CN113640886B - Method and system for exploration of ferromagnetic binary - Google Patents
Method and system for exploration of ferromagnetic binary Download PDFInfo
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Abstract
The invention aims to provide a method and a system for exploration of a ferromagnetic binary, wherein the method comprises the following steps: calculating the magnetic field of the ferromagnetic secondary body of the underground target area according to the underground target area, the spreading range of the ferromagnetic secondary body and the magnetic susceptibility distribution data of the ferromagnetic secondary body; calculating the magnetic field of the ferromagnetic binary body at the position of the horizontal observation point according to the ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic binary body of the underground target area; judging that the magnetic field of the ferromagnetic binary body at the calculated horizontal observation point is the same as the magnetic field of the ferromagnetic binary body at the horizontal observation point measured by an instrument, and if the magnetic fields are the same, taking the magnetic susceptibility distribution data of the ferromagnetic binary body as the actual magnetic susceptibility distribution data of the ferromagnetic binary body to be used for exploring the ferromagnetic binary body. The invention can meet the requirement of fine inversion imaging of high-precision magnetic prospecting data and improve the interpretation precision of magnetic measurement data.
Description
Technical Field
The invention relates to the technical field of magnetic prospecting, in particular to a method and a system for prospecting metal minerals, which are applicable to ferromagnetic binary bodies with any geometric shape and any magnetic susceptibility distribution.
Background
Mineral products are an important material basis for national economic development. With the national economic development, the demand for mineral products is increasing. Magnetic prospecting is a prospecting method based on the magnetic difference of underground objects. With the improvement of the measurement precision of magnetic measuring instruments, high-precision magnetic prospecting has become an effective means for metal mineral prospecting. Research on inversion interpretation methods of magnetic measurement data matched with high-precision and high-resolution magnetic measurement data becomes an urgent need. 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, namely, the magnetic susceptibility effect of an object is 0.1SI, 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. The method for surveying metal mineral products by using a high-precision magnetic method needs to be researched for a rapid and high-precision forward calculation method of a ferromagnetic body magnetic field considering a demagnetizing effect. At present, few methods for researching forward calculation of a ferromagnetic binary magnetic field are adopted. The document (Kostrov N P. Calculation ofmagnetic anomalies caused by 2Dbodies of arbitrary shape with consideration of demagnetization.Geophysical Prospecting,2007,55 (1): 91-115) proposes a volume-integration method using triangulation units, which allows to calculate magnetic fields with a relative permeability in the range of 2 to 20. In order to ensure the calculation accuracy, the number of triangulation units needs to be increased, so that the calculation efficiency of the method is reduced.
At present, the method for exploring the ferromagnetic binary and the forward computing method used in the exploration system have the problem that the computing efficiency and the computing precision are difficult to balance. Therefore, there is an urgent need to propose a method and a system for exploration of ferromagnetic binary bodies to solve the problems existing in the prior art.
Disclosure of Invention
Aiming at the problems that most of the prior two-degree magnetic field forward performance calculation problems only study the weak magnetic condition and do not consider the influence of demagnetizing effect, most of the prior ferromagnetic two-degree exploration methods and exploration systems have the problems of low calculation efficiency, low calculation precision and the like, the invention aims to provide the ferromagnetic two-degree exploration methods and the exploration systems so as to meet the requirement of fine inversion imaging of high-precision magnetic exploration data and improve the interpretation precision of magnetic measurement data.
In order to achieve the technical purpose of the invention, the following technical scheme is adopted:
the exploration method of the ferromagnetic binary comprises the following steps:
setting an underground target area, a spreading range of a ferromagnetic secondary body, magnetic susceptibility distribution data of the ferromagnetic secondary body, ground observation height and horizontal observation point coordinates;
calculating the magnetic field of the ferromagnetic secondary body of the underground target area according to the underground target area, the spreading range of the ferromagnetic secondary body and the magnetic susceptibility distribution data of the ferromagnetic secondary body;
calculating the magnetic field of the ferromagnetic binary body at the position of the horizontal observation point according to the ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic binary body of the underground target area;
judging that the magnetic field of the ferromagnetic binary body at the calculated horizontal observation point is the same as the magnetic field of the ferromagnetic binary body at the horizontal observation point measured by an instrument, and if the magnetic fields are the same, taking the magnetic susceptibility distribution data of the ferromagnetic binary body as the actual magnetic susceptibility distribution data of the ferromagnetic binary body to be used for exploring the ferromagnetic binary body.
