Method for dividing electric dipole source CSAMT field region

Abstract

The invention discloses a method for dividing an electric dipole source CSAMT field region, and the method comprises the steps: defining a last coincidence point of an apparent resistivity curve of a whole region and a far region of an electric field Ex component as a far region separation point from a high-frequency end to a low-frequency end, and recording a corresponding induction number as B = crifar-tran; in the direction from the low-frequency end to the high-frequency end, the last coincidence point of the whole area of the electric field Ex component and the near area apparent resistivity curve is defined as a near area separation point, and the corresponding induction number is recorded as B = critra-new. The method for dividing the field by the determined induction number can adapt to various geoelectric structures, and provides a universally applicable and non-empirical standard for defining the field.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic exploration, and in particular relates to a method for dividing an electric dipole source CSAMT field area. Background Art

[0002] In CSAMT (controlled source audio-frequency magneto-tellurics) exploration, the division of field zones is an important issue. Zonge and Hughes (1991: p723-725, 740) defined the area where the difference between Cagnird resistivity and true resistivity does not exceed 5% as the far zone based on the simulation results of the electric dipole source field on a uniform earth with a resistivity of 100 Ω.m: x and H y For the equatorial device, when B=(r min / δ FD )>4 is the far zone; for observation E x and H y Axial device, when B = (r min / δ FD )>5 is far zone; for observation E y and H x When B=(r min / δ FD )>3 is the far zone. This method of dividing the far zone based on the determined induction number B has been widely used for a long time, such as the minimum offset distance r in the technical regulations. min The selection of (such as the Ministry of Land and Resources of the People's Republic of China, 2015: p3, 27), and the recently published patent CN117031561A (Cao Qinghua and Yan Shu, 2023) all use the above B value as the standard for entering the far zone.

[0003] Since the induction numbers for dividing the field area are obtained under specific geoelectric conditions, in many cases, it is still necessary to rely on experience to divide the field area. In order to generalize the method of dividing the field area by determining the induction numbers from uniform earth with a specific resistivity to uniform earth with any resistivity, layered earth with any layer parameters, and two-dimensional and three-dimensional geoelectric structures with any geoelectric parameters, the present invention proposes a new method for dividing the electric dipole source CSAMT field area. Summary of the invention

[0004] The method for dividing the electric dipole source CSAMT field area proposed in the present invention is to determine the induction number B=cri as the standard for entering the far zone according to the far zone separation point of the defined full zone apparent resistivity curve and the far zone apparent resistivity curve. far-tranAccording to the near-area separation point between the full-area apparent resistivity curve and the near-area apparent resistivity curve, the induction number B=cri is determined as the near-area standard. tran-near The field division method proposed in the present invention is no longer limited to specific geoelectric conditions and can adapt to different geoelectric structures. The method described in the present invention not only expands the scope of application of field division methods for exploration projects and provides a more universal standard for the selection of minimum offset distance in construction design, but also provides new means and tools for exploration theory research, data interpretation, etc.

[0005] The technical solution adopted by the present invention is:

[0006] A method for dividing the CSAMT field area of ​​an electric dipole source, from the high frequency end to the low frequency direction, the electric field E x The last coincidence point of the apparent resistivity curve of the whole area and the apparent resistivity curve of the far area is defined as the far area separation point. The induction number corresponding to the far area separation point is recorded as B=cri far-tran ; From the low frequency end to the high frequency direction, the electric field E x The last coincidence point of the apparent resistivity curve of the whole area and the apparent resistivity curve of the near area is defined as the near area separation point, and the induction number corresponding to the near area separation point is recorded as B=cri tran-near ;

[0007] According to the above-defined far-zone separation point and near-zone separation point and the induction numbers corresponding to the separation points, the field area is divided into:

[0008] B≥cri far-tran The area is the far zone, cri tran-near <B<cri far-tran The area is the transition zone, B≤cri tran-near The area is the near area.

[0009] Furthermore, the electric field E at each frequency point x The apparent resistivity of the whole area It is obtained by the following simple iterative formula

[0010]

[0011] Electric field E x Far-field apparent resistivity of the component It is obtained by the following direct calculation formula

[0012]

[0013] Electric field E x Near-zone apparent resistivity of the component It is obtained by the following direct calculation formula

[0014]

[0015] The induction number B is defined by the following formula

[0016]

[0017] The detection depth δ FD It can be calculated from the skin depth formula

[0018]

[0019] Among them, I is the emission current intensity, unit A; l is the electric dipole length, unit m; r is the offset distance from the source point to the observation point, unit m; f is the operating frequency, unit Hz; j is the imaginary unit, μ0 is the vacuum permeability taken by the non-magnetic earth; is the angle between the observation point and the source point.

