Natural Source Electromagnetics

SimPEG (Simulation and Parameter Estimation in Geophysics) is a python package for simulation and gradient based parameter estimation in the context of geoscience applications.

Uses SimPEG as the framework for the forward and inverse magnetotellurics geophysical problems.

This package within SimPEG currently includes

  • Magnetotellurics

    • Impedance

    • Tipper

With support to other methods such

  • ZTEM

under development

API

NSEM Simulation

class SimPEG.electromagnetics.natural_source.simulation.BaseNSEMSimulation(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.frequency_domain.simulation.BaseFDEMSimulation

Base class for all Natural source problems.

Required Properties:

  • counter (Counter): A SimPEG.utils.Counter object, an instance of Counter

  • mesh (BaseMesh): a discretize mesh instance, an instance of BaseMesh

  • sensitivity_path (String): path to store the sensitivty, a unicode string, Default: ./sensitivity/

  • None

  • solver_opts (Dictionary): solver options as a kwarg dict, a dictionary

  • survey (Survey): a survey object, an instance of Survey

Optional Properties:

  • model (Model): Inversion model., a numpy array of <class ‘float’>, <class ‘int’> with shape (*, *) or (*)

  • mu (PhysicalProperty): Magnetic Permeability (H/m), a physical property, Default: 1.25663706212e-06

  • muMap (Mapping): Mapping of Magnetic Permeability (H/m) to the inversion model., a SimPEG Map

  • mui (PhysicalProperty): Inverse Magnetic Permeability (m/H), a physical property

  • muiMap (Mapping): Mapping of Inverse Magnetic Permeability (m/H) to the inversion model., a SimPEG Map

  • rho (PhysicalProperty): Electrical resistivity (Ohm m), a physical property

  • rhoMap (Mapping): Mapping of Electrical resistivity (Ohm m) to the inversion model., a SimPEG Map

  • sigma (PhysicalProperty): Electrical conductivity (S/m), a physical property

  • sigmaMap (Mapping): Mapping of Electrical conductivity (S/m) to the inversion model., a SimPEG Map

Other Properties:

  • muDeriv (Derivative): Derivative of Magnetic Permeability (H/m) wrt the model.

  • muiDeriv (Derivative): Derivative of Inverse Magnetic Permeability (m/H) wrt the model.

  • rhoDeriv (Derivative): Derivative of Electrical resistivity (Ohm m) wrt the model.

  • sigmaDeriv (Derivative): Derivative of Electrical conductivity (S/m) wrt the model.

Jvec(m, v, f=None)[source]

Function to calculate the data sensitivities dD/dm times a vector.

Parameters
Return type

numpy.ndarray

Returns

Jv (nData,) Data sensitivities wrt m

Jtvec(m, v, f=None)[source]

Function to calculate the transpose of the data sensitivities (dD/dm)^T times a vector.

Parameters
Return type

numpy.ndarray

Returns

Jtv (nP,) Data sensitivities wrt m

class SimPEG.electromagnetics.natural_source.simulation.Simulation1DPrimarySecondary(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.simulation.BaseNSEMSimulation

A NSEM problem soving a e formulation and primary/secondary fields decomposion.

By eliminating the magnetic flux density using

\[\mathbf{b} = \frac{1}{i \omega}\left(-\mathbf{C} \mathbf{e} \right)\]

we can write Maxwell’s equations as a second order system in \(\mathbf{e}\) only:

\[\left[ \mathbf{C}^{\top} \mathbf{M_{\mu^{-1}}^e } \mathbf{C} + i \omega \mathbf{M_{\sigma}^f} \right] \mathbf{e}_{s} = i \omega \mathbf{M_{\sigma_{s}}^f } \mathbf{e}_{p}\]

which we solve for \(\mathbf{e_s}\). The total field \(\mathbf{e} = \mathbf{e_p} + \mathbf{e_s}\).

The primary field is estimated from a background model (commonly half space ).

Required Properties:

  • counter (Counter): A SimPEG.utils.Counter object, an instance of Counter

  • mesh (BaseMesh): a discretize mesh instance, an instance of BaseMesh

  • sensitivity_path (String): path to store the sensitivty, a unicode string, Default: ./sensitivity/

  • None

  • solver_opts (Dictionary): solver options as a kwarg dict, a dictionary

  • survey (Survey): a survey object, an instance of Survey

Optional Properties:

  • model (Model): Inversion model., a numpy array of <class ‘float’>, <class ‘int’> with shape (*, *) or (*)

  • mu (PhysicalProperty): Magnetic Permeability (H/m), a physical property, Default: 1.25663706212e-06

  • muMap (Mapping): Mapping of Magnetic Permeability (H/m) to the inversion model., a SimPEG Map

  • mui (PhysicalProperty): Inverse Magnetic Permeability (m/H), a physical property

  • muiMap (Mapping): Mapping of Inverse Magnetic Permeability (m/H) to the inversion model., a SimPEG Map

  • rho (PhysicalProperty): Electrical resistivity (Ohm m), a physical property

  • rhoMap (Mapping): Mapping of Electrical resistivity (Ohm m) to the inversion model., a SimPEG Map

  • sigma (PhysicalProperty): Electrical conductivity (S/m), a physical property

  • sigmaMap (Mapping): Mapping of Electrical conductivity (S/m) to the inversion model., a SimPEG Map

Other Properties:

  • muDeriv (Derivative): Derivative of Magnetic Permeability (H/m) wrt the model.

  • muiDeriv (Derivative): Derivative of Inverse Magnetic Permeability (m/H) wrt the model.

