CN112649881A - Numerical simulation method and system for anisotropic medium transient electromagnetic field - Google Patents
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Abstract
The invention provides a numerical simulation method and a numerical simulation system for an anisotropic medium transient electromagnetic field, wherein the method comprises the following steps: establishing a full-space advanced detection model; setting an anisotropic medium model; the anisotropic medium model is added into a advanced detection model, and numerical simulation of the anisotropic medium transient electromagnetic field is realized by combining a full-space transient electromagnetic three-dimensional anisotropic forward theory and a multi-direction loop source loading mode. The system comprises: the detection model establishing unit is used for establishing a full-space advanced detection model; a medium model setting unit for setting an anisotropic medium model; and the simulation unit is used for adding the anisotropic medium model into the advanced detection model and realizing the numerical simulation of the anisotropic medium transient electromagnetic field by combining a multi-direction loop source loading mode through a full-space transient electromagnetic three-dimensional anisotropic forward theory. The invention can calculate the transient electromagnetic response characteristics of different anisotropic media.
Description
Technical Field
The invention belongs to a numerical simulation technology in the field of geophysical exploration, and particularly relates to a numerical simulation method and system for an anisotropic medium transient electromagnetic field.
Background
The water damage problem caused by complex hydrogeological conditions is often encountered in coal mine production, and the serious influence is caused on the safe and efficient production of coal mines. The mine transient electromagnetic method becomes an important method for detecting the water damage of the coal mine due to the characteristics of low resistance sensitivity and the like. In the past, the research on the theory and application of the mine transient electromagnetic method is carried out by taking an underground medium as an isotropic medium, however, a large number of rock physical experiments prove that the electrical anisotropy of some rocks reaches a non-negligible degree, and the fact that the underground medium is assumed to be the electrical anisotropy medium which is more consistent with the real situation has important practical significance.
The study of the electrical anisotropy by scholars at home and abroad obtains abundant results on frequency domain methods such as a geoelectromagnetic method, an ocean controllable source electromagnetic method, a controllable source audio frequency geoelectromagnetic method and the like, but the study of the transient electromagnetic method in the anisotropic medium mainly focuses on the electrical anisotropy of near-surface and underground half-space media, including the propagation condition of an electromagnetic field in the anisotropic medium, the calculation and analysis of transient electromagnetic field response in the anisotropic medium, the influence of different factors on the transient electromagnetic response in the anisotropic medium and the like.
At present, the research on the full-space transient electromagnetic field response of the underground anisotropic medium is less, however, many phenomena are found in practical work and are difficult to reasonably explain through an isotropic theory, meanwhile, the electrical anisotropy generally exists in the earth, in order to carry out more accurate simulation on the actual state of the underground medium, the continuous adoption of the electrical isotropy hypothesis is not a reasonable choice, so that the research on the transient electromagnetic response of the anisotropic medium is needed, the specific influence of the electrical anisotropy on an actual detection result is researched, a theoretical guidance effect is provided for the data explanation work of the mine transient electromagnetic detection, and more accurate geological explanation is favorably obtained.
Disclosure of Invention
Features and advantages of the invention will be set forth in part in the description which follows, or may be obvious from the description, or may be learned by practice of the invention.
In order to overcome the problems of the prior art, the invention provides a numerical simulation method of an anisotropic medium transient electromagnetic field, which comprises the following steps:
s1, establishing a full-space advanced detection model;
s2, setting an anisotropic medium model;
and S3, adding the anisotropic medium model into a advanced detection model, and realizing the numerical simulation of the anisotropic medium transient electromagnetic field by combining a multi-direction loop source loading mode through a full-space transient electromagnetic three-dimensional anisotropic forward theory.
Optionally, the three-dimensional anisotropic forward finite difference time domain iterative format is formed by adding the conductivity tensor to the maxwell equation system to obtain an electromagnetic field basic equation suitable for the anisotropic medium and performing difference discrete processing.
Optionally, the step S3 includes:
301. determining a detection angle according to a detection scheme, and calculating the emission magnetic moment on the detection angle in a multi-direction return line source loading mode;
302. calculating an initial electromagnetic field strength value according to the emission magnetic moment;
303. and substituting the initial electromagnetic field strength value into a full-space transient electromagnetic three-dimensional anisotropy forward modeling theory to realize the numerical simulation of the anisotropic medium transient electromagnetic field.
Optionally, the step 303 of implementing numerical simulation of the transient electromagnetic field of the anisotropic medium includes:
calculating a transient electromagnetic response; and calculating the apparent resistivity according to the transient electromagnetic response, performing time-depth conversion, and drawing an apparent resistivity profile.
