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 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, thus allowing for fast modifications of the survey plan to better focus the expected targets; (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.
A data-adaptive probability-based fast ERT inversion method
MAURIELLO, Paolo;
2009-01-01
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 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, thus allowing for fast modifications of the survey plan to better focus the expected targets; (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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
