Geoelectric Characterization of Thermal Water Aquifers Using 2.5D Inversion of VES Measurements

Abstract

This paper presents a short theoretical summary of the series expansion-based 2.5D combined geoelectric weighted inversion (CGWI) method and highlights the advantageous way with which the number of unknowns can be decreased due to the simultaneous characteristic of this inversion. 2.5D CGWI is an approximate inversion method for the determination of 3D structures, which uses the joint 2D forward modeling of dip and strike direction data. In the inversion procedure, the Steiner’s most frequent value method is applied to the automatic separation of dip and strike direction data and outliers. The workflow of inversion and its practical application are presented in the study. For conventional vertical electrical sounding (VES) measurements, this method can determine the parameters of complex structures more accurately than the single inversion method. Field data show that the 2.5D CGWI which was developed can determine the optimal location for drilling an exploratory thermal water prospecting well. The novelty of this research is that the measured VES data in dip and strike direction are jointly inverted by the 2.5D CGWI method.

Appendix

For further interpretation of the depth analysis discussed in Sect. 3.2.2, Figs. 17 and 18 show more information. Figure 17 represents the relations between the depth estimation errors, while Fig. 18 shows the relations between the errors of depth parameter estimation. Both figures show that despite the high deviation between the depths and errors estimated by single 1D, 2D CGI (dip), 2D CGI (strike) and 2.5D CGWI procedures, there is a strong correlation between them, as shown by the high correlation coefficients (r). The deviation in regression coefficients in Fig. 18 is calculated by

$$\sigma^{*} = \frac{{\sqrt {sq^{\prime } d} }}{{\sqrt {\frac{{\sum\nolimits_{i = 1}^{I} {H_{i}^{2} } }}{n}} }}\times 100\% ,$$

(15)

where sq′d means the residual mean square of the layer thicknesses H (H = h ₁ + h ₂ + h ₃ + h ₄), i is the number of layers and n is the number of VES stations. (The above quantity is not the same as the estimation error of inversion-derived model parameters.) Not only relations between the depths but also those of the estimation errors are determined for the 2D dip and 2D CGI procedures using VES data measured along dip direction. There is an outstanding relation between the errors characterizing the quality of depth estimation of the inversion methods. The errors are listed in Table 3 (Sect. 3.2.2). A linear relation between the results of 2.5D CGWI and other inversion methods is observable here. For a better representation, the values were plotted on a logarithmic scale on the ordinate axis, which may bias the linear trend between the relevant variables. Values r (r = 0.76; 0.54; 0.82) refer to a function-like relationship (Fig. 17). We emphasize here the reliability of the estimation results of 2.5D CGWI, even when this approximation causes considerable bias.

Fig. 17

Depth estimation errors obtained by 1D, 2D CGI (dip), 2D CGI (strike) inversion methods compared to that of 2.5D CGWI procedure

Fig. 18

Depth parameter errors obtained by 1D, 2D CGI (dip), 2D CGI (strike) inversion methods compared to that of 2.5D CGWI procedure