APPARENT RESISTIVITY-DEPTH SECTION GENERATING METHOD FOR SHORT-OFFSET ELECTROMAGNETIC EXPLORATION

Abstract

The present disclosure provides an apparent resistivity-depth section generating method for short-offset electromagnetic exploration, including: determining, in field zones divided quantitatively based on the induction number, positions of a recording point for each of observation points and frequencies or a time window thereof; and taking determined positions of the recording point as the assignment point for the observation point and the frequencies or the time window thereof, where one survey line of an axial configuration generates one apparent resistivity-depth section along the survey line; and one survey line of an equatorial configuration typically generates one apparent resistivity-depth section along the survey line, and apparent resistivity-depth sections along connecting lines from the observation points to the source which are the same as observation points in the number.

Claims

1. An apparent resistivity-depth section generating method for a short-offset electromagnetic exploration, comprising: dividing a field zone according to an induction number, namely a ratio of an offset to a detection depth, and determining positions of a recording point for each of observation points in a near-field zone, an intermediate-field zone and a far-field zone, specifically: dividing the field zone according to the ratio of the offset .sup.Rito the detection depth H.sub.i,j determining the field zone $\begin{array}{cc}\text{as the near-field zone if}0\le \frac{R_i}{H_{i,j}}\le 1& \text{­­­(1a)}\end{array}$ $\begin{array}{cc}\text{as the intermediate-field zone if}1<\frac{R_i}{H_{i,j}}<10& \text{­­­(1b)}\end{array}$ $\begin{array}{cc}\text{as the far-field zone if}\frac{R_i}{H_{i,j}}\ge 10& \text{­­­(1c)}\end{array}$ wherein, i = 1,2,.Math..Math..Math., m is a serial number of the observation point, and j = 1, 2,.Math..Math..Math., n is a serial number of a frequency; and determining the positions of the recording point for each of the observation points according to the divided zones: a horizontal position of the recording point: the horizontal position of the recording point in the near-field zone is a midpoint of the offset, the horizontal position of the recording point in the far-field zone is a position where the observation point is located, and the horizontal position of the recording point in the intermediate-field zone moves linearly from the midpoint of the offset to the position where the observation point is located; and a vertical position of the recording point: the vertical position of the recording point in the near-field zone and the intermediate-field zone is located at an intersection of a line from the detection depth to a source and a perpendicular line passing through the horizontal position of the recording point, and the vertical position of the recording point in the far-field zone is equal to the detection depth; and taking the positions of the recording point as an assignment point for an apparent resistivity corresponding to the each observation point and the frequency thereof, wherein (1) for an axial configuration, assuming that the source coincides with an origin .sup.O of a rectangular coordinate system, and a survey line is arranged along an .sup.x -axis, then on an .sup.xOz plane the horizontal position $P_{i,j}^x$ of the recording point for each observation point in the near-field zone is $P_{i,j}^x$ $=\frac{}{2}$ , the horizontal position $P_{i,j}^x$ of the recording point for each observation point in the far-field zone is $P_{i,j}^x$ = .sup.Ri′ ; and the horizontal position $P_{i,j}^x$ of the recording point for each observation point in the intermediate-field zone, the horizontal position $P_{i,j}^x=\frac{R_i}{2}$ of the recording point moves linearly from the midpoint of the offset to a receiving point, specifically: $\begin{array}{cc}{P}_{i,j}^x=\left\{\begin{array}{ll}\frac{R_i}{2},\hfill & 0\le \frac{R_i}{H_{i,j}}\le 1\hfill \\ \frac{R_i}{18}\left(\frac{R_i}{H_{i,j}}-1\right)+\frac{R_i}{2},\hfill & 1<\frac{R_i}{H_{i,j}}<10\hfill \\ R_i,\hfill & \text{­­­(2a)}\frac{R_i}{H_{i,j}}\ge 10\hfill \end{array}\right)& \end{array}$ the vertical position $P_{i,j}^z$ of the recording point for each observation point in the near-field zone and the intermediate-field zone is located at the intersection of the line from the .sup.Hi,j to the source and the perpendicular line passing through the $P_{i,j}^x$ , and the vertical position $P_{i,j}^z$ of the recording point for each observation point in the far-field zone is .sup.–Hi.j, specifically: $\begin{array}{cc}{P}_{i,j}^z=\left\{\begin{array}{ll}-\frac{H_{i,j}}{R_i}{P}_{i,j}^x=-\frac{H_{i,j}}{2},\hfill & \text{­­­(2b)}0\le \frac{R_i}{H_j}\le 1\hfill \\ -\frac{H_{i,j}}{R_i}{P}_{i,j}^x=-\frac{R_i+9H_{i,j}}{18},\hfill & 1<\frac{R_i}{H_{i,j}}<10\hfill \\ -H_{i,j},\hfill & \frac{R_i}{H_{i,j}}\ge 10\hfill \end{array}\right)& \end{array}$ the positions of the recording point are the assignment point for the apparent resistivity ${\rho }_{i,j}^{\text{a}}$ of each observation point of the axial configuration on the .sup.xOz plane; and one survey line of the axial configuration generates one apparent resistivity-depth section along the survey line; and (2) for an equatorial configuration, assuming that the survey line is arranged along an .sup.x′ -axis of a rectangular coordinate system, a midpoint of the survey line is taken as an origin .sup.0′, the source coincides with the origin .sup.0 of a cylindrical-coordinate system, a line from the source to the observation point is along an .sup.r-axis, a part ≥10 $\frac{R_i}{H_{i,j}}$ in the Equation (2) for the recording point of the axial configuration is taken, and the offset .sup.Ri is replaced with a position ${x^{\prime }}_i$ of the observation point on the .sup.x′ -axis, then on an .sup.x′O′z plane the horizontal position $P_{i,j}^{x^{\prime }}$ and the vertical position $P_{i,j}^z$ of the recording point for each observation point are: $\begin{array}{cc}{P}_{i,j}^{x^{\prime }}={x^{\prime }}_i,\text{if}\frac{R_i}{H_{i,j}}\ge 10& \text{­­­(3a)}\end{array}$ $\begin{array}{cc}{P}_{i,j}^z=-H_{i,j},\text{if}\frac{R_i}{H_{i,j}}\ge 10& \text{­­­(3b)}\end{array}$ a relationship between the offset .sup.Ri and the position ${x^{\prime }}_i$ of the observation point is expressed as: $\begin{array}{cc}{R}_i=\sqrt{O{O^{\prime }}^2+{x^{\prime }}_i^2}& \text{­­­(4)}\end{array}$ the positions of the recording point are the assignment point for the apparent resistivity ${\rho }_{i,j}^{\text{a}}$ of each observation point of the equatorial configuration on the .sup.x′O′z plane; on an .sup.rOz plane the horizontal position $P_{i,j}^r$ and the vertical position $P_{i,j}^z$ of the recording point for each observation point of the equatorial configuration are: $\begin{array}{cc}{P}_{i,j}^r=\left\{\begin{array}{ll}\frac{R_i}{2},\hfill & 0\le \frac{R_i}{H_{i,j}}\le 1\hfill \\ \frac{R_i}{18}\left(\frac{R_i}{H_{i,j}}-1\right)+\frac{R_i}{2},\hfill & 1<\frac{R_i}{H_{i,j}}<10\hfill \\ R_i,\hfill & \text{­­­(5a)}\frac{R_i}{H_{i,j}}\ge 10\hfill \end{array}\right)& \end{array}$ $\begin{array}{cc}{P}_{i,j}^z=\left\{\begin{array}{ll}-\frac{H_{i,j}}{R_i}{P}_{i,j}^x=-\frac{H_{i,j}}{2},\hfill & \text{­­­(5b)}0\le \frac{R_i}{H_j}\le 1\hfill \\ -\frac{H_{i,j}}{R_i}{P}_{i,j}^x=-\frac{R_i+9H_{i,j}}{18},\hfill & 1<\frac{R_i}{H_{i,j}}<10\hfill \\ -H_{i,j},\hfill & \frac{R_i}{H_{i,j}}\ge 10\hfill \end{array}\right)& \end{array}$ the positions of the recording point are the assignment point for the apparent resistivity ${\rho }_{i,j}^{\text{a}}$ of each observation point of the equatorial configuration on the rOz plane; and typically, one survey line of the equatorial configuration comprising m observation points generates one apparent resistivity-depth section along the survey line and m apparent resistivity-depth sections along connecting lines from the observation points to the source.

