Normalized Sensitivity

In addition to saving a Resistivity File (.resistivity) for each inversion iteration, MARE2DEM will save a <model name>.<iteration #>.sensistivity file that has the normalized data sensitivity computed by summing the Jacobian matrix columnwise over all n data:

\[S_j = \frac{1}{A_j} \sum_i^n | W_{ii} J_{ij} |\]

where

\[J_{ij} = \frac{\partial d_i}{\partial m_j},\]

\(W_{ii}\) is the inverse standard error for the ith datum, and \(A_j\) is the area of the jth free parameter. The normalization by the parameter area decouples the sensitivity from the size of each parameter. Normalize S has units log10(S/m)/m².

The sensitivity can be used as a relative measure of data sensitivity to structure, but be aware this is a linearized approximation for what is a non-linear inverse problem, so sensitivity plots should be taken with a grain of salt.