Noise and occam's inversion of resistivity tomography data

Abstract

! Synthetic model data are used to show the effects of noise and noise estimates on Occam’s Inversion of crossborehole resistivity data. Resolution of the images decreases with increasing noise. The reconstructions are underdetermined so that at low noise levels the images converge to an asymptotic image not the true geo-electrical section. For a noise estimate of standard deviation 10% below the correct, value the algorithm achieves an adequate data fit but the image becomes irregular. When the estimated standard deviation is twice the correct value, the resolution decreases substantially. A case history of monitoring at an EOR site is used to illustrate problems in comparing images from a site if the noise level changes. Changes in image resolution can be misinterpreted as actual geo-electrical changes. We suggest one solution to this problem is to perform smoothest but non-Occam’s inversion on later data sets using parameters found from the background data set. I