USML
reflect_loss_rayleigh Class Reference
Collaboration diagram for reflect_loss_rayleigh:

Detailed Description

Models plane wave reflection loss from a flat fluid-solid interface.

Includes the effects of both compression and shear waves in the bottom. Note that the Rayleigh model is frequency independent because all of the frequency terms cancel out.

The effect of attenuation is incorporated into the model as a complex component of the sound speed:

\[ c_w = c_{rw} \]

\[ c_b = c_{rb}-i \frac{ \alpha_b c_{rb}^2 }{ \omega } \]

\[ \alpha_b = \frac{ \alpha_{\lambda b} }{ \lambda_b 20 \log{e} } \]

where:

  • $ c_n $ = complex sound speed in medium "n" (m/s)
  • $ c_{rn} $ = real component of sound speed in medium "n" (m/s)
  • $ \alpha_{\lambda b} $ = attenuation coefficient in (dB/wavelength)
  • $ \lambda_b $ = wavelength in bottom = $ c_{rb} / f $
  • $ \alpha_b $ = attenuation coefficient in bottom (nepers/meter)

The effect of absorption on the in-water sound speed is assumed to be negligible.

The complex reflection coefficient is modeled as a combination of the acoustic impedances for compressional and shear waves. The effect of shear on the in-water impedance is assumed to be negligible.

\[ Z_{pn} = \frac{ \rho_n c_n }{ cos(\theta_{pn}) } \]

\[ Z_{sb} = \frac{ \rho_b c_{sb} }{ cos(\theta_{sb}) } \]

\[ Z_w = Z_{pw} \]

\[ Z_b = Z_{pb} sin^2(2\theta_{sn}) + Z_{sb} cos^2(2\theta_{sn}) \]

\[ R = \frac{ Z_b - Z_w }{ Z_b + Z_w } \]

where:

  • $ \rho_n $ = density of medium "n" (kg/m^3)
  • $ c_{sb} $ = complex shear speed in bottom (m/s)
  • $ \theta_{pn} $ = angle between ray and surface normal in medium "n" for compression waves (radians)
  • $ \theta_{sn} $ = angle between ray and surface normal in bottom for shear waves (radians)
  • $ Z_{pn} $ = compression waves impedance in medium "n"
  • $ Z_{sn} $ = shear wave impedance in bottom
  • $ Z_n $ = total acoustic impedance in medium "n"
  • $ R $ = complex reflection coefficient

The angles between the ray and surface normal in each medium is computed using Snell's Law:

\[ \frac{sin(\theta_w)}{c_w} = \frac{sin(\theta_{pb})}{c_{pb}} = \frac{sin(\theta_{sb})}{c_{sb}} \]

Note that the sin() and cos() terms in this derivation have been inverted from the reference to take into account the difference between grazing angle and angle to the surface normal.

References:
F.B. Jensen, W.A. Kuperman, M.B. Porter, H. Schmidt, "Computational Ocean Acoustics", pp. 35-49.

Member Enumeration Documentation

Bottom types supported by table lookup feature.

Enumerator
CLAY 
SILT 
SAND 
GRAVEL 
MORAINE 
CHALK 
LIMESTONE 
BASALT 
MUD 

Constructor & Destructor Documentation

Initialize model with a generic bottom type.

Initialize model with impedance mis-match factors.

Uses an internal lookup table to convert into impedance mis-match factors.

Parameters
typeGeneric bottom for table lookup of impedance mis-match factors.
reflect_loss_rayleigh ( double  density,
double  speed,
double  att_bottom = 0.0,
double  speed_shear = 0.0,
double  att_shear = 0.0 
)

Initialize model with impedance mis-match factors.

Defined in terms of ratios to match commonly used databases.

Parameters
densityRatio of bottom density to water density Water density is assumed to be 1000 kg/m^3.
speedRatio of compressional sound speed in the bottom to the sound speed in water. The sound speed in water is assumed to be 1500 m/s.
att_bottomCompressional wave attenuation in bottom (dB/wavelength). No attenuation if this is zero.
speed_shearRatio of shear wave sound speed in the bottom to the sound speed in water.
att_shearShear wave attenuation in bottom (dB/wavelength).

Member Function Documentation

complex< double > impedance ( double  density,
double  speed,
double  attenuation,
double  angle,
complex< double > *  cosA 
)
private

Compute impedance for compression or shear waves with attenuation.

Includes the Snell's Law computation of transmitted angle.

Parameters
densityRatio of bottom density to water density Water density is assumed to be 1000 kg/m^3.
speedRatio of compressional sound speed in the bottom to the sound speed in water. The sound speed in water is assumed to be 1500 m/s.
attenuationCompressional wave attenuation in bottom (dB/wavelength). No attenuation if this is zero.
angleReflection angle relative to the normal (radians).
cosAReturns the cosine of the transmitted angle computed using Snell's Law.
void reflect_loss ( const wposition1 location,
const seq_vector frequencies,
double  angle,
vector< double > *  amplitude,
vector< double > *  phase = NULL 
)
virtual

Computes the broadband reflection loss and phase change.

Parameters
locationLocation at which to compute attenuation.
frequenciesFrequencies over which to compute loss. (Hz)
angleReflection angle relative to the normal (radians).
amplitudeChange in ray strength in dB (output).
phaseChange in ray phase in radians (output). Phase change not computed if this is NULL.

Implements reflect_loss_model.

Member Data Documentation

const double _att_bottom
private

Compressional wave attenuation in bottom (nepers/wavelength).

const double _att_shear
private

Shear wave attenuation in bottom (nepers/wavelength).

const double _density_bottom
private

Bottom density (kg/m^3).

const double _density_water
private

Density of water (kg/m^3).

const double _speed_bottom
private

Compressional speed of sound in bottom (m/s).

const double _speed_shear
private

Shear speed of sound in bottom (m/s).

const double _speed_water
private

Speed of sound in water (m/s).