  • rhoDeriv (Derivative): Derivative of Electrical resistivity (Ohm m) wrt the model.

  • sigmaDeriv (Derivative): Derivative of Electrical conductivity (S/m) wrt the model.

fieldsPair[source]

alias of SimPEG.electromagnetics.natural_source.fields.Fields1DPrimarySecondary

property MeMui

Edge inner product matrix

property MfSigma

Edge inner product matrix

MfSigmaDeriv(u)[source]

Edge inner product matrix

property sigmaPrimary

A background model, use for the calculation of the primary fields.

getA(freq)[source]

Function to get the A matrix.

Parameters

freq (float) – Frequency

Return type

scipy.sparse.csr_matrix

Returns

A

getADeriv(freq, u, v, adjoint=False)[source]

The derivative of A wrt sigma

getRHS(freq)[source]

Function to return the right hand side for the system.

Parameters

freq (float) – Frequency

Return type

numpy.ndarray

Returns

RHS for 1 polarizations, primary fields (nF, 1)

getRHSDeriv(freq, v, adjoint=False)[source]

The derivative of the RHS wrt sigma

fields(m=None)[source]

Function to calculate all the fields for the model m.

Parameters

m (numpy.ndarray) – Conductivity model (nC,)

Return type

SimPEG.electromagnetics.natural_source.fields.Fields1DPrimarySecondary

Returns

NSEM fields object containing the solution

class SimPEG.electromagnetics.natural_source.simulation.Simulation3DPrimarySecondary(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.simulation.BaseNSEMSimulation

A NSEM problem solving a e formulation and a primary/secondary fields decompostion.

By eliminating the magnetic flux density using

\[\mathbf{b} = \frac{1}{i \omega}\left(-\mathbf{C} \mathbf{e} \right)\]

we can write Maxwell’s equations as a second order system in \(\mathbf{e}\) only:

\[\left[\mathbf{C}^{\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M_{\sigma}^e} \right] \mathbf{e}_{s} = i \omega \mathbf{M_{\sigma_{p}}^e} \mathbf{e}_{p}\]

which we solve for \(\mathbf{e_s}\). The total field \(\mathbf{e} = \mathbf{e_p} + \mathbf{e_s}\).

The primary field is estimated from a background model (commonly as a 1D model).

Required Properties:

  • counter (Counter): A SimPEG.utils.Counter object, an instance of Counter

  • mesh (BaseMesh): a discretize mesh instance, an instance of BaseMesh

  • sensitivity_path (String): path to store the sensitivty, a unicode string, Default: ./sensitivity/

  • None

  • solver_opts (Dictionary): solver options as a kwarg dict, a dictionary

  • survey (Survey): a survey object, an instance of Survey

Optional Properties:

  • model (Model): Inversion model., a numpy array of <class ‘float’>, <class ‘int’> with shape (*, *) or (*)

  • mu (PhysicalProperty): Magnetic Permeability (H/m), a physical property, Default: 1.25663706212e-06

  • muMap (Mapping): Mapping of Magnetic Permeability (H/m) to the inversion model., a SimPEG Map

  • mui (PhysicalProperty): Inverse Magnetic Permeability (m/H), a physical property

  • muiMap (Mapping): Mapping of Inverse Magnetic Permeability (m/H) to the inversion model., a SimPEG Map

  • rho (PhysicalProperty): Electrical resistivity (Ohm m), a physical property

  • rhoMap (Mapping): Mapping of Electrical resistivity (Ohm m) to the inversion model., a SimPEG Map

  • sigma (PhysicalProperty): Electrical conductivity (S/m), a physical property

  • sigmaMap (Mapping): Mapping of Electrical conductivity (S/m) to the inversion model., a SimPEG Map

Other Properties:

  • muDeriv (Derivative): Derivative of Magnetic Permeability (H/m) wrt the model.

  • muiDeriv (Derivative): Derivative of Inverse Magnetic Permeability (m/H) wrt the model.

  • rhoDeriv (Derivative): Derivative of Electrical resistivity (Ohm m) wrt the model.

  • sigmaDeriv (Derivative): Derivative of Electrical conductivity (S/m) wrt the model.

fieldsPair[source]

alias of SimPEG.electromagnetics.natural_source.fields.Fields3DPrimarySecondary

property sigmaPrimary

A background model, use for the calculation of the primary fields.

getA(freq)[source]

Function to get the A system.

Parameters

freq (float) – Frequency

Return type

scipy.sparse.csr_matrix

Returns

A

getADeriv(freq, u, v, adjoint=False)[source]

Calculate the derivative of A wrt m.

Parameters
Return type

numpy.ndarray

Returns

Calculated derivative (nP,) (adjoint=False) and (nU,)[NOTE return as a (nU/2,2) columnwise polarizations] (adjoint=True) for both polarizations

getRHS(freq)[source]

Function to return the right hand side for the system.

Parameters

freq (float) – Frequency

Return type

numpy.ndarray

Returns

RHS for both polarizations, primary fields (nE, 2)

getRHSDeriv(freq, v, adjoint=False)[source]

The derivative of the RHS with respect to the model and the source

Parameters

  • freq (float) – Frequency

  • v (numpy.ndarray) – vector of size (nU,) (adjoint=False) and size (nP,) (adjoint=True)

Return type

numpy.ndarray

Returns

Calculated derivative (nP,) (adjoint=False) and (nU,2) (adjoint=True) for both polarizations

fields(m=None)[source]

Function to calculate all the fields for the model m.

