CN114942474A - Non-coplanar transient electromagnetic tunnel forecasting device and equivalent conducting plane interpretation method thereof - Google Patents

Non-coplanar transient electromagnetic tunnel forecasting device and equivalent conducting plane interpretation method thereof Download PDF

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CN114942474A
CN114942474A CN202110492755.8A CN202110492755A CN114942474A CN 114942474 A CN114942474 A CN 114942474A CN 202110492755 A CN202110492755 A CN 202110492755A CN 114942474 A CN114942474 A CN 114942474A
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equivalent
coil
depth
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transmitting coil
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刘黎东
贾祥雨
裴世建
李耐宾
王迎晓
史存焕
闫高翔
袁真秀
雷凯
赵晓亮
程彬彬
田占峰
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China Railway Liuyuan Group Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
    • G01V3/08—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with magnetic or electric fields produced or modified by objects or geological structures or by detecting devices
    • G01V3/10—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation operating with magnetic or electric fields produced or modified by objects or geological structures or by detecting devices using induction coils
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V3/00—Electric or magnetic prospecting or detecting; Measuring magnetic field characteristics of the earth, e.g. declination, deviation
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Abstract

The invention provides a non-coplanar transient electromagnetic tunnel forecasting device which comprises a transmitting coil and a receiving coil, wherein one of the transmitting coil and the receiving coil is placed on a tunnel face, and the other one of the transmitting coil and the receiving coil is placed in front of the tunnel face. The method includes the steps of enabling a transmitting loop to be equivalent to superposition of a plurality of electric dipoles, enabling a full space to be equivalent to an infinite conducting plane, calculating an electromagnetic field generated by the electric dipoles according to a mirror image principle, and finally calculating the response of an integral return line source according to the superposition principle. The forecasting device adopts a separating coil to acquire data of single component or three components; the interpretation method is characterized in that the transmitting coil is equivalent to the superposition of a plurality of electric dipoles, approximate electromagnetic response is calculated for each electric dipole by adopting an equivalent conductive plane method, and the equivalent conductive plane interpretation of the transient electromagnetic non-coplanar device is realized according to the superposition principle or the approximate forward modeling of the whole transmitting coil, so that the mutual inductance influence between the transmitting coil and the receiving coil can be effectively avoided.

