CN113917544A - Near-surface target position rapid delineation method based on magnetic gradient tensor eigenvalue - Google Patents

Near-surface target position rapid delineation method based on magnetic gradient tensor eigenvalue Download PDF

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CN113917544A
CN113917544A CN202111170634.8A CN202111170634A CN113917544A CN 113917544 A CN113917544 A CN 113917544A CN 202111170634 A CN202111170634 A CN 202111170634A CN 113917544 A CN113917544 A CN 113917544A
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gradient tensor
target position
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张晓娟
郑垚鑫
李诗言
邢康
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Aerospace Information Research Institute of CAS
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Abstract

The invention relates to a method for quickly delineating a near-surface target position based on magnetic gradient tensor eigenvalue, which comprises the following steps: step 1, gridding a measuring area to obtain a magnetic gradient tensor matrix of each grid point; step 2, calculating the eigenvalue of the magnetic gradient tensor matrix G and arranging the eigenvalue from large to small, and recording the eigenvalue as lambda1,λ2,λ3(ii) a Step 3, establishing a target position delineation function
Figure DDA0003293016060000011
The local maximum of the function P corresponds to the target position. The method provided by the invention has good resolution while effectively overcoming the influence of oblique magnetization, and can be applied to the rapid delineation of the near-surface target position.