Parameters

(nC,) m (numpy.ndarray) – Conductivity model

Return type

SimPEG.electromagnetics.frequency_domain.fields.FieldsFDEM

Returns

Fields object with of the solution

class SimPEG.electromagnetics.natural_source.simulation.Problem3D_ePrimSec(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.simulation.Simulation3DPrimarySecondary

This class has been deprecated, see Simulation3DPrimarySecondary for documentation

class SimPEG.electromagnetics.natural_source.simulation.Problem1D_ePrimSec(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.simulation.Simulation1DPrimarySecondary

This class has been deprecated, see Simulation1DPrimarySecondary for documentation

NSEM Survey

class SimPEG.electromagnetics.natural_source.survey.Data(*args, **kwargs)[source]

Bases: SimPEG.data.Data, SimPEG.electromagnetics.natural_source.utils.plot_utils.DataNSEMPlotMethods

Data class for NSEMdata. Stores the data vector indexed by the survey.

Required Properties:

  • dobs (Array):

    Vector of the observed data. The data can be set using the survey parameters:

    data = Data(survey)
for src in survey.source_list:
    for rx in src.receiver_list:
        data[src, rx] = datum

    , a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

  • noise_floor (UncertaintyArray):

    Noise floor of the data. This can be set using an array of the same size as the data (e.g. if you want to assign a different noise floor to each datum) or as a scalar if you would like to assign a the same noise floor to all data.

    The standard_deviation is constructed as follows:

    relative_error * np.abs(dobs) + noise_floor

    For example, if you set

    data = Data(survey, dobs=dobs)
data.noise_floor = 1e-10

    then the contribution to the standard_deviation is equal to

    data.noise_floor

    , An array that can be set by a scalar value or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

  • relative_error (UncertaintyArray):

    Relative error of the data. This can be set using an array of the same size as the data (e.g. if you want to assign a different relative error to each datum) or as a scalar if you would like to assign a the same relative error to all data.

    The standard_deviation is constructed as follows:

    relative_error * np.abs(dobs) + noise_floor

    For example, if you set

    data = Data(survey, dobs=dobs)
data.relative_error = 0.05

    then the contribution to the standard_deviation is equal to

    data.relative_error * np.abs(data.dobs)

    , An array that can be set by a scalar value or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

  • survey (BaseSurvey): a SimPEG survey object, an instance of BaseSurvey

toRecArray(returnType='RealImag')[source]

Returns a numpy.recarray for a SimpegNSEM impedance data object.

Parameters

returnType (str, optional) – Switches between returning a rec array where the impedance is split to real and imaginary (‘RealImag’) or is a complex (‘Complex’)

Return type

numpy.recarray

Returns

Record array with data, with indexed columns

classmethod fromRecArray(recArray, srcType='primary')[source]

Class method that reads in a numpy record array to NSEMdata object.

Parameters

  • recArray (numpy.recarray) – Record array with the data. Has to have (‘freq’,’x’,’y’,’z’) columns and some (‘zxx’,’zxy’,’zyx’,’zyy’,’tzx’,’tzy’)

  • srcType (str, optional) – The type of SimPEG.EM.NSEM.SrcNSEM to be used

class SimPEG.electromagnetics.natural_source.sources.Planewave_xy_1DhomotD(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.frequency_domain.sources.BaseFDEMSrc

NSEM source for both polarizations (x and y) for the total Domain.

It calculates fields calculated based on conditions on the boundary of the domain.

Required Properties:

  • frequency (Float): frequency of the source, a float in range [0, inf]

  • integrate (Boolean): integrate the source term?, a boolean, Default: False

  • receiver_list (a list of BaseRx): receiver list, a list (each item is an instance of BaseRx)

Optional Properties:

  • location (SourceLocationArray): Location of the source [x, y, z] in 3D, a 1D array denoting the source location of <class ‘float’>, <class ‘int’> with shape (*)

class SimPEG.electromagnetics.natural_source.sources.Planewave_xy_1Dprimary(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.frequency_domain.sources.BaseFDEMSrc

NSEM planewave source for both polarizations (x and y) estimated from a single 1D primary models.

Required Properties:

  • frequency (Float): frequency of the source, a float in range [0, inf]

  • integrate (Boolean): integrate the source term?, a boolean, Default: False

  • receiver_list (a list of BaseRx): receiver list, a list (each item is an instance of BaseRx)

Optional Properties:

  • location (SourceLocationArray): Location of the source [x, y, z] in 3D, a 1D array denoting the source location of <class ‘float’>, <class ‘int’> with shape (*)

ePrimary(simulation)[source]

Primary electric field

Parameters

simulation (BaseFDEMSimulation) – FDEM simulation

Return type

numpy.ndarray

Returns

primary electric field

bPrimary(simulation)[source]

Primary magnetic flux density

Parameters

simulation (BaseFDEMSimulation) – FDEM simulation

Return type

numpy.ndarray

Returns

primary magnetic flux density

S_e(simulation)[source]

Get the electrical field source

S_eDeriv(simulation, v, adjoint=False)[source]

The derivative of S_e with respect to

S_eDeriv_m(simulation, v, adjoint=False)[source]

Get the derivative of S_e wrt to sigma (m)

class SimPEG.electromagnetics.natural_source.sources.Planewave_xy_3Dprimary(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.frequency_domain.sources.BaseFDEMSrc

NSEM source for both polarizations (x and y) given a 3D primary model. It assigns fields calculated from the 1D model as fields in the full space of the simulation.