2. The apparent resistivity-depth section generating method for the short-offset electromagnetic exploration according to claim 1, wherein the detection depth is calculated by the following general equations: $\begin{array}{cc}{H}_{i,j}=\sqrt{\frac{{\rho }_{i,j}^{\text{a}}}{{\mu }_0\text{}\pi \text{}{f}_{i,j}}}=\sqrt{\frac{{\rho }_{i,j}^{\text{a}}}{4\text{}\pi \times {10}^{-7}\text{}\pi \text{}{f}_{i,j}}}\approx 503\sqrt{\frac{{\rho }_{i,j}^{\text{a}}}{f_{i,j}}}& \text{­­­(6a)}\end{array}$ $\begin{array}{cc}{H}_{i,j}=\sqrt{\frac{2t_{i,j}{\rho }_{i,j}^{\text{a}}}{{\mu }_0}}=\sqrt{\frac{2t_{i,j}{\rho }_{i,j}^{\text{a}}}{4\text{}\pi \times {10}^{-7}}}\approx 1260\sqrt{t_{i,j}{\rho }_{i,j}^{\text{a}}}& \text{­­­(6b)}\end{array}$ wherein, Equation (6a) is a frequency-domain equation, ƒ.sub.i,j is the jth frequency of the observation point i, ${\rho }_{i,j}^a$ is the apparent resistivity, .Math. .sub.0 is a vacuum permeability when the ground is a nonmagnetic medium, Equation (6b) is a time-domain equation, and t.sub.i,j is observation time for a jth time window of the measuring point i.

3. The apparent resistivity-depth section generating method for the short-offset electromagnetic exploration according to claim 1, wherein the apparent resistivity ${\rho }_{i,j}^{\text{a}}$ is calculated from a definition and an algorithm of a Cagniard apparent resistivity or a single-component apparent resistivity, or from any improved apparent resistivity definition and algorithm.

4. The apparent resistivity-depth section generating method for the short-offset electromagnetic exploration according to claim 1, wherein the method is applicable to any configuration with the offset, regardless of an electric source or a magnetic source.

5. The apparent resistivity-depth section generating method for the short-offset electromagnetic exploration according to claim 1, wherein field observation records further comprise the position of the source besides the positions of the observation point, so as to determine the offset.

6. The apparent resistivity-depth section generating method for the short-offset electromagnetic exploration according to claim 1, wherein for frequency-domain or time-domain exploration, the field zone division standard is adjusted for any configuration, source and observation component.

7. The apparent resistivity-depth section generating method for the short-offset electromagnetic exploration according to claim 2, wherein the apparent resistivity ${\rho }_{i,j}^{\text{a}}$ is calculated from a definition and an algorithm of a Cagniard apparent resistivity or a single-component apparent resistivity, or from any improved apparent resistivity definition and algorithm.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] FIG. 1 illustrates the offset, detection depth and observation point.

[0027] FIG. 2 illustrates the axial configuration and apparent resistivity-depth section, where FIG. 2a is the arranged plan of the configuration, and FIG. 2b is the apparent resistivity-depth section of the configuration on the xOz plane.

[0028] FIG. 3 illustrates the equatorial configuration and apparent resistivity-depth section, where FIG. 3a is the arranged plan of the configuration, FIG. 3b is the apparent resistivity-depth section of the configuration on the x′O′z plane, and FIG. 3c is the apparent resistivity-depth section of the configuration on the rOz plane.

[0029] FIG. 4 is the arranged plan of the axial configuration in example 1.

[0030] FIG. 5 is the apparent resistivity-depth section of the axial configuration along the survey line in example 1.

[0031] FIG. 6 is the arranged plan of the equatorial configuration in example 2.

[0032] FIG. 7 is the apparent resistivity-depth section of an equatorial configuration in example 2, where FIG. 7a is the apparent resistivity-depth section along the survey line, and FIGS. 7b, 7c, 7d, 7e and 7f are apparent resistivity-depth sections along connecting lines from observation points No.1, No.2, No.3, No.4 and No.5 to the source, respectively.

[0033] In the figures: 1. source, 2. observation point, 3. offset, 4. detection depth H.sub.i,j, 5. recording point

[00031]$\left(P_{i,j}^x,P_{i,j}^z\right),\left(P_{i,j}^{x^{\prime }},P_{i,j}^z\right)\text{or}\left(P_{i,j}^r,P_{i,j}^z\right),6.$

distance, and 7. apparent resistivity contour curve.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] To clarify the purpose, technical solutions and advantages of the present disclosure, the present disclosure is further described below in conjunction with the drawings and examples. It should be understood that the examples described herein are only used to explain the present disclosure, not to limit the present disclosure.

[0035] The present disclosure provides a method for generating apparent resistivity-depth section from observed data in short-offset electromagnetic exploration. A field zone is divided according to an induction number (a ratio of an offset to a detection depth), specifically:

[0036] The field zone is divided according to the ratio of the offset R.sub.i to the detection depth H.sub.i,j, and it is determined [0037] as the near-field zone if [0038] as the intermediate-field zone if [0039] as the far-field zone if

[0040] Positions of a recording point for each of observation points are determined from this. In the foregoing equations, i=1,2,.Math.,m is a serial number of the observation point, and j = 1,2,.Math.,n is a serial number of a time window or the frequencies.

[0041] According to the above divided field zones, the positions of the recording point for the observation point are determined in the near-field zone, the intermediate-field zone and the far-field zone, and the positions of the recording point are taken as the assignment point for the apparent resistivity corresponding to each observation point and the frequencies or the time window thereof.

[0042] As shown in FIG. 1, the horizontal position of the recording point in the near-field zone is the midpoint of the offset, that in the far-field zone is the position where the observation point is located, and that in the intermediate-field zone moves linearly from the midpoint of the offset to the position where the observation point is located. The vertical position of the recording point in the near-field zone and the intermediate-field zone is located at the point of intersection between the connecting line from the detection depth to the source and the perpendicular line passing through the horizontal position of the recording point, and that in the far-field zone is equal to the detection depth.

[0043] With an axial configuration and an equatorial configuration as examples, the apparent resistivity-depth section is specifically generated as follows:

[0044] (1) The axial configuration is as shown in FIG. 2a. Assuming that the source coincides with the origin O of a rectangular coordinate system, and the survey line is arranged along the x -axis, on the xOz plane the horizontal position

[00035]$P_{i,j}^x$

of the recording point for each observation point in the near-field zone is

[00036]$P_{i.j}^x=\frac{R_i}{2},$

and that in the far-field zone is and in the intermediate-field zone, the horizontal position of the recording point moves linearly from the midpoint of the offset to a receiving point.

