Model¶

class casingSimulations.model.BaseCasingParametersMixin(**kwargs)¶

Bases: casingSimulations.base.BaseCasing

Parameters used to set up a casing in a background. This class does not function on its own. It should be mixed in with the background model of your choice

Required Properties:

casing_d (Float): diameter of the casing (m), a float, Default: 0.1
casing_l (Float): length of the casing (m), a float, Default: 1000
casing_t (Float): thickness of the casing (m), a float, Default: 0.01
casing_top (Float): top of the casing (m), a float, Default: 0.0
directory (String): Working directory, a unicode string, Default: .
filename (String): Filename to which the properties are serialized and written to, a unicode string
mur_casing (Float): relative permeability of the casing, a float, Default: 100.0
sigma_casing (Float): conductivity of the casing (S/m), a float, Default: 5500000.0
sigma_inside (Float): conductivity of the fluid inside the casing (S/m), a float, Default: 1.0
version (String): version of the software, a unicode string, Default: 0.0.4

add_mur_casing(mesh, mur)¶: add relative magnetic permeability of the casing to the provided model :param discretize.BaseMesh mesh: a discretize mesh :param numpy.ndarray mur: relative magnetic permittivity model to modify :rtype: numpy.ndarray :return: relative magnetic permeability model with casing

add_sigma_casing(mesh, sigma)¶: add the conductivity of the casing to the provided conductivity model :param discretize.BaseMesh mesh: a discretize mesh :param numpy.ndarray sigma: electrical conductivity model to modify :rtype: numpy.ndarray :return: electrical conductivity model with casing

casing_a¶

Inner casing radius

Return type:	float

casing_b¶

Outer casing radius

Return type:	float

casing_d¶: casing_d (Float): diameter of the casing (m), a float, Default: 0.1

casing_l¶: casing_l (Float): length of the casing (m), a float, Default: 1000

casing_r¶

Casing radius

Return type:	float

casing_t¶: casing_t (Float): thickness of the casing (m), a float, Default: 0.01

casing_top¶: casing_top (Float): top of the casing (m), a float, Default: 0.0

casing_z¶

z-extent of the casing

Return type:	numpy.array

ind_casing(mesh)¶

indices of the cell centers of the casing

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

ind_inside(mesh)¶

indices of the cell centers of the inside portion of the casing

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

indx_casing(mesh)¶

x-indices of the casing

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

indx_inside(mesh)¶

x indicies of the inside of the casing

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

indz_casing(mesh)¶

z-indices of the casing

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

info_casing¶

mur_casing¶: mur_casing (Float): relative permeability of the casing, a float, Default: 100.0

sigma_casing¶: sigma_casing (Float): conductivity of the casing (S/m), a float, Default: 5500000.0

sigma_inside¶: sigma_inside (Float): conductivity of the fluid inside the casing (S/m), a float, Default: 1.0

class casingSimulations.model.CasingInHalfspace(filename=None, **kwargs)¶

Bases: casingSimulations.model.Halfspace, casingSimulations.model.BaseCasingParametersMixin

A model of casing in a halfspace

Required Properties:

casing_d (Float): diameter of the casing (m), a float, Default: 0.1
casing_l (Float): length of the casing (m), a float, Default: 1000
casing_t (Float): thickness of the casing (m), a float, Default: 0.01
casing_top (Float): top of the casing (m), a float, Default: 0.0
directory (String): Working directory, a unicode string, Default: .
filename (String): Filename to which the properties are serialized and written to, a unicode string, Default: ModelParameters.json
mur_back (Float): relative permittivity of the background, a float in range [0.0, inf], Default: 1.0
mur_casing (Float): relative permeability of the casing, a float, Default: 100.0
sigma_air (Float): conductivity of the air (S/m), a float, Default: 1e-06
sigma_back (Float): conductivity of the background (S/m), a float in range [0.0, inf], Default: 0.01
sigma_casing (Float): conductivity of the casing (S/m), a float, Default: 5500000.0
sigma_inside (Float): conductivity of the fluid inside the casing (S/m), a float, Default: 1.0
src_a (Array): down-hole z-location for the source, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 0. 0. -975.]
src_b (Array): B electrode location, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 1000. 0. 0.]
surface_z (Float): elevation of the air-earth interface (m), a float, Default: 0
version (String): version of the software, a unicode string, Default: 0.0.4

