SimPEG.regularization.CrossGradient.__call__#

CrossGradient.__call__(model)[source]#

Computes the sum of all cross-gradient values at all cell centers.

Parameters

  • model (numpy.ndarray) – stacked array of individual models np.c_[model1, model2,…]

  • normalized (bool) – returns value of normalized cross-gradient if True

Return type

float

Returns

the computed value of the cross-gradient term.

..math:

\phi_c(\mathbf{m_1},\mathbf{m_2})
= \lambda \sum_{i=1}^{M} \|\nabla \mathbf{m_1}_i \times \nabla \mathbf{m_2}_i \|^2
= \sum_{i=1}^{M} \|\nabla \mathbf{m_1}_i\|^2 \ast \|\nabla \mathbf{m_2}_i\|^2
    - (\nabla \mathbf{m_1}_i \cdot \nabla \mathbf{m_2}_i )^2
= \|\phi_{cx}\|^2 + \|\phi_{cy}\|^2 + \|\phi_{cz}\|^2

(optional strategy, not used in this script)