Description

Non-coplanar transient electromagnetic tunnel forecasting device and equivalent conducting plane interpretation method thereof
Technical Field
The invention belongs to the field of advanced geological forecast electromagnetic prospecting of tunnels, and particularly relates to a non-coplanar transient electromagnetic tunnel forecasting device and an equivalent conducting plane interpretation method thereof.
Background
The tunnel construction process can face to complicated water-bearing geological structures such as water inrush, mud inrush, sand inrush and underground rivers, and the tunnel construction safety is greatly threatened. The transient electromagnetic method is an effective geophysical exploration tool, and has remarkable research results in the aspect of low-resistance anomaly detection. Through years of development and application, transient electromagnetism is widely applied to the aspect of advanced geological prediction of tunnels, particularly to the aspect of detecting water-bearing structures in front of a tunnel face. At present, a coplanar device is mainly adopted for tunnel transient electromagnetic advanced prediction, and the tunnel transient electromagnetic advanced prediction is used for transmitting and receiving on a tunnel face and detecting water-containing structures in different forms. The coplanar device needs to be close to the face for detection, so that potential safety hazards exist for constructors; in addition, the coplanar device has a higher mutual inductance effect of the receiving and transmitting coils, which affects the detection effect.
So far, tunnel transient electromagnetism mainly adopts an apparent resistivity definition interpretation method of a coplanar device to perform data interpretation, and the data interpretation is performed from a ground half-space apparent resistivity technology to transient electromagnetism full-space apparent resistivity definition. And for mutual inductance influence, a correction coefficient method is mainly adopted, so that not only is the correction coefficient determined, but also the mutual inductance influence is not avoided.
Disclosure of Invention
The invention provides a non-coplanar transient electromagnetic tunnel forecasting device and an equivalent conductive plane interpretation method thereof, aiming at the technical problems in the prior art, wherein the forecasting device adopts a separation coil to acquire data of single component or three components; the interpretation method is characterized in that the transmitting coil is equivalent to the superposition of a plurality of electric dipoles, approximate electromagnetic response is calculated for each electric dipole by adopting an equivalent conductive plane method, and the equivalent conductive plane interpretation of the transient electromagnetic non-coplanar device is realized according to the superposition principle or the approximate forward modeling of the whole transmitting coil, so that the mutual inductance influence between the transmitting coil and the receiving coil can be effectively avoided, and the data acquisition personnel can leave the tunnel face to improve the construction safety.
The technical scheme adopted by the invention is as follows: a non-coplanar transient electromagnetic tunnel forecasting device comprises
The device comprises a transmitting coil and a receiving coil, wherein one of the transmitting coil and the receiving coil is placed on the tunnel face, and the other one of the transmitting coil and the receiving coil is placed in front of the tunnel face.
The distance between the transmitting coil and the receiving coil is within 2 times of the side length of the transmitting coil.
The technical scheme adopted by the invention is as follows: the equivalent conducting plane interpretation method of the measured data of the non-coplanar transient electromagnetic tunnel forecasting device,
the transmission loop is equivalent to the superposition of a plurality of electric dipoles, the full space is equivalent to an infinite conductive plane, an electromagnetic field generated by the electric dipoles is calculated according to a mirror image principle, and finally the response of the whole return line source is calculated according to a superposition principle.
Specifically, the magnetic source is divided into m electrical sources, and the approximate calculation formula of the transient electromagnetic field at a certain point in space is
Figure BDA0003052157720000021
Wherein H z Represents the vertical magnetic field component, t is time, in seconds; i is the current intensity in the loop, h is the distance from the coil to the equivalent plane, x, y and z are space coordinates, pi is 3.14, mu 0 Is the permeability constant in vacuum;
order to
Figure BDA0003052157720000022
Then
Figure BDA0003052157720000023
For horizontal laminar media, the depth h of the equivalent conducting plane is introduced Effect of (1) ：
Figure BDA0003052157720000024
Wherein σ (z) is the conductivity of the medium, H is the depth of investigation, S is the total longitudinal conductance of the medium above the depth of investigation, and g is a relative weight parameter that determines the upper and lower formations;