Optional Properties:

freqs (Array): source frequencies, a list or numpy array of <type ‘float’> with shape (*)
timeSteps (TimeStepArray): times-steps at which to solve, an array or list of tuples specifying the mesh tensor of <type ‘float’> with shape (*)

mur(mesh)¶

put the permeability model on a mesh

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

sigma(mesh)¶

put the conductivity model on a mesh

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

class casingSimulations.model.CasingInSingleLayer(filename=None, **kwargs)¶

Bases: casingSimulations.model.SingleLayer, casingSimulations.model.BaseCasingParametersMixin

A model of casing in an earth that has a single layer

Required Properties:

casing_d (Float): diameter of the casing (m), a float, Default: 0.1
casing_l (Float): length of the casing (m), a float, Default: 1000
casing_t (Float): thickness of the casing (m), a float, Default: 0.01
casing_top (Float): top of the casing (m), a float, Default: 0.0
directory (String): Working directory, a unicode string, Default: .
filename (String): Filename to which the properties are serialized and written to, a unicode string, Default: ModelParameters.json
layer_z (Array): z-limits of the layer, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (2), Default: [-1000. -900.]
mur_back (Float): relative permittivity of the background, a float in range [0.0, inf], Default: 1.0
mur_casing (Float): relative permeability of the casing, a float, Default: 100.0
sigma_air (Float): conductivity of the air (S/m), a float, Default: 1e-06
sigma_back (Float): conductivity of the background (S/m), a float in range [0.0, inf], Default: 0.01
sigma_casing (Float): conductivity of the casing (S/m), a float, Default: 5500000.0
sigma_inside (Float): conductivity of the fluid inside the casing (S/m), a float, Default: 1.0
sigma_layer (Float): conductivity of the layer (S/m), a float, Default: 0.01
src_a (Array): down-hole z-location for the source, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 0. 0. -975.]
src_b (Array): B electrode location, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 1000. 0. 0.]
surface_z (Float): elevation of the air-earth interface (m), a float, Default: 0
version (String): version of the software, a unicode string, Default: 0.0.4

Optional Properties:

freqs (Array): source frequencies, a list or numpy array of <type ‘float’> with shape (*)
timeSteps (TimeStepArray): times-steps at which to solve, an array or list of tuples specifying the mesh tensor of <type ‘float’> with shape (*)

mur(mesh)¶

put the permeability model on a mesh

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

sigma(mesh)¶

put the conductivity model on a mesh

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

class casingSimulations.model.CasingInWholespace(filename=None, **kwargs)¶

Bases: casingSimulations.model.Wholespace, casingSimulations.model.BaseCasingParametersMixin

A model of casing in a wholespace

Required Properties:

casing_d (Float): diameter of the casing (m), a float, Default: 0.1
casing_l (Float): length of the casing (m), a float, Default: 1000
casing_t (Float): thickness of the casing (m), a float, Default: 0.01
casing_top (Float): top of the casing (m), a float, Default: 0.0
directory (String): Working directory, a unicode string, Default: .
filename (String): Filename to which the properties are serialized and written to, a unicode string, Default: ModelParameters.json
mur_back (Float): relative permittivity of the background, a float in range [0.0, inf], Default: 1.0
mur_casing (Float): relative permeability of the casing, a float, Default: 100.0
sigma_back (Float): conductivity of the background (S/m), a float in range [0.0, inf], Default: 0.01
sigma_casing (Float): conductivity of the casing (S/m), a float, Default: 5500000.0
sigma_inside (Float): conductivity of the fluid inside the casing (S/m), a float, Default: 1.0
src_a (Array): down-hole z-location for the source, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 0. 0. -975.]
src_b (Array): B electrode location, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 1000. 0. 0.]
version (String): version of the software, a unicode string, Default: 0.0.4