[0020] Furthermore, the electric field E x The components are obtained through theoretical formulas or actual measurements. The geoelectric model calculated theoretically in the exploration experiment stage is constructed based on the electrical logging data or other geological data in the survey area.

[0021] Furthermore, the minimum offset distance r required to achieve the far zone condition in actual exploration is min and the detection depth δ FD or the maximum depth that can be detected at a given offset r The induction number B corresponding to the far-field separation point is cri far-tran Estimate.

[0022] Furthermore, the detection depth may be calculated using an algorithm, such as an equivalent detection depth algorithm.

[0023] Furthermore, for the apparent resistivity of the whole area Curve and distant area apparent resistivity The coincidence points of the curves must satisfy the following formula:

[0024]

[0025] Apparent resistivity of the whole area Curve and near-area apparent resistivity The coincidence points of the curves must satisfy the following formula:

[0026]

[0027] Where α and β are the tolerance values ​​of the far zone separation point and the near zone separation point respectively.

[0028] Furthermore, the apparent resistivity of the whole area at each frequency point is The iterative calculation steps are as follows:

[0029] Step S1, start iteration from the high frequency end, set the initial apparent resistivity of the whole area to

[0030] Step S2, setting the initial value of the number of iterations n=0 and the maximum value of the number of iterations N at each frequency point;

[0031] Step S3: Initial value of apparent resistivity of the whole area Substitute the simple iterative formula of the apparent resistivity of the entire area to calculate a new apparent resistivity value if The apparent resistivity at this frequency is And terminate the iterative calculation of this frequency point. Repeat steps S2 to S3 as the initial value of the next frequency point to calculate the apparent resistivity of the entire area at the next frequency point; δ is the accuracy value.

[0032] Step S4, if Then continue the iterative calculation of the apparent resistivity of the whole area at this frequency point, the number of iterations n = n + 1, if n ≤ N, then Input to step S3, and perform the iterative calculation of steps S3 to S4 again;

[0033] Step S5, if n>N then Terminate the iterative calculation of the apparent resistivity of the entire area at this frequency point.

[0034] Further, the initial value of the apparent resistivity of the whole area in step S1 is In theoretical calculations, the resistivity value of the first layer of the geoelectric model is taken; in exploration projects, the Cagniard resistivity or the E calculated by the formula for calculating the apparent resistivity of the distant area is taken. x The first curve value of distant area apparent resistivity.

[0035] Furthermore, the maximum value of iteration is N=20.

[0036] Furthermore, the precision value is δ=10 -5 .

[0037] Beneficial Effects

[0038] 1) The existing applicable conditions for dividing the field area by determining the induction number are extended from the uniform earth with a resistivity of 100Ω.m to the uniform and layered earth with arbitrary layer parameters, as well as two-dimensional and three-dimensional geoelectric structures.

[0039] 2) The far zone separation point and the near zone separation point defined in the present invention not only make the method of dividing the field area more universal and applicable, but also supplement the missing standard of dividing the near zone by determining the induction number.

[0040] 3) The present invention not only provides a generally applicable site division method for construction design, but also provides new means and standards for research work such as CSAMT exploration theory and data interpretation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is the angle between the observation point and the source point Schematic diagram of .

[0042] Figure 2 is the uniform electric field E on the ground x Apparent resistivity curve of the component.

[0043] Figure 3 is the electric field E on the layered earth x Apparent resistivity curve of the component.

[0044] In the figure: 1 source point; 2 observation point; 3 electric field E x The apparent resistivity curve of the whole area of ​​the component; 4 Electric field E x Far-field apparent resistivity curve of component; 5 Electric field E x 1. Near zone apparent resistivity curve of the component; 2. Far zone separation point; 3. Near zone separation point. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0046] The present invention proposes a method for dividing the electric dipole source CSAMT field area, which is to divide the electric field E from the high frequency end to the low frequency end. x The last overlapping point of the full-area apparent resistivity curve 3 and the distant-area apparent resistivity curve 4 of the component is defined as the distant-area separation point 6. The induction number corresponding to the distant-area separation point 6 is recorded as B=cri far-tran ; From the low frequency end to the high frequency direction, the electric field E x The last overlapping point of the full-area apparent resistivity curve 3 and the near-area apparent resistivity curve 5 of the component is defined as the near-area separation point 7. The induction number corresponding to the near-area separation point 7 is recorded as B=cri tran-near .

