Separation of DC Electrical Method Anomaly By Using Multifractal Modelling

: A more accurate method of DC processing data to distinguish the anomalous body is important for the prediction and detection of potential risk such as goaf and water inrush. In this paper, we have performed a DC data processing process, which relies on the theory of aggregation - area(C - A). We investigate the apparent resistant log𝜌 𝑠 and apparent resistant isograms cumulative area logS as a function to search the threshold as the boundary value. Comparisons of the conventional data processing method to physical simulation that the C - A identified the higher resistance anomalous body better than the lower resistance because its sensitivity. Scoped the higher resistance area almost identical with the physical model, while the lower approach the nearest boundary. The results are in good agreement with the physical model, validating C - A multifractal theory as an effective way for DC accurate interpretation.


INTRODUCTION
Geophysics is an important tool in geological engineering, especially for solving the issues related to the safety of coal mining, as is can be used for the identification of the anomalies related to the potential threaten (e.g. water and fault). And therefore, a series of geophysical methods/models, including the DC electric method, seismic prospecting, transient electromagnetic method, audiomagnetotellurics method, radio wave tunnels perspective, have been proposed [1][2][3][4][5]. These methods/models have their unique advantages, e.g. DC exploration is very fast and economical, seismic exploration method has a high resolution and transient electromagnetic method is less affected by topographic fluctuation. Their application provides a large number of effective scientific information for identification of the geological anomalies, so as to better guarantee the safety production of coal mines.
Among these methods/models, the Direct Current electric method (DC) is an effective geophysical method to detect the conductivity structure in the shallow part of the earth's surface, and it has long been used for mineral, energy, environment, hydrology and geological structure because of its unique feature of flexible device form [6][7][8]. However, there are still some problems limited the more extensive and in-depth application of it, especially the raw and qualitative results as it can be provided, rather than quantitative information. For instance, the TEM can provide the information that there is an anomaly in front of the working face, but it is hard to determine how far away and how about the accurate scale of the anomaly. The main reason for this problem is that the geophysical interpretation results based on Kriging interpolation are continuous contour map, and it is hard to determine the mutation value (threshold). If the researcher wants to get the accurate information, more complex calculation or experience must be needed.
The methods long been used in geochemical study might be useful for solving this issue. A series of geochemical studies, for example, the identification of pollution hotspot [10] or, the determination of the metallogenic area [11], have proposed kinds of methods/models, such as the graphical methods (e.g. Quantile or probability plots), the spatial-statistical methods (Moran's I and spatial cluster analysis) and the multifractal modeling. All of them have a similar feature that their usages are friendly and effective.
In this study, these geochemical methods have been applied tentatively for the explanation of the DC data obtained from an artificial tunnel exploration, and the results suggested that they can be used for getting the quantitative information about the anomaly.

Information about the tunnel
The artificial tunnel is location in the southern campus of Suzhou University. A total of 11 survey points and 88 apparent resistivity data points were collected in the study area. The experiment adopts symmetrical quadrupole device and the dot spacing is 2m. The relationship between the line layout and the relative position of the physical simulated object (the simulated tunnel) is shown in Fig.1

DC electric exploration
Electric exploration is a kind of geophysical exploration method that uses the spatial and temporal distribution of electric field or electromagnetic field (natural of artificial) to solve the geological structure or search for useful minerals based on the differences in the electrical properties of various rocks and ores in the earth's crust.
The apparent resistivity value can be obtained by formula: The values of the above parameters can be obtained by instrument measurement.
By changing the distance of the supply electrode, the apparent resistivity of the measuring point at different depths can be detected.