Optional Properties:

freqs (Array): source frequencies, a list or numpy array of <type ‘float’> with shape (*)
timeSteps (TimeStepArray): times-steps at which to solve, an array or list of tuples specifying the mesh tensor of <type ‘float’> with shape (*)

mur(mesh)¶

put the permeability model on a mesh

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

sigma(mesh)¶

put the conductivity model on a mesh

Parameters:	mesh (discretize.BaseMesh) – a discretize mesh
Return type:	numpy.array

class casingSimulations.model.Halfspace(filename=None, **kwargs)¶

Bases: casingSimulations.model.Wholespace

Model and survey parameters for an electromagnetic survey in a halfspace

Required Properties:

directory (String): Working directory, a unicode string, Default: .
filename (String): Filename to which the properties are serialized and written to, a unicode string, Default: ModelParameters.json
mur_back (Float): relative permittivity of the background, a float in range [0.0, inf], Default: 1.0
sigma_air (Float): conductivity of the air (S/m), a float, Default: 1e-06
sigma_back (Float): conductivity of the background (S/m), a float in range [0.0, inf], Default: 0.01
src_a (Array): down-hole z-location for the source, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 0. 0. -975.]
src_b (Array): B electrode location, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 1000. 0. 0.]
surface_z (Float): elevation of the air-earth interface (m), a float, Default: 0
version (String): version of the software, a unicode string, Default: 0.0.4

Optional Properties:

freqs (Array): source frequencies, a list or numpy array of <type ‘float’> with shape (*)
timeSteps (TimeStepArray): times-steps at which to solve, an array or list of tuples specifying the mesh tensor of <type ‘float’> with shape (*)

ind_air(mesh)¶

indices where the air is

Parameters:	mesh (discretize.BaseMesh) – mesh to find the air cells of
Return type:	bool

info_model¶

sigma(mesh)¶

put the conductivity model on a mesh

Parameters:	mesh (discretize.BaseMesh) – mesh to find air cells of
Return type:	numpy.array

sigma_air¶: sigma_air (Float): conductivity of the air (S/m), a float, Default: 1e-06

surface_z¶: surface_z (Float): elevation of the air-earth interface (m), a float, Default: 0

class casingSimulations.model.PhysicalProperties(meshGenerator, modelParameters)¶

Bases: object

Physical properties on the mesh

model¶

model vector [sigma, mu]

Return type:	numpy.array

mu¶

permeability

Return type:	numpy.array

mur¶

relative permeability

Return type:	numpy.array

plot(ax=None, clim=[None, None], pcolorOpts=None)¶

plot the electrical conductivity and relative permeability

Parameters:	ax (matplotlib.axes) – axis clim (list) – list of numpy arrays: colorbar limits pcolorOpts (dict) – dictionary of pcolor options

plot_mur(ax=None, clim=None, pcolorOpts=None)¶

plot the relative permeability

Parameters:	ax (matplotlib.axes) – axis clim (numpy.array) – colorbar limits pcolorOpts (dict) – dictionary of pcolor options

plot_prop(prop, ax=None, clim=None, pcolorOpts=None, theta_ind=0)¶

Plot a cell centered property

Parameters:	prop (numpy.array) – cell centered property to plot ax (matplotlib.axes) – axis clim (numpy.array) – colorbar limits pcolorOpts (dict) – dictionary of pcolor options

plot_sigma(ax=None, clim=None, pcolorOpts=None)¶

plot the electrical conductivity

Parameters:	ax (matplotlib.axes) – axis clim (numpy.array) – colorbar limits pcolorOpts (dict) – dictionary of pcolor options

sigma¶

electrical conductivity

Return type:	numpy.array

wires¶

wires to hook up maps to sigma, mu

Return type:	SimPEG.Maps.Wires

class casingSimulations.model.SingleLayer(filename=None, **kwargs)¶

Bases: casingSimulations.model.Halfspace

A model consisting of air, subsurface and a single subsurface layer

Required Properties:

directory (String): Working directory, a unicode string, Default: .
filename (String): Filename to which the properties are serialized and written to, a unicode string, Default: ModelParameters.json
layer_z (Array): z-limits of the layer, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (2), Default: [-1000. -900.]
mur_back (Float): relative permittivity of the background, a float in range [0.0, inf], Default: 1.0
sigma_air (Float): conductivity of the air (S/m), a float, Default: 1e-06
sigma_back (Float): conductivity of the background (S/m), a float in range [0.0, inf], Default: 0.01
sigma_layer (Float): conductivity of the layer (S/m), a float, Default: 0.01
src_a (Array): down-hole z-location for the source, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 0. 0. -975.]
src_b (Array): B electrode location, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 1000. 0. 0.]
surface_z (Float): elevation of the air-earth interface (m), a float, Default: 0
version (String): version of the software, a unicode string, Default: 0.0.4