Description

Near-surface target position rapid delineation method based on magnetic gradient tensor eigenvalue
Technical Field
The invention belongs to the field of geophysical aeromagnetic method detection, and particularly relates to a method for quickly delineating a near-surface target position based on a magnetic gradient tensor eigenvalue.
Background
Through the development of more than half a century, the means of magnetic prospecting have further evolved from total field measurements, total field gradient measurements, vector measurements to magnetic field tensor measurements. Magnetic gradient tensor research has been conducted abroad since the 90 s of the 20 th century and is now in commercial use. The domestic research starts late, and the research on the aspects of theoretical analysis, system integration, data processing, interpretation and the like is not deep enough. Magnetic gradient tensor measurements have the following advantages over total magnetic field or total field gradient measurements:
(1) the interference of a background field can be shielded, and the spatial geometric information of the geologic body can be more clearly reflected;
(2) the magnetic sensor is insensitive to magnetic dip angle and magnetic declination angle and has certain anti-dip magnetization capability;
(3) the information such as the magnetization direction, the geographical trend and the like of the geologic body can be well distinguished;
(4) the defect that vector measurement is sensitive to the direction is avoided, and the requirement on the direction is lowered;
(5) redundant elements of the tensor can implement error correction and noise estimation;
(6) the formal particularity of the tensor enables some new data processing methods to be applied.
At present, magnetic gradient tensor eigenvalues have been applied in the fields of geologic body boundary detection, structure circling and the like (CN 112749493A; CN 112327383A; Zheng Qiang, Guo Hua, Zhang Guibin and the like. equilibrium boundary identification method based on magnetic gradient full tensor eigenvalue. oil geophysical exploration 2020,55(2): 454) 464). With the continuous development of unmanned aerial vehicle technology, the gradient tensor measurement of a small magnetic target near the earth surface is completely feasible, and Brilliant et al adopts a small multi-rotor unmanned aerial vehicle platform to perform gradient tensor detection on the target near the earth surface, but the influence of the oblique magnetization of the geomagnetic field on the target is not considered. (H.jin, J.Guo, H.Wang, et al, Magnetic analog Detection and Localization use the Orthogonal Basis of Magnetic transducer control, IEEE Transactions on Geoscience and Remote Sensing,2020, 58(8): 5944-.
Disclosure of Invention
The invention provides a method for quickly delineating a near-surface target position based on a magnetic gradient tensor eigenvalue, aiming at the problem that a total field extremum deviates from a target center when a target is influenced by the oblique magnetization of a geomagnetic field. Experimental results show that the method has strong anti-oblique magnetization capability and good target resolution, and can realize rapid delineation of the near-surface target position. The invention aims to provide a method for quickly delineating a near-surface target position based on magnetic gradient tensor eigenvalue, so as to solve the problems in the background technology.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: a method for quickly delineating a near-surface target position based on magnetic gradient tensor eigenvalues comprises the following steps:
(1) gridding the measuring area to obtain the magnetic gradient tensor matrix of each grid point
Figure BDA0003293016040000021
Wherein B isαβRepresents the partial derivative of the component of the magnetic field in the alpha direction in the beta direction, alpha, beta are the values in x, y, z;
(2) calculating the eigenvalue of the magnetic gradient tensor matrix G and arranging the eigenvalues from large to small, and recording the eigenvalue as lambda1,λ2,λ3；
(3) Establishing a target location delineation function
Figure BDA0003293016040000022
The local maximum of the function P corresponds to the target position.
Optionally, the physical meaning of the magnetic gradient tensor matrix G of step (1) is three components (B) of the magnetic induction density Bx,By,Bz) Spatial rate of change in three mutually orthogonal directions (x, y, z), i.e.
Figure BDA0003293016040000023
Optionally, the calculating the eigenvalue of the magnetic gradient tensor matrix G in the step (2) specifically includes: according to
Figure BDA0003293016040000024
And
Figure BDA0003293016040000025
calculating to obtain lambda1,λ2,λ3Where E is the identity matrix.
Optionally, the target position delineation function P in step (3) is uniquely determined by the eigenvalue of the magnetic gradient tensor matrix of each grid point, and the local maximum of the function P corresponds to the target position, so as to complete the fast delineation of the target position.
The invention has the beneficial effects that:
the invention provides a method for quickly delineating a near-surface target position based on magnetic gradient tensor eigenvalue, wherein a target position delineating function is established based on the gradient tensor eigenvalue, further research shows that the target position delineating function is only related to the size of a target magnetic moment and the distance from a target to an observation point, and when the distance from the observation point to the target is minimum, the function obtains the maximum value. By combining the specific embodiment and comparing with the traditional method, the method provided by the invention has good resolution while effectively overcoming the influence of oblique magnetization, and can be applied to the rapid delineation of the near-surface target position.
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The invention is described in further detail below with reference to the following figures and embodiments:
FIG. 1 is a flow chart of a method for rapidly delineating a near-surface target location based on magnetic gradient tensor eigenvalues provided by the present invention;
FIG. 2 is a schematic diagram of a target magnetic moment vector and a magnetic gradient tensor system position vector;
FIG. 3 is a schematic diagram of a gridding measurement of a magnetic gradient tensor system;
FIG. 4 is a graph of the total field result of magnetic anomalies for a target under oblique magnetization;
FIG. 5 is a graph of the position circling function results for a target under oblique magnetization.
Detailed Description
The technical solutions of the present invention are described in detail below with reference to the embodiments and the drawings, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without any creative effort belong to the protection scope of the present invention.
As shown in fig. 1, the present invention provides a method for fast delineation of a near-surface target location based on eigenvalues of magnetic gradient tensor, which comprises the following steps:
(1) gridding the measuring area to obtain the magnetic gradient tensor matrix of each grid point
Figure BDA0003293016040000031
Wherein B isαβA partial derivative in the β direction of a component representing the α direction of the magnetic field; alpha and beta are values in x, y and z;
(2) calculating the eigenvalue of the magnetic gradient tensor matrix G and arranging the eigenvalues from large to small, and recording the eigenvalue as lambda1,λ2,λ3；
(3) Establishing a target location delineation function
Figure BDA0003293016040000032
The local maximum of the function P corresponds to the target position.
Wherein, the physical meaning of the magnetic gradient tensor matrix G of the step (1) is three components (B) of the magnetic induction intensity Bx,By,Bz) Spatial rate of change in three mutually orthogonal directions (x, y, z), i.e.
Figure BDA0003293016040000033
The step (2) of calculating the eigenvalue of the magnetic gradient tensor matrix G specifically includes: according to
Figure BDA0003293016040000034
And
Figure BDA0003293016040000035
calculating to obtain lambda1,λ2,λ3Wherein E is a monoA matrix of bits.
And (3) uniquely determining the target position delineation function P by the eigenvalue of the magnetic gradient tensor matrix of each grid point, wherein the local maximum value of the function P corresponds to the target position, and thus, the rapid delineation of the target position is completed.
Example (b):
taking a magnetic dipole as an example, the fast delineation of the target position is completed through a target position delineation function based on the eigenvalue of the magnetic gradient tensor, wherein fig. 2 is a schematic diagram of a dipole target magnetic moment vector and a magnetic gradient tensor system position vector. The method comprises the following specific steps:
s1: acquiring a magnetic gradient tensor matrix G of the target at a grid point, wherein for a magnetic dipole, gradient tensor matrix elements can be expressed as:
Figure BDA0003293016040000041
wherein, mu0Denotes the magnetic permeability in vacuum, μ0＝4π×10-7H/m; m is the magnetic moment vector of the target, m ═ mx,my,mz) M is the modulus of the magnetic moment vector; r is the distance vector from the observation point to the target, and r is (r)x,ry,rz) R is the norm of the distance vector; deltaijFor the kronecker function, i, j is the value in x, y, z;
s2: calculating the eigenvalue of the magnetic gradient tensor matrix G and arranging the eigenvalues from large to small, and recording the eigenvalue as lambda1,λ2,λ3The magnetic field generated by the magnetic field generator, for a magnetic dipole,
Figure BDA0003293016040000042
wherein
Figure BDA0003293016040000043
Is a gradient tensor invariant. θ represents the angle between the distance vector and the target magnetic moment vector.
S3: establishing a target location delineation function
Figure BDA0003293016040000044
For a magnetic dipole, the magnetic dipole is,
Figure BDA0003293016040000045
it can be seen that the target position delineation function is only related to the modulus of the target magnetic moment vector and the modulus of the observation point to the target distance vector, and the local maximum of the function P corresponds to the target position.
It should be noted that although the above embodiment only considers the model of magnetic dipole, the derivation described in the present method is applicable to the magnetic gradient tensor matrix generated by the magnetic target with any shape, and the magnetic dipole is only used for simplifying the description and should not be considered as a limitation of the present invention.
Figure 3 is a schematic diagram of a magnetic gradient tensor system gridding measurement.
Comparative example:
in order to analyze the accuracy, resolution and anti-oblique magnetization capability of the invention for the target position delineation, a magnetic abnormal total field B of a magnetic dipole sub-target is adoptedtotalComparison of effects, Btotal＝Ba+Bbg，
Figure BDA0003293016040000046
Wherein, mu0Denotes the magnetic permeability in vacuum, μ0＝4π×10-7H/m; m is the magnetic moment vector of the target, m ═ mx,my,mz) (ii) a r is the distance vector from the observation point to the target, and r is (r)x，ry，rz) R is the norm of the distance vector; b isbgIs a geomagnetic background field.
Let the magnetic moment vector of the target be (1.0,1.5, -2.0) A.m2The target is located at the origin of coordinates, the magnetic gradient tensor measurement system moves from (-10m,0m,4m) to (10m,0m,4m) along the x-axis direction, the declination and declination of the geomagnetic background field are-30 degrees and 45 degrees respectively, the modulus of the geomagnetic background field is 54772nT, and the size of the measurement grid is 0.5m × 0.5 m. The result of obtaining the total magnetic anomaly field of the target under oblique magnetization is shown in fig. 4; the result of the position delineation function of the target under oblique magnetization is shown in fig. 5.
Compared with the traditional method for determining the target position through the magnetic anomaly total field, the method provided by the invention has stronger anti-oblique magnetization capability, can accurately reflect the real position of the target, has good precision and resolution and is suitable for fast delineation of the near-surface target position.
The invention is not the best known technology.
The above embodiments are merely illustrative of the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims (4)

