THE EFFECTS OF NOISE ON OCCAMS INVERSION OF RESISTIVITY TOMOGRAPHY DATA

An Occam's inversion algorithm for crosshole resistivity data that use s a finite-element method forward solution is discussed. For the inver se algorithm? the earth is discretized into a series of parameter bloc ks. each containing one or more elements, The Occam's inversion finds the smoothest 2-D model for which the Chi-squared statistic equals an a priori value. Synthetic model data are used to show the effects of n oise and noise estimates on the resulting 2-D resistivity images. Reso lution of the images decreases with increasing noise. The reconstructi ons are underdetermined so that at low noise levels the images converg e to an asymptotic image, not the true geoelectrical section, If the e stimated standard deviation is too low, the algorithm cannot achieve a n adequate data fit, the resulting image becomes rough, and irregular artifacts start to appear. When the estimated standard deviation is la rger than the correct value, the resolution decreases substantially (t he image is too smooth), The same effects are demonstrated for field d ata from a site near Livermore, California, However, when the correct noise values are known, the Occam's results are independent of the dis cretization used. A case history of monitoring at an enhanced oil reco very site is used to illustrate problems in comparing successive image s over time from a site where the noise level changes. In this case, c hanges in image resolution can be misinterpreted as actual geoelectric al changes. 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.