for varying depths of investigation H, formula (4) H z As a function of H to
Figure BDA0003052157720000031
Wherein
Figure BDA0003052157720000032
Gradually increasing H by formula (6), calculating a transition curve for each H value to obtain a set of H z (H) The envelope equation of the set of curves is obtained as
Figure BDA0003052157720000033
Solving equation (7) can obtain
Figure BDA0003052157720000034
Wherein
Figure BDA0003052157720000035
I.e. the equivalent conductive plane depth corresponding to a certain study depth H, therefore
Figure BDA0003052157720000036
According to the optimization principle, when g is 4.25 and C is 1.4, the linearity of the transient response obtained by the equivalent conducting plane algorithm and the filter solution under the log-log coordinate is the highest, and then the corresponding approximate magnetic field strength calculation formula is as follows:
Figure BDA0003052157720000037
when the collected data is voltage, according to the formula (11), the calculation formula of the time derivative of the magnetic induction intensity can be obtained as follows:
Figure BDA0003052157720000041
the equivalent conducting plane longitudinal conductance S value can be calculated by the formula (12), so that the resistivity of the underground medium can be calculated.
Further, according to the formula (11), the study depth expression is:
Figure BDA0003052157720000042
from equation (13), the study depth equation is derived as:
Figure BDA0003052157720000043
where N denotes an N-layer medium,. sigma. i And h i The conductivity and the thickness of the ith layer of medium are expressed, and the conductivity of each layer of medium stratum can be obtained according to the formula;
the conductivity of the subsurface medium can be calculated from the longitudinal conductance and the study depth formula relationship:
Figure BDA0003052157720000044
to obtain S τ (t) and h τ And (t) performing primary and secondary differentiation on the apparent longitudinal conductance data with respect to the depth to obtain apparent longitudinal conductance differential imaging data.
The second differential of the apparent longitudinal conductance has good identification capability on the interface of the earth electric model, and the direction of curve take-off reflects the resistivity variation trend of the adjacent interface; the amplitude reflects the magnitude of the resistivity difference between adjacent interfaces.
Compared with the prior art, the invention has the beneficial effects that:
1. the improvement of the tunnel transient electromagnetic device can effectively avoid mutual inductance between coils, and can improve the emission magnetic moment by increasing the current intensity so as to improve the detection depth.
2. The calculation of the resistivity parameter of the invention not only meets the full-space form of the tunnel, but also is simpler.
3. The method can give the electrical distribution of the medium and also can approximately give the geometric boundary of the abnormal body based on the equivalent conductive plane, and provides a more visual and accurate explanation method for the tunnel transient electromagnetic advanced prediction.
Drawings
FIG. 1 is a schematic perspective view of a tilted fault model designed according to the present invention;
FIG. 2 is a schematic cross-sectional view of a tilted fault model designed according to the present invention;
FIG. 3 is an equivalent diagram of a magnetic source electric dipole according to the present invention;
FIG. 4 is a schematic diagram of an equivalent conductive plane of a tunnel according to the present invention;
FIG. 5 is a schematic diagram illustrating the depth of transient electromagnetic resistivity of a tilted fault model non-coplanar device according to the present invention;
FIG. 6 is a schematic diagram for explaining transient electromagnetic differential conductance of the inclined fault model non-coplanar device.
In the figure, 1-transmitting coil, 2-receiving coil, 3-tunnel face.
Detailed Description
In order to make the technical solutions of the present invention better understood, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Model design: as shown in fig. 1-2, a tunnel face front inclined fault model is designed, the fault is inclined by 15 degrees, the interface center point is located at 20m in front of the face, the first layer resistivity is 200 Ω · m, and the second layer resistivity is 2000 Ω · m.
The embodiment of the invention provides a non-coplanar transient electromagnetic tunnel forecasting device, which comprises a transmitting coil and a receiving coil, wherein the transmitting coil is placed on a tunnel face, and the length of a transmitting side is 3 m; the receiving coil is placed in front of the tunnel face and 5m away from the tunnel face.
The embodiment of the invention also provides an equivalent conducting plane interpretation method of the measured data of the non-coplanar transient electromagnetic tunnel prediction device,
the transmission loop is equivalent to the superposition of a plurality of electric dipoles, the full space is equivalent to an infinite conducting plane, an electromagnetic field generated by the electric dipoles is calculated according to a mirror image principle, and finally the response of the whole return line source is calculated according to a superposition principle.