Optional Properties:

freqs (Array): source frequencies, a list or numpy array of <type ‘float’> with shape (*)
timeSteps (TimeStepArray): times-steps at which to solve, an array or list of tuples specifying the mesh tensor of <type ‘float’> with shape (*)

ind_layer(mesh)¶: Indices where the layer is

info_model¶

layer_z¶: layer_z (Array): z-limits of the layer, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (2), Default: [-1000. -900.]

sigma(mesh)¶

Construct the conductivity model on a mesh

Parameters:	mesh (discretize.BaseMesh) – mesh to put conductivity model on

sigma_layer¶: sigma_layer (Float): conductivity of the layer (S/m), a float, Default: 0.01

class casingSimulations.model.SurveyParametersMixin(**kwargs)¶

Bases: properties.base.base.HasProperties

A mixin that has the properties of the survey. It doesn’t do anything on its own

Required Properties:

src_a (Array): down-hole z-location for the source, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 0. 0. -975.]
src_b (Array): B electrode location, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 1000. 0. 0.]

Optional Properties:

freqs (Array): source frequencies, a list or numpy array of <type ‘float’> with shape (*)
timeSteps (TimeStepArray): times-steps at which to solve, an array or list of tuples specifying the mesh tensor of <type ‘float’> with shape (*)

freqs¶: freqs (Array): source frequencies, a list or numpy array of <type ‘float’> with shape (*)

info_survey¶

src_a¶: src_a (Array): down-hole z-location for the source, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 0. 0. -975.]

src_b¶: src_b (Array): B electrode location, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 1000. 0. 0.]

timeSteps¶: timeSteps (TimeStepArray): times-steps at which to solve, an array or list of tuples specifying the mesh tensor of <type ‘float’> with shape (*)

class casingSimulations.model.TimeStepArray(doc, **kwargs)¶

Bases: properties.math.Array

class_info = 'an array or list of tuples specifying the mesh tensor'¶

validate(instance, value)¶

class casingSimulations.model.Wholespace(filename=None, **kwargs)¶

Bases: casingSimulations.model.SurveyParametersMixin, casingSimulations.base.BaseCasing

Model and survey parameters for an electromagnetic survey in a wholespace

Required Properties:

directory (String): Working directory, a unicode string, Default: .
filename (String): Filename to which the properties are serialized and written to, a unicode string, Default: ModelParameters.json
mur_back (Float): relative permittivity of the background, a float in range [0.0, inf], Default: 1.0
sigma_back (Float): conductivity of the background (S/m), a float in range [0.0, inf], Default: 0.01
src_a (Array): down-hole z-location for the source, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 0. 0. -975.]
src_b (Array): B electrode location, a list or numpy array of <type ‘float’>, <type ‘int’> with shape (*), Default: [ 1000. 0. 0.]
version (String): version of the software, a unicode string, Default: 0.0.4

Optional Properties:

freqs (Array): source frequencies, a list or numpy array of <type ‘float’> with shape (*)
timeSteps (TimeStepArray): times-steps at which to solve, an array or list of tuples specifying the mesh tensor of <type ‘float’> with shape (*)

diffusion_distance(t=None, sigma=None, mu=None)¶: Difusion distance

\[\]

filename¶: filename (String): Filename to which the properties are serialized and written to, a unicode string, Default: ModelParameters.json

info¶

info_model¶

mu(mesh)¶: Magnetic permeability on a mesh :param discretize.BaseMesh mesh: a discretize mesh :rtype: numpy.ndarray :return: magnetic permeability on the mesh

mur(mesh)¶: Relative magnetic permeability on a mesh :param discretize.BaseMesh mesh: a discretize mesh :rtype: numpy.ndarray :return: relative magnetic permeability on the mesh

mur_back¶: mur_back (Float): relative permittivity of the background, a float in range [0.0, inf], Default: 1.0

sigma(mesh)¶: Electrical conductivity on a mesh :param discretize.BaseMesh mesh: a discretize mesh :rtype: numpy.ndarray :return: electrical conductivity on the mesh

sigma_back¶: sigma_back (Float): conductivity of the background (S/m), a float in range [0.0, inf], Default: 0.01

skin_depth(sigma=None, mu=None, f=None)¶: Skin depth

\[\delta = \sqrt(\frac{2}{\omega \mu \sigma})\]