SimPEG.regularization.SmoothnessFirstOrder.deriv2

SmoothnessFirstOrder.deriv2(m, v=None) → csr_matrix

Second derivative

Parameters

• m (numpy.ndarray) – geophysical model

• v (numpy.ndarray) – vector to multiply

Return type

scipy.sparse.csr_matrix

Returns

WtW, or if v is supplied WtW*v (numpy.ndarray)

The regularization is:

\[R(m) = \frac{1}{2}\mathbf{(m-m_\text{ref})^\top W^\top W(m-m_\text{ref})}\]

So the second derivative is straight forward:

\[R(m) = \mathbf{W^\top W}\]