esys.downunder.forwardmodels Package — esys.escript 5.6 documentation

# esys.downunder.forwardmodels Package

## Classes

- `AcousticWaveForm`
- `DcRes`
- `ForwardModel`
- `ForwardModelWithPotential`
- `GravityModel`
- `IsostaticPressure`
- `MT2DModelTEMode`
- `MT2DModelTMMode`
- `MagneticIntensityModel`
- `MagneticModel`
- `SelfDemagnetizationModel`
- `Subsidence`

class `esys.downunder.forwardmodels.` `AcousticWaveForm`(domain, omega, w, data, F, coordinates=None, fixAtBottom=False, tol=1e-10, saveMemory=True, scaleF=True)

  Bases: `esys.downunder.forwardmodels.base.ForwardModel`

  Forward Model for acoustic waveform inversion in the frequency domain. It defines a cost function:

  Math: | `defect = 1/2 integrate( ( w * ( a * u - data ) ) ** 2 )`

  where w are weighting factors, data are the measured data (as a 2-comp vector of real and imaginary part) for real frequency omega, and u is the corresponding result produced by the forward model. u (as a 2-comp vector) is the solution of the complex Helmholtz equation for frequency omega, source F and complex, inverse, squared p-velocity sigma:

  Math: | `-u_{ii} - omega**2 * sigma * u = F`

  It is assumed that the exact scale of source F is unknown and the scaling factor a of F is calculated by minimizing the defect.

  `__init__`(domain, omega, w, data, F, coordinates=None, fixAtBottom=False, tol=1e-10, saveMemory=True, scaleF=True)

    initializes a new forward model with acoustic wave form inversion.

    Parameters: | domain (`Domain`) – domain of the model w (`Scalar`) – weighting factors data (`escript.Data` of shape (2,)) – real and imaginary part of data F (`escript.Data` of shape (2,)) – real and imaginary part of source given at Dirac points, on surface or at volume. coordinates (`ReferenceSystem` or `SpatialCoordinateTransformation`) – defines coordinate system to be used (not supported yet) tol (positive `float`) – tolerance of underlying PDE saveMemory (`bool`) – if true stiffness matrix is deleted after solution of PDE to minimize memory requests. This will require more compute time as the matrix needs to be reallocated. scaleF (`bool`) – if true source F is scaled to minimize defect. fixAtBottom (`bool`) – if true pressure is fixed to zero at the bottom of the domain

  `getArguments`(sigma)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | sigma (`escript.Data` of shape (2,)) – a suggestion for complex 1/V**2
    Returns: | solution, uTar, uTai, uTu
    Return type: | `escript.Data` of shape (2,), 3 x `float`

  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getDefect`(sigma, u, uTar, uTai, uTu)

    Returns the defect value.

    Parameters: | sigma (`escript.Data` of shape (2,)) – a suggestion for complex 1/V**2 u (`escript.Data` of shape (2,)) – a u vector uTar (`float`) – equals `integrate( w * (data[0]*u[0]+data[1]*u[1]))` uTai – equals `integrate( w * (data[1]*u[0]-data[0]*u[1]))` uTu (`float`) – equals `integrate( w * (u,u))`
    Return type: | `float`

  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(sigma, u, uTar, uTai, uTu)

    Returns the gradient of the defect with respect to density.

    Parameters: | sigma (`escript.Data` of shape (2,)) – a suggestion for complex 1/V**2 u (`escript.Data` of shape (2,)) – a u vector uTar (`float`) – equals `integrate( w * (data[0]*u[0]+data[1]*u[1]))` uTai – equals `integrate( w * (data[1]*u[0]-data[0]*u[1]))` uTu (`float`) – equals `integrate( w * (u,u))`

  `getSourceScaling`(u)

    returns the scaling factor s required to rescale source F to minimize defect `|s * u- data|^2`

    Parameters: | u (`escript.Data` of shape (2,)) – value of pressure solution (real and imaginary part)
    Return type: | `complex`

  `getSurvey`(index=None)

    Returns the pair (data, weight)

    If argument index is ignored.

  `rescaleWeights`(scale=1.0, sigma_scale=1.0)

    rescales the weights such that

    Math: | integrate( ( w omega**2 * sigma_scale * data * ((1/L_j)**2)**-1) +1 )/(data*omega**2 * ((1/L_j)**2)**-1) * sigma_scale )=scale
    Parameters: | scale (positive `float`) – scale of data weighting factors sigma_scale (`Scalar`) – scale of 1/vp**2 velocity.

