An Algorithm for the Fast and Accurate Three-Dimensional DC Resistivity Inversion

M.Emin CANDANSAYAR^1,2 and Nikos G. PAPADOPOULOS²

¹Ankara University, Department of Geophysical Engineering, 06100, Ankara, TURKEY

² Laboratory of Geophysical-Satellite Remote Sensing & Archaeo-environment, IMS-FORTH Rethymnon, GREECE

Direct Current Resistivity (DCR) method is one of the most useful geophysical methods in archaeological prospection. During the last decade DCR data acquisition systems have been greatly improved and currently thousands of data can be measured relatively fast (e.g. less than an hour) using multi-channel and multi-electrode measurement systems. Furthermore, the development of three-dimensional (3-D) DCR inversion algorithms for processing the apparent resistivity data has rendered the 3-D electrical resistivity tomography (ERT) very popular among geoscientists.

Nowadays in archaeological areas, DCR data are mostly collected along dense parallel lines and are interpreted by using 3-D inversion algorithms. The main issues that are of major concern in DCR method include: a) the choice of the optimum array to effectively investigate buried archaeological remains and b) data processing time when using the 3-D inversion algorithms.

In this study, we suggested two new improvements in 3-D inversion of DCR data set. The first is the calculation of the compressed sensitivity matrix (Papadopoulos et al. 2008) in initial iteration and the subsequent updating of this matrix with Broyden' s method during the latter iterations. The second is the collections of data by using left- and right-sided pole-dipole and dipole-dipole arrays and the jointly inversion of these data sets (Candansayar, 2008) to get more accurate result than any individual use of these arrays.

We showed these improvements with a synthetic data inversion. The synthetic data sets were calculated by using 441 electrodes (21 by 21 in x- and y-direction) for the model shown in Figure 1. The model consisted of two layer. The surface layer resistivity is 75 ohm-m and the basement resistivity is 50 ohm-m. There is also a tumulus like structure having 500 ohm-m resistivity that is buried in the basement. Dipole-Dipole, left- and right-sided pole-dipole arrays data sets were calculated along x-direction that yielded 11088 apparent resistivity data.

Inversion with full sensitivity matrix inversion obtained after 96 minutes CPU time (Figure 2). Inversion result with sparse sensitivity calculation in initial iteration and Broyden's update for the following iterations is obtained after 18 minutes CPU time. Although both inversion results are of comparable accuracy and similar to the original model, our suggestion converges to an inversion model in shorter time compared to conventional inversion approach. We also compared individual inversion of each array data sets with each other and with the joint inversion of all the data sets calculated for the model explained above. We showed that (not presented here) joint inversion of left- and right-side pole-dipole and dipole-dipole arrays data sets gives more accurate results than individual inversion of any of these data sets.

Acknowledgements

This work was supported by the european project "ArchaeoLandscapes - ARCLAND" Europe. (2010-2015) European multiannual project (2010-2015) - European Commission - Directorate General Education and Culture, Programme « Culture » (2007-2013).

References

Candansayar,M.E.,2008. Two-dimensional individual and joint inversion of three- and four-electrode array dc resistivity data. J. Geophys. Eng.,5,290-300.

Papadopoulos, N.G., Tsourlos P., Papazachos C., Tsokas G.N., Sarris A. and Kim J.H., 2011. An algorithm for fast 3D inversion of surface electrical resistivity tomography data: application on imaging buried antiquities. Geophysical Prospecting, 59, 557-575.