Required Properties:

  • frequency (Float): frequency of the source, a float in range [0, inf]

  • integrate (Boolean): integrate the source term?, a boolean, Default: False

  • receiver_list (a list of BaseRx): receiver list, a list (each item is an instance of BaseRx)

Optional Properties:

  • location (SourceLocationArray): Location of the source [x, y, z] in 3D, a 1D array denoting the source location of <class ‘float’>, <class ‘int’> with shape (*)

ePrimary(simulation)[source]

Primary electric field

Parameters

simulation (BaseFDEMSimulation) – FDEM simulation

Return type

numpy.ndarray

Returns

primary electric field

bPrimary(simulation)[source]

Primary magnetic flux density

Parameters

simulation (BaseFDEMSimulation) – FDEM simulation

Return type

numpy.ndarray

Returns

primary magnetic flux density

S_e(simulation)[source]

Get the electrical field source

S_eDeriv_m(simulation, v, adjoint=False)[source]

Get the derivative of S_e wrt to sigma (m)

Module RxNSEM.py

Receivers for the NSEM problem

class SimPEG.electromagnetics.natural_source.receivers.BaseRxNSEM_Point(*args, **kwargs)[source]

Bases: SimPEG.survey.BaseRx

Natural source receiver base class.

Assumes that the data locations are xyz coordinates.

param numpy.ndarray locs

receiver locations (ie. np.r_[x,y,z])

param string orientation

receiver orientation ‘x’, ‘y’ or ‘z’

param string component

real or imaginary component ‘real’ or ‘imag’

Required Properties:

  • component (StringChoice): component of the field (real or imag), either “real” or “imag”

  • locations (RxLocationArray): Locations of the receivers (nRx x nDim), an array of receiver locations of <class ‘float’>, <class ‘int’> with shape (*, *)

  • projGLoc (StringChoice): Projection grid location, default is CC, any of “CC”, “Fx”, “Fy”, “Fz”, “Ex”, “Ey”, “Ez”, “N”, Default: CC

  • storeProjections (Boolean): Store calls to getP (organized by mesh), a boolean, Default: True

property component

component (StringChoice): component of the field (real or imag), either “real” or “imag”

property mesh
property src
property f
property Pex
property Pey
property Pbx
property Pby
property Pbz
eval(src, mesh, f, return_complex=False)[source]

Function to evaluate datum for this receiver

evalDeriv(src, mesh, f, v, adjoint=False)[source]

Function to evaluate datum for this receiver

class SimPEG.electromagnetics.natural_source.receivers.Point1DImpedance(*args, **kwargs)[source]

Bases: SimPEG.survey.BaseRx

Natural source 1D impedance receiver class

param string component

real or imaginary component ‘real’ or ‘imag’

Required Properties:

  • component (StringChoice): component of the field (real or imag), either “real” or “imag”

  • locations (RxLocationArray): Locations of the receivers (nRx x nDim), an array of receiver locations of <class ‘float’>, <class ‘int’> with shape (*, *)

  • projGLoc (StringChoice): Projection grid location, default is CC, any of “CC”, “Fx”, “Fy”, “Fz”, “Ex”, “Ey”, “Ez”, “N”, Default: CC

  • storeProjections (Boolean): Store calls to getP (organized by mesh), a boolean, Default: True

orientation = 'yx'
property component

component (StringChoice): component of the field (real or imag), either “real” or “imag”

property mesh
property src
property f
property Pex
property Pbx
eval(src, mesh, f, return_complex=False)[source]

Project the fields to natural source data.

Parameters
Return type

numpy.ndarray

Returns

Evaluated data for the receiver

evalDeriv(src, mesh, f, v, adjoint=False)[source]

method evalDeriv

The derivative of the projection wrt u

Parameters
Return type

numpy.ndarray

Returns

Calculated derivative (nD,) (adjoint=False) and (nP,2) (adjoint=True) for both polarizations

class SimPEG.electromagnetics.natural_source.receivers.Point3DImpedance(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.receivers.BaseRxNSEM_Point

Natural source 3D impedance receiver class

param numpy.ndarray locs

receiver locations (ie. np.r_[x,y,z])

param string orientation

receiver orientation ‘xx’, ‘xy’, ‘yx’ or ‘yy’

param string component

real or imaginary component ‘real’ or ‘imag’

Required Properties:

  • component (StringChoice): component of the field (real or imag), either “real” or “imag”

  • locations (RxLocationArray): Locations of the receivers (nRx x nDim), an array of receiver locations of <class ‘float’>, <class ‘int’> with shape (*, *)

  • orientation (StringChoice): orientation of the receiver. Must currently be ‘xx’, ‘xy’, ‘yx’, ‘yy’, any of “xx”, “xy”, “yx”, “yy”

  • projGLoc (StringChoice): Projection grid location, default is CC, any of “CC”, “Fx”, “Fy”, “Fz”, “Ex”, “Ey”, “Ez”, “N”, Default: CC

  • storeProjections (Boolean): Store calls to getP (organized by mesh), a boolean, Default: True

property orientation

orientation (StringChoice): orientation of the receiver. Must currently be ‘xx’, ‘xy’, ‘yx’, ‘yy’, any of “xx”, “xy”, “yx”, “yy”

eval(src, mesh, f, return_complex=False)[source]

Project the fields to natural source data.

