CN113640887B - Aviation exploration method and exploration system for complex ferromagnetic body - Google Patents
Aviation exploration method and exploration system for complex ferromagnetic body Download PDFInfo
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Abstract
An aviation exploration method and an exploration system of a complex ferromagnetic body calculate a magnetic field of the ferromagnetic body in an underground target area according to the underground target area, the spreading range of the ferromagnetic body and the magnetic susceptibility distribution data of the ferromagnetic body; calculating the magnetic field of the high-intensity ferromagnetic body and the magnetic field gradient tensor according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area; and if the magnetic field and the magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body are respectively the same as the actual magnetic field and the magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body measured by an instrument, taking the magnetic susceptibility distribution data of the ferromagnetic body as the actual magnetic susceptibility distribution data of the ferromagnetic body to be used for aviation exploration of the ferromagnetic body. The method can be efficiently and accurately applied to calculating the magnetic field and the magnetic field gradient tensor of the ferromagnetic body, thereby improving the precision of fine inversion and interpretation by utilizing the magnetic field and the magnetic field gradient data.
Description
Technical Field
The invention relates to the technical field of aeromagnetic prospecting, in particular to an aeromagnetic prospecting method and system for metal mineral prospecting, which are suitable for complex ferromagnetic bodies with any observing height, any geometric shape and any magnetic susceptibility distribution.
Background
Metal mineral is an important material foundation for national economic development, and development of metal mineral exploration is of great significance for maintaining national safety and benefits. Because metal minerals are magnetic, magnetic prospecting has become an effective means of metal mineral prospecting. With the development of unmanned plane technology, magnetometers and magnetic gradiometers, the aviation magnetic measurement technology is mature, and compared with the ground magnetic measurement, the magnetic measurement device has high measurement efficiency, is not limited by water areas, forests, marshes, deserts and mountains, and provides technical support for realizing metal mineral exploration in complex areas. Meanwhile, research on a data inversion interpretation method matched with aviation magnetic measurement data becomes urgent. The forward calculation is the basis of inversion interpretation of magnetic measurement data, and the calculation accuracy and calculation efficiency directly influence the effect of inversion interpretation. Most of the current magnetic field forward computing methods are mainly oriented to weak magnetic conditions, and the influence of the demagnetizing effect is small and negligible. However, for most metallic minerals, such as magnetite, the demagnetizing effect is not negligible when exhibiting strong magnetism. The calculation of the strong magnetic field by the weak magnetic field calculation method can generate larger errors. In addition, the forward calculation of the ferromagnetic magnetic field gradient tensor has little research. In order to meet the mineral exploration requirement of aviation magnetic measurement metal, a rapid and high-precision forward computing method for researching a ferromagnetic magnetic field and gradient tensor thereof considering a demagnetizing effect becomes an urgent problem to be solved.
At present, the research on forward calculation of the ferromagnetic magnetic field and the gradient tensor thereof is less. Patent document with publication number CN109254327a discloses a three-dimensional ferromagnetic body exploration method and exploration system, wherein a method for forward computing of a ferromagnetic body magnetic field is proposed, and fast and high-precision forward computing of the ferromagnetic body magnetic field is realized by means of a fast fourier transform algorithm. The method is suitable for calculating the magnetic fields of the earth surface and the underground area, is not suitable for calculating the magnetic field of the height above the earth surface, cannot meet the technical requirements of aviation magnetic measurement exploration, and cannot calculate the magnetic field gradient tensor.
At present, the forward computing method used in the exploration method and the exploration system of the ferromagnetic body can not solve the problem of rapid and high-precision computing of the magnetic field and the magnetic field gradient tensor at any altitude. Therefore, those skilled in the art are in urgent need to propose an aeronautical exploration method and exploration system of ferromagnetic body suitable for calculation of magnetic field and magnetic field gradient tensor at arbitrary altitude, so as to solve the problems existing in the prior art.
Disclosure of Invention
Aiming at the problems that most of magnetic field forward calculation problems in the prior art only study weak magnetic conditions and do not consider influence of demagnetizing effect, most of existing ferromagnetic exploration methods and exploration systems have the problems of low calculation efficiency and calculation precision, incapability of calculating magnetic field and magnetic field gradient tensor of any altitude surface and the like, the invention provides an aviation exploration method of a complex ferromagnetic body, so that the requirement of fine inversion imaging of aviation magnetic exploration data is met, and the interpretation precision of magnetic measurement data is improved.
In order to achieve the technical purpose of the invention, the following technical scheme is adopted:
an aviation exploration method of a complex ferromagnetic body comprises the following steps:
calculating the magnetic field of the ferromagnetic body in the underground target area according to the distribution range of the ferromagnetic body and the magnetic susceptibility distribution data of the ferromagnetic body in the underground target area;
calculating the magnetic field of the high-intensity ferromagnetic body according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area;
calculating the magnetic field gradient tensor of the high-altitude ferromagnetic body according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area;
and if the magnetic field and the magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body are respectively the same as the actual magnetic field and the actual magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body obtained by the instrument measurement, taking the magnetic susceptibility distribution data of the ferromagnetic body as the actual magnetic susceptibility distribution data of the ferromagnetic body for aviation exploration.
