volume | PIER Journals

2009-10-15

A Data-Adaptive Probability-Based Fast ERT Inversion Method

Paolo Mauriello,

Dr. Paolo Mauriello

Department of Science and Technology for Environment and Territory

University of Molise

Italy

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Domenico Patella

Prof. Domenico Patella

Department of Physical Sciences

University Federico II

Italy

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Progress In Electromagnetics Research, Vol. 97, 275-290, 2009

doi:10.2528/PIER09092307

Abstract

An easy and fast Probability-based Electrical Resistivity Tomography Inversion (PERTI) algorithm is proposed. The simplest theory follows from the principles of the probability tomography imaging, previously developed for the ERT method of geophysical prospecting. The new inversion procedure is based on a formula which provides the resistivity at any point of the surveyed volume as a weighted average of the apparent resistivity data. The weights are obtained as the Frechet derivatives of the apparent resistivity function of a homogeneous half-space, where a resistivity perturbation is produced in an arbitrary small cell of the discretised surveyed volume. Some 2D and 3D synthetic examples are presented, for which the results of the PERTI method are compared with the inverted models derived from the application of the commercial inversion softwares ERTLAB by Multi-Phase Technologies and Geostudi Astier, and RES2DINV and RES3DINV by Geotomo Software. The comparison shows that the new approach is generally as efficacious as the previous methods in detecting, distinguishing and shaping the sources of the apparent resistivity anomalies. Less certain appears, however, its ability to approach the true resistivity of the source bodies. Main peculiarities of the new method are: (i) unnecessity of a priori information and hence full and unconstrained data-adaptability; (ii) decrease of computing time, even two orders of magnitude shorter than that required by commercial softwares in complex 3D cases using the same PC; (iii) real-time inversion directly in the field in complex 3D cases using the same PC; (iii) real-timein complex 3D cases using the same PC; (iii) real-timein complex 3D cases using the same PC; (iii) real-time; (iv) total independence from data acquisition techniques and spatial regularity, (v) possibility to be used as an optimum starting model in standard iterative inversion processes in order to speed up convergence.

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Paolo Mauriello, and Domenico Patella, "A Data-Adaptive Probability-Based Fast ERT Inversion Method," Progress In Electromagnetics Research, Vol. 97, 275-290, 2009.
doi:10.2528/PIER09092307

References

1. Patella, D., "Introduction to ground surface self-potential tomography," Geophys. Prosp., Vol. 45, 653-681, 1997.
doi:10.1046/j.1365-2478.1997.430277.x

2. Mauriello, P. and D. Patella, "Resistivity anomaly imaging by probability tomography," Geophys. Prosp., Vol. 47, 411-429, 1999.
doi:10.1046/j.1365-2478.1999.00137.x

3. Mauriello, P. and D. Patella, "Resistivity tensor probability tomography," Progress In Electromagnetics Research B, Vol. 8, 129-146, 2008.
doi:10.2528/PIERB08051604

4. Mauriello, P. and D. Patella, "Geoelectrical anomalies imaged by polar and dipolar probability tomography," Progress In Electromagnetics Research, Vol. 87, 63-88, 2008.
doi:10.2528/PIER08092201

5. Alaia, R., D. Patella, and P. Mauriello, "Application of geoelectrical 3D probability tomography in a test-site of the archaeological park of Pompei (Naples, Italy) ," J. Geophys. Eng., Vol. 5, 67-76, 2008.
doi:10.1088/1742-2132/5/1/007

6. Alaia, R., D. Patella, and P. Mauriello, "Imaging multipole self-potential sources by 3D probability tomography," Progress In Electromagnetics Research B, Vol. 14, 311-339, 2009.
doi:10.2528/PIERB09021614

7. Compare, V., M. Cozzolino, P. Mauriello, and D. Patella, "Three-dimensional resistivity probability tomography at the prehistoric site of Grotta Reali (Molise, Italy) ," Archaeol. Prosp., Vol. 16, 53-63, 2009.
doi:10.1002/arp.347

8. Zhou, B. and S. A. Greenhalgh, "Rapid 2D/3D crosshole resistivity imaging using the analytic sensitivity function," Geophysics, Vol. 67, 755-765, 2002.
doi:10.1190/1.1484518

9. Loke, M. H. and R. D. Barker, "Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method," Geophys. Prosp., Vol. 44, 131-152, 1996.
doi:10.1111/j.1365-2478.1996.tb00142.x

10. Gnedenko, B. V., Kurs Teorii Verojatnostej, Mir, Moscow, 1979.

11. Barker, R. D., "A simple algorithm for electrical imaging of the subsurface," First Break, Vol. 10, 53-62, 1992.