SimPEG.regularization.Smallness

class SimPEG.regularization.Smallness(mesh, **kwargs)

Bases: SimPEG.regularization.base.BaseRegularization

Small regularization - L2 regularization on the difference between a model and a reference model.

$$r(m)=\frac{1}{2}(\mathbf{m}-{\mathbf{m}}_{\mathbf{ref}}{)}^{o}p{\mathbf{V}}^T{\mathbf{W}}^T\mathbf{W}\mathbf{V}(\mathbf{m}-{\mathbf{m}}_{\mathbf{ref}})$$

where $\mathbf{m}$ is the model, ${\mathbf{m}}_{\mathbf{ref}}$ is a reference model, $\mathbf{V}$ are square root of cell volumes and $\mathbf{W}$ is a weighting matrix (default Identity). If fixed or

free weights are provided, then it is diag(np.sqrt(weights))).

Optional Inputs

Parameters

• mesh (discretize.base.BaseMesh) – SimPEG mesh

• shape (int) – number of parameters

• mapping (IdentityMap) – regularization mapping, takes the model from model space to the space you want to regularize in

• reference_model (numpy.ndarray) – reference model

• active_cells (numpy.ndarray) – active cell indices for reducing the size of differential operators in the definition of a regularization mesh

• weights (numpy.ndarray) – cell weights

Methods

f_m(m)	Model residual
f_m_deriv(m)	Derivative of the model residual

Galleries and Tutorials using SimPEG.regularization.Smallness

Method of Equivalent Sources for Removing VRM Responses

Method of Equivalent Sources for Removing VRM Responses