Mo 21P1 08 Comparison of Different Acquisition Patterns for 2D Tomographic Resistivity Surveys

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1 Mo 21P1 08 Comparison of Different Acquisition Patterns for 2D Tomographic Resistivity Surveys R. Martorana* (University of Palermo), P. Capizzi (University of Palermo), A. D'Alessandro (INGV - Roma) & D. Luzio (University of Palermo) SUMMARY A systematic comparison is presented between some 2D resistivity models and their images by the inversion of synthetic datasets relating to three different arrays, suitable for multichannel data acquisitions (dipole-dipole (DD), Wenner-Schlumberger (WS) and multiple gradient (MG)). The goal is to study how the measurement errors affects the resolution of the tomographic models and the ability to retrieve correct information on buried targets. We considered different data acquisition patterns, gradually increasing the complexity of the combinations of potential spacing and dipolar distance. To this end we increased the number of current dipoles to obtain approximately the same amount of measures, increasing the investigation time. Results from noise-free and noisy data are discussed and compared with those from field data. The results show that: the quality of the inversion models, for a fixed noise level, depends significantly on the data acquisition pattern; the information recovery and the resolution, being equal the number of measurements, is overall better for WS and worse for DD; the decrease of sensitivity with depth is lower for particular acquisition patterns that allow to better resolve deeper targets; the MG array can be preferred because it provides comparable results, using a smaller number of current electrodes.

2 Introduction The recent development of multi-channel resistivity-meters, capable of acquiring in a short time a large number of apparent resistivity data, has caused the increasing use of electrical resistivity tomography. Recently many authors have dealt the optimization of acquisition sequences of data, which can be formed by various combinations of measurements with different electrode arrays and different dipolar lengths and distances, in order to obtain the best resolution and an efficient retrieval of information. The goal should be to seek the optimal sequences that ensure a realistic imaging, without the need for an excessive number of measurements that would compromise the economic viability of the survey. Stummer et al. (2004) have experienced an accurate approach that uses sensitivity distributions to calculate an estimate of the resolution matrix of the model. However, most of the optimization techniques used so far have not sufficiently taken into account the effects of noise on apparent resistivity data. Wilkinson et al. (2012) have addressed some aspects of this problem. Generally, in ERT the problem due to errors on data caused by improper electrode positioning is not adequately considered. To reduce the effect of this kind of error it is possible to select data sets that include arrays with relatively low geometric factors and therefore less sensitive to position errors (Wilkinson et al., 2008). The goal of this work is to study how error affects the model resolution and the ability to retrieve correct information of the subsurface. This in order to understand how the performance depends on a few basic parameters, as the combination of potential spacing and dipolar distance and, consequently, the number of measurements and of current dipoles. The latter is crucial, when using multichannel resistivitymeters, because it determines the overall acquisition time. Choice of the acquisition patterns and forward modeling Several simulations on 2D model have been made, using the software RES2DMOD (Loke, 2014). Data sets of apparent resistivity values have been calculated using the multiple gradient array (Dahlin and Zhou, 2004; 2006) and the two most common arrays for multichannel measurements: dipole-dipole (DD) and Wenner-Schlumberger (WS). For DD and WS arrays, we have choose sequences that retain approximately the same depth of investigation and a not so different total amount of data. For both arrays eight data sets were generated in which the maximum potential spacing a gradually increases Array Pattern DD WS MG parameters N. of measures N. of current dipoles 1 a=1; n= a=1-2; n= a=1-3; n= a=1-4; n= a=1-5; n= a=1-6; n= a=1-7; n= a=1-8; n= a=1; n= a=1-2; n= a=1-3; n= a=1-4; n= a=1-5; n= a=1-6; n= a=1-7; n= a=1-8; n= e=1-8; c = e=1-8; c = e=1-8; c = e=1-8; c = e=1-8; c = e=1-8; c = Table 1 Parameters used, number of measures and of current dipoles current for each data set considered. and the maximum n factor decreases (Table 1). In this way the total number of current dipoles increases, and therefore the time of acquisition. For the multiple gradient array (MG) we choose particular sequences, in order to minimize the number of current dipoles (and therefore time), but maintaining a resolution comparable to those of the DD and WS arrays (Fiandaca et al., 2005). The choice of number and positions of the current dipoles was determined by subdividing the electrode layout AB max into equal parts and by locating the current electrodes at the ends of each part (Martorana et al., 2009). In this way, for a simulation with 72 electrodes, only 36 different current dipoles are chosen. The current electrode separations AB=(s+2)a are chosen considering different lenghts AB=AB max/e (e varying from 1 to 8). In this basic sequence, the forwarding step of the current dipole is the same of the current electrode separation. However, this sequence does not ensure a uniform lateral coverage comparable to the classical sequences in which all the electrodes are in turn used as the current electrodes. To overcome this drawback, the dipoles of the current are increased by dividing the

