# SimPEG.regularization.Smallness#

class SimPEG.regularization.Smallness(mesh, **kwargs)[source]#

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

$r(m) = \frac{1}{2}(\mathbf{m} - \mathbf{m_ref})^ op \mathbf{V}^T \mathbf{W}^T \mathbf{W} \mathbf{V} (\mathbf{m} - \mathbf{m_{ref}})$

where $$\mathbf{m}$$ is the model, $$\mathbf{m_{ref}}$$ 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

 Model residual 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