As a preferred embodiment of the present invention, wherein: calculating a magnetic field of a ferromagnetic body of a subsurface target region, comprising:
(a) Establishing an initial three-dimensional prism model according to the underground target area and the spreading range of the ferromagnetic body;
(b) Uniformly dividing the initial three-dimensional prism model into a plurality of regular small prisms;
(c) Assigning a value to the magnetic susceptibility of each small prism according to the magnetic susceptibility distribution data of the ferromagnetic body to obtain a target three-dimensional prism model corresponding to the ferromagnetic body;
(d) Calculating a model magnetic field weighting coefficient according to the target three-dimensional prism model;
(e) Calculating according to the target three-dimensional prism model to obtain a compact operator;
(f) Calculating an earth main magnetic field at the geometric center of each small prism according to the earth main magnetic field model;
(g) Taking the main magnetic field of the earth at the geometric center of each small prism as the corresponding magnetic field initial value;
(h) Calculating to obtain a space domain abnormal magnetic field according to the target three-dimensional prism model, the magnetic field initial value and the model magnetic field weighting coefficient;
(i) Calculating to obtain a total magnetic field according to the magnetic field initial value, the compact operator and the space domain abnormal magnetic field;
(j) If the total magnetic field meets a given iteration convergence condition, taking the total magnetic field as the magnetic field of the ferromagnetic body of the underground target area;
(k) And (c) if the total magnetic field does not meet the given iteration convergence condition, taking the total magnetic field as the magnetic field initial value, and repeatedly executing the steps (h) to (k).
Further, in the step (d), for each small prism in the three-dimensional prism model, the model magnetic field weighting coefficients include 6, which are respectively:
wherein: the region where the three-dimensional prism model is located, that is, the region where the magnetic field of the ferromagnetic body of the underground target region is located coincides with the region of the observation point of the strong magnetic field of the underground target region, and the geometric center of each small prism is simultaneously used as the observation point in the region of the observation point of the strong magnetic field of the underground target region, (x) i ,y j ,z k ) And (xi) m ,η n ,ζ l ) Respectively representing the geometric center coordinates of small prisms in the three-dimensional prism model and the coordinates of observation points in the strong magnetic field observation point area of the underground target area, i=1, 2, … and N x ，j＝1,2,…,N y ，k＝1,2,…,N z ，m＝1,2,…,N x ，n＝1,2,…,N y ，l＝1,2,…,N z Where N is x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively, Δx, Δy and Δz are the dimensions of the small prisms in the x, y and z directions, respectively, arctan represents the arctangent operation, ln represents the logarithmic operation,ζ, η, ζ respectively represent the upper and lower integral limits in the weighting coefficient calculation formula, the upper limit taking ζ=x i -ξ m +0.5Δx，η＝y j -η n +0.5Δy，ζ＝z k -ζ l +0.5Δz, lower limit taken ζ=x i -ξ m -0.5Δx，η＝y j -η n -0.5Δy，ζ＝z k -ζ l -0.5Δz。
Further, in the step (e), the tightening operator includes:
wherein: alpha (x) i ,y j ,z k ) And beta (x) i ,y j ,z k ) Expressed as (x) i ,y j ,z k ) Tight operator, χ (x i ,y j ,z k ) Expressed as (x) i ,y j ,z k ) The magnetic susceptibility of a small prism as the geometric center coordinate, i=1, 2, …, N x ，j＝1,2,…,N y And k=1, 2, …, N z ，N x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively.
Further, in the step (H), the spatial domain abnormal magnetic field H a The three components of (a) are as follows:
wherein: m is m x (ξ m ,η n ,ζ l )，m y (ξ m ,η n ,ζ l ) And m z (ξ m ,η n ,ζ l ) Respectively represent geometric center coordinates (ζ) m ,η n ,ζ l ) The spatial domain magnetization M (x i ,y j ,z k ) An x component, a y component and a z component; m (x) i ,y j ,z k )＝χ(x i ,y j ,z k )H (0) (x i ,y j ,z k )，H (0) (x i ,y j ,z k ) Is of the order of (x i ,y j ,z k ) The initial value of the magnetic field of the small prism body which is the geometric center coordinate, H (0) (x i ,y j ,z k )＝H b (x i ,y j ,z k )，H b (x i ,y j ,z k ) Is the geometric center coordinates (x i ,y j ,z k ) The main magnetic field of the earth is calculated by the main magnetic field model of the earth; m=1, 2, …, N x ，n＝1,2,…,N y ，l＝1,2,…,N z ，N x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively.
Further, in the step (i), the total magnetic field
H (1) (x i ,y j ,z k )＝α(x i ,y j ,z k )(H a (x i ,y j ,z k )+H b (x i ,y j ,z k ))+β(x i ,y j ,z k )H (0) (x i ,y j ,z k )
Further, in the step (j), the given iteration convergence condition is:
ε 0 is of desired numerical accuracy.