3 forwarding step of the current dipole by a coverage factor c. Six different sequences were considered, with c ranging from 1 to 6 (table 1). The adopted resistivity model is similar to those used by Szalai et al. (2013) and shows ten resistive prisms (100 Ωm) of the same square section (2m*2m), equally spaced and a background of 10 Ωm. The depth of the center of the first prism to the left is 2m and the following prisms are gradually deeper 25 cm until a maximum depth of 3.75 m. 72 electrodes are considered with a spacing of 1 m (Fig. 3). Noise was added to the synthetic data by simulating errors both on electrode spacing and on potential. A standard deviation of 3% was considered to add noise to the electrode positions. The potential errors were generated by simulating the trend showed by Zhou and Dahlin (2003). We used the formula: noisy data = U(1+R*β/100), where U is the potential reading, R is a random number and β = (c 1/U) c2 denotes absolute relative errors of the potential observations (Dahlin and Zhou, 2004). From observed data we considered, as reasonable values, c 1= 10 4 and c 2 = 0.4 (Figure 1, left) in order to obtain an average error on resistivity data of approximatively 5% (Figure 1, right). Figure 1 Simulations of the potential noise for 2D resistivity imaging surveys (left) and corresponding cross plot of noisy vs. noise-free resistivity data (right). Data inversion and calculation of related parameters Inversion was performed using the EarthImager 2D Software (2009), considering always the same optimized parameter settings, in order to compare the results obtained from the different data sets of noise-free data as well as of noisy and field data. Generally, the main parameter used to evaluate the effectiveness of an inversion is the RMS error, which quantifies the misfit between the observed and predicted data. However, simulated models gives the possibility to define quantitative parameters that describe the discrepancy between the tomographic model and the original one. The inversion program uses an arrangement of cells according to the pseudo-section and to the sensitivity function. This is obviously different from the arrangement of the original model. For this reason, in order to evaluate the resistivity mismatch between inverted and original models, a new refined mesh was designed, obtained from the superposition of the boundaries of all the blocks of the inverted and the original models. For the j-th refined mesh the model misfit is defined as where and are respectively the resistivity in the inverse model and in the original model. A useful parameter to evaluate the model resolution is the relative model sensitivity, i.e. the main diagonal of J T J, where J is Jacobian. A high sensitivity often leads to high model resolution. The inversion process will better resolve model blocks with a higher relative model sensitivity. Figure 2 shows some examples of the obtained results for the above mentioned model, which highlight how the resolution strongly depends on the choice of the data set and how the information recovery decreases with the target depth. Results obtained by noisy data (Figure 2 a) are poorer of information than noise-free data (Figure 2 b) but the gap between results decreases considering more complex and time requiring data sets. In this example the comparison is made between data set 1 (a=1; n=1-35) and data set 5 (a=1-5; n=1-6) for DD and WS, and between data set 1 (e=1-8; c = 1) and data set 6 (e=1-8; c = 6) for MG. Generally, as the data set number increases, the model misfit (Figure 2 c) decreases in correspondence of the targets and overall the shapes are better resolved and artifacts are more limited. This can be explained by the comparison of the correspondent images of relative model sensitivity (Figure 2 d) that show a more uniform distribution and higher values at greater depths.