[00037]$\begin{array}{cc}{P}_{i,j}^x=\left\{\begin{array}{ll}\frac{R_i}{2},\hfill & 0\le \frac{R_i}{H_{i,j}}\le 1\hfill \\ \frac{R_i}{18}\left(\frac{R_i}{H_{i,j}}-1\right)+\frac{R_i}{2},\hfill & 1<\frac{R_i}{H_{i,j}}<10\hfill \\ R_i,\hfill & \frac{R_i}{H_{i,j}}\ge 10\hfill \end{array}\right)& \text{­­­(2a)}\end{array}$

[0045] The vertical position

[00038]$P_{i,j}^z$

of the recording point for each observation point inthe near-field zone and the intermediate-field zone is located at the intersection of the line from H.sub.i,j to the source and the perpendicular line passing through

[00039]$P_{i,j}^x,$

and that in the far-field -H.sub.i,j zone is

[00040]$\begin{array}{cc}{P}_{i,j}^z=\left\{\begin{array}{ll}-\frac{H_{i,j}}{R_i}{P}_{i,j}^x=-\frac{H_{i,j}}{2},\hfill & 0\le \frac{R_i}{H_{i,j}}\le 1\hfill \\ -\frac{H_{i,j}}{R_i}{P}_{i,j}^x=-\frac{R_i+8H_{i,j}}{18},\hfill & 1<\frac{R_i}{H_{i,j}}<10\hfill \\ -H_{i,j},\hfill & \frac{R_i}{H_{i,j}}\ge 10\hfill \end{array}\right)& \text{­­­(2b)}\end{array}$

[0046] The positions of the recording point are the assignment point for the apparent resistivity

[00041]${\rho }_{i,j}^{\text{a}}$

of each observation point of the axial configuration on the xOz plane. One survey line of the axial configuration generates one apparent resistivity-depth section along the survey line (FIG. 2b).

[0047] (2) The equatorial configuration is as shown in FIG. 3a. Assuming that the survey line is arranged along the x′ -axis of a rectangular coordinate system, the midpoint of the survey line is taken as the origin O′, the source coincides with the origin O of a cylindrical-coordinate system, the line from the source to the observation point is along the r -axis, the part

[00042]$\frac{R_i}{H_{i,j}}\ge 10$

in Equation (2) for the recording point of the axial configuration is taken, and the offset R.sub.i, is replaced with the position

[00043]${x^{\prime }}_i$

of each observation point on the x′ -axis, then on the x́Óz plane the horizontal position

[00044]$P_{i,j}^{x^{\prime }}$

and the vertical position

[00045]$P_{i,j}^z$

of the recording point for each observation point are:

[00046]$\begin{array}{cc}{P}_{i,j}^{x^{\prime }}={x^{\prime }}_i,\text{if}\frac{R_i}{H_{i,j}}\ge 10& \text{­­­(3a)}\end{array}$

[00047]$\begin{array}{cc}{P}_{i,j}^z=-H_{i,j},\text{if}\frac{R_i}{H_{i,j}}\ge 10& \text{­­­(3b)}\end{array}$

[0048] The relationship between the offset R.sub.i and the position

[00048]${x^{\prime }}_i$

of the observation point is expressed as:

[00049]$\begin{array}{cc}{R}_i=\sqrt{O{O^{\prime }}^2+{x^{\prime }}_i^2}& \text{­­­(4)}\end{array}$

[0049] The above positions of the recording point are the assignment point for the apparent resistivity

[00050]${\rho }_{i,j}^{\text{a}}$

of the observation point of the equatorial configuration on the x′O′z plane.

[0050] If the superscript x in Equation (2) for the recording point of the axial configuration is replaced as r, then on the rOz plane the horizontal position

[00051]$P_{i,j}^r$

and the vertical position

[00052]$P_{i,j}^z$

of the recording point for each observation point of the equatorial configuration are:

[00053]$\begin{array}{cc}{P}_{i,j}^r=\left\{\begin{array}{ll}\frac{R_i}{2},\hfill & 0\le \frac{R_i}{H_{i,j}}\le 1\hfill \\ \frac{R_i}{18}\left(\frac{R_i}{H_{i,j}}-1\right)+\frac{R_i}{2},\hfill & 1<\frac{R_i}{H_{i,j}}<10\hfill \\ R_i,\hfill & \frac{R_i}{H_{i,j}}\ge 10\hfill \end{array}\right)& \text{­­­(5a)}\end{array}$

[00054]$\begin{array}{cc}{P}_{i,j}^z=\left\{\begin{array}{ll}-\frac{H_{i,j}}{R_i}{P}_{i,j}^r=-\frac{H_{i,j}}{2},\hfill & 0\le \frac{R_i}{H_{i,j}}\le 1\hfill \\ -\frac{H_{i,j}}{R_i}{P}_{i,j}^r=-\frac{R_i+8H_{i,j}}{18},\hfill & 1<\frac{R_i}{H_{i,j}}<10\hfill \\ -H_{i,j},\hfill & \frac{R_i}{H_{i,j}}\ge 10\hfill \end{array}\right)& \text{­­­(5b)}\end{array}$

[0051] The above positions of the recording point are the assignment point for the apparent resistivity

[00055]${\rho }_{i,j}^{\text{a}}$

of each observation point of the equatorial configuration on the rOz plane.

[0052] Typically, one survey line of the equatorial configuration including m observation points generates one apparent resistivity-depth section along the survey line (FIG. 3b) and m apparent resistivity-depth sections along connecting lines from the observation points to the source. (FIG. 3c illustrates an i th profile).

[0053] The present disclosure will be further described below in conjunction with two specific examples.

[0054] Example 1: Generation of the apparent resistivity-depth section of an axial configuration. FIG. 4 is the arranged plan of the configuration, with nine observation points in total. The right part of Table 1 gives the offsets of each observation point, and the left part gives the geoelectric models for calculating Cagniard apparent resistivities of each observation point :

[00056]${\rho }_{i,j}^{\text{a}}=\frac{1}{\mu \text{}\omega }\frac{{\left|E_x\right|}^2}{{\left|H_y\right|}^2}$

[0055] The second column of Table 2 shows operating frequencies of each observation point, and the third column shows calculated results.

TABLE-US-00001 Geoelectric models and offsets for observation points of the axial configuration Geoelectric model Observation point Offset R.sub.i Observation point Offset R.sub.i ρ.sub.1 = 200 Ω.m h.sub.1 = 100 m No.1 R.sub.1 = 600 m No.6 R.sub.6 = 1600 m ρ.sub.2 = 100 Ω.m h.sub.2 = 200 m No.2 R.sub.2 = 800 m No.7 R.sub.7 = 1800 m ρ.sub.3 = 50 Ω.m No.3 R.sub.3 = 1000 m No.8 R.sub.8 = 2000 m No.4 R.sub.4 = 1200 m No.9 R.sub.9 = 2200 m Electric source arranged along the x -axis No.5 R.sub.5 = 1400 m Observed E.sub.x and H.sub.y components

[0056] Substituting the Cagniard apparent resistivities

[00057]${\rho }_{i,j}^{\text{a}}$

a (third column in Table 2) into Equation (6a) yields detection depths H.sub.i,j, which are listed in the fourth column in Table 2. The fifth column shows induction numbers

[00058]$\frac{R_i}{H_{i,j}}.$

[0057] For the field zones divided according to Equation (1), substituting the offsets R.sub.i and the detection depths H.sub.i,j into Equation (2) yields the horizontal positions

[00059]$P_{i,j}^x$

and the vertical positions

[00060]$P_{i,j}^z$

of the recording points for each observation point, which are listed in the sixth and seventh columns of Table 2 respectively to serve as the assignment points for the apparent resistivities

[00061]${\rho }_{i,j}^{\text{a}}$

in the third column. Then in the table,

[00062]$P_{i,j}^x$

as Column A,

[00063]$P_{i,j}^z$

as Column B, and a

[00064]${\rho }_{i,j}^{\text{a}}$

as Column C are listed in Table 3, thereby forming data of one apparent resistivity-depth section along the survey line. Therefore, the apparent resistivity-depth section drawn with Surfer software is as shown in FIG. 5.