As shown in fig. 3(a), the transmission loop is equivalent to a combination of multiple electric dipoles; as can be seen from fig. 3(a), the field of a single dipole at the measurement point is known, and the field of the transmission loop at any point can be equivalent to the superposition of multiple electric dipoles. As shown in fig. 4, the tunnel medium is replaced by an infinite large conducting plane, using the mirror principleCan calculate the field generated by any dipole, A in the figure 1 B 1 -A i B i Represents a source, A 1 ’B 1 ’-A i ’B i ' denotes a mirror field.
Specifically, the magnetic source is divided into m electrical sources, and the approximate calculation formula of the transient electromagnetic field at a certain point in space is
Figure BDA0003052157720000061
Wherein H z Represents the vertical magnetic field component, t is time, in seconds; i is the current intensity in the loop, h is the distance from the coil to the equivalent plane, x, y and z are space coordinates, pi is 3.14, mu 0 Is the permeability constant in vacuum;
order to
Figure BDA0003052157720000062
Then
Figure BDA0003052157720000063
For a horizontal laminar medium, the depth h of the equivalent conductive plane is introduced Effect(s) of promoting digestion ：
Figure BDA0003052157720000064
Wherein σ (z) is the conductivity of the medium, H is the depth of investigation, S is the total longitudinal conductance of the medium above the depth of investigation, and g is a relative weight parameter that determines the upper and lower formations;
for varying depths of investigation H, formula (4) H z As a function of H to
Figure BDA0003052157720000065
Wherein
Figure BDA0003052157720000066
Gradually increasing H by formula (6), calculating a transition curve for each H value to obtain a set of H z (H) The envelope equation of the set of curves is obtained as
Figure BDA0003052157720000071
Solving equation (7) can obtain
Figure BDA0003052157720000072
Wherein
Figure BDA0003052157720000073
I.e. the equivalent conductive plane depth corresponding to a certain study depth H, therefore
Figure BDA0003052157720000074
Fitting and optimizing coefficients C and g according to a uniform half-space analytic solution and an equivalent conductive plane solution, wherein when g is 4.25 and C is 1.4, the linearity degree of a transient response obtained by an equivalent conductive plane algorithm and a filtering solution under a log-log coordinate is the highest, and at the moment, a corresponding approximate magnetic field strength calculation formula is as follows:
Figure BDA0003052157720000075
when the collected data is voltage, according to the formula (11), the calculation formula of the time derivative of the magnetic induction intensity can be obtained as follows:
Figure BDA0003052157720000076
the equivalent conducting plane longitudinal conductance S value can be calculated by the formula (12), so that the resistivity of the underground medium can be calculated.
According to the formula (11), the study depth expression is:
Figure BDA0003052157720000081
from equation (13), the study depth formula can be derived as:
Figure BDA0003052157720000082
where N denotes an N-layer medium,. sigma. i And h i The conductivity and the thickness of the ith layer of medium are expressed, and the conductivity of each layer of medium stratum can be obtained according to the formula;
the conductivity of the subsurface medium can be calculated according to the longitudinal conductance and the research depth formula relation:
Figure BDA0003052157720000083
to obtain S τ (t) and h τ And (t) carrying out primary and secondary differentiation on the apparent longitudinal conductance data with respect to the depth to obtain apparent longitudinal conductance differential imaging data. The second differential of the apparent longitudinal conductance has good identification capability on the interface of the earth-electricity model, and the curve take-off direction reflects the resistivity variation trend of the adjacent interface; the amplitude reflects the magnitude of the resistivity difference between adjacent interfaces. The final result of the interpretation method is shown in fig. 5 and 6, the transformation of the medium resistivity can be seen from fig. 5, the inclination and the depth position of the dip fault can be determined from fig. 6, and the result is consistent with the model design.
The present invention has been described in detail with reference to the embodiments, but the description is only illustrative of the present invention and should not be construed as limiting the scope of the invention. The scope of the invention is defined by the claims. The technical solutions of the present invention or those skilled in the art, based on the teaching of the technical solutions of the present invention, should be considered to be within the scope of the present invention, and all equivalent changes and modifications made within the scope of the present invention or equivalent technical solutions designed to achieve the above technical effects are also within the scope of the present invention.