  `setUpPDE`()

    Creates and returns the underlying PDE.

    Return type: | `lpde.LinearPDE`

class `esys.downunder.forwardmodels.` `DcRes`(domain, locator, delphiIn, sampleTags, phiPrimary, sigmaPrimary, w=1.0, coordinates=None, tol=1e-08, saveMemory=True, b=None)

  Bases: `esys.downunder.forwardmodels.base.ForwardModel`

  Forward Model for DC resistivity, with a given source pair. The cost function is defined as:

  Math: | defect = 1/2 (sum_s sum_pq w_pqs * ((phi_sp-phi_sq)-v_pqs)**2

  `__init__`(domain, locator, delphiIn, sampleTags, phiPrimary, sigmaPrimary, w=1.0, coordinates=None, tol=1e-08, saveMemory=True, b=None)

    setup new forward model

    Parameters: | domain – the domain of the model locator – contains locator to the measurement pairs sampleTags (list of tuples) – tags of measurement points from which potential differences will be calculated. phiPrimary (`Scalar`) – primary potential.
    Type: | escript domain
    Type: | `list` of `Locator`
    Param: | delphiIn: this is v_pq, the potential difference for the current source and a set of measurement pairs. A list of measured potential differences is expected. Note this should be the secondary potential only.

  `getArguments`(sigma)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | sigma (`Data` of shape (1,)) – conductivity
    Returns: | phi
    Return type: | `Data` of shape (1,)

  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getDefect`(sigma, phi, loc_phi)

    Returns the defect value.

    Parameters: | sigma (`Data` of shape (1,)) – a suggestion for conductivity phi (`Data` of shape (1,)) – potential field
    Return type: | `float`

  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(sigma, phi, loc_phi)

    Returns the gradient of the defect with respect to density.

    Parameters: | sigma (`Data` of shape (1,)) – a suggestison for conductivity phi (`Data` of shape (1,)) – potential field

  `getPrimaryPotential`()

    returns the primary potential :rtype: `Data`

  `setUpPDE`()

    Return the underlying PDE.

    Return type: | `LinearPDE`

class `esys.downunder.forwardmodels.` `ForwardModel`

  Bases: `object`

  An abstract forward model that can be plugged into a cost function. Subclasses need to implement `getDefect()`, `getGradient()`, and possibly `getArguments()` and ‘getCoordinateTransformation’.

  `__init__`()

    Initialize self. See help(type(self)) for accurate signature.

  `getArguments`(x)
  `getCoordinateTransformation`()
  `getDefect`(x, *args)
  `getGradient`(x, *args)

class `esys.downunder.forwardmodels.` `ForwardModelWithPotential`(domain, w, data, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

  Bases: `esys.downunder.forwardmodels.base.ForwardModel`

  Base class for a forward model using a potential such as magnetic or gravity. It defines a cost function:

  > defect = 1/2 sum_s integrate( ( weight_i[s] * ( r_i - data_i[s] ) )**2 )

  where s runs over the survey, weight_i are weighting factors, data_i are the data, and r_i are the results produced by the forward model. It is assumed that the forward model is produced through postprocessing of the solution of a potential PDE.

  `__init__`(domain, w, data, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

    initializes a new forward model with potential.

    Parameters: | domain (`Domain`) – domain of the model w (`Vector` or list of `Vector`) – data weighting factors data (`Vector` or list of `Vector`) – data coordinates (`ReferenceSystem` or `SpatialCoordinateTransformation`) – defines coordinate system to be used fixPotentialAtBottom (`bool`) – if true potential is fixed to zero at the bottom of the domain in addition to the top. tol (positive `float`) – tolerance of underlying PDE

  `getArguments`(x)
  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getData`()

    Returns the data

    Return type: | `list` of `Data`

  `getDataFunctionSpace`()

    Returns the `FunctionSpace` of the data

    Return type: | `FunctionSpace`

  `getDefect`(x, *args)
  `getDefectGradient`(result)
  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(x, *args)
  `getMisfitWeights`()

    Returns the weights of the misfit function

    Return type: | `list` of `Data`

  `getPDE`()

    Return the underlying PDE.

