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

Bases: SimPEG.regularization.base.BaseRegularization

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

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

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

  • 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



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