Parameters
Return type

numpy.ndarray

Returns

component of the impedance evaluation

evalDeriv(src, mesh, f, v, adjoint=False)[source]

The derivative of the projection wrt u

Parameters
Return type

numpy.ndarray

Returns

Calculated derivative (nD,) (adjoint=False) and (nP,2) (adjoint=True) for both polarizations

class SimPEG.electromagnetics.natural_source.receivers.Point3DTipper(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.receivers.BaseRxNSEM_Point

Natural source 3D tipper receiver base class

param numpy.ndarray locs

receiver locations (ie. np.r_[x,y,z])

param string orientation

receiver orientation ‘x’, ‘y’ or ‘z’

param string component

real or imaginary component ‘real’ or ‘imag’

Required Properties:

  • component (StringChoice): component of the field (real or imag), either “real” or “imag”

  • locations (RxLocationArray): Locations of the receivers (nRx x nDim), an array of receiver locations of <class ‘float’>, <class ‘int’> with shape (*, *)

  • orientation (StringChoice): orientation of the receiver. Must currently be ‘zx’, ‘zy’, either “zx” or “zy”

  • projGLoc (StringChoice): Projection grid location, default is CC, any of “CC”, “Fx”, “Fy”, “Fz”, “Ex”, “Ey”, “Ez”, “N”, Default: CC

  • storeProjections (Boolean): Store calls to getP (organized by mesh), a boolean, Default: True

property orientation

orientation (StringChoice): orientation of the receiver. Must currently be ‘zx’, ‘zy’, either “zx” or “zy”

eval(src, mesh, f, return_complex=False)[source]

Project the fields to natural source data.

Parameters
Return type

numpy.ndarray

Returns

Evaluated component of the impedance data

evalDeriv(src, mesh, f, v, adjoint=False)[source]

The derivative of the projection wrt u

Parameters
Return type

numpy.ndarray

Returns

Calculated derivative (nD,) (adjoint=False) and (nP,2) (adjoint=True) for both polarizations

class SimPEG.electromagnetics.natural_source.receivers.Point_impedance1D(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.receivers.Point1DImpedance

This class has been deprecated, see Point1DImpedance for documentation

class SimPEG.electromagnetics.natural_source.receivers.Point_impedance3D(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.receivers.Point3DImpedance

This class has been deprecated, see Point3DImpedance for documentation

class SimPEG.electromagnetics.natural_source.receivers.Point_tipper3D(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.receivers.Point3DTipper

This class has been deprecated, see Point3DTipper for documentation

class SimPEG.electromagnetics.natural_source.Data(*args, **kwargs)[source]

Data class for NSEMdata. Stores the data vector indexed by the survey.

Required Properties:

  • dobs (Array):

    Vector of the observed data. The data can be set using the survey parameters:

    data = Data(survey)
for src in survey.source_list:
    for rx in src.receiver_list:
        data[src, rx] = datum

    , a list or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

  • noise_floor (UncertaintyArray):

    Noise floor of the data. This can be set using an array of the same size as the data (e.g. if you want to assign a different noise floor to each datum) or as a scalar if you would like to assign a the same noise floor to all data.

    The standard_deviation is constructed as follows:

    relative_error * np.abs(dobs) + noise_floor

    For example, if you set

    data = Data(survey, dobs=dobs)
data.noise_floor = 1e-10

    then the contribution to the standard_deviation is equal to

    data.noise_floor

    , An array that can be set by a scalar value or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

  • relative_error (UncertaintyArray):

    Relative error of the data. This can be set using an array of the same size as the data (e.g. if you want to assign a different relative error to each datum) or as a scalar if you would like to assign a the same relative error to all data.

    The standard_deviation is constructed as follows:

    relative_error * np.abs(dobs) + noise_floor

    For example, if you set

    data = Data(survey, dobs=dobs)
data.relative_error = 0.05

    then the contribution to the standard_deviation is equal to

    data.relative_error * np.abs(data.dobs)

    , An array that can be set by a scalar value or numpy array of <class ‘float’>, <class ‘int’> with shape (*)

  • survey (BaseSurvey): a SimPEG survey object, an instance of BaseSurvey

toRecArray(returnType='RealImag')[source]

Returns a numpy.recarray for a SimpegNSEM impedance data object.

Parameters

returnType (str, optional) – Switches between returning a rec array where the impedance is split to real and imaginary (‘RealImag’) or is a complex (‘Complex’)

Return type

numpy.recarray

Returns

Record array with data, with indexed columns

classmethod fromRecArray(recArray, srcType='primary')[source]

Class method that reads in a numpy record array to NSEMdata object.

Parameters

  • recArray (numpy.recarray) – Record array with the data. Has to have (‘freq’,’x’,’y’,’z’) columns and some (‘zxx’,’zxy’,’zyx’,’zyy’,’tzx’,’tzy’)

  • srcType (str, optional) – The type of SimPEG.EM.NSEM.SrcNSEM to be used

NSEM Fields

class SimPEG.electromagnetics.natural_source.fields.Fields1DPrimarySecondary(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.frequency_domain.fields.FieldsFDEM

Fields storage for the 1D NSEM solution.

Solving for e fields, using primary/secondary formulation

Required Properties:

  • simulation (BaseSimulation): a SimPEG simulation, an instance of BaseSimulation

knownFields = {'e_1dSolution': 'F'}
aliasFields = {'b_1d': ['e_1dSolution', 'E', '_b'], 'b_1dPrimary': ['e_1dSolution', 'E', '_bPrimary'], 'b_1dSecondary': ['e_1dSolution', 'E', '_bSecondary'], 'e_1d': ['e_1dSolution', 'F', '_e'], 'e_1dPrimary': ['e_1dSolution', 'F', '_ePrimary'], 'e_1dSecondary': ['e_1dSolution', 'F', '_eSecondary']}
class SimPEG.electromagnetics.natural_source.fields.Fields3DPrimarySecondary(*args, **kwargs)[source]

Bases: SimPEG.fields.Fields

Fields storage for the 3D NSEM solution. Labels polarizations by px and py.

