simpeg.regularization.AmplitudeSmoothnessFirstOrder.f_m_deriv#

AmplitudeSmoothnessFirstOrder.f_m_deriv(m)[source]#

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:

$$\begin{array}{r}\frac{\partial {\mathbf{f}}_{\mathbf{m}}}{\partial \mathbf{m}}=\left[\begin{array}{cc}{\mathbf{G}}_{\mathbf{x}}& \mathbf{0}\\ \mathbf{0}& {\mathbf{G}}_{\mathbf{x}}\end{array}\right]\end{array}$$

where ${\mathbf{G}}_{\mathbf{x}}$ 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.