As a preferred embodiment of the present invention, wherein the magnetic field of the high-intensity ferromagnetic body is computationally observed, comprising:
calculating six above-ground observation height magnetic field weighting coefficients according to the above-ground observation height and the horizontal observation point coordinates:
wherein: omega 7 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 8 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 9 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 10 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 11 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) And omega 12 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) Representing six above-ground observation height magnetic field weighting coefficients, m=1, 2, …, N x ，n＝1,2,…,N y ，l＝1,2,…,N z Where N is x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively, Δx, Δy and Δz are the dimensions of the small prisms in the x, y and z directions, respectively, arctan represents the arctangent operation, ln represents the logarithmic operation,Z 0 indicating the observed height, X p ，Y q Respectively representing the coordinates of the observation points at the observation height level, wherein p=1, 2, … and N p ，q＝1,2,…,N q ，N p And N q The number of the observation points with the height level in the x and y directions is respectively represented, and the coordinate intervals of the observation points with the height level are deltax and deltay respectively;
according to the above-ground observation height magnetic field weighting coefficient, three components of an abnormal magnetic field of the ferromagnetic body at the observation height level observation point are calculated:
as a preferred embodiment of the present invention, wherein: computationally viewing a magnetic field gradient tensor for a highly ferromagnetic body, comprising:
calculating ten above-ground observation height magnetic field gradient tensor weighting coefficients according to the above-ground observation height and the horizontal observation point coordinates;
wherein: omega 13 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 14 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 15 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 16 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 17 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 18 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 19 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 20 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 21 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) And omega 22 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) Representing ten above-ground observation height magnetic field gradient tensor weighting coefficients, Z 0 Indicating the observed height, X p ，Y q Respectively representing the coordinates of the observation points at the observation height level, wherein p=1, 2, … and N p ，q＝1,2,…,N q ，N p And N q The number of the observation points with the height level in the x and y directions is respectively represented, and the coordinate intervals of the observation points with the height level are deltax and deltay respectively;
according to the weighting coefficient of the observed height magnetic field gradient tensor, six components of the magnetic field gradient tensor of the observed height horizontal observation point ferromagnetic body are calculated:
the invention provides an aeromagnetic prospecting system of a complex ferromagnetic body, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the following steps when executing the computer program:
calculating the magnetic field of the ferromagnetic body in the underground target area according to the distribution range of the ferromagnetic body and the magnetic susceptibility distribution data of the ferromagnetic body in the underground target area;
calculating the magnetic field of the high-intensity ferromagnetic body according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area;
calculating the magnetic field gradient tensor of the high-altitude ferromagnetic body according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area;
and if the magnetic field and the magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body are respectively the same as the actual magnetic field and the actual magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body obtained by the instrument measurement, taking the magnetic susceptibility distribution data of the ferromagnetic body as the actual magnetic susceptibility distribution data of the ferromagnetic body for aviation exploration.
Compared with the prior art, the invention has the following technical effects:
the invention can be very conveniently applied to the discretization of the ferromagnetic body with complex magnetic susceptibility distribution and the relief topography situation by finely describing the complex ferromagnetic body by utilizing the small prism with the advantages of simplicity, flexibility and the like;
the method can be efficiently and accurately applied to calculating the magnetic field and the magnetic field gradient tensor of the ferromagnetic body with larger magnetic susceptibility, thereby improving the precision of fine inversion and interpretation by utilizing the magnetic field and the magnetic field gradient data, and can also be applied to the weak magnetic body;
the invention can be suitable for calculating magnetic field and magnetic field gradient data of any observation height, including areas above and below the ground, and is particularly suitable for aeromagnetic exploration;
further, in an embodiment of the present invention, a three-dimensional discrete convolution fast algorithm is used to calculate the abnormal magnetic field H a (x i ,y j ,z k ) Is included in the three components of (a). Repeatedly calling N by adopting a two-dimensional discrete convolution fast algorithm z And thirdly, three components of the abnormal magnetic field of the ferromagnetic body at the observation point of the high level are calculated. Repeatedly calling N by adopting a two-dimensional discrete convolution fast algorithm z Next, six minutes of magnetic field gradient tensor of the ferromagnetic body at the observation point of the high level are calculatedAmount of the components. Because the two-dimensional discrete convolution and the three-dimensional discrete convolution rapid algorithm are adopted, the number of the model magnetic field weighting coefficients is the same as the number of the three-dimensional prism models, the number of the observation height magnetic field gradient tensor weighting coefficients is the same as the number of the observation height observation points, and the number of the observation height magnetic field gradient tensor weighting coefficients is the same as the number of the observation height observation points.
Drawings
FIG. 1 is a flow chart of a method for calculating magnetic field and magnetic field gradient tensor of a ferromagnetic body according to an embodiment;
FIG. 2 is a schematic diagram of a three-dimensional prism model, a sphere anomaly, and an observation plane according to an embodiment;
FIG. 3 is a diagram illustrating a magnetic field z-component numerical solution in one embodiment;
FIG. 4 is a schematic diagram of a magnetic field z-component resolution in one embodiment;
FIG. 5 is a diagram showing the absolute error of a numerical solution and an analytical solution of the z-component of the magnetic field according to an embodiment;
FIG. 6 is a diagram illustrating a numerical solution of the xy tensor component of the magnetic field gradient in one embodiment;
FIG. 7 is a schematic diagram of an exemplary analysis of the xy tensor component of the magnetic field gradient;
FIG. 8 is a diagram of the absolute error of a numerical solution and an analytical solution of the xy tensor of the magnetic field gradient in one embodiment;
the symbols in the drawings are as follows:
bz: the z component of the magnetic field in nT;
bxx: the magnetic field gradient tensor xx component, in nT/m;
the achievement of the objects, functional features and advantages of the present invention will be further described with reference to the accompanying drawings, in conjunction with the embodiments.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Aiming at the problems that the numerical calculation method of the magnetic field of the ferromagnetic body in the prior art is difficult to balance calculation efficiency and calculation precision, is not suitable for calculating any observed high-altitude magnetic field and magnetic field gradient tensor, cannot meet the requirement of fine inversion imaging of the exploration data of the aeromagnetic method and the like, the invention provides the aeromagnetic exploration method of the complex ferromagnetic body, which can realize high-efficiency and high-precision forward calculation of the magnetic field and magnetic field gradient tensor of the ferromagnetic body at any observed altitude, so as to meet the requirement of fine inversion imaging of the exploration data of the aeromagnetic method and improve the interpretation precision of magnetic measurement data.