param SimPEG object mesh

The solution mesh

param SimPEG object survey

A survey object

Required Properties:

  • simulation (BaseSimulation): a SimPEG simulation, an instance of BaseSimulation

dtype

alias of builtins.complex

knownFields = {'e_pxSolution': 'E', 'e_pySolution': 'E'}
aliasFields = {'b_px': ['e_pxSolution', 'F', '_b_px'], 'b_pxPrimary': ['e_pxSolution', 'F', '_b_pxPrimary'], 'b_pxSecondary': ['e_pxSolution', 'F', '_b_pxSecondary'], 'b_py': ['e_pySolution', 'F', '_b_py'], 'b_pyPrimary': ['e_pySolution', 'F', '_b_pyPrimary'], 'b_pySecondary': ['e_pySolution', 'F', '_b_pySecondary'], 'e_px': ['e_pxSolution', 'E', '_e_px'], 'e_pxPrimary': ['e_pxSolution', 'E', '_e_pxPrimary'], 'e_pxSecondary': ['e_pxSolution', 'E', '_e_pxSecondary'], 'e_py': ['e_pySolution', 'E', '_e_py'], 'e_pyPrimary': ['e_pySolution', 'E', '_e_pyPrimary'], 'e_pySecondary': ['e_pySolution', 'E', '_e_pySecondary']}
class SimPEG.electromagnetics.natural_source.fields.Fields1D_ePrimSec(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.fields.Fields1DPrimarySecondary

This class has been deprecated, see Fields1DPrimarySecondary for documentation

class SimPEG.electromagnetics.natural_source.fields.Fields3D_ePrimSec(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.fields.Fields3DPrimarySecondary

This class has been deprecated, see Fields3DPrimarySecondary for documentation

NSEM Utilities

SimPEG.electromagnetics.natural_source.utils.analytic_1d.getEHfields(m1d, sigma, freq, zd, scaleUD=True, scaleValue=1)[source]

Analytic solution for MT 1D layered earth. Returns E and H fields.

Parameters

  • object m1d (discretize.base.BaseMesh,) – Mesh object with the 1D spatial information.

  • vector sigma (numpy.ndarray,) – Physical property of conductivity corresponding with the mesh.

  • freq (float,) – Frequency to calculate data at.

  • vector zd (numpy.ndarray,) – location to calculate EH fields at

  • scaleUD (bool,) – scales the output to be scaleValue at the top, increases numerical stability.

Assumes a halfspace with the same conductive as the deepest cell.

SimPEG.electromagnetics.natural_source.utils.analytic_1d.getImpedance(m1d, sigma, freq)[source]

Analytic solution for MT 1D layered earth. Returns the impedance at the surface.

Parameters
SimPEG.electromagnetics.natural_source.utils.data_utils.rotate_data(NSEMdata, rot_angle)[source]
Function that rotates clockwise by rotation angle

(- negative for a counter-clockwise rotation)

Parameters
SimPEG.electromagnetics.natural_source.utils.data_utils.extract_data_info(NSEMdata)[source]

Simple function that extracts data, frequency and receiver type lists.

Useful when assigning uncertainties to data based on frequencies and receiver types.

Parameters

NSEMdata (SimPEG.electromagnetics.natural_source.Data) – NSEM data object to process

SimPEG.electromagnetics.natural_source.utils.data_utils.resample_data(NSEMdata, locs='All', freqs='All', rxs='All', verbose=False)[source]

Function that selects locations from all the receivers in the survey (uses the numerator location as a reference). Also gives the option of selecting frequencies and receiver.

Parameters

  • NSEMdata (SimPEG.electromagnetics.natural_source.Data) – NSEM data object to process

  • locs (numpy.ndarray, optional) – receiver locations to use (default is ‘All’ locations)

  • freqs (numpy.ndarray, optional) – frequencies to use (default is ‘All’ frequencies))

  • rxs (str, optional) – list of receiver sting types to use (default is ‘All’ types). Can be any componation of [‘zxx’,’zxy’,’zyx’,’zyy’,’tzx’,’tzy’]

SimPEG.electromagnetics.natural_source.utils.data_utils.convert3Dto1Dobject(NSEMdata, rxType3D='yx')[source]

Function that converts a 3D NSEMdata of a list of 1D NSEMdata objects for running 1D inversions for.

Parameters
SimPEG.electromagnetics.natural_source.utils.data_utils.appResPhs(freq, z)[source]
SimPEG.electromagnetics.natural_source.utils.data_utils.skindepth(rho, freq)[source]

Function to calculate the skindepth of EM waves

SimPEG.electromagnetics.natural_source.utils.data_utils.rec_to_ndarr(rec_arr, data_type=<class 'float'>)[source]

Function to transform a numpy record array to a nd array.

SimPEG.electromagnetics.natural_source.utils.data_utils.makeAnalyticSolution(mesh, model, elev, freqs)[source]
SimPEG.electromagnetics.natural_source.utils.data_utils.plotMT1DModelData(problem, models, symList=None)[source]
SimPEG.electromagnetics.natural_source.utils.data_utils.plotImpAppRes(dataArrays, plotLoc, textStr=[])[source]

Plots amplitude impedance and phase

SimPEG.electromagnetics.natural_source.utils.data_utils.printTime()[source]

Small function to print the current time

class SimPEG.electromagnetics.natural_source.utils.data_viewer.NSEM_data_viewer(*args, **kwargs)[source]

Bases: properties.base.base.HasProperties

An interactive SimPEG NSEM Data viewer.