Optionally, in step S2, the method further includes: and establishing an isotropic medium model for comparison with other anisotropic medium models.
The invention provides a numerical simulation system of an anisotropic medium transient electromagnetic field, which comprises:
the detection model establishing unit is used for establishing a full-space advanced detection model;
a medium model setting unit for setting an anisotropic medium model;
and the simulation unit is used for adding the anisotropic medium model into a advanced detection model and realizing the numerical simulation of the anisotropic medium transient electromagnetic field by combining a multi-direction loop source loading mode through a full-space transient electromagnetic three-dimensional anisotropic forward modeling theory.
Optionally, the simulation unit is specifically configured to:
determining a detection angle according to a detection scheme, and calculating the emission magnetic moment on the detection angle in a multi-direction return line source loading mode;
calculating an initial electromagnetic field strength value according to the emission magnetic moment;
and substituting the initial electromagnetic field strength value into a full-space transient electromagnetic three-dimensional anisotropy forward modeling theory to realize the numerical simulation of the anisotropic medium transient electromagnetic field.
Optionally, the simulation unit is specifically configured to: calculating a transient electromagnetic response; and calculating the apparent resistivity according to the transient electromagnetic response, performing time-depth conversion, and drawing an apparent resistivity profile.
Optionally, the medium model setting unit is further configured to: and establishing an isotropic medium model for comparison with other anisotropic medium models.
The present invention provides a computer-readable storage medium storing at least one program executable by a computer, the at least one program, when executed by the computer, causing the computer to perform the steps of a method provided by any of the embodiments of the present invention.
The method realizes forward numerical simulation of transient electromagnetic fields of different anisotropic media under the condition of full space, calculates transient electromagnetic response characteristics of different anisotropic media, and can be used for analyzing influence factors of transient electromagnetic response of the anisotropic media.
Drawings
FIG. 1 is a flow chart of a numerical simulation method of an anisotropic medium transient electromagnetic field according to an embodiment of the present invention.
FIG. 2 is a schematic structural diagram of a system for numerical simulation of transient electromagnetic fields of anisotropic media according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of a Yee's staggered grid in an anisotropic medium.
Fig. 4 is a schematic diagram of a full-space advanced detection model.
FIG. 5 is a schematic view of sector measuring point arrangement.
Fig. 6A is a schematic view of an isotropic media model.
Fig. 6B is a schematic diagram of a VTI media model.
FIG. 6C is a schematic representation of the HTI-X media model.
Figure 6D is a schematic diagram of a TTI medium model.
FIG. 7 is a diagram showing a look-ahead resistivity profile for a bedding direction probing scheme.
FIG. 8 is a diagram showing a prior probe apparent resistivity profile for a vertical probing scheme.
Detailed Description
The invention adds the conductivity tensor into the Maxwell equation set to obtain an electromagnetic field basic equation suitable for the anisotropic medium, improves the Yee's staggered grid so as to conveniently carry out differential discrete processing on the transient electromagnetic field in the anisotropic medium, forms a full-space transient electromagnetic three-dimensional anisotropic forward theory on the basis, and realizes the numerical simulation of the transient electromagnetic field of the anisotropic medium by combining a loading method of a multidirectional return line source.
The theory of the forward three-dimensional anisotropy of the full-space transient electromagnetic is further described as follows:
firstly, establishing an electromagnetic field equation suitable for an anisotropic medium;
more specifically, the conductivity tensor is added into a Maxwell equation set to obtain an electromagnetic field basic equation suitable for the anisotropic medium;
the time domain Maxwell equation set is:
wherein, B is magnetic field induction intensity, E is electric field intensity, H is magnetic field intensity, gamma is dielectric constant, and sigma is electric conductivity.
In electrically anisotropic media, the electrical conductivity σ is replaced by an arbitrary direction tensor conductivity
An electromagnetic field suitable for anisotropic media can be established:
the basic equation of the electromagnetic field is expanded, and meanwhile, the improvement is carried out on the anisotropic medium, so that the formula (3) and the formula (4) are shown as follows:
then, carrying out difference discrete processing on the electromagnetic field equation of the anisotropic medium, and forming a time domain finite difference iterative format of three-dimensional anisotropic forward modeling on the basis;
more specifically, in the Yee's staggered grid in the anisotropic medium shown in FIG. 3, the electric field in the direction of X, Y, Z is substituted for the conductivity σ in the corresponding direction, respectively, at the time of calculationx'、σy'、σz'。
The time domain finite difference iterative format of the three-dimensional anisotropy forward model finally formed on the basis is as follows, wherein the electric field equations are formulas (5.1) to (5.3), and the magnetic field equations are formulas (6.1) to (6.3):
wherein, i, j and k respectively represent grid positions in x, y and z directions; n represents the order of iterative computation, and iteration is carried out continuously from front to back; Δ t represents the time interval of iteration, n is 0 represents the initial time, when n is 1, one step of iteration is carried out, the electromagnetic field value of the next step is calculated by using the electromagnetic field value calculated by the previous step, and the time between the two steps is Δ t;
and finally, combining a loading method of a multi-direction wire returning source on the time domain finite difference iteration format of the three-dimensional anisotropic forward modeling to form a full-space transient electromagnetic three-dimensional anisotropic forward modeling theory.