Specifically, in an embodiment of the present invention, an aeronautical exploration method for complex ferromagnetic bodies is provided, including:
s1: giving the coordinates of an underground target area, the spreading range of the ferromagnetic body, the magnetic susceptibility distribution data of the ferromagnetic body, the ground observation height and the horizontal observation point;
s2: calculating the magnetic field of the ferromagnetic body in the underground target area according to the distribution range of the ferromagnetic body and the magnetic susceptibility distribution data of the ferromagnetic body in the underground target area;
s3: calculating the magnetic field of the high-intensity ferromagnetic body according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area;
s4: calculating the magnetic field gradient tensor of the high-altitude ferromagnetic body according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area;
s5: and if the magnetic field and the magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body are respectively the same as the actual magnetic field and the actual magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body obtained by the instrument measurement, taking the magnetic susceptibility distribution data of the ferromagnetic body as the actual magnetic susceptibility distribution data of the ferromagnetic body for aviation exploration.
Referring to fig. 1, a flowchart of an aeronautical exploration method of a complex ferromagnetic body according to an embodiment of the present invention includes a calculation flow of a magnetic field of a ferromagnetic body in an underground target area, a magnetic field of a high-intensity ferromagnetic body observed above ground, and a magnetic field gradient tensor of a high-intensity ferromagnetic body observed above ground.
In one embodiment of the present invention, in S2, a magnetic field of a ferromagnetic substance in an underground target area is calculated based on an underground target area, a spread range of the ferromagnetic substance, and magnetic susceptibility distribution data of the ferromagnetic substance, including:
(a) And establishing an initial three-dimensional prism model according to the underground target area and the spreading range of the ferromagnetic body.
(b) Uniformly dividing the initial three-dimensional prism model into a plurality of regular small prisms;
and selecting any point in the space as a coordinate origin, establishing a three-dimensional rectangular coordinate system Oxyz, and determining the initial positions of the three-dimensional prism model in the x, y and z directions.
The initial three-dimensional prism model is then uniformly divided into a plurality of regular small prisms by a series of straight lines parallel to the x, y, z axes, the geometric center coordinates of the small prisms being (x i ,y j ,z k ) The dimensions in the x, y and z directions are Δx, Δy and Δz, respectively, where the x, y and z directions are split at equal intervals. The three-dimensional prism model has the number of small prisms N in the x, y and z directions respectively x ，N y And N z 。
(c) Assigning a value to the magnetic susceptibility of each small prism according to the magnetic susceptibility distribution data of the ferromagnetic body to obtain a target three-dimensional prism model corresponding to the ferromagnetic body;
the magnetic susceptibility of each small prism is assigned according to the magnetic susceptibility distribution data of the given ferromagnetic body, and the magnetic susceptibility in each small prism is constant, so that the magnetic susceptibility of the small rectangular center (x i ,y j ,z k ) The magnetic susceptibility at that point represents the magnetic susceptibility of the entire small prism.
(d) Calculating a model magnetic field weighting coefficient according to the target three-dimensional prism model;
for each small prism in the three-dimensional prism model, the model magnetic field weighting coefficients include 6, respectively:
wherein: omega 1 (x i -ξ m ,y j -η n ,z k -ζ l )，ω 2 (x i -ξ m ,y j -η n ,z k -ζ l )，ω 3 (x i -ξ m ,y j -η n ,z k -ζ l )，ω 4 (x i -ξ m ,y j -η n ,z k -ζ l )，ω 5 (x i -ξ m ,y j -η n ,z k -ζ l ) And omega 6 (x i -ξ m ,y j -η n ,z k -ζ l ) Respectively representing model magnetic field weighting coefficients for calculating the magnetic field of the subsurface target region.
The region where the three-dimensional prism model is located, namely, the region where the magnetic field of the ferromagnetic substance is located in the underground target region, and the region where the magnetic field of the ferromagnetic substance is located in the underground target region and the strong magnetic field of the underground target regionThe observation point areas are overlapped, the geometric center of each small prism is simultaneously used as the observation point in the strong magnetic field observation point area of the underground target area, (x) i ,y j ,z k ) And (xi) m ,η n ,ζ l ) Respectively representing the geometric center coordinates of small prisms in the three-dimensional prism model and the coordinates of observation points in the strong magnetic field observation point area of the underground target area, i=1, 2, … and N x ，j＝1,2,…,N y ，k＝1,2,…,N z ，m＝1,2,…,N x ，n＝1,2,…,N y ，l＝1,2,…,N z Where N is x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively, Δx, Δy and Δz are the dimensions of the small prisms in the x, y and z directions, respectively, arctan represents the arctangent operation, ln represents the logarithmic operation,ζ, η, ζ are respectively proportional to the upper and lower limits of the integral in the expression representing the weighting coefficient calculation, the upper limit taking ζ=x i -ξ m +0.5Δx，η＝y j -η n +0.5Δy，ζ＝z k -ζ l +0.5Δz, lower limit taken ζ=x i -ξ m -0.5Δx，η＝y j -η n -0.5Δy，ζ＝z k -ζ l -0.5Δz。
(e) Calculating according to the target three-dimensional prism model to obtain a compact operator;
wherein: alpha (x) i ,y j ,z k ) And beta (x) i ,y j ,z k ) Expressed as (x) i ,y j ,z k ) Tight operator, χ (x i ,y j ,z k ) Expressed as (x) i ,y j ,z k ) The magnetic susceptibility of a small prism as the geometric center coordinate, i=1, 2, …, N x ，j＝1,2,…,N y And k=1, 2, …, N z ，N x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively.
