Micro-geofísica de alta resolución: Tomografía eléctrica para muros High-resolution micro-geophysics: electrical tomography for walls

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Proceeding uf the 3 Asamblea Hispano Portuguesa de Geodesia y Geofísica

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Micro-geofísica de alta resolución: Tomografía eléctrica para muros High-resolution micro-geophysics: electrical tomography for walls P.L. Cosentino(1), R. Martorana(2) (1) Dipartimento di Chimica e Fisica della Terra ed Applicazioni alle Georisorse ed ai Rischi Naturali, University of Palermo (Italy), [email protected]; (2) Idem, [email protected]

SUMMARY In this paper we describe a new electrical tomography technique which has been theoretically developed and finally tested in ancient walls and floors. The technique is based on the simultaneous acquisition of a number of potentials (up to 256 channels) and a successive back-projection of the data, using normalized sensitivity coefficients, in order to obtain 3D electrical imaging of the internal structure. A successive filtering technique has been in addition developed to increase the contrast of the images taking as a reference sharp-boundary electrical models. Finally some results are presented which have been obtained on a floor and a wall of the Steri palace, in Palermo.

1. INTRODUCTION The framework of the High-Resolution integrated research project we are developing include the following main problems: − Detection of thin layers (external and internal gypsum and calcium-oxalate patinas, oxidation layers, fractured surfaces, etc.); − Characterization of materials (rocks, concrete, and wood); − Internal constitution of artifacts. Particular challenges which have been partially overcame in this field are: − Detection of layers thinner or much thinner than the wavelength used (1000, 1500 and 1600 MHz antennas) by analysis of both kinematical and dynamic properties of the e.m. signals; − Study and optimization of suitable markers: metal bars and/or “ad hoc” solutions with the property of being selectively adsorbed by layers characterized by different physico-chemical properties; − Characterization of “ad hoc” properties of materials (i.e. concrete, rocks and wood) by means of: - Seismic (sonic and ultrasonic) and GPR (both transmission and reflection): both using kinematical and dynamical analysis; - Self Potential, Resistivity and Polarization; - Microscopy and structural analysis of the samples; - E.M. and electrical tomography using 256-channel resistivity grid. In particular we present here the tomographic electrical approach that has been developed by our research unit.

2. FOREWORDS Tomographic approach, that is a more or less detailed reconstruction of 2D and 3D images obtained by recovering the space behavior of a physical parameter along a set of pixels (2D) or voxels (3D), is increasingly used in Geophysics, especially for shallow targets. The main potential-fields used for tomographic geophysical investigations are electric, magnetic and gravimetric fields. The electric one is generally much more powerful and flexible than the others due to the large possibility of different ways to energize the sample (direction, size and shape of the field sources, etc.): most of them are easy to be applied for most of the samples to be investigated. The inverse problem can sometime be solved by means of a simple “back-projection” of the experimental data, leading to interpretative models sometime very useful as preliminary “images” of the “final” model. The back-projection does not require any a priori interpretative model other than a fragmentation of the sample in a number of elementary 3D or 2½D cells (called

voxels, VOlume piXELS): the only subjective choices are the size of the voxels and the matching of the grid with the sample. The apparent resistivity measurements, even if carried out by means of different electrode arrays, can be used all together in order to obtain the back-projected resistivity voxels of the subsoil. The back-projection methodology (Cosentino et al., 1997; 1998), already tested for the sub-soil, using different electrode arrays, is now optimized for wall structures. Let we describe the wall using a model, which is discretized in a lot of elementary cells. The “anomalous” resistivity of a voxel can modify an experimental resistivity measurement (apparent resistivity) carried out using a general four-electrode array. The influence factors (Cosentino et al., 1997) of all the voxels have been calculated in a discrete set of representative points of a homogeneous thick plate, by means of the formulas given for the influence of the elementary volumes (“sensitivity”, after Roy and Apparao, 1971; Roy, 1972; 1974). 3. MATHEMATICAL OUTLINE In a confined medium having h thickness and ρ1 resistivity (two horizontal layers, the second having infinite resistivity), a d.c. source of I intensity, located at (xC, yC, 0), gives in the point (x, y, z) the following potential: ρ I ⎧⎪ 1 + V1 = 1 ⎨ 1 2 2π ⎪ ( x − x ) + ( y − y )2 + z 2 2 C C ⎩ ∞ kn +∑ + (1) 1 2 2 2 2 n =1 ( x − x ) + ( y − y ) + ( z + 2nh ) C C