The multidirectional loop source is as follows: for an emission loop with a total area S, let the emission current be I, then the emitted magnetic moment of the loop is:
M＝IS
the elevation angle and the azimuth angle of the return line detection direction are respectively set to be theta and
the component of the emitted magnetic moment in the rectangular coordinate system is:
Mz＝IScosθ
the small loop line sources in the three directions are loaded simultaneously, and the loop line source in the synthesis target direction can realize the loading of the multidirectional loop line source. And by adopting a multidirectional wire return source loading mode, the emitted magnetic moment at a specific angle can be calculated. From the emitted magnetic moments, an initial electromagnetic field strength can be calculated to iteratively calculate subsequent electromagnetic field strengths.
Based on the above-mentioned full-space transient electromagnetic three-dimensional anisotropy forward theory, referring to fig. 1, the invention provides a numerical simulation method of an anisotropic medium transient electromagnetic field, comprising the steps of:
s1, establishing a full-space advanced detection model;
the total-space advanced detection model can be established according to an engineering example, as shown in fig. 4, a tunnel face (namely one end of a tunnel) is arranged at the center of the whole model space, the tunnel trend extends along the X-axis direction, a transmitting coil is arranged on the tunnel face, a receiving coil and the transmitting coil are overlapped, and the resistivity and the thickness of each layer are respectively set for a total-space stratum. The anisotropic medium is used as the detection region, which is represented in the model as a cube.
Relevant parameters of the advanced detection model, such as the size of the whole space, the size of the subdivided grid, medium parameters of the space where the model is located, the boundary of the model and the like can be set according to requirements.
S2, setting an anisotropic medium model;
in this embodiment, a VTI media model shown in fig. 6B, an HTI-X media model shown in fig. 6C, and a TTI media model shown in fig. 6D are respectively set according to actual operating conditions. A corresponding isotropic media model (as shown in fig. 6A) may also be provided for comparison with other anisotropic media models.
And S3, adding the anisotropic medium model into a advanced detection model, and realizing the numerical simulation of the anisotropic medium transient electromagnetic field by combining a multi-direction loop source loading mode through a full-space transient electromagnetic three-dimensional anisotropic forward theory.
In one embodiment of the present invention, the step S3 includes:
301. determining a detection angle according to a detection scheme, and calculating the emission magnetic moment on the detection angle in a multi-direction return line source loading mode;
the detection scheme can be designed according to the working mode in practical engineering, and the anisotropic medium can be detected in all directions. For example, by adopting a conventional mine transient electromagnetic detection arrangement, as shown in fig. 5, 11 direction measuring points are arranged along the bedding direction on the tunnel face to realize the detection of the front side and the left and right side walls of the tunnel face, and 9 direction measuring points are arranged in the vertical direction to realize the detection of the front side and the top bottom plate of the tunnel face. Different detection schemes are provided with different detection angles, and a multi-direction wire return source loading mode is adopted to calculate the emission magnetic moment at a specific angle.
302. Calculating an initial electromagnetic field strength value according to the emission magnetic moment;
303. and substituting the initial electromagnetic field strength value into a full-space transient electromagnetic three-dimensional anisotropy forward modeling theory to realize the numerical simulation of the anisotropic medium transient electromagnetic field.
More specifically, the initial electromagnetic field strength value is substituted into formulas (5.1) to (6.3) in the full-space transient electromagnetic three-dimensional anisotropy forward theory.
When numerical simulation of the transient electromagnetic field of the anisotropic medium is carried out, transient electromagnetic response, namely induced electromotive force, is calculated, apparent resistivity is calculated according to the induced electromotive force, time-depth conversion is carried out, and finally an apparent resistivity section diagram is drawn.
More specifically, the transient electromagnetic field of the anisotropic medium under the bedding direction detection scheme is calculated, and transient electromagnetic responses of an isotropic medium model, a VTI medium model, an HTI-X medium model and a TTI medium model are calculated respectively.
