Abstract
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.
Similar content being viewed by others
References
Andersen, W. (1973), FORTRAN IV programs for the determination of the transient tangential electric field and vertical magnetic field about a vertical magnetic dipole for an m-layer stratified earth by numerical integration and digital linear filtering, NTIS No. PB-221240.
Anderson, W. L. (1975), Improved digital filters for evaluating Fourier and Hankel transform integrals, NTIS No. PB-242800.
Backus, G. E., andGilbert, J. F. (1968),The Resolving Power of Gross Earth Data, Geophys. J. R. astr. Soc.16, 169–205.
Jupp, D., andVozoff, K. (1975),Stable Iterative Methods for the Inversion of Geophysical Data, Geophys. J. R. astr. Soc.42, 957–975.
Koeford, O.,The Application of the Kernel Function in Interpreting Geoelectric Resistivity Measurements (Gebruder, Borntraeger, Berlin 1968), p. 14.
Koeford, O., Ghosh, D. G., andPolman, G. J. (1972),Computation of the Curves for Electromagnetic Depth Soundings with a Horizontal Transmitting Coil by Means of a Digital Linear Filter, Geophys. Prospect.20, 406–420.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Barakat, R., Stoyer, C.H. The effect of intrinsic model noise upon resistivity inversion. PAGEOPH 119, 841–853 (1980). https://doi.org/10.1007/BF01131261
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01131261