4 Figure 2 Results of the inversion of some data sets starting from the synthetic model above traced in images: (a) Inverse models for noisy data sets; (b) inverse models for noise-free data sets; (c) images of the model misfit; (d) images of the relative model sensitivity. To obtain inclusive parameters that express the overall effectiveness and resolution of each data set, we calculated the average of the values the model misfit and the relative model sensitivity of all the cells of the refined mesh, weighted according to cell size. Figure 3 shows the results. Figure 3 Parameters that express the quality of inversions depending on the data set number: (a) data misfit (RMS error %); (b) average model misfit; (c) average relative model sensitivity. The comparison of the data misfit of inversions for each data set of DD, WS an MG arrays (figure 3 a) obviously shows sensibly higher values for noisy and field data than for noise-free data. Moreover, there is a similar trend for both field and noisy data. As the complexity and time required of data sets increases (data set number increasing from 1 to 8) the RMS% decreases, rapidly for DD and slowly for WS, instead practically it does not vary for MG. The average model misfit (figure 3 b) is highly depending on noise. In noisy data it is generally higher for MG and DD than for WS. The trends show a decreasing parameter as data set number increases (very strong for the MG) that probably is related to the increase of number of current dipoles. The average relative model sensitivity (figure 3 c) is few

5 Figure 4. Trend of the average relative model sensitivity as a function of the depth of the target. Colored zones show the areas of variation of the parameter for each array, from the data set number lower (dotted line) to the highest (solid line). influenced by the presence of noise and its trend is very similar between noisy and field data because probably the only difference is the different resistivity trend in the subsoil. WS data sets show higher values than DD ones. In every array, sensitivity increases with data set number, very quickly for MG. We also calculated the normalized values of the average model misfit and of the average relative model sensitivity, on windows of the same size as each resistive square anomaly. Figure 4 shows the exponential decrease of the sensitivity values as the target depth increases. We note that the slope of the curves decreases considering more complex data sets. Ultimately, the best sensitivity is obtained for WS array, and the worst for DD array. Conclusions The comparison between 2D synthetic geoelectrical models and their inversion images, obtained by WS, DD and MG data sets, showed that the information recovery and the resolution are overall better for WS and worse for DD. Anyway, they can be improved by considering data set with higher numbers of current dipoles but at the expense of the measurement times. In this context, the MG array is definitely preferable because it provides comparable results, with a number of current dipoles substantially lower. References Advanced Geosciences, Inc. [2009] Instruction manual for EarthImager 2D, Version 2.4.0, Resistivity and IP inversion software, 139 pp. Dahlin, T. and Zhou, B. [2004] A numerical comparison of 2D resistivity imaging with ten electrode arrays. Geophysical Prospecting, 52 (5), Dahlin, T. and Zhou B. [2006] Multiple-gradient array measurements for multichannel 2D resistivity imaging. Near Surface Geophysics, 4 (2), Fiandaca G., Martorana R., Cosentino P.L Use of the linear grid array in 2D resistivity tomography. Near Surface 2005, A023 Loke, M.H. [2014] RES2DMOD ver Rapid 2D resistivity forward modelling using the finitedifference and finite-element methods. Martorana, R., Fiandaca, G., Casas Ponsati, A. and Cosentino, P.L. [2009] Comparative tests on different multi-electrode arrays using models in near-surface geophysics. Journal of Geophysics and Engineering, 6 (1), Stummer, P., Maurer, H. and Green, A.G. [2004] Experimental design: Electrical resistivity data sets that provide optimum subsurface information. Geophysics, 69 (1), Szalai, S., Koppán, A., Szokoli, K., and Szarka, L. [2013] Geoelectric imaging properties of traditional arrays and of the optimized Stummer configuration. Near Surface Geophysics, 11 (1), Wilkinson, P.B., Chambers, J.E., Lelliott, M., Wealthall, G.P., and Ogilvy, R.D. [2008] Extreme sensitivity of crosshole electrical resistivity tomography measurements to geometric errors. Geophysical Journal International, 173 (1), Wilkinson, P.B., Loke, M.H., Meldrum, P.I., Chambers, J.E., Kuras, O., Gunn, D.A., and Ogilvy, R.D. [2012] Practical aspects of applied optimized survey design for electrical resistivity tomography. Geophysical Journal International, 189 (1), Zhou B., and Dahlin T. [2003]. Properties and effects of measurement errors on 2D resistivity imaging. Near Surface Geophysics. 1 (3),