[0047] According to the above-defined far zone separation point 6 and near zone separation point 7 and the induction numbers corresponding to the separation points, the field area is divided into:

[0048] B≥cri far-tran The area is the far zone, cri tran-near <B<cri far-tran The area is the transition zone, B≤cri tran-near The area is the near area.

[0049] In this embodiment, the electric field E x The components can be calculated by theoretical formulas or obtained by actual measurements. The geoelectric model calculated theoretically during the exploration experiment phase is constructed based on the electrical logging data or other geological data of the survey area.

[0050] In this embodiment, the electric field E at each frequency point x The apparent resistivity of the whole area (unit Ω·m) can be obtained by the following simple iterative formula

[0051]

[0052] In this embodiment, the electric field E x Far-field apparent resistivity of the component (unit Ω·m) is obtained by the following direct calculation formula

[0053]

[0054] In this embodiment, the electric field E x Near-zone apparent resistivity of the component (unit Ω·m) is obtained by the following direct calculation formula

[0055]

[0056] The induction number B is defined by the following formula

[0057]

[0058] The detection depth δ FD It can be calculated from the skin depth formula

[0059]

[0060] In the above formulas, I is the emission current intensity (unit A), l is the electric dipole length (unit m), r is the offset distance from the source point to the observation point (unit m), f is the operating frequency (unit Hz), j is the imaginary unit, μ0 = 4π × 10 -7 H / m is the vacuum magnetic permeability of the non-magnetic earth. is the angle between the observation point and the source point (e.g. Figure 1 shown).

[0061] In this embodiment, for the apparent resistivity of the whole area Curve and distant area apparent resistivity The curve coincidence point (i.e., the far zone separation point 6) must satisfy the following formula:

[0062]

[0063] In this embodiment, for the apparent resistivity of the whole area Curve and near-area apparent resistivity The curve overlap point (near zone separation point 7) must satisfy the following formula:

[0064]

[0065] Where α and β are the tolerance values ​​of the far zone separation point and the near zone separation point respectively. The tolerance values ​​can be determined according to the actual project.

[0066] In this embodiment, since the apparent resistivity of the whole area at each frequency point is It needs to be calculated iteratively, so the apparent resistivity of the whole area The calculation can be performed using the following steps:

[0067] Step S1, start iteration from the high frequency end, set the initial apparent resistivity of the whole area to

[0068] Step S2, setting the initial value of the number of iterations n=0 and the maximum value of the number of iterations N at each frequency point;

[0069] Step S3: Initial value of apparent resistivity of the whole area Substitute the simple iterative formula (1) to calculate a new apparent resistivity value If the absolute value of the difference in apparent resistivity of the entire area before and after iteration is less than or equal to the accuracy value The apparent resistivity at this frequency is And terminate the iterative calculation of this frequency point. Repeat steps S2 to S3 as the initial value of the next frequency point to calculate the apparent resistivity of the whole area at the next frequency point;

[0070] Step S4: If the absolute value of the apparent resistivity difference of the whole area before and after the iteration is greater than the accuracy value Then continue the iterative calculation of the apparent resistivity of the whole area at this frequency point, the number of iterations n = n + 1, if n ≤ N, then Input to step S3, and perform the iterative calculation of steps S3 to S4 again;

[0071] Step S5, if n>N, then Terminate the iterative calculation of the apparent resistivity of the entire area at this frequency point.

[0072] In this embodiment, the precision value δ in the above steps is 10 -5 .