(f) Calculating an earth main magnetic field at the geometric center of each small prism according to the earth main magnetic field model;
from the earth's main magnetic field model, the center (x i ,y j ,z k ) The earth's main magnetic field H at b Wherein: i=1, 2, …, N x ，j＝1,2,…,N y And k=1, 2, …, N z Where N is x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively.
(g) Taking the main magnetic field of the earth at the geometric center of each small prism as the corresponding magnetic field initial value;
using the main magnetic field of the earth as the initial magnetic field value of the three-dimensional prism model, namely
H (0) (x i ,y j ,z k )＝H b (x i ,y j ,z k ) (7)
(h) Calculating to obtain a space domain abnormal magnetic field according to the target three-dimensional prism model, the magnetic field initial value and the model magnetic field weighting coefficient;
calculating the space domain magnetization intensity of each small prism in the target three-dimensional prism model:
M(x i ,y j ,z k )＝χ(x i ,y j ,z k )H (0) (x i ,y j ,z k ) (8)
in the formula (8), χ (x) i ,y j ,z k ) Expressed as (x) i ,y j ,z k ) The magnetic susceptibility of the small prism as the center.
Calculating the space domain abnormal magnetic field H a (x i ,y j ,z k ) Is as follows:
wherein: m is m x (ξ m ,η n ,ζ l )，m y (ξ m ,η n ,ζ l ) And m z (ξ m ,η n ,ζ l ) Respectively represent geometric center coordinates (ζ) m ,η n ,ζ l ) The spatial domain magnetization M (x i ,y j ,z k ) An x component, a y component and a z component; m=1, 2, …, N x ，n＝1,2,…,N y ，l＝1,2,…,N z ，N x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively.
(i) Calculating to obtain a total magnetic field according to the magnetic field initial value, the compact operator and the space domain abnormal magnetic field;
H (1) (x i ,y j ,z k )＝α(x i ,y j ,z k )(H a (x i ,y j ,z k )+H b (x i ,y j ,z k ))+β(x i ,y j ,z k )H (0) (x i ,y j ,z k ) (12)
(j) Judging the total magnetic field H (1) Whether the iteration convergence condition is satisfied:
in the formula (13), ε 0 Is of desired numerical accuracy.
(k) If the total magnetic field H (1) (x i ,y j ,z k ) Satisfying the iteration convergence condition, and setting the total magnetic field H (1) (x i ,y j ,z k ) Outputting the magnetic field as the ferromagnetic material in the subsurface target region; if the total magnetic field H (1) (x i ,y j ,z k ) Failing to satisfy the given iteration convergence condition, the total magnetic field H (1) (x i ,y j ,z k ) And (3) as the initial value of the magnetic field, repeating the steps (h) to (k) until the iteration convergence condition is met.
In the step (H), a three-dimensional discrete convolution fast algorithm is adopted to calculate the abnormal magnetic field H in the spatial domain a (x i ,y j ,z k ) Wherein the three-dimensional discrete convolution fast algorithm comprises the steps of:
(1) The weighting coefficient omega (x i -ξ 1 ,y j -η 1 ,z k -ζ 1 ) Arranged in a three-dimensional matrix t, denoted as
Wherein the matrix element t m,n,l And a weighting coefficient omega (x i -ξ 1 ,y j -η 1 ,z k -ζ 1 ) There is a relationship
t m,n,l ＝ω(x m -ξ 1 ,y n -η 1 ,z l -ζ 1 )
(2) Dividing the three-dimensional matrix t into eight three-dimensional block matrices, and recording as
/>
(3) The block matrix is interchanged to obtain a three-dimensional matrix c ext
(4) The magnetization component m (ζ) m ,η n ,ζ l ) Where m=1, 2, …, N x ，n＝1,2,…,N y ，l＝1,2,…,N z Arranged in a three-dimensional matrix g, matrix elements g m,n,l In relation to magnetization
g m,n,l ＝m(ξ m ,η n ,ζ l )
Zero padding and expanding the matrix g into a three-dimensional matrix g ext
Wherein, the liquid crystal display device comprises a liquid crystal display device, respectively represent the dimension N x ×(N y -1)×N z ，(N x -1)×N y ×N z ，(N x -1)×(N y -1)×N z ，N x ×N y ×(N z -1)，(N x -1)×N y ×(N z -1)，N x ×(N y -1)×(N z -1)，(N x -1)×(N y -1)×(N z -1) a three-dimensional zero matrix;
(5) Calculation ofWherein fft3 () represents a three-dimensional fast fourier transform;
(6) Calculation of
Wherein "..x" denotes a corresponding element multiplication operation;
(7) Calculation of
Wherein ifft3 () represents the three-dimensional inverse fast fourier transform;
(8) Extracting matrix f ext Is N the first of (2) x Front N y Front N z And the elements form a three-dimensional matrix f, namely a three-dimensional discrete convolution result. When ω and m in the calculation of f are ω given by the formulas (9), (10), (11), respectively 1 ，ω 2 ，ω 3 ，ω 4 ，ω 5 ，ω 6 ，m x ，m y ，m z At this time, 9 three-dimensional discrete convolutions can be obtained:
/>
in S3 of an embodiment of the present invention, calculating the magnetic field of the high-altitude ferromagnetic body from the above-ground observation height, the horizontal observation point coordinates, and the magnetic field of the ferromagnetic body of the subsurface target area, includes:
(3.1) calculating a ground observation height magnetic field weighting coefficient according to the ground observation height and the horizontal observation point coordinates:
wherein: omega 7 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 8 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 9 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 10 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 11 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) And omega 12 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) Representing six above-ground observation height magnetic field weighting coefficients, (ζ) m ,η n ,ζ l ) Representing the center coordinates of the small prisms, m=1, 2, …, N x ，n＝1,2,…,N y ，l＝1,2,…,N z Where N is x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively, Δx, Δy and Δz are the dimensions of the small prisms in the x, y and z directions, respectively, arctan represents the arctangent operation, ln represents the logarithmic operation,Z 0 indicating the observed height, X p ，Y q Respectively representing the coordinates of the observation points at the observation height level, wherein p=1, 2, … and N p ，q＝1,2,…,N q Where N is p And N q The number of observed height horizontal observation points in the x and y directions are represented, respectively, where the horizontal observation point coordinate intervals are Δx and Δy, respectively.
