+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ This is the API reference for the echoSMs package.
+Each type of model is contained in a separate Python class (with name ending in Model), but with common calling signatures across all model classes, as defined in ScatterModelBase. There are also classes to provide ready access to the benchmark models and reference model definitions. There are also utility functions.
+ Bases: ABC
Base class for a class that provides a scattering model.
+All scattering models should inherit from this class, have a name that +ends with 'Model', and provide initialisation and calculate_ts_single() functions.
+ + + +Attributes:
+| Name | +Type | +Description | +
|---|---|---|
long_name |
+
+ str
+ |
+
+
+
+ The long name of the model. + |
+
short_name |
+
+ str
+ |
+
+
+
+ A short version of the model's long name, typically an ancronym. + |
+
analytical_type |
+
+ str
+ |
+
+
+
+ Whether the model implements an |
+
boundary_types |
+
+ list[str]
+ |
+
+
+
+ The types of boundary conditions that the model provides, e.g., 'fixed rigid', +'pressure release', 'fluid filled' + |
+
shapes |
+
+ list[str]
+ |
+
+
+
+ The target shapes that the model can represent. + |
+
max_ka |
+
+ float
+ |
+
+
+
+ An approximate maximum ka value that will result in accurate target strength results. Note +that ka is often not the only parameter that determines the accuracy of the model (e.g., +aspect ratio and incident angle can also affect the accuracy). + |
+
no_expand_parameters |
+
+ list[str]
+ |
+
+
+
+ The model parameters that are not expanded into Pandas DataFrame columns or
+Xarray DataArray coordinates. They will instead end up as a dict in the DataFrame or
+DataArray |
+
src/echosms/scattermodelbase.pycalculate_ts(data, expand=False, inplace=False, multiprocess=False)
+
+Calculate the target strength (TS) for many parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
data |
+
+ Pandas DataFrame, Xarray DataArray or dict
+ |
+
+
+
+ Requirements for the different input data types are: +
|
+ + required + | +
multiprocess |
+
+ bool
+ |
+
+
+
+ Split the ts calculation across CPU cores. Multiprocessing is currently provided by
+mapply with little customisation. For more
+sophisticated uses it may be preferred to use a multiprocessing package of your choice
+directly on the |
+
+ False
+ |
+
expand |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
inplace |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ None, list[float], Series, or DataFrame
+ |
+
+
+
+ The return type and value are determined by the type of the input variable (
|
+
src/echosms/scattermodelbase.py60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 | |
+ Bases: ScatterModelBase
Modal series deformed cylinder model (DCM).
+This class contains methods to calculate acoustic scatter from finite straight cylinders with +various boundary conditions.
+ +src/echosms/dcmmodel.pycalculate_ts(data, expand=False, inplace=False, multiprocess=False)
+
+Calculate the target strength (TS) for many parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
data |
+
+ Pandas DataFrame, Xarray DataArray or dict
+ |
+
+
+
+ Requirements for the different input data types are: +
|
+ + required + | +
multiprocess |
+
+ bool
+ |
+
+
+
+ Split the ts calculation across CPU cores. Multiprocessing is currently provided by
+mapply with little customisation. For more
+sophisticated uses it may be preferred to use a multiprocessing package of your choice
+directly on the |
+
+ False
+ |
+
expand |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
inplace |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ None, list[float], Series, or DataFrame
+ |
+
+
+
+ The return type and value are determined by the type of the input variable (
|
+
src/echosms/scattermodelbase.py60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 | |
calculate_ts_single(medium_c, medium_rho, a, b, theta, f, boundary_type, target_c=None, target_rho=None, **kwargs)
+
+Calculate the scatter from a finite cylinder using the modal series deformed cylinder model.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
medium_c |
+
+ float
+ |
+
+
+
+ Sound speed in the fluid medium surrounding the target [m/s]. + |
+ + required + | +
medium_rho |
+
+ float
+ |
+
+
+
+ Density of the fluid medium surrounding the target [kg/m³]. + |
+ + required + | +
a |
+
+ float
+ |
+
+
+
+ Radius of the cylinderical target [m]. + |
+ + required + | +
b |
+
+ float
+ |
+
+
+
+ Length of the cylinderical target [m]. + |
+ + required + | +
theta |
+
+ float
+ |
+
+
+
+ Pitch angle to calculate the scattering at [°]. An angle of 0 is head on, +90 is dorsal, and 180 is tail on. + |
+ + required + | +
f |
+
+ float
+ |
+
+
+
+ Frequency to calculate the scattering at [Hz]. + |
+ + required + | +
boundary_type |
+
+ str
+ |
+
+
+
+ The model type. Supported model types are given in the |
+ + required + | +
target_c |
+
+ float
+ |
+
+
+
+ Sound speed in the fluid inside the sphere [m/s].