TABLE-US-00002 Operating frequencies, apparent resistivities, detection depths, induction numbers and recording points for each observation point of the axial configuration Recording points of observation point No. 1 (R.sub.1=600 m) at each of frequencies j ƒ.sub.1,j / Hz [00065]${\rho }_{1,j}^{\text{n}}/\text{Ω}\text{.m}$ H.sub.1,j/m R.sub.1/H.sub.1,j [00066]$P_{1,j}^x\text{/m}$ [00067]$P_{1,j}^{\text{z}}\text{/m}$ 1 8192 209.9 80.53 7.45 515.0 -69.12 2 4096 207.3 113.1 5.30 443.3 -83.63 3 2048 180.3 149.2 4.01 400.6 -99.67 4 1024 138.3 184.8 3.24 374.8 -115.4 5 512 143.9 266.6 2.24 341.6 -151.8 6 256 254.1 501.1 1.19 306.5 -256.0 7 128 527.4 1021. 0.58 300.0 -510.5 8 64 1078. 2064. 0.29 300.0 -1032. 9 32 2143. 4117. 0.14 300.0 -2058. 10 16 4207. 8156. 0.07 300.0 -4078. 11 8 8249. 16152 0.03 300.0 -8076. 12 4 16241 32051 0.01 300.0 -16025

TABLE-US-00003 Recording points of observation point No. 2 (R.sub.2=800 m) at each of frequencies j ƒ.sub.2,j / Hz [00068]${\rho }_{2,j}^{\text{a}}\text{/Ω}\text{.m}$ H.sub.2,j/m R.sub.2/H.sub.2,j [00069]$P_{2,j}^x\text{/m}$ [00070]$P_{2,j}^{\text{z}}\text{/m}$ 1 8192 209.9 80.52 9.93 797.1 -80.23 2 4096 206.1 112.8 7.08 670.6 -94.59 3 2048 192.1 154.0 5.19 586.3 -112.9 4 1024 165.3 202.1 3.95 531.4 -134.2 5 512 129.3 252.7 3.16 496.2 -156.7 6 256 125.8 352.7 2.26 456.3 -201.2 7 128 196.8 623.7 1.28 412.5 -321.6 8 64 393.1 1246 0.64 400.0 -623.3 9 32 802.7 2519 0.31 400.0 -1259. 10 16 1602. 5033 0.15 400.0 -2516. 11 8 3155. 9989 0.08 400.0 -4994. 12 4 6200. 19804 0.04 400.0 -9902.

TABLE-US-00004 Recording points of observation point No. 3 (R.sub.3=1,000 m) at each of frequencies j ƒ.sub.3,j / Hz [00071]${\rho }_{3,j}^{\text{a}}\text{/Ω}\text{.m}$ H.sub.3,j/m R.sub.3/H.sub.3,j/m [00072]$P_{3,j}^x\text{/m}$ [00073]$P_{3,j}^{\text{z}}\text{/m}$ 1 8192 209.4 80.42 12.4 1000. -80.42 2 4096 205.4 112.6 8.87 937.5 -105.6 3 2048 190.1 153.2 6.52 806.9 -123.6 4 1024 174.4 207.6 4.81 712.0 -147.8 5 512 148.5 270.9 3.69 649.4 -175.9 6 256 117.0 340.0 2.94 607.8 -206.7 7 128 112.6 471.8 2.11 562.1 -265.2 8 64 177.4 837.5 1.19 510.7 -427.8 9 32 360.5 1688 0.59 500.0 -844.1 10 16 741.6 3424 0.29 500.0 -1712. 11 8 1485. 6853 0.14 500.0 -3426. 12 4 2933. 13620 0.07 500.0 -6810.

TABLE-US-00005 Recording points of observation point No. 4 (R.sub.4=1,200 m) at each of frequencies j ƒ.sub.4,j/Hz [00074]${\rho }_{4,j}^{\text{a}}\text{/Ω}\text{.m}$ H.sub.4,j/m R.sub.4/H.sub.4,j [00075]$P_{4,j}^x\text{/m}$ [00076]$P_{4,j}^{\text{z}}\text{/m}$ 1 8192 209.3 80.40 14.9 1200. -80.40 2 4096 206.8 113.0 10.6 1200. -113.0 3 2048 189.3 152.9 7.84 1056. -134.6 4 1024 173.5 207.0 5.79 919.6 -158.7 5 512 157.7 279.2 4.29 819.8 -190.7 6 256 129.0 357.1 3.35 757.3 -225.4 7 128 99.13 442.6 2.71 714.0 -263.4 8 64 104.5 643.0 1.86 657.7 -352.4 9 32 188.3 1220. 0.98 600.0 -610.1 10 16 396.8 2505. 0.47 600.0 -1252. 11 8 816.5 5081. 0.23 600.0 -2540. 12 4 1632. 10161 0.11 600.0 -5080.

TABLE-US-00006 Recording points at of observation point No. 5 (R.sub.5=1,400 m) at each of frequencies j ƒ.sub.5,j / Hz [00077]${\rho }_{5,j}^{\text{a}}\text{/Ω}\text{.m}$ H.sub.5,j/m R.sub.5/H.sub.5,j [00078]$P_{5,j}^x\text{/m}$ [00079]$P_{5,j}^{\text{z}}\text{/m}$ 1 8192 209.3 80.40 17.4 1400. -80.40 2 4096 205.2 112.6 12.4 1400. -112.6 3 2048 188.9 152.7 9.16 1334. -145.6 4 1024 172.4 206.4 6.78 1149. -169.5 5 512 158.8 280.1 4.99 1010. -202.3 6 256 137.5 368.7 3.79 917.5 -241.6 7 128 104.9 455.3 3.07 861.3 -280.1 8 64 82.83 572.2 2.44 812.5 -332.1 9 32 114.3 950.7 1.47 736.7 -500.3 10 16 237.2 1937. 0.72 700.0 -968.5 11 8 503.5 3990. 0.35 700.0 -1995. 12 4 1025. 8052. 0.17 700.0 -4026.