Generates a clickble location map of the data, plotting data curves in a separate window.

Parameters

  • data (SimPEG.electromagnetics.natural_source.Data) – Data object, needs to have assigned relative_error and noise_floor

  • data_dict (dict, optional) – A dictionary of other NSEM Data objects

  • backend (str, optional) – Flag to control the backend used in matplotlib

property dict_comp
view()[source]

Excute the viewer and show the matplotlib window

class SimPEG.electromagnetics.natural_source.utils.edi_files_utils.EDIimporter(EDIfilesList, compList=None, outEPSG=None)[source]

Bases: object

A class to import EDIfiles.

filesList = None
comps = None
importFiles()[source]

Function to import EDI files into a object.

SimPEG.electromagnetics.natural_source.utils.plot_data_types.plotIsoFreqNSimpedance(ax, freq, array, flag, par='abs', colorbar=True, colorNorm='SymLog', cLevel=True, contour=True)[source]
SimPEG.electromagnetics.natural_source.utils.plot_data_types.plotIsoFreqNSDiff(ax, freq, arrayList, flag, par='abs', colorbar=True, cLevel=True, mask=None, contourLine=True, useLog=False)[source]
SimPEG.electromagnetics.natural_source.utils.plot_data_types.plotIsoFreqNStipper(ax, freq, array, flag, par='abs', colorbar=True, colorNorm='SymLog', cLevel=True, contour=True)[source]
SimPEG.electromagnetics.natural_source.utils.plot_data_types.plotIsoStaImpedance(ax, loc, array, flag, par='abs', pSym='s', pColor=None, addLabel='', zorder=1)[source]
SimPEG.electromagnetics.natural_source.utils.plot_data_types.plotPsudoSectNSimpedance(ax, sectDict, array, flag, par='abs', colorbar=True, colorNorm='None', cLevel=None, contour=True)[source]
SimPEG.electromagnetics.natural_source.utils.plot_data_types.plotPsudoSectNSDiff(ax, sectDict, arrayList, flag, par='abs', colorbar=True, colorNorm='SymLog', cLevel=None, contour=True, mask=None, useLog=False)[source]
class SimPEG.electromagnetics.natural_source.utils.plot_utils.BaseDataNSEMPlots(*args, **kwargs)[source]

Bases: properties.base.base.HasProperties

A class container of matplotlib panels for plotting NSEM data.

Optional Properties:

  • axes (a list of Axes): List of plot axes, a list (each item is an instance of Axes)

  • fig (Figure): Figure plotting, an instance of Figure

property fig

fig (Figure): Figure plotting, an instance of Figure

property axes

axes (a list of Axes): List of plot axes, a list (each item is an instance of Axes)

setup()[source]

Setup up the plot window.

Should populate the

self.fig and self.axes properties

draw()[source]
clear_axes()[source]

Function to clear all of the axes

class SimPEG.electromagnetics.natural_source.utils.plot_utils.TipperAmplitudeStationPlot(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.utils.plot_utils.BaseDataNSEMPlots

Class for setting up 2 axes figure with:

tipper amplitudes | tipper phase setup.

Optional Properties:

  • axes (a list of Axes): List of plot axes, a list (each item is an instance of Axes)

  • fig (Figure): Figure plotting, an instance of Figure

setup()[source]

Setup a station data plot figure.

draw(data_list, location)[source]

Function to draw on the axes

Parameters

  • data_list – List of NSEM data objects to plot. Has to be of length >= 1. First item is treat as a observed data (Hast to have relative_error and noise_floor) assigned) and the others are plotted on top.

  • location – Location of the station to plot

class SimPEG.electromagnetics.natural_source.utils.plot_utils.ApparentResPhsStationPlot(*args, **kwargs)[source]

Bases: SimPEG.electromagnetics.natural_source.utils.plot_utils.BaseDataNSEMPlots

Class for setting up 4 axes figure with:

apparent resistivity

phase

impedance amplitudes

impedance phase

setup.

Optional Properties:

  • axes (a list of Axes): List of plot axes, a list (each item is an instance of Axes)

  • fig (Figure): Figure plotting, an instance of Figure

setup()[source]

Setup a station data plot figure.

draw(data_list, location)[source]

Function to draw on the axes

Parameters

  • data_list – List of NSEM data objects to plot. Has to be of length >= 1. First item is treat as a observed data (Hast to have relative_error and noise_floor) assigned) and the others are plotted on top.

  • location – Location of the station to plot

class SimPEG.electromagnetics.natural_source.utils.plot_utils.DataNSEMPlotMethods[source]

Bases: object

Class container for properties and methods for plotting of NSEM data.

plot_app_res(location, components=['xy', 'yx'], ax=None, errorbars=False, comp_plot_dict={'xx': {'color': 'green', 'label': 'Imp_xx', 'ls': 'None', 'marker': '_'}, 'xy': {'color': 'blue', 'label': 'Imp_xy', 'ls': 'None', 'marker': '_'}, 'yx': {'color': 'red', 'label': 'Imp_yx', 'ls': 'None', 'marker': '_'}, 'yy': {'color': 'yellow', 'label': 'Imp_yy', 'ls': 'None', 'marker': '_'}, 'zx': {'color': 'brown', 'label': 'Tip_zx', 'ls': 'None', 'marker': '_'}, 'zy': {'color': 'purple', 'label': 'Tip_zy', 'ls': 'None', 'marker': '_'}})[source]

Plot apperent resistivity curves at a given location

Parameters

  • location (axes) – Location of the data point

  • components (list) – List of the components to plot. Default = [‘xy’,’yx’]

