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/V2 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/V2 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 )/(dataomega2 ((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

esys.downunder.forwardmodels Package¶

Classes¶

Functions¶

Others¶

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