+Only required for |
+
+ None
+ |
+
target_rho |
+
+ float
+ |
+
+
+
+ Density of the fluid inside the sphere [kg/m³].
+Only required for |
+
+ None
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The target strength (re 1 m²) of the target [dB]. + |
+
The class implements the code in Section B.1 of Ject et al. (2015).
+Jech, J.M., Horne, J.K., Chu, D., Demer, D.A., Francis, D.T.I., Gorska, N., Jones, B., +Lavery, A.C., Stanton, T.K., Macaulay, G.J., Reeder, D.B., Sawada, K., 2015. +Comparisons among ten models of acoustic backscattering used in aquatic ecosystem +research. Journal of the Acoustical Society of America 138, 3742–3764. +https://doi.org/10.1121/1.4937607
+src/echosms/dcmmodel.py27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 | |
There are several models that use the distorted-wave Born approximation, documented below:
+
+ Bases: ScatterModelBase
Distorted-wave Born approximation scattering model.
+ + +The DWBA model is not yet functional.
+src/echosms/dwbamodel.pycalculate_ts(data, expand=False, inplace=False, multiprocess=False)
+
+Calculate the target strength (TS) for many parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
data |
+
+ Pandas DataFrame, Xarray DataArray or dict
+ |
+
+
+
+ Requirements for the different input data types are: +
|
+ + required + | +
multiprocess |
+
+ bool
+ |
+
+
+
+ Split the ts calculation across CPU cores. Multiprocessing is currently provided by
+mapply with little customisation. For more
+sophisticated uses it may be preferred to use a multiprocessing package of your choice
+directly on the |
+
+ False
+ |
+
expand |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
inplace |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ None, list[float], Series, or DataFrame
+ |
+
+
+
+ The return type and value are determined by the type of the input variable (
|
+
src/echosms/scattermodelbase.py60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 | |
calculate_ts_single(theta, phi, f, target_rho, target_c)
+
+Distorted-wave Born approximation scattering model.
+Implements the distorted-wave Born approximation +model for calculating the acoustic backscatter from weakly scattering bodies.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
theta |
+
+ float
+ |
+
+
+
+ Incident wave pitch angle [°]. + |
+ + required + | +
phi |
+
+ float
+ |
+
+
+
+ Incident wave roll angle [°]. + |
+ + required + | +
f |
+
+ float
+ |
+
+
+
+ Frequency to run the model at [Hz] + |
+ + required + | +
target_rho |
+
+ iterable[float]
+ |
+
+
+
+ Densities of each material. Must have at least the same number of entries as unique
+integers in |
+ + required + | +
target_c |
+
+ iterable[float]
+ |
+
+
+
+ Sound speed of each material. Must have at least the same number of entries as unique
+integers in |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The target strength (re 1 m²) [dB] of the target. + |
+
This class implements the method presented in Chu et al. (1993).
+Chu, D., Foote, K. G., & Stanton, T. K. (1993). Further analysis of target strength +measurements of Antarctic krill at 38 and 120 kHz: Comparison with deformed cylinder +model and inference or orientation distribution. The Journal of the Acoustical Society +of America, 93(5), 2985–2988. https://doi.org/10.1121/1.405818
+src/echosms/dwbamodel.py
+ Bases: ScatterModelBase
Phase-tracking distorted-wave Born approximation scattering model.
+ +src/echosms/ptdwbamodel.pycalculate_ts(data, expand=False, inplace=False, multiprocess=False)
+
+Calculate the target strength (TS) for many parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
data |
+
+ Pandas DataFrame, Xarray DataArray or dict
+ |
+
+
+
+ Requirements for the different input data types are: +
|
+ + required + | +
multiprocess |
+
+ bool
+ |
+
+
+
+ Split the ts calculation across CPU cores. Multiprocessing is currently provided by
+mapply with little customisation. For more
+sophisticated uses it may be preferred to use a multiprocessing package of your choice
+directly on the |
+
+ False
+ |
+
expand |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
inplace |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ None, list[float], Series, or DataFrame
+ |
+
+
+
+ The return type and value are determined by the type of the input variable (
|
+
src/echosms/scattermodelbase.py60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 | |
calculate_ts_single(volume, theta, phi, f, voxel_size, rho, c, **kwargs)
+
+Phase-tracking distorted-wave Born approximation scattering model.