[0073] The following two specific examples are used to further illustrate:

[0074] Example 1: Calculate the electric field E on the uniform ground using a theoretical formula xComponent (Table 1), according to step S1, iterate from the high frequency end f = 8192Hz of the second column of Table 1, and the initial value of the apparent resistivity of the whole area is the resistivity of the first layer of the geoelectric model The maximum number of iterations N = 20, the precision value δ = 10 -5 Then execute steps S2 to S5 to obtain the apparent resistivity of the whole area. Together with the distant area apparent resistivity calculated using formula (2) And the near-zone apparent resistivity calculated by formula (3) They are listed in columns 4, 5, and 6 of Table 1 and plotted on Figure 2 Columns 7 and 8 of Table 1 use formula (5) and formula (4) to calculate the skin depth δ corresponding to each frequency point FD and induction number B. According to Table 1 and Figure 2 , from high frequency to low frequency, and The last coincidence point of the curve is approximately at the frequency point f = 2048 Hz. From formula (6a), we know that the tolerance value of this point α≈0.386%, which is considered to meet the engineering requirements. Therefore, the corresponding induction number B = cri far-tran =5.69 as the far zone separation point. From low frequency to high frequency, and The last coincidence point of the curve is approximately at the frequency point f = 2 Hz. From formula (6b), we know that the tolerance value β at this point is ≈ 0.361%, which is considered to meet the engineering requirements. Therefore, the corresponding induction number B = cri tran-near =0.17 as the near zone separation point.

[0075] In the given case of the first embodiment, the region where B≥5.69 is the far region, the region where 0.17<B<5.69 is the transition region, and the region where B≤0.17 is the near region.

[0076] From Table 1: Skin depth δ corresponding to the far zone separation point (f = 2048 Hz) FD =351.48m. According to formula (4) It can be seen that the minimum offset distance r required to detect a depth of 351.48 m is min = 2000m. In other words, the maximum detection depth given an offset distance r = 2000m

[0077] Table 1 Operating frequency and electric field E of the CSAMT electric dipole source on uniform ground x Component, apparent resistivity, skin depth and induction

[0078]

[0079]

[0080] Example 2: Calculate the electric field E on the layered earth using a theoretical formula x Component (Table 2), according to step S1, iterate from the high frequency end f = 8192Hz of the second column of Table 2, and the initial value of the apparent resistivity of the whole area is the resistivity of the first layer of the geoelectric model. The maximum number of iterations N = 20, the precision value δ = 10 -5 Then execute steps S2 to S5 to obtain the apparent resistivity of the whole area. Together with the distant area apparent resistivity calculated using formula (2) And the near-zone apparent resistivity calculated by formula (3) They are listed in columns 4, 5, and 6 of Table 2 and plotted on Figure 3 ; The 7th and 8th columns of Table 2 are the skin depths δ calculated using formulas (5) and (4) FD and induction number B. According to Table 2 and Figure 3 , from high frequency to low frequency, and The last coincidence point of the curve is approximately at the frequency point f = 32 Hz. From formula (6a), we can know that the tolerance value of this point α≈0.534%, which is considered to meet the engineering requirements. Therefore, the corresponding induction number B=cri far-tran =5.20 as the far zone separation point; from low frequency to high frequency, and The last coincidence point of the curve is approximately at the frequency point f = 0.25 Hz. From formula (6b), we know that the tolerance value β at this point is ≈ 0.658%, which is considered to meet the engineering requirements. Therefore, the corresponding induction number B = cri tran-near =0.21 as the near zone separation point.

[0081] In the given case of the second embodiment: the area where B≥5.20 is the far area, the area where 0.21<B<5.20 is the transition area, and the area where B≤0.21 is the near area.

[0082] Table 2: Skin depth δ corresponding to the far zone separation point (f = 32 Hz) FD =384.8m, according to formula (4) It can be seen that the minimum offset distance r required to detect a depth of 384.8 m is min = 2000m. In other words, the maximum detection depth given an offset distance r = 2000m

[0083] Table 2 Operating frequency and electric field E of the layered earth electric dipole source CSAMT x Component, apparent resistivity, skin depth and induction

[0084]

[0085] The detection depth calculated by the skin depth formula (5) can also be obtained by other improved algorithms.

[0086] In summary, the method for dividing the electric dipole source CSAMT field zone provided by the present invention provides the definition and confirmation rules of the far zone separation point and the near zone separation point, thereby dividing the far zone, transition zone and near zone, providing a universally applicable and non-empirical standard for the definition of the field zone.

[0087] The above embodiments of the present invention only cite two one-dimensional geoelectric structures, namely uniform earth and layered earth. However, the method proposed in the present invention is not limited to the above geoelectric structures, but can also be applied to two-dimensional and three-dimensional geoelectric structures.