Claims (5)

1. A non-coplanar transient electromagnetic tunnel forecasting device, comprising: the device comprises a transmitting coil and a receiving coil, wherein one of the transmitting coil and the receiving coil is placed on a palm surface, and the other one of the transmitting coil and the receiving coil is placed in front of the palm surface.
2. The non-coplanar transient electromagnetic tunnel forecasting device of claim 1, wherein: the distance between the transmitting coil and the receiving coil is within 2 times of the side length of the transmitting coil.
3. A method of equivalent conducting plane interpretation of measurement data using a non-coplanar transient electromagnetic tunnel forecasting device as claimed in claim 1 or 2, characterized in that:
the transmission loop is equivalent to the superposition of a plurality of electric dipoles, the full space is equivalent to an infinite conductive plane, an electromagnetic field generated by the electric dipoles is calculated according to a mirror image principle, and finally the response of the whole return line source is calculated according to a superposition principle.
4. The equivalent conductive plane interpretation method of claim 3, wherein: the magnetic source is divided into m electric sources, and the approximate calculation formula of the transient electromagnetic field at a certain point in space is as follows
Figure FDA0003052157710000011
Wherein H z Representing the vertical magnetic field component, t is time in seconds(ii) a I is the current intensity in the loop, h is the distance from the coil to the equivalent plane, x, y and z are space coordinates, pi is 3.14, mu 0 Is the permeability constant in vacuum;
order to
Figure FDA0003052157710000012
Then
Figure FDA0003052157710000013
For a horizontal laminar medium, the depth h of the equivalent conductive plane is introduced Effect of (1) ：
Figure FDA0003052157710000014
Wherein σ (z) is the conductivity of the medium, H is the depth of investigation, S is the total longitudinal conductance of the medium above the depth of investigation, and g is a relative weight parameter that determines the upper and lower formations;
for varying depths of investigation H, H of formula (4) z As a function of H to
Figure FDA0003052157710000021
Wherein
Figure FDA0003052157710000022
Gradually increasing H by formula (6), calculating a transition curve for each H value to obtain a set of H z (H) The envelope equation of the set of curves is obtained as
Figure FDA0003052157710000023
Solving equation (7) can obtain
Figure FDA0003052157710000024
Wherein
Figure FDA0003052157710000025
I.e. the equivalent conductive plane depth corresponding to a certain study depth H, therefore
Figure FDA0003052157710000026
According to the optimization principle, when g is 4.25 and C is 1.4, the linearity degree of the transient response obtained by the equivalent conducting plane algorithm and the filter solution under the log-log coordinate is the highest, and then the corresponding approximate magnetic field strength calculation formula is as follows:
Figure FDA0003052157710000031
when the collected data is voltage, according to the formula (11), the calculation formula of the time derivative of the magnetic induction intensity can be obtained as follows:
Figure FDA0003052157710000032
the equivalent conducting plane longitudinal conductance S value can be calculated by the formula (12), so that the resistivity of the underground medium can be calculated.
5. The equivalent conductive plane interpretation method of claim 4, wherein: according to the formula (11), the study depth expression is:
Figure FDA0003052157710000033
from equation (13), the study depth formula can be derived as:
Figure FDA0003052157710000034
where N denotes an N-layer medium,. sigma. i And h i Represents the conductivity and thickness of the ith layer medium;
the conductivity of the subsurface medium can be calculated from the longitudinal conductance and the study depth formula relationship:
Figure FDA0003052157710000035
to obtain S τ (t) and h τ And (t) performing primary and secondary differentiation on the apparent longitudinal conductance data with respect to the depth to obtain apparent longitudinal conductance differential imaging data.
CN202110492755.8A 2021-05-06 2021-05-06 Non-coplanar transient electromagnetic tunnel forecasting device and equivalent conducting plane interpretation method thereof Pending CN114942474A (en)

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106646638A (en) * 2017-01-24 2017-05-10 山东大学 Solid source transient electromagnetic three-dimensional tunnel advanced forecasting method

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106646638A (en) * 2017-01-24 2017-05-10 山东大学 Solid source transient electromagnetic three-dimensional tunnel advanced forecasting method

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
伍小刚 等: "传统瞬变电磁法的改进及其在隧道超前地质预报中的应用", 水文地质工程地质, vol. 48, no. 01, 31 January 2021 (2021-01-31), pages 163 - 170 *
张莹莹: "地空瞬变电磁法逆合成孔径成像方法研究", 中国博士学位论文全文数据库·基础科学辑, no. 02, 15 February 2017 (2017-02-15), pages 49 - 56 *

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