The effect of intrinsic model noise upon resistivity inversion

Model uncertainty is introduced into direct-current resistivity data by adding random changes to layer thicknesses in a ten-layer model. The resulting information is then aliased by generating a sounding curve which contains less information than the ten resistivities and nine thicknesses. These sounding curves are then inverted via the Backus-Gilbert algorithm using singular value decomposition to obtain solutions in terms of simpler two-or three-layer models. Quantitative results confirm what has been known qualitatively for many years as the principle of equivalence. An interesting result is that the geometric average of a given suite of noisy models is virtually identical to the best-fit model for the average of the noisy curves. The results show that the inversion of resistivity data by nonlinear least-squares parameter fitting is stable in the sense that noise in the data inverts to the same magnitude of noise in the model.