SimPEG.regularization.LinearCorrespondence

class SimPEG.regularization.LinearCorrespondence(mesh, wire_map, coefficients=None, **kwargs)

Bases: BaseSimilarityMeasure

Linear correspondence regularization for joint inversion with two physical properties.

LinearCorrespondence is used to recover a model where the differences between the model parameter values for two physical property types are minimal. LinearCorrespondence can also be used to minimize the squared L2-norm of a linear combination of model parameters for two physical property types. See the Notes section for a comprehensive description.

Parameters:

meshSimPEG.regularization.RegularizationMesh, discretize.base.BaseMesh

Mesh on which the regularization is discretized. This is not necessarily the same as the mesh on which the simulation is defined.

active_cellsNone, (n_cells, ) numpy.ndarray of bool

Boolean array defining the set of RegularizationMesh cells that are active in the inversion. If None, all cells are active.

wire_mapSimPEG.maps.Wires

Wire map connecting physical properties defined on active cells of the RegularizationMesh` to the entire model.

coefficientsNone, (3) numpy.ndarray of float

Coefficients $\{{\lambda }_1,{\lambda }_2,{\lambda }_3\}$ for the linear relationship between model parameters. If None, the coefficients are set to $\{1,-1,0\}$.

Notes

Let $\mathbf{m}$ be a discrete model consisting of two physical property types such that:

$$\begin{array}{r}\mathbf{m}=\left[\begin{array}{c}{\mathbf{m}}_{\mathbf{1}}\\ {\mathbf{m}}_{\mathbf{2}}\end{array}\right]\end{array}$$

Where $\{{\lambda }_1,{\lambda }_2,{\lambda }_3\}$ define scalar coefficients for a linear combination of vectors ${\mathbf{m}}_{\mathbf{1}}$ and ${\mathbf{m}}_{\mathbf{2}}$, the regularization function (objective function) is given by:

$$\varphi (\mathbf{m})=\frac{1}{2}\Vert {\lambda }_1{\mathbf{m}}_{\mathbf{1}}+{\lambda }_2{\mathbf{m}}_{\mathbf{2}}+{\lambda }_3{\Vert }^2$$

Scalar coefficients $\{{\lambda }_1,{\lambda }_2,{\lambda }_3\}$ are set using the coefficients property. For a true linear correspondence constraint, we set $\{{\lambda }_1,{\lambda }_2,{\lambda }_3\}$ to $\{1,-1,0\}$.

Attributes

coefficients

Coefficients for the linear relationship between model parameters.

Methods

__call__(model)	Evaluate the regularization function for the model provided.
deriv(model)	Gradient of the regularization function evaluated for the model provided.
deriv2(model[, v])	Hessian of the regularization function evaluated for the model provided.
relation(model)	Computes the relation vector for the model provided.