(3.2) repeatedly calling N by adopting a two-dimensional discrete convolution fast algorithm according to the observed height magnetic field weighting coefficient z Third, three components of an abnormal magnetic field of the ferromagnetic body at the observation point of the height level are calculated:
in S4 of an embodiment of the present invention, calculating a magnetic field gradient tensor of a high-strength ferromagnetic body from an above-ground observation height, a horizontal observation point coordinate, and a magnetic field of a ferromagnetic body of an underground target area, includes:
(4.1) calculating a weighting coefficient of the magnetic field gradient tensor of the above-ground observation height according to the above-ground observation height and the horizontal observation point coordinates:
/>
wherein: omega 13 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 14 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 15 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 16 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 17 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 18 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 19 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 20 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 21 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) And omega 22 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) The observed height magnetic field gradient tensor weighting coefficients respectively representing the calculated observed height magnetic field gradient tensor (ζ) m ,η n ,ζ l ) Representing the center coordinates of the small prisms, m=1, 2, …, N x ，n＝1,2,…,N y ，l＝1,2,…,N z Where N is x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively, Δx, Δy and Δz are the dimensions of the small prisms in the x, y and z directions, respectively,Z 0 indicating the observed height, X p ，Y q Respectively representing the coordinates of the observation points at the observation height level, wherein p=1, 2, … and N p ，q＝1,2,…,N q Where N is p And N q The number of observed height horizontal observation points in the x and y directions are represented, respectively, where the horizontal observation point coordinate intervals are Δx and Δy, respectively.
(4.2) repeatedly calling N by adopting a two-dimensional discrete convolution fast algorithm according to the weighting coefficient of the gradient tensor of the observed height magnetic field z Secondly, six components of a magnetic field gradient tensor of the ferromagnetic body at the observation point of the high level are calculated:
/>
in the above embodiment of the present invention, the two-dimensional discrete convolution fast algorithm adopted in both the (3.2) step of S3 and the (4.2) step of S4 includes the following steps:
(1) Given l, the weighting coefficient ω (X p -ξ 1 ,Y q -η 1 ,Z 0 -ζ l ) Arranged in a two-dimensional matrix t, denoted as
Wherein the matrix element t m,n And a weighting coefficient omega (X p -ξ 1 ,Y q -η 1 ,Z 0 -ζ l ) There is a relationship
t m,n ＝ω(X m -ξ 1 ,Y n -η 1 ,Z 0 -ζ l )
(2) Dividing the matrix t into four two-dimensional block matrices, denoted as
Wherein the dimensions of the four block matrices are:is (N) x -1)×(N y -1)，/>Is (N) x -1)×N q ，/>Is N p ×(N y -1)，/>Is N p ×N q 。
(3) The block matrix is interchanged to obtain a matrixc ext
(4) The magnetization component m (ζ) m ,η n ,ζ l ) Where m=1, 2, …, N x ，n＝1,2,…,N y Arranged in a matrix g, matrix elements g m,n In relation to magnetization
g m,n ＝m(ξ m ,η n ,ζ l )
Zero padding and expanding the matrix g into the matrix g ext
Wherein, the liquid crystal display device comprises a liquid crystal display device,respectively represent the dimension N x ×(N q -1)，(N p -1)×N y ，(N p -1)×(N q -1) zero matrix;
(5) Calculation ofWherein fft2 () represents a two-dimensional fast fourier transform;
(6) Calculation of/>
Wherein "..x" denotes a corresponding element multiplication operation;
(7) Calculation of
Wherein ifft2 () represents a two-dimensional inverse fast fourier transform;
(8) Extracting matrix f ext Is N the first of (2) p Front N of line q Column elements forming a matrix f, i.e. two-dimensionalAnd (3) discrete convolution results. When ω and m in the calculation of f are ω given by the formulas (20), (21), (22), (34), (35), (36), (37), (38) and (39), respectively 7 ，ω 8 ，ω 9 ，ω 10 ，ω 11 ，ω 12 ，ω 13 ，ω 14 ，ω 15 ，ω 16 ，ω 17 ，ω 18 ，ω 19 ，ω 20 ，ω 21 ，ω 22 ，m x ，m y ，m z When the method is used, 27 two-dimensional discrete convolutions can be obtained:
the effect of the aeronautical prospecting method for complex ferromagnetic bodies provided by the above-described embodiments of the present invention is examined below.