Data analysis
Two kinds of methods have been used in this study: the graphical methods (e.g. electric sounding curve and contour) and the multifractal modeling.
(1) The electric sounding curve (VES) The electric sounding curve (VES) describes the variation of apparent resistivity with depth at a certain point. In general, the AB/2 relative to depth is taken as the Abscissa, and the apparent resistivity measured at the point is taken as the ordinate, and the coordinates are Log-log plot [18] .
(2) The apparent resistivity section chart The apparent resistivity section chart reflects the apparent resistivity distribution of the section where the survey line is located. The relative distance of all the survey points is taken as the horizontal coordinate, and the depth of the survey (AB/2) is taken as the vertical coordinate [19] .
(3) The multifractal modeling There are a series of multifractal models have been proposed, e.g. these include

Results of traditional analysis
The apparent resistivity profile is commonly used in electrical data processing, and the shape of the object is deduced by analyzing the equivalent and relative values of the apparent resistivity. Sometimes the position of the anomaly is estimated from the overall variation of the electrical sounding curve from the original data. It can be seen from the electrical sounding curve (Fig.2b) Figure (Fig.2d) shows the variation of apparent resistivity with depth at survey point 7 to 11. The subsurface formation information is assumed to be similar.
In the analysis of electric sounding data, it is necessary to combine the data point by point for many times in order to infer the starting and stopping position of abnormal body. If the field work is large and there are more survey points, the work efficiency will be seriously affected. If there are more disturbance factors in the data collection, the variation law of the electric sounding curve will not be easy to be induced and the The apparent resistivity contour map is shown in figure 3.

Fig.3 apparent resistivity profile
It can be concluded that the shallow layer (about 0-6m) is obviously stratified, and the apparent resistivity is larger than that of the lower layer, especially when there is a high resistivity anomaly (the simulation tunnel) in the middle position (the red area), which location is about 5 meters above the buried depth, within 3-14 meters of the relative coordinates of the survey line, which corresponds roughly to the relative position of the physical simulation tunnel. Since the apparent resistivity contour map is drawn and the apparent resistivity value is the overall reflection of the resistivity value of the surrounding rocks and minerals, therefore, the interpretation of the target body can only qualitatively infer the relatively high and low resistance bodies, while for the boundary of the target body, but they can't be identified by contour lines.

Result based on multifractal modeling
Based on the multifractal theory, the isograms of apparent resistivity are drawn with surfer software, and then the different apparent resistivity s  is constructed to delineate the aggregation-area maps of accumulative area. A scatter plot of apparent resistivity and distribution area (Fig.4) is obtained by least squares fitting.

Discussion
The two simulated objects of physical model in Figure 5 show the shape and distribution. The tunnel shows a higher resistance because of air-filled, while the floor water is lower resistance. Comparisons show that the shape of area C the same as the tunnel, the position of the physical model is located between the 3 rd and 8 th measuring points of the experiment line. The horizontal coordinates of 3 to 13 meters and 7 to 9 meters with respect to the vertical coordinates (the buried depth) of about 2 to 5 and 5 to 7 meters is the higher resistance tunnel, and the lower resistance floor water, respectively. The objects identified by the method of multifractal theory (C-A) is located: at the horizontal coordinates of 3 to 13 meters is regarded as the length of tunnel surface, 5 to 11 meters is the bottom at the depth of 3 meter. The relative height matches the original object, but the burial depth various, shifting up 4 meters. Because of the sensitivity and the influence of the water, it can get the nearest location of the C D lower resistance floor water at 6 meters, but can't correspond to its shape and boundary. The delineation of boundary position plays an important role in the prediction of mine water inrush.

Conclusion
By using C-A multifractal method to deal with the study of the separation of abnormal objects from DC electrical data, the following conclusions are obtained: (1) Using multifractal theory to select the threshold value of object, and then dividing the boundary of Anomaly object, it provides a qualitative explanation for analyzing object anomaly object, and it is also a quantitative exploration.
(2) Constructing multifractal model to extract abnormal information, and reducing the dependence on other information, such as known geological information, drilling verification, etc..
(3) Because there are some errors in the inversion of depth by DC method, the result of lateral detection is more accurate than that of longitudinal detection.
(4) The detection effect of higher resistance is better than the lower, especially the sharp and the boundary.
(5) Although the proposed method is based on the results of the geochemistry, the applicability of the geophysical prospecting method and the accuracy of the interpretation need to be further studied.