Transient electromagnetic responses of the isotropic medium model, the VTI medium model, the HTI-X medium model and the TTI medium model are calculated respectively by calculating the transient electromagnetic responses of the anisotropic medium transient electromagnetic field under the vertical direction detection scheme.
The apparent resistivity is obtained through transient electromagnetic response data calculation, then time-apparent resistivity data is converted into depth-apparent resistivity data by applying a time-depth conversion calculation formula, a sector-view resistivity section diagram is drawn according to the actual detection direction of each measuring point according to the arrangement of the measuring points, namely, data in a plurality of detection directions are arranged according to respective angles and are drawn in the same diagram, and a multi-angle section diagram is obtained, as shown in fig. 7 and 8. In fig. 7, (a) is an isotropic medium bedding direction advance detection apparent resistivity sectional view, (b) is a VTI medium bedding direction advance detection apparent resistivity sectional view, (c) is an HTI-X medium bedding direction advance detection apparent resistivity sectional view, and (d) is a TTI medium bedding direction advance detection apparent resistivity sectional view. In fig. 8, (a) is an isotropic medium vertical direction advanced detection apparent resistivity sectional view, (b) is a VTI medium vertical direction advanced detection apparent resistivity sectional view, (c) is an HTI-X medium vertical direction advanced detection apparent resistivity sectional view, and (d) is a TTI medium vertical direction advanced detection apparent resistivity sectional view.
As shown in FIG. 2, the present invention provides a system for numerical simulation of transient electromagnetic field of anisotropic medium, comprising: a detection model establishing unit 10, a medium model setting unit 20 and a simulation unit 30. Wherein:
the detection model establishing unit 10 is used for establishing a full-space advanced detection model; more specifically, a full-space advanced detection model can be established according to an engineering example, as shown in fig. 4, a tunnel face (i.e., one end of a tunnel) is arranged at the center of the whole model space, the tunnel trend extends along the X-axis direction, a transmitting coil is arranged on the tunnel face, a receiving coil and the transmitting coil are overlapped, and the resistivity and the thickness of each layer are respectively set for the full-space stratum. The anisotropic medium is used as the detection region, which is represented in the model as a cube. Relevant parameters of the advanced detection model, such as the size of the whole space, the size of the subdivided grid, medium parameters of the space where the model is located, the boundary of the model and the like can be set according to requirements.
The medium model setting unit 20 is used for setting an anisotropic medium model; in this embodiment, a VTI media model shown in fig. 6B, an HTI-X media model shown in fig. 6C, and a TTI media model shown in fig. 6D are respectively set according to actual operating conditions. The medium model setting unit 20 may further set a corresponding isotropic medium model (as shown in fig. 6A) for comparison with other anisotropic medium models.
The simulation unit 30 is connected with the detection model establishing unit 10 and the medium model setting unit 20, and the simulation unit 30 is used for adding the anisotropic medium model into the advanced detection model and realizing the numerical simulation of the anisotropic medium transient electromagnetic field by combining a full-space transient electromagnetic three-dimensional anisotropic forward modeling theory and a multi-direction loop source loading mode.
More specifically, the simulation unit 30 is configured to: determining a detection angle according to a detection scheme, and calculating the emission magnetic moment on the detection angle in a multi-direction return line source loading mode; calculating an initial electromagnetic field strength value according to the emission magnetic moment; and substituting the initial electromagnetic field strength value into a full-space transient electromagnetic three-dimensional anisotropy forward modeling theory to realize the numerical simulation of the anisotropic medium transient electromagnetic field.
The detection scheme can be designed according to the working mode in actual engineering, and the anisotropic medium can be detected in all directions. For example, by adopting a conventional mine transient electromagnetic detection arrangement, as shown in fig. 5, 11 direction measuring points are arranged along the bedding direction on the tunnel face to realize the detection of the front side and the left and right side walls of the tunnel face, and 9 direction measuring points are arranged in the vertical direction to realize the detection of the front side and the top bottom plate of the tunnel face. Different detection schemes are provided with different detection angles, and a multi-direction wire return source loading mode is adopted to calculate the emission magnetic moment at a specific angle.
When numerical simulation of the transient electromagnetic field of the anisotropic medium is carried out, transient electromagnetic response, namely induced electromotive force, is calculated, apparent resistivity is calculated according to the induced electromotive force, time-depth conversion is carried out, and finally an apparent resistivity section diagram is drawn.
