PerfectlyElectricConducting())
environment.z_max = 300
environment.M_profile = lambda x, z: elevated_duct(z)
environment.knife_edges = [KnifeEdge(range=70e3, height=150)]
max_range = 100000
```

--------------------------------

### Visualize field results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/std_atmosphere.html

Creates visual representations of the calculated field data.

```python
vis300mhz = FieldVisualiser(field, env=environment, label='Pade + Transparent BC: 300 MHz', x_mult=1E-3)
```

```python
plt = vis300mhz.plot2d(min=-120, max=0)
plt.title('10log|u|')
plt.xlabel('Range (km)')
plt.ylabel('Height (m)')
plt.tight_layout()
plt.grid(True)
plt.show()
```

```python
vis3ghz = FieldVisualiser(field, env=environment, label='Pade + Transparent BC: 3 GHz', x_mult=1E-3)
```

```python
plt = vis3ghz.plot_hor(30, vis300mhz)
plt.xlabel('Range (km)')
plt.ylabel('10log|u| (dB)')
plt.grid(True)
plt.tight_layout()
plt.show()
```

```python
plt = vis3ghz.plot2d(min=-120, max=0)
plt.title('10log|u|')
plt.xlabel('Range (km)')
plt.ylabel('Height (m)')
plt.tight_layout()
plt.grid(True)
plt.show()
```

--------------------------------

### Plot horizontal field comparison

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Plots a comparison of the horizontal field values between the Pade propagator and the two-ray model.

```python
plt = pade_vis.plot_hor(50, trm_vis)
plt.xlabel('Range (m)')
plt.ylabel('10log|u| (dB)')
plt.tight_layout()
plt.grid(True)
plt.show()
```

--------------------------------

### Configure transmitting antenna

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/knife_edge_in_elevated_duct.html

Defines the Gaussian antenna properties including wavelength, height, and beam characteristics.

```python
antenna = GaussAntenna(wavelength=0.1,
                       height=30,
                       beam_width=2,
                       elevation_angle=0,
                       polarz='H')
```

--------------------------------

### Plot two-ray model results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Generates a 2D plot for the two-ray model field.

```python
plt = trm_vis.plot2d(min=-40, max=0)
plt.xlabel('Range (m)')
plt.ylabel('Height (m)')
plt.grid(True)
plt.tight_layout()
plt.show()
```

--------------------------------

### Configure transmitting antenna

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Sets the antenna parameters, including the elevation angle calculated based on the Brewster angle.

```python
freq_hz = 3000e6
b_angle = brewster_angle(1, ground_material.complex_permittivity(freq_hz)).real
antenna = GaussAntenna(freq_hz=freq_hz, height=50, beam_width=5, elevation_angle=90-b_angle, polarz='V')
h1 = antenna.height_m
h2 = 0
a = abs((h1 - h2) / cm.tan(abs(antenna.elevation_angle) * cm.pi / 180))
max_range = 2 * a + 200
```

--------------------------------

### Calculate electromagnetic field

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Executes the propagation task using the defined antenna, environment, and computational parameters.

```python
pade_task = TroposphericRadioWaveSSPadePropagator(antenna=antenna, env=environment, max_range_m=max_range, comp_params=pade_params)
pade_field = pade_task.calculate()
```

--------------------------------

### Compute electromagnetic field

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/std_atmosphere.html

Calculates the field using the Pade approximation based on the provided environment, antenna, and computational parameters.

```python
params = RWPSSpadeComputationalParams(
    max_range_m=150E3,
    max_height_m=300,
    dx_m = 100, # output grid steps affects only on the resulting field, NOT the computational grid
    dz_m = 1
)


field = rwp_ss_pade(antenna=antenna, env=environment, params=params)
```

```python
field = rwp_ss_pade(antenna=antenna, env=environment, params=params)
```

--------------------------------

### Plot Pade propagator results

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Generates a 2D plot for the Pade propagator field.

```python
plt = pade_vis.plot2d(min=-40, max=0)
plt.xlabel('Range (m)')
plt.ylabel('Height (m)')
plt.tight_layout()
plt.grid(True)
plt.show()
```

--------------------------------

### Plot 2D field distribution

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/elevated_duct.html

Generates a 2D heatmap of the field amplitude over the range and height.

```python
plt = vis.plot2d(min=-70, max=0)
plt.title('10log|u|')
plt.xlabel('Range (km)')
plt.ylabel('Height (m)')
plt.tight_layout()
plt.show()
```

--------------------------------

### Specify elevated duct M-profile

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/elevated_duct.html

Defines the refractive index profile using a 1D interpolation function applied to the environment.

```python
profile1d = interp1d(x=[0, 100, 150, 300], y=[0, 32, 10, 45], fill_value="extrapolate")
environment.M_profile = lambda x, z: profile1d(z)
```

--------------------------------

### Define tropospheric environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/brewster_angle.html

Configures the simulation environment with a flat troposphere and custom ground material properties.

```python
environment = Troposphere(flat=True)
environment.z_max = 100
ground_material = CustomMaterial(eps=3, sigma=0)
environment.terrain = Terrain(ground_material=ground_material)
```

--------------------------------

### Plot horizontal field amplitude

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/elevated_duct.html

Generates a 1D plot of the field amplitude at a specific height.

```python
plt = vis.plot_hor(30)
plt.xlabel('Range (km)')
plt.ylabel('10log|u| (dB)')
plt.grid(True)
plt.tight_layout()
plt.show()
```

--------------------------------

### Define tropospheric environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/elevated_duct.html

Configures the base troposphere environment with ground terrain and a maximum propagation range.

```python
environment = Troposphere()
environment.terrain = Terrain(ground_material=WetGround())
max_range = 150e3
```

--------------------------------

### Define troposphere environment

Source: https://wave-propagation.readthedocs.io/en/latest/notebooks/std_atmosphere.html

Configures the troposphere with a specific terrain type.

```python
environment = Troposphere()
environment.terrain = Terrain(ground_material=WetGround())
```
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