Discrimination And Classification Of Uxo Using Magnetometry: Inversion And Error Analysis Using Robust Statistics
Stephen D. Billings, Leonard R. Pasion and Douglas W. Oldenburg
Event name: 16th EEGS Symposium on the Application of Geophysics to Engineering and Environmental Problems
Session: Unexploded Ordnance
Publication date: 06 April 2003
Info: Extended abstract, PDF ( 243.8Kb )
Geophysical inversion using least-squares has been a very successful method for UXO discrimination
of magnetics. However, the residuals do not follow a normal distribution, which means
that the assumptions underlying the inverse problem are violated. Two consequences of this are (i)
model bias and (ii) incorrect estimates of model parameter uncertainties. We have found that the
residuals are better modeled by an Ekblom distribution which can be designed to be more tolerant
of statistical outliers than the Gaussian.
To reformulate the inverse problem we are left with the issue of determining the two parameters
that define the Ekblom distribution. We appeal to the concept of self-consistency to resolve
these parameters; i.e. the statistical distribution used to determine the model parameters should
be the same as the distribution of the residuals. To achieve this aim, we set the problem up as a
two parameter inverse problem and use the maximum difference between the cumulative density
functions of the Ekblom distribution and the residuals as a misfit measure.
For magnetic data collected in Montana, the recovered dipole parameters using the Ekblom
distribution could be significantly different than those obtained by least-squares. In one case considered
in detail, the 95.4% confidence regions for the different solutions didn’t even overlap.