TABLE-US-00007 Recording points of observation point No. 6 (R.sub.6=1,600 m) at each of frequencies j ƒ.sub.6,j / Hz [00080]${\rho }_{6,j}^{\text{a}}\text{/Ω}\text{.m}$ H.sub.6,j/m R.sub.6/H.sub.6,j [00081]$P_{6,j}^x\text{/m}$ [00082]$P_{6,j}^{\text{z}}\text{/m}$ 1 8192 209.3 80.40 19.9 1600. -80.40 2 4096 205.1 112.5 14.2 1600. -112.5 3 2048 189.3 152.9 10.4 1600. -152.9 4 1024 171.9 206.1 7.76 1401. -180.5 5 512 157.9 279.3 5.72 1220. -213.0 6 256 140.3 372.3 4.29 1093. -254.3 7 128 112.7 472.0 3.38 1012. -298.6 8 64 80.55 564.3 2.83 963.1 -339.6 9 32 81.52 802.8 1.99 888.2 -445.7 10 16 154.8 1564. 1.02 802.0 -784.2 11 8 336.9 3264. 0.49 800.0 -1632. 12 4 701.4 6661. 0.24 800.0 -3330.

TABLE-US-00008 Recording points of observation point No. 7 (R.sub.7=1,800 m) at each of frequencies j ƒ.sub.7,j/Hz [00083]${\rho }_{7,j}^{}\text{/Ω}\text{.m}$ H.sub.7,j/m R.sub.7 / H.sub.7,j [00084]$P_{7,j}^x\text{/m}$ [00085]$P_{7,j}^{\text{z}}\text{/m}$ 1 8192 209.2 80.39 22.3 1800. -80.39 2 4096 205.0 112.5 15.9 1800. -112.5 3 2048 188.8 152.7 11.7 1800. -152.7 4 1024 171.7 205.9 8.73 1673. -191.5 5 512 157.2 278.7 6.45 1445. -223.8 6 256 140.1 372.1 4.83 1283. -265.4 7 128 117.6 482.1 3.73 1173. -314.3 8 64 85.09 580.0 3.10 1110. -357.7 9 32 68.05 733.5 2.45 1045. -426.0 10 16 108.8 1311. 1.37 937.1 -683.1 11 8 238.9 2749. 0.65 900.0 -1374. 12 4 509.6 5677. 0.31 900.0 -2838.

TABLE-US-00009 Recording points of observation point No. 8 (R.sub.8=2,000 m) at each of frequencies j ƒ.sub.8,j / Hz [00086]${\rho }_{8,j}^{\text{a}}\text{/Ω}\text{.m}$ H.sub.8,j/m R.sub.8/H.sub.8,j [00087]$P_{8,j}^x\text{/m}$ [00088]$P_{8,j}^{\text{z}}\text{/m}$ 1 8192 209.2 80.39 24.8 2000. -80.39 2 4096 205.0 112.5 17.7 2000. -112.5 3 2048 188.7 152.6 13.0 2000. -152.6 4 1024 171.5 205.8 9.71 1968. -202.6 5 512 156.8 278.4 7.18 1687. -234.8 6 256 139.3 371.1 5.38 1487. -276.0 7 128 119.4 485.9 4.11 1346. -327.1 8 64 90.93 599.5 3.33 1259. -377.5 9 32 64.32 713.1 2.80 1200. -428.0 10 16 82.24 1140. 1.75 1083. -617.9 11 8 176.8 2364. 0.84 1000. -1182. 12 4 386.2 4942. 0.40 1000. -2471.

TABLE-US-00010 Recording points of observation point No. 9 (R.sub.9=2,200 m) at each of frequencies j ƒ.sub.9,j/Hz [00089]${\rho }_{9,j}^{\text{a}}\text{/Ω}\text{.m}$ H.sub.9,j/m R.sub.9/H.sub.9,j [00090]$P_{9,j}^x\text{/m}$ [00091]$P_{9,j}^{\text{z}}\text{/m}$ 1 8192 209.2 80.39 27.3 2200. -80.39 2 4096 204.9 112.5 19.5 2200. -112.5 3 2048 188.5 152.6 14.4 2200. -152.6 4 1024 171.7 205.9 10.6 2200. -205.9 5 512 156.6 278.1 7.90 1944. -245.8 6 256 138.7 370.2 5.94 1703. -286.7 7 128 119.4 485.9 4.52 1531. -338.2 8 64 95.73 615.1 3.57 1414. -395.6 9 32 65.54 719.8 3.05 1351. -442.1 10 16 66.87 1028. 2.13 1239. -579.2 11 8 135.3 2068. 1.06 1107. -1041. 12 4 301.6 4368. 0.50 1100. -2184.

TABLE-US-00011 Data for plotting the apparent resistivity-depth section of the axial configuration Column A corresponds to P.sup.x.sub.i,j, Column B corresponds to P.sup.z.sub.i,j, and Column C corresponds to p.sup.a.sub.i,j.Math. 800.0 -3330. 701.4 A B C 500.0 -6810. 2933. 1800. -80.39 209.2 515.0 -69.12 209.9 1200. -80.40 209.3 1800. -112.5 205.0 443.3 -83.63 207.3 1200. -113.0 206.8 1800. -152.7 188.8 400.6 -99.67 180.3 1056. -134.6 189.3 1673. -191.5 171.7 374.8 -115.4 138.3 919.6 -158.7 173.5 1445. -223.8 157.2 341.6 -151.8 143.9 819.8 -190.7 157.7 1283. -265.4 140.1 306.5 -256.0 254.1 757.3 -225.4 129.0 1173. -314.3 117.6 300.0 -510.5 527.4 714.0 -263.4 99.13 1110. -357.7 85.09 300.0 -1032. 1078. 657.7 -352.4 104.5 1045. -426.0 68.05 300.0 -2058. 2143. 600.0 -610.1 188.3 937.1 -683.1 108.8 300.0 -4078. 4207. 600.0 -1252. 396.8 900.0 -1374. 238.9 300.0 -8076. 8249. 600.0 -2540. 816.5 900.0 -2838. 509.6 300.0 -16025 16241 600.0 -5080. 1632. 2000. -80.39 209.2 797.1 -80.23 209.9 1400. -80.40 209.3 2000. -112.5 205.0 670.6 -94.59 206.1 1400. -112.6 205.2 2000. -152.6 188.7 586.3 -112.9 192.1 1334. -145.6 188.9 1968. -202.6 171.5 531.4 -134.2 165.3 1149. -169.5 172.4 1687. -234.8 156.8 496.2 -156.7 129.3 1010. -202.3 158.8 1487. -276.0 139.3 456.3 -201.2 125.8 917.5 -241.6 137.5 1346. -327.1 119.4 412.5 -321.6 196.8 861.3 -280.1 104.9 1259. -377.5 90.93 400.0 -623.3 393.1 812.5 -332.1 82.83 1200. -428.0 64.32 400.0 -1259. 802.7 736.7 -500.3 114.3 1083. -617.9 82.24 400.0 -2516. 1602. 700.0 -968.5 237.2 1000. -1182. 176.8 400.0 -4994. 3155. 700.0 -1995. 503.5 1000. -2471. 386.2 400.0 -9902. 6200. 700.0 -4026. 1025. 2200. -80.39 209.2 1000. -80.42 209.4 1600. -80.40 209.3 2200. -112.5 204.9 937.5 -105.6 205.4 1600. -112.5 205.1 2200. -152.6 188.5 806.9 -123.6 190.1 1600. -152.9 189.3 2200. -205.9 171.7 712.0 -147.8 174.4 1401. -180.5 171.9 1944. -245.8 156.6 649.4 -175.9 148.5 1220. -213.0 157.9 1703. -286.7 138.7 607.8 -206.7 117.0 1093. -254.3 140.3 1531. -338.2 119.4 562.1 -265.2 112.6 1012. -298.6 112.7 1414. -395.6 95.73 510.7 -427.8 177.4 963.1 -339.6 80.55 1351. -442.1 65.54 500.0 -844.1 360.5 888.2 -445.7 81.52 1239. -579.2 66.87 500.0 -1712. 741.6 802.0 -784.2 154.8 1107. -1041. 135.3 500.0 -3426. 1485. 800.0 -1632. 336.9 1100. -2184. 301.6

[0058] Example 2: Generation of the apparent resistivity-depth section of an equatorial configuration. FIG. 6 is the arranged plan of the configuration. The distance between the survey line and the source is 2,000 m, with nine observation points in total. The right part of Table 4 gives the offsets of each observation point calculated from Equation (4), and the left part gives the geoelectric models for calculating Cagniard apparent resistivities of each observation point:

[00092]${\rho }_{i,j}^{\text{a}}=\frac{1}{\mu \text{}\omega }\frac{{\left|E_x\right|}^2}{{\left|H_y\right|}^2}$

[0059] The second column of Table 5 shows the operating frequencies of each observation point, and the third column shows calculated results.