[0088] The above embodiments are only used to illustrate the design ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. A method for dividing the electric dipole source CSAMT field region, characterized in that: From the high frequency end to the low frequency direction, the electric field E x The last overlapping point of the full-area apparent resistivity curve (3) and the distant-area apparent resistivity curve (4) of the component is defined as the distant-area separation point (6). The induction number corresponding to the distant-area separation point (6) is recorded as B=cri far-tran ; From the low frequency end to the high frequency direction, the electric field E x The last overlapping point of the full-area apparent resistivity curve (3) and the near-area apparent resistivity curve (5) of the component is defined as the near-area separation point (7), and the induction number corresponding to the near-area separation point (7) is recorded as B=cri tran-near ; According to the above-defined far zone separation point (6) and near zone separation point (7) and the induction numbers corresponding to the separation points, the field area is divided into: B≥cri far-tran The area is the far zone, cri tran-near <B<cri far-tran The area is the transition zone, B≤cri tran-near The area is the near area.

2. A method for dividing the electric dipole source CSAMT field area according to claim 1, characterized in that: The electric field E at each frequency point x The apparent resistivity of the whole area It is obtained by the following simple iterative formula Electric field E x Far-field apparent resistivity of the component It is obtained by the following direct calculation formula Electric field E x Near-zone apparent resistivity of the component It is obtained by the following direct calculation formula The induction number B is defined by the following formula The detection depth δ FD It can be calculated from the skin depth formula Among them, I is the emission current intensity, unit A; l is the electric dipole length, unit m; r is the offset distance from the source point to the observation point, unit m; f is the operating frequency, unit Hz; j is the imaginary unit, μ0 is the vacuum permeability taken by the non-magnetic earth; is the angle between the observation point and the source point.

3. A method for dividing the electric dipole source CSAMT field area according to claim 1, characterized in that: Electric field E x The components are obtained through theoretical formulas or actual measurements. The geoelectric model calculated theoretically in the exploration experiment stage is constructed based on the electrical logging data or other geological data in the survey area.

4. A method for dividing the electric dipole source CSAMT field area according to claim 1, characterized in that: The minimum offset distance r required to achieve far zone conditions in actual exploration min and the detection depth δ FD or the maximum depth that can be detected at a given offset r The induction number B corresponding to the far-field separation point is cri far-tran Estimate.

5. A method for dividing the electric dipole source CSAMT field area according to claim 2, characterized in that: The detection depth may be calculated using an algorithm.

6. A method for dividing the electric dipole source CSAMT field area according to claim 1, characterized in that: For the apparent resistivity of the whole area Curve and distant area apparent resistivity The coincidence points of the curves must satisfy the following formula: Apparent resistivity of the whole area Curve and near-area apparent resistivity The coincidence points of the curves must satisfy the following formula: Where α and β are the tolerance values ​​of the far zone separation point and the near zone separation point respectively.

7. A method for dividing the electric dipole source CSAMT field area according to claim 1, characterized in that: The apparent resistivity of the whole area at each frequency point The iterative calculation steps are as follows: Step S1, start iteration from the high frequency end, set the initial value of apparent resistivity of the whole area to be Step S2, setting the initial value of the number of iterations n=0 and the maximum value of the number of iterations N at each frequency point; Step S3: Initial value of apparent resistivity of the whole area Substitute the simple iterative formula of the apparent resistivity of the entire area to calculate a new apparent resistivity value if The apparent resistivity at this frequency is And terminate the iterative calculation of this frequency point. Repeat steps S2 to S3 as the initial value of the next frequency point to calculate the apparent resistivity of the whole area at the next frequency point; δ is the accuracy value; Step S4, if Then continue the iterative calculation of the apparent resistivity of the whole area at this frequency point, the number of iterations n = n + 1, if n ≤ N, then Input to step S3, and perform the iterative calculation of steps S3 to S4 again; Step S5, if n>N then Terminate the iterative calculation of the apparent resistivity of the entire area at this frequency point.

8. A method for dividing the electric dipole source CSAMT field area according to claim 7, characterized in that: The initial value of apparent resistivity of the whole area in step S1 In theoretical calculations, the resistivity value of the first layer of the geoelectric model is taken; in exploration projects, the Cagniard resistivity or the E calculated by the formula for calculating the apparent resistivity of the distant area is taken. x The first curve value of distant area apparent resistivity.

9. A method for dividing the electric dipole source CSAMT field area according to claim 7, characterized in that: The maximum value of iteration is N=20.

10. A method for dividing the electric dipole source CSAMT field area according to claim 7, characterized in that: The precision value is δ=10 -5 .

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