    Return type: | `LinearPDE`

  `getSurvey`(index=None)

    Returns the pair (data_index, weight_index), where data_i is the data of survey i, weight_i is the weighting factor for survey i. If index is None, all surveys will be returned in a pair of lists.

class `esys.downunder.forwardmodels.` `GravityModel`(domain, w, g, gravity_constant=6.6742e-11, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

  Bases: `esys.downunder.forwardmodels.base.ForwardModelWithPotential`

  Forward Model for gravity inversion as described in the inversion cookbook.

  `__init__`(domain, w, g, gravity_constant=6.6742e-11, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

    Creates a new gravity model on the given domain with one or more surveys (w, g).

    Parameters: | domain (`Domain`) – domain of the model w (`Vector` or list of `Vector`) – data weighting factors g (`Vector` or list of `Vector`) – gravity anomaly data coordinates (ReferenceSystem` or `SpatialCoordinateTransformation`) – defines coordinate system to be used tol (positive `float`) – tolerance of underlying PDE fixPotentialAtBottom (`bool`) – if true potential is fixed to zero at the base of the domain in addition to the top
    Note: | It is advisable to call rescaleWeights() to rescale weights before starting the inversion.

  `getArguments`(rho)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | rho (`Scalar`) – a suggestion for the density distribution
    Returns: | gravity potential and corresponding gravity field.
    Return type: | `Scalar`, `Vector`

  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getData`()

    Returns the data

    Return type: | `list` of `Data`

  `getDataFunctionSpace`()

    Returns the `FunctionSpace` of the data

    Return type: | `FunctionSpace`

  `getDefect`(rho, phi, gravity_force)

    Returns the value of the defect

    Parameters: | rho (`Scalar`) – density distribution phi (`Scalar`) – corresponding potential gravity_force (`Vector`) – gravity force
    Return type: | `float`

  `getDefectGradient`(result)
  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(rho, phi, gravity_force)

    Returns the gradient of the defect with respect to density.

    Parameters: | rho (`Scalar`) – density distribution phi (`Scalar`) – corresponding potential gravity_force (`Vector`) – gravity force
    Return type: | `Scalar`

  `getMisfitWeights`()

    Returns the weights of the misfit function

    Return type: | `list` of `Data`

  `getPDE`()

    Return the underlying PDE.

    Return type: | `LinearPDE`

  `getPotential`(rho)

    Calculates the gravity potential for a given density distribution.

    Parameters: | rho (`Scalar`) – a suggestion for the density distribution
    Returns: | gravity potential
    Return type: | `Scalar`

  `getSurvey`(index=None)

    Returns the pair (data_index, weight_index), where data_i is the data of survey i, weight_i is the weighting factor for survey i. If index is None, all surveys will be returned in a pair of lists.

  `rescaleWeights`(scale=1.0, rho_scale=1.0)

    rescales the weights such that

    sum_s integrate( ( w_i[s] *g_i[s]) (w_j[s]*1/L_j) * L**2 * 4*pi*G*rho_scale )=scale

    Parameters: | scale (positive `float`) – scale of data weighting factors rho_scale (`Scalar`) – scale of density.

class `esys.downunder.forwardmodels.` `IsostaticPressure`(domain, p0=0.0, level0=0, gravity0=-9.81, background_density=2670.0, gravity_constant=6.6742e-11, coordinates=None, tol=1e-08)

  Bases: `object`

  class to calculate isostatic pressure field correction due to gravity forces

  `__init__`(domain, p0=0.0, level0=0, gravity0=-9.81, background_density=2670.0, gravity_constant=6.6742e-11, coordinates=None, tol=1e-08)

    Parameters: | domain (`Domain`) – domain of the model p0 (scalar `Data` or `float`) – pressure at level0 background_density (`float`) – defines background_density in kg/m^3 coordinates (ReferenceSystem` or `SpatialCoordinateTransformation`) – defines coordinate system to be used tol (positive `float`) – tolerance of underlying PDE level0 (`float`) – pressure for z>=`level0` is set to zero. gravity0 (`float`) – vertical background gravity at `level0`

  `getPressure`(g=None, rho=None)

    return the pressure for gravity force anomaly `g` and density anomaly `rho`

    Parameters: | g (`Vector`) – gravity anomaly data rho (`Scalar`) – gravity anomaly data
    Returns: | pressure distribution
    Return type: | `Scalar`

class `esys.downunder.forwardmodels.` `MT2DModelTEMode`(domain, omega, x, Z_XY, eta=None, w0=1.0, mu=1.2566370614359173e-06, sigma0=0.01, airLayerLevel=None, coordinates=None, Ex_top=1, fixAtTop=False, tol=1e-08, saveMemory=False, directSolver=True)