TABLE-US-00012 Geoelectric models and offsets for observation points of the equatorial configuration Geoelectric model Observation point Offset R.sub.i Observation point Offset R.sub.i ρ.sub.1 = 200 Ω.m h.sub.1 = 100 m No.1 R.sub.1 = 2154 m No.6 R.sub.6 = 2010 m ρ.sub.2 = 100 Ω.m h.sub.2 = 200 m No.2 R.sub.2 = 2088 m No.7 R.sub.7 = 2040 m ρ.sub.3 =50 Ω.m No.3 R.sub.3 = 2040 m No.8 R.sub.8 = 2088 m No.4 R.sub.4 = 2010 m No.9 R.sub.9 = 2154 m Electric source arranged along the x-axis No.5 R.sub.5 = 2000 m Observed E.sub.x and H.sub.y components

[0060] Substituting the Cagniard apparent resistivities

[00093]${\rho }_{i,j}^{\text{a}}$

a (third column in Table 5) into Equation (6a) yields detection depths H.sub.i,j, which are listed in the fourth column in Table 5. The fifth column shows induction numbers

[00094]$\frac{R_i}{H_{i,j}}.$

[0061] For the field zones divided according to Equation (1), substituting the offsets R.sub.i and the detection depths H.sub.i,j into Equation (3) and Equation (5) yields the horizontal positions

[00095]$P_{i,j}^r$

and the vertical positions

[00096]$P_{i,j}^z$

of the recording points for each observation point, which are respectively listed in the sixth and seventh columns of Table 5 to serve as the assignment points for the apparent resistivities

[00097]${\rho }_{i,j}^{\text{a}}$

in the third column. For each observation point selected from the table,

[00098]${x^{\prime }}_i,P_{i,j}^z$

and

[00099]${\rho }_{i,j}^{\text{a}}$

corresponding to the recording point

[00100]$R_i=P_{i,j}^r$

in the far-field zone are respectively taken as Column A, Column B and Column C to list in No.1-No.9 in Table 6, thereby forming data of one apparent resistivity-depth section along the survey line. Then, for each observation point,

[00101]$P_{i,j}^r$

as Column A,

[00102]$P_{i,j}^z$

as Column B, and

[00103]${\rho }_{i,j}^{\text{a}}$

a as Column C are listed in No.1-S to No.9-S in Table 6, thereby forming data of nine apparent resistivity-depth section along connecting lines from the observation points to the source. The apparent resistivity-depth sections drawn from these with the Surfer software are as shown by 7a-7f in FIG. 7 (only five sections are drawn due to the symmetry property).

TABLE-US-00013 Operating frequencies, apparent resistivities, detection depths, induction numbers and recording points for each observation point of the equatorial configuration Recording points of observation point No.1[00104]$\left(R_1=2,154\text{m,}{x}_1^{\prime }=\text{-}800\text{m}\right)$at each of frequencies j ƒ.sub.1,j/Hz [00105]${\rho }_{1,j}^{\text{a}}/\text{Ω}\text{.m}$ H.sub.1,j/m R.sub.1/H.sub.1,j [00106]$P_{1,j}^{\text{r}}/\text{m}$ [00107]$P_{1,j}^{\text{z}}/\text{m}$ 1 8192 209.1 80.36 26.8 2154. -80.36 2 4096 205.6 112.7 19.1 2154. -112.7 3 2048 190.1 153.2 14.0 2154. -153.2 4 1024 170.5 205.2 10.4 2154. -205.2 5 512 158.8 280.1 7.68 1877. -244.1 6 256 141.6 374.2 5.75 1646. -285.9 7 128 121.9 490.9 4.38 1482. -337.8 8 64 106.3 648.5 3.32 1354. -407.8 9 32 104.6 909.4 2.36 1240. -523.8 0 16 114.1 1343. 1.60 1149. -716.8 11 8 128.2 2013. 1.06 1085. -1014. 12 4 145.7 3036. 0.70 1077. -1518.

Recording points of observation point No.2 (R.sub.2=2,088 m,

[00108]${x^{\prime }}_2=$

-600 m) at each of frequencies

TABLE-US-00014 j ƒ.sub.2,j/Hz ρ.sub.2,j/Ω.m H.sub.2,j /m R.sub.2/H.sub.2,j P.sub.2,j/m P.sub.2,j/m 1 8192 209.1 80.36 25.9 2088. -80.36 2 4096 205.6 112.7 18.5 2088. -112.7 3 2048 190.1 153.2 13.6 2088. -153.2 4 1024 171.8 206.0 10.1 2088. -206.0 5 512 158.8 280.1 7.45 1792. -240.5 6 256 141.8 374.3 5.57 1574. -282.3 7 128 122.2 491.6 4.24 1420. -334.5 8 64 107.1 650.9 3.20 1300. -405.3 9 32 105.0 911.5 2.29 1193. -521.1 10 16 113.7 1341. 1.55 1108. -712.1 11 8 128.4 2015. 1.03 1048. -1011. 12 4 151.2 3093. 0.67 1044. -1546.

Recording points of observation point No. 3 (R.sub.3=2,040 m,

[00109]$\left({x^{\prime }}_3=-400\text{m}\right)$

at each of frequencies

TABLE-US-00015 j ƒ.sub.3,j/Hz ρ.sub.3,j/Ω.m H.sub.3,j/m R.sub.3/H.sub.3,j P.sub.3,j/m P.sub.3,j/m 1 8192 209.1 80.36 25.3 2040. -80.36 2 4096 205.6 112.7 18.1 2040. -112.7 3 2048 190.1 153.2 13.3 2040. -153.2 4 1024 172.4 206.4 9.88 2026. -205.0 5 512 158.8 280.2 7.28 1731. -237.8 6 256 141.9 374.5 5.44 1523. -279.7 7 128 122.5 492.2 4.14 1376. -332.1 8 64 107.7 652.7 3.12 1260. -403.4 9 32 105.4 913.1 2.23 1159. -519.1 0 16 113.7 1341. 1.52 1079. -709.4 11 8 129.4 2023. 1.00 1020. -1012. 12 4 156.9 3150. 0.64 1020. -1575.