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where k = (ρ2 – ρ1)/ (ρ2 + ρ1). Proceeding as in the case of a homogeneous and isotropic halfspace (Roy and Apparao, 1971), the contribution to the above potential measured in the surface in a point P(xP, yP, 0), due to an infinitesimal volume dxdydz centered in the point (x, y, z), with z ≤ h, is given by: ∞ ∞ kn kn ⎤ ρ I ⎪⎧⎡ 1 dVP = 1 2 ⎨⎢ 3 + ∑ 3 + ∑ 3 ⎥⋅ 4π ⎪⎩⎣ A 2 n =1 C1 (n ) 2 n =1 C2 (n ) 2 ⎦ (x − xP )(x − xC ) + ( y − yP )( y − yC ) + (2) 3 B2 ∞ ⎡ z k n ( z + 2nh ) ∞ k n (z − 2nh ) ⎤ z ⎪⎫ + ⎢ 3 +∑ +∑ ⎥ ⋅ 3 ⎬dxdydz 3 3 2 C1 (n ) 2 C2 (n ) 2 ⎦ B 2 ⎪⎭ n =1 n =1 ⎣A

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where 2 2 A = (x − xC ) + ( y − yC ) + z 2

B = ( x − xP ) + ( y − y P ) + z 2 2

2

C1 (n ) = ( x − xC ) + ( y − yC ) + ( z + 2nh ) 2

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C2 (n ) = ( x − xC ) + ( y − yC ) + ( z − 2nh ) We can think of a wall structure as a two-layered horizontal model, in which the first layer (the wall) has thickness h equal to the wall thickness and resistivity ρ1 = ρ, while the resistivity of the second layer is infinite. In this case k = 1, and equation (2) is simplified as follow: ∞ ∞ ρI ⎪⎧⎡ 1 1 1 ⎤ dV P = ⋅ + + ⎢ ⎨ ∑ ∑ 3 3 3 ⎥ 2 2 2 2 4π ⎪⎩⎣⎢ A n =1 C1 (n ) n =1 C 2 (n ) ⎦ ⎥ (3) (x − x P )(x − xC ) + (x − x P )(x − xC ) + 3 B2 ∞ ⎡ z z + 2nh ∞ z − 2nh ⎤ z ⎫⎪ ⋅ 3 ⎬dxdydz + ⎢ 3 +∑ +∑ 3 3 ⎥ 2 2 2 n =1 C1 (n ) n =1 C 2 (n ) ⎦ ⎥ B 2 ⎪⎭ ⎣⎢ A 2

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To find the influence of a voxel, the integral of the function (3) must be extended to the whole volume of the voxel. The result is the sensitivity coefficient of the voxel of the tomographic 3D grid, which represents the model of the subsoil under study. The back-projection of the data (Cosentino et al., 1997; 1998) is carried out, making a convolution, by means of the sensitivity coefficients, in which all the experimental data are re-distributed to each voxel of the tomographic 3D model. A new “filtered” back projection can be subsequently obtained taking as a reference a sharp-boundary model. It is necessary to select a probabilistic correction of the coefficients: most of them are put to zero, when the correlation between the value of the resistivity obtained in the voxel and the selected datum is poor. Then the whole set of coefficients for each voxel is again normalized to make a new convolution process. The final result is a new 3D tomographic matrix in which the resistivity contrasts are increased. The back-projection technique, already tested for different types of electrode arrays, is now optimized for a new electrode arrangement, called resistivity grid (Cosentino et al., 1999; Cosentino, 2000). In this array (fig. 1), the potential electrodes are placed in a grid with regular meshes, while current electrodes are placed symmetrically outside the grid, having dipoles in different directions and of various lengths, in order to “illuminate” the subsoil under different corners and to reach different investigation depths. Potential measures are carried out between each pair of

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Fig. 2 – The MGS 256 (Micro Geoelectric System) produced by GF Instruments (Czech Republic).