  • ax (axes) – The ax object to add the, , Default: None

  • errorbars (bool) – Controls if errorbars are plotted Default = True

  • comp_plot_dict (dict) – Dictionary with additional kwargs for matplotlib.plot

plot_app_phs(location, components=['xy', 'yx'], ax=None, errorbars=False, comp_plot_dict={'xx': {'color': 'green', 'label': 'Imp_xx', 'ls': 'None', 'marker': '_'}, 'xy': {'color': 'blue', 'label': 'Imp_xy', 'ls': 'None', 'marker': '_'}, 'yx': {'color': 'red', 'label': 'Imp_yx', 'ls': 'None', 'marker': '_'}, 'yy': {'color': 'yellow', 'label': 'Imp_yy', 'ls': 'None', 'marker': '_'}, 'zx': {'color': 'brown', 'label': 'Tip_zx', 'ls': 'None', 'marker': '_'}, 'zy': {'color': 'purple', 'label': 'Tip_zy', 'ls': 'None', 'marker': '_'}})[source]

Plot apperent resistivity curves at a given location

Parameters

  • location (axes) – Location of the data point

  • components (list) – List of the components to plot. Default = [‘xy’,’yx’]

  • ax (axes) – The ax object to add the, , Default: None

  • errorbars (bool) – Controls if errorbars are plotted Default = True

  • comp_plot_dict (dict) – Dictionary with additional kwargs for matplotlib.plot settings

plot_imp_amp(location, components=['xy', 'yx'], ax=None, errorbars=False, comp_plot_dict={'xx': {'color': 'green', 'label': 'Imp_xx', 'ls': 'None', 'marker': '_'}, 'xy': {'color': 'blue', 'label': 'Imp_xy', 'ls': 'None', 'marker': '_'}, 'yx': {'color': 'red', 'label': 'Imp_yx', 'ls': 'None', 'marker': '_'}, 'yy': {'color': 'yellow', 'label': 'Imp_yy', 'ls': 'None', 'marker': '_'}, 'zx': {'color': 'brown', 'label': 'Tip_zx', 'ls': 'None', 'marker': '_'}, 'zy': {'color': 'purple', 'label': 'Tip_zy', 'ls': 'None', 'marker': '_'}})[source]

Plot impedance amplitude curves at a given location

Parameters

  • location (axes) – Location of the data point

  • components (list) – List of the components to plot. Default = [‘xy’,’yx’]

  • ax (axes) – The ax object to add the, , Default: None

  • errorbars (bool) – Controls if errorbars are plotted Default = True

  • comp_plot_dict (dict) – Dictionary with additional kwargs for matplotlib.plot

plot_tip_amp(location, components=['zx', 'zy'], ax=None, errorbars=False, comp_plot_dict={'xx': {'color': 'green', 'label': 'Imp_xx', 'ls': 'None', 'marker': '_'}, 'xy': {'color': 'blue', 'label': 'Imp_xy', 'ls': 'None', 'marker': '_'}, 'yx': {'color': 'red', 'label': 'Imp_yx', 'ls': 'None', 'marker': '_'}, 'yy': {'color': 'yellow', 'label': 'Imp_yy', 'ls': 'None', 'marker': '_'}, 'zx': {'color': 'brown', 'label': 'Tip_zx', 'ls': 'None', 'marker': '_'}, 'zy': {'color': 'purple', 'label': 'Tip_zy', 'ls': 'None', 'marker': '_'}})[source]

Plot tipper amplitude curves at a given location

Parameters

  • location (axes) – Location of the data point

  • components (list) – List of the components to plot. Default = [‘xy’,’yx’]

  • ax (axes) – The ax object to add the, , Default: None

  • errorbars (bool) – Controls if errorbars are plotted Default = True

  • comp_plot_dict (dict) – Dictionary with additional kwargs for matplotlib.plot

map_data_locations(ax=None, **plot_kwargs)[source]
Function that plots all receiver locations of the data

(all discreate data locations).

Parameters

ax (axes) – The ax object for mapping to. Default: None

station_component(location, orientation, component, ax=None, **plot_kwargs)[source]
Parameters
station_errorbars(location, orientation, component, ax=None, **plot_kwargs)[source]
Parameters
frequency_map(frequency, orientation, component, ax=None, plot_error=True, **plot_kwargs)[source]

Function to generate a iso-frequency map

Parameters
SimPEG.electromagnetics.natural_source.utils.solutions_1d.get1DEfields(m1d, sigma, freq, sourceAmp=1.0)[source]

Function to get 1D electrical fields

SimPEG.electromagnetics.natural_source.utils.source_utils.homo1DModelSource(mesh, freq, sigma_1d)[source]

Function that calculates and return background fields

Parameters

  • mesh (discretize.base.BaseMesh) – Holds information on the discretization

  • freq (float) – The frequency to solve at

  • sigma_1d (numpy.ndarray) – Background model of conductivity to base the calculations on, 1d model.

Return type

numpy.ndarray

Returns

eBG_bp, E fields for the background model at both polarizations with shape (mesh.nE, 2).

SimPEG.electromagnetics.natural_source.utils.source_utils.analytic1DModelSource(mesh, freq, sigma_1d)[source]

Function that calculates and return background fields

Parameters

  • mesh (discretize.base.BaseMesh) – Holds information on the discretization

  • freq (float) – The frequency to solve at

  • sigma_1d (numpy.ndarray) – Background model of conductivity to base the calculations on, 1d model.

Return type

numpy.ndarray

Returns

eBG_bp, E fields for the background model at both polarizations with shape (mesh.nE, 2).