simpeg.regularization.AmplitudeSmoothnessFirstOrder.f_m_deriv

AmplitudeSmoothnessFirstOrder.f_m_deriv(m)

Derivative of the regularization kernel function.

For first-order smoothness regularization in the x-direction, the derivative of the regularization kernel function with respect to the model is given by:

\[\begin{split}\frac{\partial \mathbf{f_m}}{\partial \mathbf{m}} = \begin{bmatrix} \mathbf{G_x} & \mathbf{0} \\ \mathbf{0} & \mathbf{G_x} \end{bmatrix}\end{split}\]

where \(\mathbf{G_x}\) is the partial cell gradient operator along x (i.e. the x-derivative).

Parameters:

mnumpy.ndarray

The model.

Returns:

scipy.sparse.csr_matrix

The derivative of the regularization kernel function.