1. A method for quickly delineating a near-surface target position based on magnetic gradient tensor eigenvalues is characterized by comprising the following steps of:
step 1, gridding the measuring area to obtain the magnetic gradient tensor matrix of each grid point
Figure FDA0003293016030000011
Wherein B isαβA partial derivative in the β direction of a component representing the α direction of the magnetic field; alpha and beta are values in x, y and z;
step 2, calculating the eigenvalue of the magnetic gradient tensor matrix G and arranging the eigenvalue from large to small, and recording the eigenvalue as lambda1,λ2,λ3；
Step 3, establishing a target position delineation function
Figure FDA0003293016030000012
The local maximum of the function P corresponds to the target position.
2. The method for fast delineation of a near-surface target location based on magnetic gradient tensor eigenvalues according to claim 1, wherein in step 1, the physical significance of the magnetic gradient tensor matrix G is three components of magnetic induction intensity B (B)x,By,Bz) Spatial rates of change in three mutually orthogonal directions (x, y, z), namely:
Figure FDA0003293016030000013
3. the method for rapidly delineating a near-surface target location based on magnetic gradient tensor eigenvalues as claimed in claim 1, wherein the step 2 of calculating eigenvalues of a magnetic gradient tensor matrix G specifically comprises: according to
Figure FDA0003293016030000014
And
Figure FDA0003293016030000015
Byz＝Bzycalculating to obtain lambda1,λ2,λ3Where E is the identity matrix.
4. The method for fast delineation of a near-surface target position based on magnetic gradient tensor eigenvalues as claimed in claim 1, wherein the step 3 of delineating the target position is uniquely determined by eigenvalues of a magnetic gradient tensor matrix of each grid point, and a local maximum value of the function P corresponds to the target position, thereby completing fast delineation of the target position.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114488326A (en) * 2022-02-15 2022-05-13 中国自然资源航空物探遥感中心 Method and system for improving capability of detecting aeromagnetic data geologic body boundary
CN116360000A (en) * 2023-02-17 2023-06-30 中国自然资源航空物探遥感中心 Aeromagnetic detection technology for crust material structure

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111551996A (en) * 2020-04-30 2020-08-18 南京理工大学 Cooperative magnetic target real-time positioning method based on magnetic tensor
CN112749493A (en) * 2021-01-25 2021-05-04 中国自然资源航空物探遥感中心 Geologic body boundary detection method and system based on full magnetic gradient tensor eigenvalue

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111551996A (en) * 2020-04-30 2020-08-18 南京理工大学 Cooperative magnetic target real-time positioning method based on magnetic tensor
CN112749493A (en) * 2021-01-25 2021-05-04 中国自然资源航空物探遥感中心 Geologic body boundary detection method and system based on full magnetic gradient tensor eigenvalue

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114488326A (en) * 2022-02-15 2022-05-13 中国自然资源航空物探遥感中心 Method and system for improving capability of detecting aeromagnetic data geologic body boundary
CN116360000A (en) * 2023-02-17 2023-06-30 中国自然资源航空物探遥感中心 Aeromagnetic detection technology for crust material structure
CN116360000B (en) * 2023-02-17 2023-09-05 中国自然资源航空物探遥感中心 Aeromagnetic detection method for crust material structure

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