+Implements the phase-tracking distorted-wave Born approximation +model for calculating the acoustic backscatter from weakly scattering bodies.
+ + +Input parameters theta, phi, and the orientation of volume do not currently follow the
+echoSMs coordinate system.
Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
volume |
+
+ Numpy ndarray[int]
+ |
+
+
+
+ The object to be modelled as a 3D volume of voxels. Array contents should be 0
+for the surrounding medium, then increasing by 1 for each additional material
+type (i.e., 1, 2, 3, etc).
|
+ + required + | +
theta |
+
+ float
+ |
+
+
+
+ Incident wave pitch angle [°]. + |
+ + required + | +
phi |
+
+ float
+ |
+
+
+
+ Incident wave roll angle [°]. + |
+ + required + | +
f |
+
+ float
+ |
+
+
+
+ Frequency to run the model at [Hz] + |
+ + required + | +
voxel_size |
+
+ iterable[float]
+ |
+
+
+
+ The size of the voxels in |
+ + required + | +
rho |
+
+ iterable[float]
+ |
+
+
+
+ Densities of each material. Must have at least the same number of entries as unique
+integers in |
+ + required + | +
c |
+
+ iterable[float]
+ |
+
+
+
+ Sound speed of each material. Must have at least the same number of entries as unique
+integers in |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The target strength (re 1 m²) [dB] of the target. + |
+
This class implements the method presented in Jones et. al. (2009). The code is +based closely on the Matlab code in Jones (2006).
+Jones, B. A. (2006). Acoustic scattering of broadband echolocation signals +from prey of Blainville's beaked whales: Modeling and analysis. Master of Science, +Massachusetts Institute of Technology. https://doi.org/10.1575/1912/1283
+Jones, B. A., Lavery, A. C., & Stanton, T. K. (2009). Use of the distorted +wave Born approximation to predict scattering by inhomogeneous objects: +Application to squid. The Journal of the Acoustical Society of America, +125(1), 73-88. https://doi.org/10.1121/1.3021298
+src/echosms/ptdwbamodel.py21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 +150 +151 +152 +153 +154 +155 +156 +157 +158 +159 +160 +161 +162 +163 | |
+ Bases: ScatterModelBase
Stochastic distorted-wave Born approximation scattering model.
+ + +The SDWBA model is not yet functional.
+src/echosms/sdwbamodel.pycalculate_ts(data, expand=False, inplace=False, multiprocess=False)
+
+Calculate the target strength (TS) for many parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
data |
+
+ Pandas DataFrame, Xarray DataArray or dict
+ |
+
+
+
+ Requirements for the different input data types are: +
|
+ + required + | +
multiprocess |
+
+ bool
+ |
+
+
+
+ Split the ts calculation across CPU cores. Multiprocessing is currently provided by
+mapply with little customisation. For more
+sophisticated uses it may be preferred to use a multiprocessing package of your choice
+directly on the |
+
+ False
+ |
+
expand |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
inplace |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ None, list[float], Series, or DataFrame
+ |
+
+
+
+ The return type and value are determined by the type of the input variable (
|
+
src/echosms/scattermodelbase.py60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 | |
calculate_ts_single(theta, phi, f, target_rho, target_c)
+
+Stochastic distorted-wave Born approximation scattering model.
+Implements the stochastic distorted-wave Born approximation +model for calculating the acoustic backscatter from weakly scattering bodies.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
theta |
+
+ float
+ |
+
+
+
+ Incident wave pitch angle [°]. + |
+ + required + | +
phi |
+
+ float
+ |
+
+
+
+ Incident wave roll angle [°]. + |
+ + required + | +
f |
+
+ float
+ |
+
+
+
+ Frequency to run the model at [Hz] + |
+ + required + | +
target_rho |
+
+ iterable[float]
+ |
+
+
+
+ Densities of each material. Must have at least the same number of entries as unique
+integers in |
+ + required + | +
target_c |
+
+ iterable[float]
+ |
+
+
+
+ Sound speed of each material. Must have at least the same number of entries as unique
+integers in |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The target strength (re 1 m²) [dB] of the target. + |
+
This class implements the method presented in Demer & Conti (2003), Demer & Conti (2004), +and Conti & Demer (2006).