Recording points of observation point No.4 (R.sub.4=2,010 m,

[00110]$\left({x^{\prime }}_4=-200\text{m}\right)$

at each of frequencies

TABLE-US-00016 j ƒ.sub.4,j/Hz ρ.sub.4,j/Ω.m H.sub.4,j /m R.sub.4/H.sub.4,j P.sub.4,j/m P.sub.4,j/m 1 8192 209.1 80.37 25.0 2010. -80.37 2 4096 205.6 112.7 17.8 2010. -112.7 3 2048 190.1 153.2 13.1 2010. -153.2 4 1024 172.5 206.4 9.73 1980. -203.4 5 512 158.9 280.2 7.17 1694. -236.2 6 256 142.0 374.6 5.36 1492. -278.1 7 128 122.7 492.6 4.08 1348. -330.6 8 64 108.1 653.8 3.07 1236. -402.2 9 32 105.7 914.2 2.19 1138. -517.9 0 16 113.8 1341. 1.49 1060. -708.0 11 8 130.3 2030. 0.99 1005. -1015. 12 4 161.0 3191. 0.62 1005. -1595.

Recording points of observation point No.5 (R.sub.5=2,000 m,

[00111]$\left({x^{\prime }}_5=0\text{m}\right)$

at each of frequencies

TABLE-US-00017 j ƒ.sub.5,j / Hz ρ.sub.5,j/Ω.m H.sub.5,j/m R.sub.5/H.sub.5,j P.sub.5,j/m P.sub.5,j/m 1 8192 209.1 80.37 24.8 2000. -80.37 2 4096 205.6 112.7 17.7 2000. -112.7 3 2048 190.1 153.2 13.0 2000. -153.2 4 1024 172.9 206.7 9.67 1963. -202.9 5 512 158.9 280.2 7.13 1681. -235.6 6 256 142.0 374.6 5.33 1481. -277.6 7 128 122.8 492.7 4.05 1339. -330.1 8 64 108.2 654.2 3.05 1228. -401.8 9 32 105.7 914.5 2.18 1131. -517.5 10 16 113.9 1342. 1.49 1054. -707.6 11 8 130.6 2032. 0.98 1000. -1016. 12 4 162.5 3206. 0.62 1000. -1603.

Recording points of observation point No.6 (R.sub.6=2,010 m,

[00112]$\left({x^{\prime }}_6=200\text{m}\right)$

at each of frequencies

TABLE-US-00018 j ƒ.sub.6,j / Hz ρ.sub.6,j/Ω.m H.sub.6,j /m R.sub.6/H.sub.6,j P.sub.6,j/m P.sub.6,j/m 1 8192 209.1 80.37 25.0 2010. -80.37 2 4096 205.6 112.7 17.8 2010. -112.7 3 2048 190.1 153.2 13.1 2010. -153.2 4 1024 172.5 206.4 9.73 1980. -203.4 5 512 158.9 280.2 7.17 1694. -236.2 6 256 142.0 374.6 5.36 1492. -278.1 7 128 122.7 492.6 4.08 1348. -330.6 8 64 108.1 653.8 3.07 1236. -402.2 9 32 105.7 914.2 2.19 1138. -517.9 10 16 113.8 1341. 1.49 1060. -708.0 11 8 130.3 2030. 0.99 1005. -1015. 12 4 161.0 3191. 0.62 1005. -1595.

Recording points of observation point No.7 (R.sub.7=2,040 m,

[00113]${x^{\prime }}_7=$

400 m) at each of frequencies

TABLE-US-00019 j f.sub.7,j / Hz ρ.sub.7,j/Ω.m H.sub.7,j /m R.sub.7 / H.sub.7,j P.sub.7,j/m P.sub.7,j/m 1 8192 209.1 80.36 25.3 2040. -80.36 2 4096 205.6 112.7 18.1 2040. -112.7 3 2048 190.1 153.2 13.3 2040. -153.2 4 1024 172.4 206.4 9.88 2026. -205.0 5 512 158.8 280.2 7.28 1731. -237.8 6 256 141.9 374.5 5.44 1523. -279.7 7 128 122.5 492.2 4.14 1376. -332.1 8 64 107.7 652.7 3.12 1260. -403.4 9 32 105.4 913.1 2.23 1159. -519.1 0 16 113.7 1341. 1.52 1079. -709.4 11 8 129.4 2023. 1.00 1020. -1012. 12 4 156.9 3150. 0.64 1020. -1575.

Recording points of observation point No.8 (R.sub.8=2,088 m,

[00114]${x^{\prime }}_8=$

= 600 m) at each of frequencies

TABLE-US-00020 j f.sub.8,j / Hz ρ.sub.8,j / Ω.m H.sub.8,j/m R.sub.8/H.sub.8,j P.sub.8,j/m P.sub.8,j/m 1 8192 209.1 80.36 25.9 2088. -80.36 2 4096 205.6 112.7 18.5 2088. -112.7 3 2048 190.1 153.2 13.6 2088. -153.2 4 1024 171.8 206.0 10.1 2088. -206.0 5 512 158.8 280.1 7.45 1792. -240.5 6 256 141.8 374.3 5.57 1574. -282.3 7 128 122.2 491.6 4.24 1420. -334.5 8 64 107.1 650.9 3.20 1300. -405.3 9 32 105.0 911.5 2.29 1193. -521.1 10 16 113.7 1341. 1.55 1108. -712.1 11 8 128.4 2015. 1.03 1048. -1011. 12 4 151.2 3093. 0.67 1044. -1546.

Recording points of observation point No.9 (R.sub.9=2,154 m,

[00115]$\left({x^{\prime }}_9=800\text{m}\right)$

at each of frequencies

TABLE-US-00021 j f.sub.9,j / Hz ρ.sub.9,j / Ω.m H.sub.9,j /m R.sub.9 /H.sub.9,j P.sub.9,j/m P.sub.9,j/m 1 8192 209.1 80.36 26.8 2154. -80.36 2 4096 205.6 112.7 19.1 2154. -112.7 3 2048 190.1 153.2 14.0 2154. -153.2 4 1024 170.5 205.2 10.4 2154. -205.2 5 512 158.8 280.1 7.68 1877. -244.1 6 256 141.6 374.2 5.75 1646. -285.9 7 128 121.9 490.9 4.38 1482. -337.8 8 64 106.3 648.5 3.32 1354. -407.8 9 32 104.6 909.4 2.36 1240. -523.8 10 16 114.1 1343. 1.60 1149. -716.8 11 8 128.2 2013. 1.06 1085. -1014. 12 4 145.7 3036. 0.70 1077. -1518.

