# Geo-Electrical Detection of Impermeable Membranes in the Subsurface
## 3 Concept of Looking Ahead  
A simulation exercise was performed as a preparation for the prototype design and the laboratory test. As mentioned, a larger separation of the electrodes allows the current to flow deeper in the subsurface and subsequently to look further ahead. However, since the electrodes will be implemented into a sort of logging tool there are limitations on the dimension of the tool and electrode spacing. Our tool has a \"T\" shape with electrodes on the horizontal and vertical axes (Figure 1d). There are also remote electrodes, installed on the surface far away from the tool. Remote electrodes are typically positioned about 10 times the depth of target away. Two modes are defined, which are schematically sketched in Figure 1c:  
1. Mode 1: All electrodes are located on the horizontal axis of the tool. No remote electrodes are being used. 2. Mode 2: At least two electrodes are located on the horizontal axis and use of remote electrodes (1 or 2 depending on the array). A variation of these modes would be using electrodes on the vertical axis, or a combination of electrodes from the horizontal and the vertical axes. Modes 1 and 2, however, demonstrate the idea of looking ahead. We expect that Mode 1 is sensitive to the resistivity structure close to the tool, because the two current electrodes are located on the tool. We refer to this configuration as near-looking. In Mode 2, however, the current will travel through a much larger volume, because of the position on the remote electrodes. We expect this mode to be sensitive to the resistivity further away from the tool. We refer to this configuration as far-looking. The final tool will include a combination of all modes and electrodes, as we will explain in the later section. All simulations are performed using COMSOL(www.comsol.com, accessed on 1 June 2018). We simulate a homogeneous saturated sand body with a resistivity of 30 Ohm-m and an insulator (i.e., membrane) at 6.00 m depth. For every location of the tool and for every possible location of the membrane, we simulate the forward response of the measurements, which we call kernel. In other words, the kernel is the theoretical response of tool, if we know the background resistivity structure and the location of the membrane. This kernel will be the basis of the calculations. The kernels were calculated for Mode 1 and Mode 2 for a range of electrode spacings (Figure 3). For example, the light blue line in Figure 3 (left panel) shows the model resistivity result for a spacing between A and N of 60 cm. For Mode 2 (Figure 3, right panel), the number in the legend refers to the spacing between the electrodes A and M, since only two electrodes are used on the tool in this configuration. The vertical axis indicates the position of the tool at various distances relative to the membrane. The looking ahead capabilities are qualitatively assessed by the position of the curvature of the kernels in Figure 3. We consider the position where the curvature is changing as detection distance. As expected for Mode 1, the array is mostly influenced by the resistivity in the vicinity of the four electrodes on the tool. Consequently, the array needs to be relatively close to the membrane to \"sense\" it. The increased electrode spacing only slightly increases the capability of looking ahead. For example, when the array is 10 cm wide (corresponding to 3.3 cm electrode spacing), the membrane can be sensed at 20 cm distance (at a depth of 580 cm). When the array is much bigger, e.g., 60 cm, it senses the membrane at a distance of 60 cm (depth of 540 cm). For Mode 2, however, the presence of the membrane is sensed by the tool at a much larger distance. The curves presented here are shown as part of the explanation of the methodology, in Section 8 we discuss the process of determining the position of the membrane. In the field situation, the ground above the membrane might not be homogeneous (as in the simulation) and the background resistivities might be unknown.