+Demer, D. A., & Conti, S. G. (2003). Reconciling theoretical versus empirical target +strengths of krill: Effects of phase variability on the distorted-wave Born approximation. +ICES Journal of Marine Science, 60, 429-434. +https://doi.org/10.1016/S1054-3139(03)00002-X
+Demer, D. A., & Conti, S. G. (2004). Reconciling theoretical versus empirical +target strengths of krill: Effects of phase variability on the distorted-wave Born +approximation. ICES Journal of Marine Science, 61(1), 157-158. +https://doi.org/10.1016/j.icesjms.2003.12.003
+Conti, S. G., & Demer, D. A. (2006). Improved parameterization of the SDWBA for estimating +krill target strength. ICES Journal of Marine Science, 63(5), 928-935. +https://doi.org/10.1016/j.icesjms.2006.02.007
+src/echosms/sdwbamodel.py
+ Bases: ScatterModelBase
Elastic sphere (ES) scattering model.
+This class calculates acoustic backscatter from elastic spheres.
+ +src/echosms/esmodel.pycalculate_ts(data, expand=False, inplace=False, multiprocess=False)
+
+Calculate the target strength (TS) for many parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
data |
+
+ Pandas DataFrame, Xarray DataArray or dict
+ |
+
+
+
+ Requirements for the different input data types are: +
|
+ + required + | +
multiprocess |
+
+ bool
+ |
+
+
+
+ Split the ts calculation across CPU cores. Multiprocessing is currently provided by
+mapply with little customisation. For more
+sophisticated uses it may be preferred to use a multiprocessing package of your choice
+directly on the |
+
+ False
+ |
+
expand |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
inplace |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ None, list[float], Series, or DataFrame
+ |
+
+
+
+ The return type and value are determined by the type of the input variable (
|
+
src/echosms/scattermodelbase.py60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 | |
calculate_ts_single(medium_c, medium_rho, a, f, target_longitudinal_c, target_transverse_c, target_rho, **kwargs)
+
+Calculate the backscatter from an elastic sphere for one set of parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
medium_c |
+
+ float
+ |
+
+
+
+ Sound speed in the fluid medium surrounding the sphere [m/s]. + |
+ + required + | +
medium_rho |
+
+ float
+ |
+
+
+
+ Density of the fluid medium surrounding the sphere [kg/m³]. + |
+ + required + | +
a |
+
+ float
+ |
+
+
+
+ Radius of the sphere [m]. + |
+ + required + | +
f |
+
+ float
+ |
+
+
+
+ Frequency to calculate the scattering at [Hz]. + |
+ + required + | +
target_longitudinal_c |
+
+ float
+ |
+
+
+
+ Longitudinal sound speed in the material inside the sphere [m/s]. + |
+ + required + | +
target_transverse_c |
+
+ float
+ |
+
+
+
+ Transverse sound speed in the material inside the sphere [m/s]. + |
+ + required + | +
target_rho |
+
+ float
+ |
+
+
+
+ Density of the material inside the sphere [kg/m³]. + |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The target strength (re 1 m²) of the sphere [dB]. + |
+
The class implements the code in MacLennan (1981).
+MacLennan, D. N. (1981). The Theory of Solid Spheres as Sonar Calibration Targets. +Scottish Fisheries Research Report Number 22. Department of Agriculture and Fisheries +for Scotland.
+src/echosms/esmodel.py
+ Bases: ScatterModelBase
Modal series solution (MSS) scattering model.
+This class calculates acoustic scatter from spheres and shells with various
+boundary conditions, as listed in the boundary_types class attribute.
src/echosms/mssmodel.pycalculate_ts(data, expand=False, inplace=False, multiprocess=False)
+
+Calculate the target strength (TS) for many parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
data |
+
+ Pandas DataFrame, Xarray DataArray or dict
+ |
+
+
+
+ Requirements for the different input data types are: +
|
+ + required + | +
multiprocess |
+
+ bool
+ |
+
+
+
+ Split the ts calculation across CPU cores. Multiprocessing is currently provided by
+mapply with little customisation. For more
+sophisticated uses it may be preferred to use a multiprocessing package of your choice
+directly on the |
+
+ False
+ |
+
expand |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
inplace |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ None, list[float], Series, or DataFrame
+ |
+
+
+
+ The return type and value are determined by the type of the input variable (
|
+
src/echosms/scattermodelbase.py60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 | |
calculate_ts_single(medium_c, medium_rho, a, theta, f, boundary_type, target_c=None, target_rho=None, shell_c=None, shell_rho=None, shell_thickness=None, **kwargs)
+
+Calculate the scatter using the mss model for one set of parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
medium_c |
+
+ float
+ |
+
+
+
+ Sound speed in the fluid medium surrounding the target [m/s]. + |
+ + required + | +
medium_rho |
+
+ float
+ |
+
+
+
+ Density of the fluid medium surrounding the target [kg/m³]. + |
+ + required + | +
a |
+
+ float
+ |
+
+
+
+ Radius of the spherical target [m]. + |
+ + required + | +
theta |
+
+ float
+ |
+
+
+
+ Pitch angle to calculate the scattering at [°]. An angle of 0 is head on, +90 is dorsal, and 180 is tail on. + |
+ + required + | +
f |
+
+ float
+ |
+
+
+
+ Frequency to calculate the scattering at [Hz]. + |
+ + required + | +
boundary_type |
+
+ str
+ |
+
+
+
+ The boundary type. Supported types are given in the |
+ + required + | +
target_c |
+
+ float
+ |
+
+
+
+ Sound speed in the fluid inside the sphere [m/s].