  Bases: `esys.downunder.forwardmodels.magnetotelluric2d.MT2DBase`

  Forward Model for two dimensional MT model in the TE mode for a given frequency omega. It defines a cost function:

  > - defect = 1/2 integrate( sum_s w^s * ( E_x/H_y - Z_XY^s ) ) ** 2 *

  where E_x is the horizontal electric field perpendicular to the YZ-domain, horizontal magnetic field H_y=1/(i*omega*mu) * E_{x,z} with complex unit i and permeability mu. The weighting factor w^s is set to

  > - w^s(X) = w_0^s *

  if length(X-X^s) <= eta and zero otherwise. X^s is the location of impedance measurement Z_XY^s, w_0^s is the level of confidence (eg. 1/measurement error) and eta is level of spatial confidence.

  E_x is given as solution of the PDE

  > - -E_{x,ii} - i omega * mu * sigma * E_x = 0

  where E_x at top and bottom is set to solution for background field. Homogeneous Neuman conditions are assumed elsewhere.

  `__init__`(domain, omega, x, Z_XY, eta=None, w0=1.0, mu=1.2566370614359173e-06, sigma0=0.01, airLayerLevel=None, coordinates=None, Ex_top=1, fixAtTop=False, tol=1e-08, saveMemory=False, directSolver=True)

    initializes a new forward model. See base class for a description of the arguments.

  `getArguments`(sigma)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | sigma (`Data` of shape (2,)) – conductivity
    Returns: | E_x, E_z
    Return type: | `Data` of shape (2,)

  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getDefect`(sigma, Ex, dExdz)

    Returns the defect value.

    Parameters: | sigma (`Data` of shape ()) – a suggestion for conductivity Ex (`Data` of shape (2,)) – electric field dExdz (`Data` of shape (2,)) – vertical derivative of electric field
    Return type: | `float`

  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(sigma, Ex, dExdz)

    Returns the gradient of the defect with respect to density.

    Parameters: | sigma (`Data` of shape ()) – a suggestion for conductivity Ex (`Data` of shape (2,)) – electric field dExdz (`Data` of shape (2,)) – vertical derivative of electric field

  `getWeightingFactor`(x, wx0, x0, eta)

    returns the weighting factor

  `setUpPDE`()

    Return the underlying PDE.

    Return type: | `LinearPDE`

class `esys.downunder.forwardmodels.` `MT2DModelTMMode`(domain, omega, x, Z_YX, eta=None, w0=1.0, mu=1.2566370614359173e-06, sigma0=0.01, airLayerLevel=None, coordinates=None, tol=1e-08, saveMemory=False, directSolver=True)

  Bases: `esys.downunder.forwardmodels.magnetotelluric2d.MT2DBase`

  Forward Model for two-dimensional MT model in the TM mode for a given frequency omega. It defines a cost function:

  > - defect = 1/2 integrate( sum_s w^s * ( rho*H_x/Hy - Z_YX^s ) ) ** 2 *

  where H_x is the horizontal magnetic field perpendicular to the YZ-domain, horizontal magnetic field H_y=1/(i*omega*mu) * E_{x,z} with complex unit i and permeability mu. The weighting factor w^s is set to

  > - w^s(X) = w_0^s *

  if length(X-X^s) <= eta and zero otherwise. X^s is the location of impedance measurement Z_XY^s, w_0^s is the level of confidence (eg. 1/measurement error) and eta is level of spatial confidence.

  H_x is given as solution of the PDE

  > - -(rho*H_{x,i})_{,i} + i omega * mu * H_x = 0

  where H_x at top and bottom is set to solution for background field. Homogeneous Neuman conditions are assumed elsewhere.

  `__init__`(domain, omega, x, Z_YX, eta=None, w0=1.0, mu=1.2566370614359173e-06, sigma0=0.01, airLayerLevel=None, coordinates=None, tol=1e-08, saveMemory=False, directSolver=True)

    initializes a new forward model. See base class for a description of the arguments.