In order to illustrate the efficiency and the accuracy of the complex ferromagnetic body aviation exploration method provided by the embodiment of the invention applied to calculating the complex ferromagnetic body abnormal magnetic field and magnetic field gradient tensor with any observation height, any geometric shape and any magnetic susceptibility distribution, a three-dimensional prism, a sphere abnormal body and an observation plane model as shown in fig. 2 are designed, and the specific details are as follows:
in this embodiment, a ferromagnetic abnormal sphere is arranged in the three-dimensional prism model, and the range of the three-dimensional prism model is as follows: x-direction from 0m to 1000m, y-direction from 0m to 1000m, z-direction from 0m to 1000m (positive in z-axis downward); the sphere center of the ferromagnetic abnormal sphere coincides with the center of the model, the space coordinates are (500 m ), and the sphere radius is 200m; the magnetic susceptibility is 10; the main magnetic field of the earth in the target area is 50000nT and the magnetic field is 50000nTThe tilt angle is 45 degrees and the declination angle is 30 degrees. Dividing the three-dimensional prism model into 100 x 100 small prisms with the same size, calculating observation plane (Z) 0 -100 meters) of the magnetic field and the magnetic field gradient tensor (plane above the prism model in fig. 2, the prism upper height plane is denoted as 0 meters), the observation plane spread is: the x direction is from-500 m to 1500m, the y direction is from-500 m to 1500m, and the number of observation points is 200 x 200. The expected relative root mean square error magnitude |ε 0 |＝10 -3 ％。
The magnetic field calculation method of the ferromagnetic body of the present embodiment is implemented by using Fortran language, and the configuration of the operation platform is as follows: CPU is i7-4810MQ, main frequency is 2.80GHz, and memory is 32GB. For a model of 100 x 100, the method for calculating the magnetic field of the ferromagnetic body of the subsurface target area according to the embodiment of the invention is iterated once for about 1.5 seconds, the relative root mean square error converges to 10 -3 % requires 20 iterations, and the time required to calculate the x-, y-, and z-components of the magnetic field in the elevation plane is about 1.5 seconds, and the time required to calculate the xx-, xy-, xz-, yy-, yz-, and zz-components of the magnetic field gradient tensor is about 1.5 seconds, thus providing a high degree of visual efficiency. The numerical solution of the magnetic field z component, the analytical solution, and the absolute errors of the two are shown in fig. 3, 4, and 5, respectively, and the numerical solution of the magnetic field gradient tensor xx component, the analytical solution, and the absolute errors of the two are shown in fig. 6, 7, and 8, respectively, and are identical from a morphological point of view. The numerical accuracy of the embodiment of the invention is measured by using the absolute error of the numerical solution and the analytic solution, and the forward calculation accuracy of the magnetic field and the magnetic field gradient tensor is high.
An embodiment of the present invention further provides an aerospace exploration system of a ferromagnetic body, including: a memory and one or more processors coupled to the memory, the memory storing computer program code, the processor configured to execute the computer program code to implement the method of aero-prospecting for complex ferromagnetic bodies according to the previous embodiments.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (3)
1. The aviation exploration method of the complex ferromagnetic body is characterized by comprising the following steps of:
the method for calculating the magnetic field of the ferromagnetic material in the underground target area based on the underground target area, the spread range of the ferromagnetic material, and the magnetic susceptibility distribution data of the ferromagnetic material, comprises:
(a) Establishing an initial three-dimensional prism model according to the underground target area and the spreading range of the ferromagnetic body;
(b) Uniformly dividing the initial three-dimensional prism model into a plurality of regular small prisms;
(c) Assigning a value to the magnetic susceptibility of each small prism according to the magnetic susceptibility distribution data of the ferromagnetic body to obtain a target three-dimensional prism model corresponding to the ferromagnetic body;
(d) Calculating a model magnetic field weighting coefficient according to the target three-dimensional prism model;
for each small prism in the three-dimensional prism model, the model magnetic field weighting coefficients include 6, respectively:
wherein: the region where the three-dimensional prism model is located, that is, the region where the magnetic field of the ferromagnetic body of the underground target region is located coincides with the region of the observation point of the strong magnetic field of the underground target region, and the geometric center of each small prism is simultaneously used as the observation point in the region of the observation point of the strong magnetic field of the underground target region, (x) i ,y j ,z k ) And (xi) m ,η n ,ζ l ) Respectively representing the geometric center coordinates of small prisms in the three-dimensional prism model and the coordinates of observation points in the strong magnetic field observation point area of the underground target area, i=1, 2, … and N x ，j＝1,2,…,N y ，k＝1,2,…,N z ，m＝1,2,…,N x ，n＝1,2,…,N y ，l＝1,2,…,N z Where N is x ，N y And N z The number of small prisms in the x, y and z directions of the three-dimensional prism model, respectively, Δx, Δy and Δz are the dimensions of the small prisms in the x, y and z directions, respectively, arctan represents the arctangent operation, ln represents the logarithmic operation,ζ, η, ζ respectively represent the upper and lower integral limits in the weighting coefficient calculation formula, the upper limit taking ζ=x i -ξ m +0.5Δx，η＝y j -η n +0.5Δy，ζ＝z k -ζ l +0.5Δz, lower limit taken ζ=x i -ξ m -0.5Δx，η＝y j -η n -0.5Δy，ζ＝z k -ζ l -0.5Δz；
(e) Calculating according to the target three-dimensional prism model to obtain a compact operator;
the tightening operator comprises:
wherein: alpha (x) i ,y j ,z k ) And beta (x) i ,y j ,z k ) Expressed as (x) i ,y j ,z k ) Tight operator, χ (x i ,y j ,z k ) Expressed as (x) i ,y j ,z k ) Magnetic susceptibility of the small prism body which is the geometric center coordinate;
(f) Calculating an earth main magnetic field at the geometric center of each small prism according to the earth main magnetic field model;
(g) Taking the main magnetic field of the earth at the geometric center of each small prism as the corresponding magnetic field initial value;
(h) Calculating to obtain a space domain abnormal magnetic field according to the target three-dimensional prism model, the magnetic field initial value and the model magnetic field weighting coefficient;
abnormal magnetic field H in space domain a (x i ,y j ,z k ) The three components of (a) are as follows:
wherein: m is m x (ξ m ,η n ,ζ l )，m y (ξ m ,η n ,ζ l ) And m z (ξ m ,η n ,ζ l ) Respectively represent geometric center coordinates (ζ) m ,η n ,ζ l ) The spatial domain magnetization M (x i ,y j ,z k ) An x component, a y component and a z component; m (x) i ,y j ,z k )＝χ(x i ,y j ,z k )H (0) (x i ,y j ,z k )，H (0) (x i ,y j ,z k ) Is of the order of (x i ,y j ,z k ) The initial value of the magnetic field of the small prism body which is the geometric center coordinate, H (0) (x i ,y j ,z k )＝H b (x i ,y j ,z k )，H b (x i ,y j ,z k ) Is the geometric center coordinates (x i ,y j ,z k ) The main magnetic field of the earth is calculated by the main magnetic field model of the earth; m=1, 2, …, N x ，n＝1,2,…,N y ，l＝1,2,…,N z ；
Calculating according to the magnetic field initial value, the compact operator and the space domain abnormal magnetic field to obtain a total magnetic field H (1) (x i ,y j ,z k ) The method comprises the following steps:
H (1) (x i ,y j ,z k )＝α(x i ,y j ,z k )(H a (x i ,y j ,z k )+H b (x i ,y j ,z k ))+β(x i ,y j ,z k )H (0) (x i ,y j ,z k )
(j) If the total magnetic field meets a given iteration convergence condition, taking the total magnetic field as the magnetic field of the ferromagnetic body of the underground target area;
(k) If the total magnetic field does not meet the given iteration convergence condition, taking the total magnetic field as the magnetic field initial value, and repeatedly executing the steps (h) to (k);
calculating the magnetic field of the high-intensity ferromagnetic body according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area, comprising:
calculating six above-ground observation height magnetic field weighting coefficients according to the above-ground observation height and the horizontal observation point coordinates:
wherein: omega 7 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 8 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 9 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 10 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 11 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) And omega 12 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) Representing the weighting coefficients of the magnetic fields of six above-ground observations, Z 0 Indicating the observed height, X p ，Y q Respectively representing the coordinates of the observation points at the observation height level, wherein p=1, 2, … and N p ，q＝1,2,…,N q ，N p And N q Respectively represent the number of the observation points of the observation height level in the x and y directionsThe coordinate intervals of the horizontal observation points are delta x and delta y respectively;
according to the above-ground observation height magnetic field weighting coefficient, three components of an abnormal magnetic field of the ferromagnetic body at the observation height level observation point are calculated:
calculating a magnetic field gradient tensor of the high-altitude ferromagnetic body according to the above-ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic body of the underground target area, wherein the magnetic field gradient tensor comprises the following steps:
calculating ten above-ground observation height magnetic field gradient tensor weighting coefficients according to the above-ground observation height and the horizontal observation point coordinates;
wherein: omega 13 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 14 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 15 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 16 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 17 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 18 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 19 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 20 (X p -ξ m ,Y q -η n ,Z 0 -ζ l )，ω 21 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) And omega 22 (X p -ξ m ,Y q -η n ,Z 0 -ζ l ) Representing ten above-ground observation height magnetic field gradient tensor weighting coefficients, Z 0 Indicating the observed height, X p ，Y q Respectively representing the coordinates of the observation points at the observation height level, wherein p=1, 2, … and N p ，q＝1,2,…,N q ，N p And N q The number of the observation points with the height level in the x and y directions is respectively represented, and the coordinate intervals of the observation points with the height level are deltax and deltay respectively;
according to the weighting coefficient of the observed height magnetic field gradient tensor, six components of the magnetic field gradient tensor of the observed height horizontal observation point ferromagnetic body are calculated:
and if the magnetic field and the magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body are respectively the same as the actual magnetic field and the actual magnetic field gradient tensor of the above-ground observation high-altitude ferromagnetic body obtained by the instrument measurement, taking the magnetic susceptibility distribution data of the ferromagnetic body as the actual magnetic susceptibility distribution data of the ferromagnetic body for aviation exploration.
2. The method of airborne exploration of complex ferromagnetic bodies according to claim 1, wherein in step (j), the given iteration convergence conditions are:
ε 0 is of desired numerical accuracy.
3. An aero-magnetic prospecting system for complex ferromagnetic bodies, comprising a memory and a processor, said memory storing a computer program, characterized in that said processor, when executing said computer program, implements the steps of the aero-prospecting method for complex ferromagnetic bodies according to claim 1.
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