+Only required for |
+
+ None
+ |
+
target_rho |
+
+ float
+ |
+
+
+
+ Density of the fluid inside the sphere [kg/m³].
+Only required for |
+
+ None
+ |
+
shell_c |
+
+ float
+ |
+
+
+
+ Sound speed in the spherical shell [m/s].
+Only required for |
+
+ None
+ |
+
shell_rho |
+
+ float
+ |
+
+
+
+ Density in the spherical shell [kg/m³].
+Only required for |
+
+ None
+ |
+
shell_thickness |
+
+ float
+ |
+
+
+
+ Thickness of the spherical shell [m]. This value is subtracted from |
+
+ None
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The target strength (re 1 m²) of the target [dB]. + |
+
The class implements the code in Section A.1 of Jech et al. (2015).
+Jech, J.M., Horne, J.K., Chu, D., Demer, D.A., Francis, D.T.I., Gorska, N., +Jones, B., Lavery, A.C., Stanton, T.K., Macaulay, G.J., Reeder, D.B., Sawada, K., 2015. +Comparisons among ten models of acoustic backscattering used in aquatic ecosystem +research. Journal of the Acoustical Society of America 138, 3742–3764. +https://doi.org/10.1121/1.4937607
+src/echosms/mssmodel.py30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 | |
+ Bases: ScatterModelBase
Prolate spheroidal modal series (PSMS) scattering model.
+ +src/echosms/psmsmodel.pycalculate_ts(data, expand=False, inplace=False, multiprocess=False)
+
+Calculate the target strength (TS) for many parameters.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
data |
+
+ Pandas DataFrame, Xarray DataArray or dict
+ |
+
+
+
+ Requirements for the different input data types are: +
|
+ + required + | +
multiprocess |
+
+ bool
+ |
+
+
+
+ Split the ts calculation across CPU cores. Multiprocessing is currently provided by
+mapply with little customisation. For more
+sophisticated uses it may be preferred to use a multiprocessing package of your choice
+directly on the |
+
+ False
+ |
+
expand |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
inplace |
+
+ bool
+ |
+
+
+
+ Only applicable if |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ None, list[float], Series, or DataFrame
+ |
+
+
+
+ The return type and value are determined by the type of the input variable (
|
+
src/echosms/scattermodelbase.py60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 +127 +128 +129 +130 +131 +132 +133 +134 +135 +136 +137 +138 +139 +140 +141 +142 +143 +144 +145 +146 +147 +148 +149 | |
calculate_ts_single(medium_c, medium_rho, a, b, theta, f, boundary_type, target_c=None, target_rho=None)
+
+Prolate spheroid modal series (PSMS) solution model.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
medium_c |
+
+ float
+ |
+
+
+
+ Sound speed in the fluid medium surrounding the target [m/s]. + |
+ + required + | +
medium_rho |
+
+ float
+ |
+
+
+
+ Density of the fluid medium surrounding the target [kg/m³]. + |
+ + required + | +
a |
+
+ float
+ |
+
+
+
+ Prolate spheroid major axis radius [m]. + |
+ + required + | +
b |
+
+ float
+ |
+
+
+
+ Prolate spheroid minor axis radius [m]. + |
+ + required + | +
theta |
+
+ float
+ |
+
+
+
+ Pitch angle to calculate the scattering at [°]. An angle of 0 is head on, +90 is dorsal, and 180 is tail on. + |
+ + required + | +
f |
+
+ float
+ |
+
+
+
+ Frequency to calculate the scattering at [Hz]. + |
+ + required + | +
boundary_type |
+
+ str
+ |
+
+
+
+ The model type. Supported model types are given in the |
+ + required + | +
target_c |
+
+ float
+ |
+
+
+
+ Sound speed in the fluid inside the target [m/s].
