Geophysical inversion using least-squares has been a very successful method for UXO discrimination<br>of magnetics. However, the residuals do not follow a normal distribution, which means<br>that the assumptions underlying the inverse problem are violated. Two consequences of this are (i)<br>model bias and (ii) incorrect estimates of model parameter uncertainties. We have found that the<br>residuals are better modeled by an Ekblom distribution which can be designed to be more tolerant<br>of statistical outliers than the Gaussian.<br>To reformulate the inverse problem we are left with the issue of determining the two parameters<br>that define the Ekblom distribution. We appeal to the concept of self-consistency to resolve<br>these parameters; i.e. the statistical distribution used to determine the model parameters should<br>be the same as the distribution of the residuals. To achieve this aim, we set the problem up as a<br>two parameter inverse problem and use the maximum difference between the cumulative density<br>functions of the Ekblom distribution and the residuals as a misfit measure.<br>For magnetic data collected in Montana, the recovered dipole parameters using the Ekblom<br>distribution could be significantly different than those obtained by least-squares. In one case considered<br>in detail, the 95.4% confidence regions for the different solutions didn’t even overlap.


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