  `getArguments`(rho)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | rho (`Data` of shape (2,)) – resistivity
    Returns: | Hx, grad(Hx)
    Return type: | `tuple` of `Data`

  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getDefect`(rho, Hx, g_Hx)

    Returns the defect value.

    Parameters: | rho (`Data` of shape ()) – a suggestion for resistivity Hx (`Data` of shape (2,)) – magnetic field g_Hx (`Data` of shape (2,2)) – gradient of magnetic field
    Return type: | `float`

  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(rho, Hx, g_Hx)

    Returns the gradient of the defect with respect to resistivity.

    Parameters: | rho (`Data` of shape ()) – a suggestion for resistivity Hx (`Data` of shape (2,)) – magnetic field g_Hx (`Data` of shape (2,2)) – gradient of magnetic field

  `getWeightingFactor`(x, wx0, x0, eta)

    returns the weighting factor

  `setUpPDE`()

    Return the underlying PDE.

    Return type: | `LinearPDE`

class `esys.downunder.forwardmodels.` `MagneticIntensityModel`(domain, w, b, background_magnetic_flux_density, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

  Bases: `esys.downunder.forwardmodels.base.ForwardModelWithPotential`

  Forward Model for magnetic intensity inversion as described in the inversion cookbook.

  `__init__`(domain, w, b, background_magnetic_flux_density, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

    Creates a new magnetic intensity model on the given domain with one or more surveys (w, b).

    Parameters: | domain (`Domain`) – domain of the model w (`Scalar` or list of `Scalar`) – data weighting factors b (`Scalar` or list of `Scalar`) – magnetic intensity field data tol (positive `float`) – tolerance of underlying PDE background_magnetic_flux_density (`Vector` or list of `float`) – background magnetic flux density (in Tesla) with components (B_east, B_north, B_vertical) coordinates (None) – defines coordinate system to be used fixPotentialAtBottom (`bool`) – if true potential is fixed to zero at the bottom of the domain in addition to the top

  `getArguments`(k)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | k (`Scalar`) – susceptibility
    Returns: | scalar magnetic potential and corresponding magnetic field
    Return type: | `Scalar`, `Vector`

  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getData`()

    Returns the data

    Return type: | `list` of `Data`

  `getDataFunctionSpace`()

    Returns the `FunctionSpace` of the data

    Return type: | `FunctionSpace`

  `getDefect`(k, phi, magnetic_flux_density)

    Returns the value of the defect.

    Parameters: | k (`Scalar`) – susceptibility phi (`Scalar`) – corresponding potential magnetic_flux_density (`Vector`) – magnetic field
    Return type: | `float`

  `getDefectGradient`(result)
  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(k, phi, magnetic_flux_density)

    Returns the gradient of the defect with respect to susceptibility.

    Parameters: | k (`Scalar`) – susceptibility phi (`Scalar`) – corresponding potential magnetic_flux_density (`Vector`) – magnetic field
    Return type: | `Scalar`

  `getMisfitWeights`()

    Returns the weights of the misfit function

    Return type: | `list` of `Data`

  `getPDE`()

    Return the underlying PDE.

    Return type: | `LinearPDE`

  `getPotential`(k)

    Calculates the magnetic potential for a given susceptibility.

    Parameters: | k (`Scalar`) – susceptibility
    Returns: | magnetic potential
    Return type: | `Scalar`

  `getSurvey`(index=None)

    Returns the pair (data_index, weight_index), where data_i is the data of survey i, weight_i is the weighting factor for survey i. If index is None, all surveys will be returned in a pair of lists.

  `rescaleWeights`(scale=1.0, k_scale=1.0)

    rescales the weights such that

    sum_s integrate( ( w_i[s] *B_i[s]) (w_j[s]*1/L_j) * L**2 * (background_magnetic_flux_density_j[s]*1/L_j) * k_scale )=scale

    Parameters: | scale (positive `float`) – scale of data weighting factors k_scale (`Scalar`) – scale of susceptibility.

class `esys.downunder.forwardmodels.` `MagneticModel`(domain, w, B, background_magnetic_flux_density, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

  Bases: `esys.downunder.forwardmodels.base.ForwardModelWithPotential`

  Forward Model for magnetic inversion as described in the inversion cookbook.

  `__init__`(domain, w, B, background_magnetic_flux_density, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

    Creates a new magnetic model on the given domain with one or more surveys (w, B).