The invention provides a specific numerical simulation method for solving the transient electromagnetic field response problem of the anisotropic medium, designs a full-space transient electromagnetic three-dimensional anisotropy finite difference forward simulation method, realizes the transient electromagnetic field three-dimensional forward modeling of the anisotropic medium, realizes the numerical simulation of the transient electromagnetic field of different anisotropic media under the full-space condition, provides theoretical guidance for the underground full-space transient electromagnetic method data processing and interpretation work under the anisotropic condition, and has important guiding significance for improving the detection precision of the transient electromagnetic method.
The above-described embodiment is only one embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and variations can be easily made based on the application and principle of the present invention disclosed in the present application, and the present invention is not limited to the method described in the above-described embodiment of the present invention, so that the above-described embodiment is only preferred, and not restrictive.
Claims (10)
1. A numerical simulation method of transient electromagnetic fields of anisotropic media is characterized by comprising the following steps:
s1, establishing a full-space advanced detection model;
s2, setting an anisotropic medium model;
and S3, adding the anisotropic medium model into a advanced detection model, and realizing the numerical simulation of the anisotropic medium transient electromagnetic field by combining a multi-direction loop source loading mode through a full-space transient electromagnetic three-dimensional anisotropic forward theory.
2. The method for numerical simulation of the transient electromagnetic field of the anisotropic medium as claimed in claim 1, wherein the full-space transient electromagnetic three-dimensional anisotropic forward modeling theory is formed by adding the conductivity tensor to the maxwell equation system to obtain the basic equation of the electromagnetic field suitable for the anisotropic medium and performing the differential discrete processing.
3. The method for numerical simulation of transient electromagnetic fields of anisotropic media as claimed in claim 1, wherein said step S3 comprises:
301. determining a detection angle according to a detection scheme, and calculating the emission magnetic moment on the detection angle in a multi-direction return line source loading mode;
302. calculating an initial electromagnetic field strength value according to the emission magnetic moment;
303. and substituting the initial electromagnetic field strength value into a full-space transient electromagnetic three-dimensional anisotropy forward modeling theory to realize the numerical simulation of the anisotropic medium transient electromagnetic field.
4. The method for numerical simulation of transient electromagnetic fields of anisotropic media as claimed in claim 3, wherein said step 303 of performing numerical simulation of transient electromagnetic fields of anisotropic media comprises:
calculating a transient electromagnetic response; and calculating the apparent resistivity according to the transient electromagnetic response, performing time-depth conversion, and drawing an apparent resistivity profile.
5. The method for numerical simulation of transient electromagnetic fields of anisotropic media as claimed in claim 1, wherein said step S2 further comprises: and establishing an isotropic medium model for comparison with other anisotropic medium models.
6. A system for numerical simulation of transient electromagnetic fields of anisotropic media, comprising:
the detection model establishing unit is used for establishing a full-space advanced detection model;
a medium model setting unit for setting an anisotropic medium model;
and the simulation unit is used for adding the anisotropic medium model into a advanced detection model and realizing the numerical simulation of the anisotropic medium transient electromagnetic field by combining a multi-direction loop source loading mode through a full-space transient electromagnetic three-dimensional anisotropic forward modeling theory.
7. The system for numerical simulation of transient electromagnetic fields of anisotropic media of claim 6, wherein said simulation unit is specifically configured to:
determining a detection angle according to a detection scheme, and calculating the emission magnetic moment on the detection angle in a multi-direction return line source loading mode;
calculating an initial electromagnetic field strength value according to the emission magnetic moment;
and substituting the initial electromagnetic field strength value into a full-space transient electromagnetic three-dimensional anisotropy forward modeling theory to realize the numerical simulation of the anisotropic medium transient electromagnetic field.
8. The system for numerical simulation of transient electromagnetic fields of anisotropic media of claim 7, wherein said simulation unit is specifically configured to: calculating a transient electromagnetic response; and calculating the apparent resistivity according to the transient electromagnetic response, performing time-depth conversion, and drawing an apparent resistivity profile.
9. The system for numerical simulation of transient electromagnetic fields of anisotropic media of claim 6, wherein said media model setup unit is further configured to: and establishing an isotropic medium model for comparison with other anisotropic medium models.
10. A computer-readable storage medium storing at least one program executable by a computer, the at least one program, when executed by the computer, causing the computer to perform the steps of the method of any one of claims 1 to 5.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113671581A (en) * | 2021-08-19 | 2021-11-19 | 中国自然资源航空物探遥感中心 | Transient electromagnetic three-dimensional finite difference forward modeling method and system |
| CN113671581B (en) * | 2021-08-19 | 2023-12-22 | 中国自然资源航空物探遥感中心 | Transient electromagnetic three-dimensional finite difference forward modeling method and system |
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