TABLE-US-00022 Data for plotting the apparent resistivity-depth section of the equatorial configuration Column A corresponds to [00116]${x^{\prime }}_i$or [00117]$P^r{}_{i,j},$Column B corresponds to[00118]$P^z{}_{i,j},$and Column C corresponds to[00119]${\rho }^{\text{a}}{}_{i,j}.$ No.1-No.9 1792. -240.5 158.8 2010. -112.7 205.6 A B C 1574. -282.3 141.8 2010. -153.2 190.1 -800.0 -80.36 209.1 1420. -334.5 122.2 1980. -203.4 172.5 -800.0 -112.7 205.6 1300. -405.3 107.1 1694. -236.2 158.9 -800.0 -153.2 190.1 1193. -521.1 105.0 1492. -278.1 142.0 -800.0 -205.2 170.5 1108. -712.1 113.7 1348. -330.6 122.7 -600.0 -80.36 209.1 1048. -1011. 128.4 1236. -402.2 108.1 -600.0 -112.7 205.6 1044. -1546. 151.2 1138. -517.9 105.7 -600.0 -153.2 190.1 No.3-Source 1060. -708.0 113.8 -600.0 -206.0 171.8 A B C 1005. -1015. 130.3 -400.0 -80.36 209.1 2040. -80.36 209.1 1005. -1595. 161.0 -400.0 -112.7 205.6 2040. -112.7 205.6 No.7-Source -400.0 -153.2 190.1 2040. -153.2 190.1 A B C -200.0 -80.37 209.1 2026. -205.0 172.4 2040. -80.36 209.1 -200.0 -112.7 205.6 1731. -237.8 158.8 2040. -112.7 205.6 -200.0 -153.2 190.1 1523. -279.7 141.9 2040. -153.2 190.1 0.0 -80.37 209.1 1376. -332.1 122.5 2026. -205.0 172.4 0.0 -112.7 205.6 1260. -403.4 107.7 1731. -237.8 158.8 0.0 -153.2 190.1 1159. -519.1 105.4 1523. -279.7 141.9 200.0 -80.37 209.1 1079. -709.4 113.7 1376. -332.1 122.5 200.0 -112.7 205.6 1020. -1012. 129.4 1260. -403.4 107.7 200.0 -153.2 190.1 1020. -1575. 156.9 1159. -519.1 105.4 400.0 -80.36 209.1 No.4-Source 1079. -709.4 113.7 400.0 -112.7 205.6 A B C 1020. -1012. 129.4 400.0 -153.2 190.1 2010. -80.37 209.1 1020. -1575. 156.9 600.0 -80.36 209.1 2010. -112.7 205.6 No.8-Source 600.0 -112.7 205.6 2010. -153.2 190.1 A B C 600.0 -153.2 190.1 1980. -203.4 172.5 2088. -80.36 209.1 600.0 -206.0 171.8 1694. -236.2 158.9 2088. -112.7 205.6 800.0 -80.36 209.1 1492. -278.1 142.0 2088. -153.2 190.1 800.0 -112.7 205.6 1348. -330.6 122.7 2088. -206.0 171.8 800.0 -153.2 190.1 1236. -402.2 108.1 1792. -240.5 158.8 800.0 -205.2 170.5 1138. -517.9 105.7 1574. -282.3 141.8 No.1-Source 1060. -708.0 113.8 1420. -334.5 122.2 A B C 1005. -1015. 130.3 1300. -405.3 107.1 2154. -80.36 209.1 1005. -1595. 161.0 1193. -521.1 105.0 2154. -112.7 205.6 No.5-Source 1108. -712.1 113.7 2154. -153.2 190.1 A B C 1048. -1011. 128.4 2154. -205.2 170.5 2000. -80.37 209.1 1044. -1546. 151.2 1877. -244.1 158.8 2000. -112.7 205.6 No.9-Source 1646. -285.9 141.6 2000. -153.2 190.1 A B C 1482. -337.8 121.9 1963. -202.9 172.9 2154. -80.36 209.1 1354. -407.8 106.3 1681. -235.6 158.9 2154. -112.7 205.6 1240. -523.8 104.6 1481. -277.6 142.0 2154. -153.2 190.1 1149. -716.8 114.1 1339. -330.1 122.8 2154. -205.2 170.5 1085. -1014. 128.2 1228. -401.8 108.2 1877. -244.1 158.8 1077. -1518. 145.7 1131. -517.5 105.7 1646. -285.9 141.6 No.2-Source 1054. -707.6 113.9 1482. -337.8 121.9 A B C 1000. -1016. 130.6 1354. -407.8 106.3 2088. -80.36 209.1 1000. -1603. 162.5 1240. -523.8 104.6 2088. -112.7 205.6 No.6-Source 1149. -716.8 114.1 2088. -153.2 190.1 A B C 1085. -1014. 128.2 2088. -206.0 171.8 2010. -80.37 209.1 1000. -1518. 145.7

[0062] In addition, according to the present application, the detection depth may be calculated by the following general equations, or other detection depth equations:

[00120]$\begin{array}{cc}{H}_{i,j}=\sqrt{\frac{{\rho }_{i,j}^{\text{a}}}{{\mu }_0\pi f_{i,j}}}=\sqrt{\frac{{\rho }_{i,j}^{\text{a}}}{4\pi \times {10}^{-7}\pi f_{i,j}}}\approx 503\sqrt{\frac{{\rho }_{i,j}^{\text{a}}}{f_{i,j}}}& \text{­­­(6a)}\end{array}$

[00121]$\begin{array}{cc}{H}_{i,j}=\sqrt{\frac{2t_{i,j}{\rho }_{i,j}^{\text{a}}}{{\mu }_0}}=\sqrt{\frac{2t_{i,j}{\rho }_{i,j}^{\text{a}}}{4\pi \times {10}^{-7}}}\approx 1260\sqrt{t_{i,j}{\rho }_{i,j}^{\text{a}}}& \text{­­­(6b)}\end{array}$

where Equation (6a) is a frequency-domain equation,

[00122]$f_{i,j}$

is the .sup.jth frequency of the observation point .sup.i, Equation (6b) is a time-domain equation, and .sup.ti,j is observation time for a .sup.jth time window of the measuring point .sup.i.

[0063] The apparent resistivity

[00123]${\rho }_{i,j}^{\text{a}}$

can further be obtained from any definition or algorithm, such as a single-component apparent resistivity, or any future improved apparent resistivity definition and algorithm.

[0064] The above method is applicable to any configuration with the offset, regardless of an electric source or a magnetic source.

[0065] Field observation records further include a position of the source besides the positions of the observation point, so as to determine the offset.

[0066] For field zone division in Equations (1), (2), (3), and (5), a value 10 is used as a field zone division standard. The field zone division standard can further be adjusted to other values regardless of frequency-domain exploration or time-domain exploration. Such an adjustment can be made for any configuration, source and observation component.

[0067] In conclusion, the present disclosure determines, in field zones divided quantitatively based on an induction number, the positions of the recording point for each observation point and the frequency or the time window thereof. The horizontal position of the recording point in the near-field zone is a midpoint of the offset, that in the far-field zone is a position where the observation point is located, and that in the intermediate-field zone moves linearly from the midpoint of the offset to the position where the observation point is located, as the induction number increases. The vertical position of the recording point in the near-field zone and the intermediate-field zone is located at a point of intersection of the line from the detection depth to the source and the perpendicular line passing through the horizontal position of the recording point, and that in the far-field zone is equal to the detection depth. The positions of the recording point are the assignment point for the apparent resistivity corresponding to each observation point and the frequency or the time window thereof. One survey line of the axial configuration generates one apparent resistivity-depth section extending along the survey line. One survey line of the equatorial configuration typically generates one apparent resistivity-depth section along the survey line and apparent resistivity-depth sections along connecting lines from the observation points to the source which are the same as observation points in the number. The generated apparent resistivity-depth section provides a simple method to solve the shadow effect caused by nonplanarwaves in short-offset exploration, which widens the application scope of the original apparent resistivity-depth section (Phoenix Geophysics Limited and China University of Geosciences, 2010; Phoenix Geophysics Limited, 2010) interpretation method for representing the geoelectric response below the observation point.

[0068] The above examples are only used for illustrating the design ideas and characteristics of the present disclosure, and the purpose thereof is to enable the person skilled in the art to understand the contents of the present disclosure and make implementation; and the protection scope of the present disclosure is not limited to the above examples. Therefore, the equivalent changes or modifications made on the basis of principles and design idea disclosed in the present disclosure are within the protection scope of the present disclosure.