# 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 *i*th datum, and
\(A_j\) is the area of the *j*th free parameter. The normalization
by the parameter area decouples the sensitivity from the size of each
parameter. Normalize *S* has units log10(S/m)/m^{2}.

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.