+Only required for |
+
+ None
+ |
+
target_rho |
+
+ float
+ |
+
+
+
+ Density of the fluid inside the target [kg/m³].
+Only required for |
+
+ None
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The target strength (re 1 m²) of the target [dB]. + |
+
The backscattered target strength of a pressure release or fluid-filled prolate spheroid +is calculated using the PSMS method of Furusawa (1988) and corrections in +Furusawa et al. (1994).
+Furusawa, M. (1988). "Prolate spheroidal models for predicting general + trends of fish target strength," J. Acoust. Soc. Jpn. 9, 13-24. +Furusawa, M., Miyanohana, Y., Ariji, M., and Sawada, Y. (1994). + “Prediction of krill target strength by liquid prolate spheroid + model,” Fish. Sci., 60, 261–265.
+src/echosms/psmsmodel.py21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74 + 75 + 76 + 77 + 78 + 79 + 80 + 81 + 82 + 83 + 84 + 85 + 86 + 87 + 88 + 89 + 90 + 91 + 92 + 93 + 94 + 95 + 96 + 97 + 98 + 99 +100 +101 +102 +103 +104 +105 +106 +107 +108 +109 +110 +111 +112 +113 +114 +115 +116 +117 +118 +119 +120 +121 +122 +123 +124 +125 +126 | |
Provide access to reference scattering model parameters.
+Reference models are the models and parameters defined in Jech et al. (2015). +The parameters are stored in a TOML-formatted file in the echoSMs repository +and this class provides easy access to the data in that file. Additional reference +models may be defined in the future and added to the TOML file (for example, entries +have been added for all known calibration sphere sizes).
+ + +Attributes:
+| Name | +Type | +Description | +
|---|---|---|
definitions |
+
+ dict
+ |
+
+
+
+ A dict representation of the |
+
Raises:
+| Type | +Description | +
|---|---|
+ TOMLDecodeError
+ |
+
+
+
+ If the |
+
+ KeyError
+ |
+
+
+
+ If the |
+
Jech, J.M., Horne, J.K., Chu, D., Demer, D.A., Francis, D.T.I., Gorska, N., Jones, B., +Lavery, A.C., Stanton, T.K., Macaulay, G.J., Reeder, D.B., Sawada, K., 2015. +Comparisons among ten models of acoustic backscattering used in aquatic ecosystem research. +Journal of the Acoustical Society of America 138, 3742–3764. https://doi.org/10.1121/1.4937607
+src/echosms/referencemodels.pynames()
+
+Names of all model definitions.
+ + +Returns:
+| Type | +Description | +
|---|---|
+ iterable of str
+ |
+
+
+
+ All model names in the |
+
src/echosms/referencemodels.pyparameters(name)
+
+Model parameters for a particular model.
+Model parameters are a subset of the model specification where the metadata items have +been removed.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
name |
+
+ str
+ |
+
+
+
+ The name of a model in the |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ dict
+ |
+
+
+
+ The model parameters for the requested model or an empty set if no model with that name. + |
+
src/echosms/referencemodels.pyspecification(name)
+
+Model definitions for a particular model.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
name |
+
+ str
+ |
+
+
+
+ The name of a model in the |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ dict
+ |
+
+
+
+ The model definitions for the requested model or an empty set if no model +with that name. + |
+
src/echosms/referencemodels.pyConvenient interface to the benchmark dataset.
+This dataset contains the TS results from Jech et al. (2015).
+ + +Attributes:
+| Name | +Type | +Description | +
|---|---|---|
angle_dataset |
+
+ Pandas DataFrame
+ |
+
+
+
+ The angle dataset from the benchmark model runs. + |
+
freq_dataset |
+
+ Pandas DataFrame
+ |
+
+
+
+ The frequency dataset from the benchmark model runs. + |
+
The column names in the source benchmark files have been changed to be the same as those used +in the ReferenceModels model definitions.
+Jech, J.M., Horne, J.K., Chu, D., Demer, D.A., Francis, D.T.I., Gorska, N., Jones, B., +Lavery, A.C., Stanton, T.K., Macaulay, G.J., Reeder, D.B., Sawada, K., 2015. +Comparisons among ten models of acoustic backscattering used in aquatic ecosystem research. +Journal of the Acoustical Society of America 138, 3742-3764. https://doi.org/10.1121/1.4937607
+src/echosms/benchmarkdata.pyMiscellaneous utility functions.