    Parameters: | domain (`Domain`) – domain of the model w (`Vector` or list of `Vector`) – data weighting factors B (`Vector` or list of `Vector`) – magnetic field data tol (positive `float`) – tolerance of underlying PDE background_magnetic_flux_density (`Vector` or list of `float`) – background magnetic flux density (in Tesla) with components (B_east, B_north, B_vertical) coordinates (`ReferenceSystem` or `SpatialCoordinateTransformation`) – defines coordinate system to be used fixPotentialAtBottom (`bool`) – if true potential is fixed to zero at the bottom of the domain in addition to the top

  `getArguments`(k)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | k (`Scalar`) – susceptibility
    Returns: | scalar magnetic potential and corresponding magnetic field
    Return type: | `Scalar`, `Vector`

  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getData`()

    Returns the data

    Return type: | `list` of `Data`

  `getDataFunctionSpace`()

    Returns the `FunctionSpace` of the data

    Return type: | `FunctionSpace`

  `getDefect`(k, phi, magnetic_flux_density)

    Returns the value of the defect.

    Parameters: | k (`Scalar`) – susceptibility phi (`Scalar`) – corresponding potential magnetic_flux_density (`Vector`) – magnetic field
    Return type: | `float`

  `getDefectGradient`(result)
  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(k, phi, magnetic_flux_density)

    Returns the gradient of the defect with respect to susceptibility.

    Parameters: | k (`Scalar`) – susceptibility phi (`Scalar`) – corresponding potential magnetic_flux_density (`Vector`) – magnetic field
    Return type: | `Scalar`

  `getMisfitWeights`()

    Returns the weights of the misfit function

    Return type: | `list` of `Data`

  `getPDE`()

    Return the underlying PDE.

    Return type: | `LinearPDE`

  `getPotential`(k)

    Calculates the magnetic potential for a given susceptibility.

    Parameters: | k (`Scalar`) – susceptibility
    Returns: | magnetic potential
    Return type: | `Scalar`

  `getSurvey`(index=None)

    Returns the pair (data_index, weight_index), where data_i is the data of survey i, weight_i is the weighting factor for survey i. If index is None, all surveys will be returned in a pair of lists.

  `rescaleWeights`(scale=1.0, k_scale=1.0)

    rescales the weights such that

    sum_s integrate( ( w_i[s] *B_i[s]) (w_j[s]*1/L_j) * L**2 * (background_magnetic_flux_density_j[s]*1/L_j) * k_scale )=scale

    Parameters: | scale (positive `float`) – scale of data weighting factors k_scale (`Scalar`) – scale of susceptibility.

class `esys.downunder.forwardmodels.` `SelfDemagnetizationModel`(domain, w, B, background_magnetic_flux_density, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

  Bases: `esys.downunder.forwardmodels.base.ForwardModelWithPotential`

  Forward Model for magnetic inversion with self-demagnetization as described in the inversion cookbook.

  `__init__`(domain, w, B, background_magnetic_flux_density, coordinates=None, fixPotentialAtBottom=False, tol=1e-08)

    Creates a new magnetic model on the given domain with one or more surveys (w, B).

    Parameters: | domain (`Domain`) – domain of the model w (`Vector` or list of `Vector`) – data weighting factors B (`Vector` or list of `Vector`) – magnetic field data background_magnetic_flux_density (`Vector` or list of `float`) – background magnetic flux density (in Tesla) with components (B_east, B_north, B_vertical) coordinates (`ReferenceSystem` or `SpatialCoordinateTransformation`) – defines coordinate system to be used fixPotentialAtBottom (`bool`) – if true potential is fixed to zero at the bottom of the domain in addition to the top tol (positive `float`) – tolerance of underlying PDE

  `getArguments`(k)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | k (`Scalar`) – susceptibility
    Returns: | scalar magnetic potential and corresponding magnetic field
    Return type: | `Scalar`, `Vector`

  `getCoordinateTransformation`()

    returns the coordinate transformation being used

    Return type: | `CoordinateTransformation`

  `getData`()

    Returns the data

    Return type: | `list` of `Data`

  `getDataFunctionSpace`()

    Returns the `FunctionSpace` of the data

    Return type: | `FunctionSpace`

  `getDefect`(k, phi, grad_phi, magnetic_flux_density)

    Returns the value of the defect.

