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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:

$S_{j} = \frac{1}{A_{j}} \sum_{i}^{n} | W_{i i} J_{i j} |$

where

J_{i j} = \frac{\partial d_{i}}{\partial m_{j}},

$W_{i i}$ 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.