The typical measuring configuration consists of a rectangular grid of potential electrodes (max. 16 x 16 rows) situated over the object under study with the generating electrodes placed symmetrically outside the grid. The MGS-256 set consists of two electrically separated units. One of them is the transmitter which is electrically connected with a 12 V battery supply. The second one is the receiver, connected with the grid of potential electrodes using multi-channel shielded cables (for each channel, with input impedance higher than 10 GΩ, input voltage ± 5V). The receiver operates using a PC notebook with dedicated software for data acquisition and processing. The system is connected to the sensor units (fig. 3), which are similar to those used in medicine to produce electrocardiograms: on a rubber sheet, a thin and round metal cap (0.7 - 1 cm in diameter) is imbedded in a conductive silicon gel which is semiconfined by a small sponge. Silicon gel gives a contact resistance of 0.5 - 5 MΩ. Obviously when there are no restrictions, copper or silver nails (2 - 3 cm long, 3 mm diameter) may be preferred. Electrode

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adjacent electrodes, oriented in parallel direction with respect to the current dipoles. In order to carry out measures on walls, a new instrument was designed and realized by GF Instruments (Czech Republic). The Micro-Geoelectric System MGS-256 is designed for highresolution resistivity and self-potential measures, to be carried out in the field, as well as on artificial structures such as walls, floors and columns. With its ability to carry out true 256 channels voltage measurements, the MGS-256 instrument represents a useful tool for surveys of historical buildings, archeological sites and other shallow structures and buried objects (fig. 2).

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Fig. 3 - Sketch of a typical ECG electrode.

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Fig. 1- Sketch of electrode disposal for the resistivity grid, showing the potential grid and various couples of current sources.

4. EXPERIMENTAL TESTS In order to verify the quality, reliability and resolution of this method, some preliminary experimental tests were carried out. A test in a stone floor in Palazzo Steri, an ancient Arab-Norman building, is presented. In the lobby of the building, the pavement is

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made by ornamental limestone slabs. The resistivity grid size chosen was 3m x 3m, with a mesh of 20 cm (fig. 4). In this case, the number of potential electrodes was 256 (the maximum controllable by the instrumentation). The ECG electrodes above mentioned are used as potential electrodes, while as current electrodes iron nail was used.

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In order to improve contact between electrodes, two or more neighboring electrodes for each pole are used to increase the current intensity. Four different directions of current dipole are used: the directions parallel to the grid sides and those at 45° with them (diagonal directions). Parallel dipoles were 3.20 m long, while diagonal dipoles were 4.5 m long. The total number of measures was 1024. The resistivity measures are presented in form of maps of average resistivity obtained considering the average of apparent resistivities along two orthogonal directions (ª and ±) and that obtained from all directions. This in order to minimize distortions due to the variation of shape of volume which is investigated by each current dipole. The apparent resistivity maps so obtained are quite independent from dipole directions (fig. 5). In each of these maps a high positive anomaly is visible. Its shape is clearly determined in the 4-directions average maps. These anomalies perfectly correspond to the air-conditioned pipes standing under the limestone slabs of the floor. The data back projection allows a 3D reconstruction of the subsoil (fig. 6). It clearly shows that the pipes are immediately under the pavement, and below them there are not others relevant heterogeneities. This agrees with the hypothesis that basement is made by homogeneous and compact calcarenite blocks. This is, however, confirmed by an inspection in a neighboring zone, where the basement brought to light. The electrocardiogram electrodes turned out to be very suitable, thanks to their perfect adhesion to the floor since the silicon gel that allows a good coupling with the limestone. As previously mentioned, there were some problems regarding the current electrodes. At times, in fact, we needed to drive two or more nails for each current pole, in order to increase current intensity in the subsoil. The conduction, however, was increased putting a little water around the current electrodes. Another test was performed on an external wall of the Steri ancient prisons, grid size and electrode number being the same as in the previous test (fig. 7). The ECG electrodes were also used. However, the highly deteriorated plaster gave problems for sticking of the potential electrodes. This in turn produced somewhere high contact resistivity both for potential and current electrodes, consequently decreasing the signal/noise ratio. Only in the map regarding the horizontal direction of the current dipole, the S/N ratio seems to be acceptable. A detail of this map, superimposed on the photograph of the wall is shown in fig. 8. One should note the clear correspondence between the high resistivity anomaly areas and the external tracks of former moisture, probable indication of a change of micro-porosity in some internal parts of the calcarenite blocks.