+ + + +Neumann(m)
+
+Neumann number.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
m |
+
+ int
+ |
+
+
+
+ The input integer. + |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ int
+ |
+
+
+
+ The Neumann number. + |
+
as_dataarray(params, no_expand=[])
+
+Convert model parameters from dict form to a Xarray DataArray.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
params |
+
+ dict
+ |
+
+
+
+ The model parameters. + |
+ + required + | +
no_expand |
+
+ list
+ |
+
+
+
+ Key values of the non-expandable model parameters in |
+
+ []
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ DataArray
+ |
+
+
+
+ Returns a multi-dimensional DataArray generated from the Cartesian product of all
+expandable items in the input dict. Non-expandable items are added to the DataArray
+attrs property. Expandable items are those that can be sensibly expanded into
+DataArray coordinates. Not all models have non-expandable items.
+The array is named |
+
src/echosms/utils.pyas_dataframe(params, no_expand=[])
+
+Convert model parameters from dict form to a Pandas DataFrame.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
params |
+
+ dict
+ |
+
+
+
+ The model parameters. + |
+ + required + | +
no_expand |
+
+ list
+ |
+
+
+
+ Key values of the non-expandable model parameters in |
+
+ []
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ DataFrame
+ |
+
+
+
+ Returns a Pandas DataFrame generated from the Cartesian product of all expandable +items in the input dict. DataFrame column names are obtained from the dict keys. +Non-expandable items are added to the DataFrame attrs property. Expandable items are +those that can be sensibly expanded into DataFrame columns. Not all models have +non-expandable items. + |
+
src/echosms/utils.pyh1(n, z, derivative=False)
+
+Spherical Hankel function of the first kind or its' derivative.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
n |
+
+ int
+ |
+
+
+
+ Order (n ≥ 0). + |
+ + required + | +
z |
+
+ float
+ |
+
+
+
+ Argument of the Hankel function. + |
+ + required + | +
derivative |
+ + | +
+
+
+ if True, the value of the derivative (rather than the function itself) is returned. + |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ complex
+ |
+
+
+
+ Value of the spherical Hankel function + |
+
Raises:
+| Type | +Description | +
|---|---|
+ ValueError
+ |
+
+
+
+ For negative n values. + |
+
The value of the Hankel function is calculated from spherical Bessel functions [1].
+The derivative is computed from spherical Hankel functions [2].
+src/echosms/utils.pypro_ang1(m, n, c, eta, norm=False)
+
+Prolate spheroidal angular function of the first kind and derivative.
+Calculates the prolate spheroidal angular function of the first kind and its'
+derivative with respect to eta.
Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
m |
+
+ int
+ |
+
+
+
+ The order parameter (≥ 0) + |
+ + required + | +
n |
+
+ int
+ |
+
+
+
+ The degree parameter (≥ |
+ + required + | +
c |
+
+ float
+ |
+
+
+
+ The size parameter. + |
+ + required + | +
eta |
+
+ float
+ |
+
+
+
+ The angular coordinate, η, where |η| ≤ 1. + |
+ + required + | +
norm |
+ + | +
+
+
+ If |
+
+ False
+ |
+
Returns:
+| Type | +Description | +
|---|---|
+ tuple[float, float]
+ |
+
+
+
+ The value of the prolate spheroidal angular function and its' derivative. + |
+
This method uses the prolate spheroidal wave function code for non complex
+arguments (van Buren & Boisvert, 2002, and van Buren & Boisvert, 2024), available on
+github. This code is in Fortran90
+and was interfaced to Python using numpy.f2py then wrapped with the current method to
+provide a similar calling convention as the Scipy function of the same name.
Van Buren, A. L., & Boisvert, J. E. (2002). Accurate calculation of prolate spheroidal +radial functions of the first kind and their first derivatives. Quarterly of Applied +Mathematics, 60(3), 589-599. https://doi.org/10.1090/qam/1914443
+Van Buren, A. L., & Boisvert, J. E. (2004). Improved Calculation of Prolate Spheroidal +Radial Functions of the Second Kind and Their First Derivatives. Quarterly of Applied +Mathematics, 62(3), 493-507. https://doi.org/10.1090/qam/2086042
+src/echosms/utils.pypro_rad1(m, n, c, xi)
+
+Prolate spheroidal radial function of the first kind and derivative.
+Calculates the prolate spheroidal radial function of the first kind and its'
+derivative with respect to xi.
Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
m |
+
+ int
+ |
+
+
+
+ The order parameter (≥ 0). + |
+ + required + | +
n |
+
+ int
+ |
+
+
+
+ The degree parameter (≥ |
+ + required + | +
c |
+
+ float
+ |
+
+
+
+ The size parameter. + |
+ + required + | +
xi |
+
+ float
+ |
+
+
+
+ The radial coordinate, ξ, where ξ ≥ 1. + |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ tuple[float, float]
+ |
+
+
+
+ The value of the prolate spheroidal radial function and its' derivative. + |
+
This method uses the prolate spheroidal wave function code for non complex
+arguments (van Buren & Boisvert, 2002, and van Buren & Boisvert, 2024), available on
+github. This code is in Fortran90
+and was interfaced to Python using numpy.f2py then wrapped with the current method to
+provide a similar calling convention as the Scipy function of the same name.
Van Buren, A. L., & Boisvert, J. E. (2002). Accurate calculation of prolate spheroidal +radial functions of the first kind and their first derivatives. Quarterly of Applied +Mathematics, 60(3), 589-599. https://doi.org/10.1090/qam/1914443
+Van Buren, A. L., & Boisvert, J. E. (2004). Improved Calculation of Prolate Spheroidal +Radial Functions of the Second Kind and Their First Derivatives. Quarterly of Applied +Mathematics, 62(3), 493-507. https://doi.org/10.1090/qam/2086042
+src/echosms/utils.pypro_rad2(m, n, c, xi)
+
+Prolate spheroidal radial function of the second kind and derivative.
+Calculates the prolate spheroidal radial function of the second kind and its'
+derivative with respect to xi.
Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
m |
+
+ int
+ |
+
+
+
+ The order parameter (≥ 0). + |
+ + required + | +
n |
+
+ int
+ |
+
+
+
+ The degree parameter (≥ |
+ + required + | +
c |
+
+ float
+ |
+
+
+
+ The size parameter. + |
+ + required + | +
xi |
+
+ float
+ |
+
+
+
+ The radial coordinate, ξ, where ξ ≥ 1. + |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ tuple[float, float]
+ |
+
+
+
+ The value of the prolate spheroidal radial function and its' derivative. + |
+
This method uses the prolate spheroidal wave function code for non complex
+arguments (van Buren & Boisvert, 2002, and van Buren & Boisvert, 2024), available on
+github. This code is in Fortran90
+and was interfaced to Python using numpy.f2py then wrapped with the current method to
+provide a similar calling convention as the Scipy function of the same name.
Van Buren, A. L., & Boisvert, J. E. (2002). Accurate calculation of prolate spheroidal +radial functions of the first kind and their first derivatives. Quarterly of Applied +Mathematics, 60(3), 589-599. https://doi.org/10.1090/qam/1914443
+Van Buren, A. L., & Boisvert, J. E. (2004). Improved Calculation of Prolate Spheroidal +Radial Functions of the Second Kind and Their First Derivatives. Quarterly of Applied +Mathematics, 62(3), 493-507. https://doi.org/10.1090/qam/2086042
+src/echosms/utils.py318 +319 +320 +321 +322 +323 +324 +325 +326 +327 +328 +329 +330 +331 +332 +333 +334 +335 +336 +337 +338 +339 +340 +341 +342 +343 +344 +345 +346 +347 +348 +349 +350 +351 +352 +353 +354 +355 +356 +357 +358 +359 +360 +361 +362 +363 +364 +365 +366 +367 +368 +369 +370 +371 +372 +373 +374 +375 +376 +377 +378 +379 +380 | |
spherical_jnpp(n, z)
+
+Second derivative of the spherical Bessel function.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
n |
+
+ int
+ |
+
+
+
+ Order (n ≥ 0) + |
+ + required + | +
z |
+
+ float
+ |
+
+
+
+ Argument of the Bessel function. + |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The second derivative of the spherical Bessel function. + |
+
src/echosms/utils.pysplit_dict(d, s)
+
+Split a dict into two dicts based on a list of keys.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
d |
+
+ dict
+ |
+
+
+
+ Dict to be split. + |
+ + required + | +
s |
+
+ list
+ |
+
+
+
+ List of dict keys to use for splitting |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ tuple(dict, dict)
+ |
+
+
+
+ The |
+
src/echosms/utils.pywavenumber(c, f)
+
+Calculate the acoustic wavenumber.
+ + +Parameters:
+| Name | +Type | +Description | +Default | +
|---|---|---|---|
c |
+
+ float
+ |
+
+
+
+ Sound speed [m/s] + |
+ + required + | +
f |
+
+ float
+ |
+
+
+
+ Frequency [Hz] + |
+ + required + | +
Returns:
+| Type | +Description | +
|---|---|
+ float
+ |
+
+
+
+ The acoustic wavenumber [m⁻¹]. + |
+
src/echosms/utils.py