    Parameters: | k (`Scalar`) – susceptibility phi (`Scalar`) – corresponding potential magnetic_flux_density (`Vector`) – magnetic field
    Return type: | `float`

  `getDefectGradient`(result)
  `getDomain`()

    Returns the domain of the forward model.

    Return type: | `Domain`

  `getGradient`(k, phi, grad_phi, magnetic_flux_density)

    Returns the gradient of the defect with respect to susceptibility.

    Parameters: | k (`Scalar`) – susceptibility phi (`Scalar`) – corresponding potential magnetic_flux_density (`Vector`) – magnetic field
    Return type: | `Scalar`

  `getMisfitWeights`()

    Returns the weights of the misfit function

    Return type: | `list` of `Data`

  `getPDE`()

    Return the underlying PDE.

    Return type: | `LinearPDE`

  `getPotential`(k)

    Calculates the magnetic potential for a given susceptibility.

    Parameters: | k (`Scalar`) – susceptibility
    Returns: | magnetic potential
    Return type: | `Scalar`

  `getSurvey`(index=None)

    Returns the pair (data_index, weight_index), where data_i is the data of survey i, weight_i is the weighting factor for survey i. If index is None, all surveys will be returned in a pair of lists.

  `rescaleWeights`(scale=1.0, k_scale=1.0)

    rescales the weights such that

    sum_s integrate( ( w_i[s] *B_i[s]) (w_j[s]*1/L_j) * L**2 * (background_magnetic_flux_density_j[s]*1/L_j) * k_scale )=scale

    Parameters: | scale (positive `float`) – scale of data weighting factors k_scale (`Scalar`) – scale of susceptibility.

class `esys.downunder.forwardmodels.` `Subsidence`(domain, w, d, lam, mu, coordinates=None, tol=1e-08)

  Bases: `esys.downunder.forwardmodels.base.ForwardModel`

  Forward Model for subsidence inversion minimizing integrate( (inner(w,u)-d)**2) where u is the surface displacement due to a pressure change P

  `__init__`(domain, w, d, lam, mu, coordinates=None, tol=1e-08)

    Creates a new subsidence on the given domain

    Parameters: | domain (`Domain`) – domain of the model w (`Vector` with `FunctionOnBoundary`) – data weighting factors and direction d (`Scalar` with `FunctionOnBoundary`) – displacement measured at surface lam (`Scalar` with `Function`) – 1st Lame coefficient lam – 2st Lame coefficient/Shear modulus coordinates (`ReferenceSystem` or `SpatialCoordinateTransformation`) – defines coordinate system to be used (not supported yet)) tol (positive `float`) – tolerance of underlying PDE

  `getArguments`(P)

    Returns precomputed values shared by `getDefect()` and `getGradient()`.

    Parameters: | P (`Scalar`) – pressure
    Returns: | displacement u
    Return type: | `Vector`

  `getCoordinateTransformation`()
  `getDefect`(P, u)

    Returns the value of the defect.

    Parameters: | P (`Scalar`) – pressure u (`Vector`) – corresponding displacement
    Return type: | `float`

  `getGradient`(P, u)

    Returns the gradient of the defect with respect to susceptibility.

    Parameters: | P (`Scalar`) – pressure u (`Vector`) – corresponding displacement
    Return type: | `Scalar`

  `rescaleWeights`(scale=1.0, P_scale=1.0)

    rescales the weights

    Parameters: | scale (positive `float`) – scale of data weighting factors P_scale (`Scalar`) – scale of pressure increment

## Functions

## Others

## Packages

- esys.downunder.forwardmodels.acoustic Package
  - Classes
  - Functions
  - Others
  - Packages
- esys.downunder.forwardmodels.base Package
  - Classes
  - Functions
  - Others
  - Packages
- esys.downunder.forwardmodels.dcresistivity Package
  - Classes
  - Functions
  - Others
  - Packages
- esys.downunder.forwardmodels.gravity Package
  - Classes
  - Functions
  - Others
  - Packages
- esys.downunder.forwardmodels.magnetic Package
  - Classes
  - Functions
  - Others
  - Packages
- esys.downunder.forwardmodels.magnetotelluric2d Package
  - Classes
  - Functions
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  - Packages
- esys.downunder.forwardmodels.pressure Package
  - Classes
  - Functions
  - Others
  - Packages
- esys.downunder.forwardmodels.subsidence Package
  - Classes
  - Functions
  - Others
  - Packages