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Fig. 5 – Apparent resistivity maps: map obtained using ± current directions (top); map obtained using ª current directions (middle); map obtained with integrated data (bottom).

5. CONCLUSIONS The technique is relatively fast to use (total time for acquisition of one tomography is about three hours) and to process (about one hour). The results of electrical tomographies are surprisingly detailed and useful, even if only images of the interior are obtained using the back projection procedure. Other data, collected using different arrays can be added before the back projection, to improve the final images. A subsequent inversion, however, can be carried out, but only when the experimental data are collected using the only grid array.

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STERI PALACE PALERMO AB = 3.20 m

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Back projection after 73% FILTERING

Fig. 6 – Back projection obtained using all experimental data collected in the test site located in the lobby of Steri Palace, in Palermo.

Fig. 7 – Experimental test on an external wall of the neoclassic building in the neighboring of Steri Palace, in Palermo.

6. REFERENCES COSENTINO, P., 2000. Approaching electrical tomography. Annali di Geofisica, 43, 1131-1146. COSENTINO, P. and D. LUZIO, 1997. Tomographic pseudo-inversion of resistivity profiles. Annali di Geofisica, 40, 5, 1127-1144. COSENTINO, P., D. LUZIO and R. MARTORANA, 1997. Filters for fast 2D and 3D pseudo-inversion of the resistivity profiles. In Proceedings of the III Meeting of the Environmental and Engineering Geophysical Society, European Section, Aarhus, 367-370. COSENTINO, P., D. LUZIO and R. MARTORANA, 1998. Tomographic resistivity 3D mapping: filters coefficients and depth corrections. In Proceedings of the IV Meeting of the Environmental and Engineering Geophysical Society (European Section), Barcelona, 279-282 COSENTINO, P., D. LUZIO, R. MARTORANA and L.M. TERRANOVA, 1995. Tomographic techniques for pseudo-section representation. In Proceedings of the 1st Meeting Environmental and Engineering Geophysics, European Section, Torino, 485-488.

Fig. 8 – High contrast picture (left) of the external wall investigated (fig. 7). On the right the corresponding resistivity map. COSENTINO, P., R. MARTORANA and L.M. TERRANOVA, 1999. The resistivity grid to optimize tomographic 3d imaging. In Proceedings of the V Meeting of the Environmental and Engineering Geophysical Society (European Section), Budapest, Em 12, 2 p. LOKE, M.H. and R.D. BARKER, 1995. Least-squares deconvolution of apparent resistivity pseudosections. Geophysics, 60, 1682-1690. LOKE M.H. and R.D. BARKER, 1996. Practical techniques for 3D resistivity surveys and data inversion. Geophysical Prospecting, 44, 499-523. ROY, A., 1972. Depth of investigation in Wenner, three-electrode and dipole-dipole resistivity methods. Geophysical Prospecting, 20, 329340. ROY, A., 1974. Resistivity signal partition in layered media. Geophysics, 39, 190-204. ROY, A. and A. APPARAO, 1971. Depth of investigation in direct current methods. Geophysics, 36 , 943-959.