Further, in the present invention, calculating a magnetic field of a ferromagnetic binary body of a subsurface target area includes:
(a) Establishing an initial two-dimensional rectangular model according to the underground target area and the spreading range of the ferromagnetic binary;
(b) Uniformly dividing the spreading range of the initial ferromagnetic binary body into a plurality of unit rectangles;
(c) Assigning a value to the magnetic susceptibility of each unit rectangle according to the magnetic susceptibility distribution data of the ferromagnetic binary body to obtain a target two-dimensional rectangular model corresponding to the initial ferromagnetic binary body;
(d) Calculating according to the target two-dimensional rectangular model to obtain a model weighting coefficient;
(e) Calculating an earth main magnetic field at the center of each unit rectangle in the target two-dimensional rectangle model according to the earth main magnetic field model;
(f) Taking the main magnetic field of the earth at the center of each unit rectangle as the magnetic field initial value;
(g) Calculating to obtain a space domain abnormal magnetic field according to the target two-dimensional rectangular model, the magnetic field initial value and the model weighting coefficient;
(h) Calculating to obtain a total magnetic field according to the magnetic field initial value and the space domain abnormal magnetic field;
(i) Setting an iteration convergence condition, judging whether the total magnetic field meets the iteration convergence condition, taking the total magnetic field as a magnetic field of a strong magnetic binary body of an underground target area if the total magnetic field meets the iteration convergence condition, taking the total magnetic field as the magnetic field initial value if the total magnetic field does not meet the given iteration convergence condition, and repeatedly executing the steps (g) to (i) until the given iteration convergence condition is met;
further, in the step (d) of the present invention, the model weighting coefficient ω (x) 1 -ξ m ,z 1 -ζ n ) Including omega x (x i -ξ m ,z j -ζ n ) And omega z (x i -ξ m ,z j -ζ n ) Two components are respectively:
wherein: the region where the target two-dimensional rectangular model is located, namely, the region where the magnetic field of the underground target region ferromagnetic binary is located coincides with the magnetic field observation point region of the underground target region ferromagnetic binary, and the center of each unit rectangle is simultaneously used as the observation point of the magnetic field observation point region of the underground target region ferromagnetic binary, (x) i ,z j ) And (xi) m ,ζ n ) Respectively representing the central coordinates of unit rectangles in the target two-dimensional rectangular model and the observation point coordinates of the magnetic field observation point region of the strong magnetic binary body of the underground target region, i=1, 2, …, N x ，j＝1,2,…,N z ，m＝1,2,…,N x ，n＝1,2,…,N z ，N x And N z The number of unit rectangles divided in the x and z directions of the two-dimensional rectangular model, and Δx and Δz are the sizes of the unit rectangles in the x and z directions of the two-dimensional rectangular model, respectively, arctan represents an arctangent operation, and ln represents a logarithmic operation.
Further, in the step (g) of the present invention, the spatial domain abnormal magnetic field H a (x i ,z j ) Is composed of two components in the x-direction and in the z-direction, as follows:
wherein: m is m x (ξ m ,ζ n ) And m z (ξ m ,ζ n ) Respectively represent the center (xi) of the unit rectangle m ,ζ n ) The spatial domain magnetization M (x i ,z j ) Is the x-component and z-component of (2), M (x i ,z j )＝χ(x i ,z j )H (0) (x i ,z j )，H (0) (x i ,z j )＝H b (x i ,z j )，H b (x i ,z j ) Is the earth's main magnetic field at the center of the cell rectangle.
Further, in the step (g) of the invention, a two-dimensional discrete convolution fast algorithm is adopted to calculate the space domain abnormal magnetic field H a (x i ,z j ) Is defined by two components H ax (x i ,z j ) And H az (x i ,z j )。
Further, in the step (H) of the present invention, the total magnetic field H (1) (x i ,z j )＝H a (x i ,z j )+H b (x i ,z j )。
Further, the iteration convergence condition set in the step (i) of the present invention is:
wherein ε 0 Is of desired numerical accuracy.
Further, in the present invention, calculating the magnetic field of the ferromagnetic binary at the position of the horizontal observation point includes:
calculating the observation point weighting coefficient omega (X) p -ξ m ,Z 0 -ζ n )：
Wherein: omega x (X p -ξ m ,Z 0 -ζ n ) And omega z (X p -ξ m ,Z 0 -ζ n ) Two components of the observation point weighting coefficient respectively representing the observation height magnetic field, Z 0 Indicating the observed height, X p Representing coordinates of the horizontal observation point, p=1, 2, …, N 0 ，N 0 The number of observation points is represented, and the coordinate interval of the horizontal observation points is deltax;
calculating the magnetic field H of the ferromagnetic binary body at the position of the horizontal observation point a (X p ,Z 0 ) Its two components in the x-direction and in the z-direction are as follows:
further, the invention adopts a one-dimensional discrete convolution fast algorithm to repeatedly call N z Secondly, calculating the magnetic field H of the ferromagnetic binary body at the position of the horizontal observation point a (X p ,Z 0 ) Its two components in the x-direction and in the z-direction.
The invention provides a ferromagnetic binary exploration system, 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:
setting an underground target area, a spreading range of a ferromagnetic secondary body, magnetic susceptibility distribution data of the ferromagnetic secondary body, ground observation height and horizontal observation point coordinates;
calculating the magnetic field of the ferromagnetic secondary body of the underground target area according to the underground target area, the spreading range of the ferromagnetic secondary body and the magnetic susceptibility distribution data of the ferromagnetic secondary body;
calculating the magnetic field of the ferromagnetic binary body at the position of the horizontal observation point according to the ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic binary body of the underground target area;
judging that the magnetic field of the ferromagnetic binary body at the calculated horizontal observation point is the same as the magnetic field of the ferromagnetic binary body at the horizontal observation point measured by an instrument, and if the magnetic fields are the same, taking the magnetic susceptibility distribution data of the ferromagnetic binary body as the actual magnetic susceptibility distribution data of the ferromagnetic binary body to be used for exploring the ferromagnetic binary body.
Compared with the prior art, the invention has the following technical effects:
the invention can be very conveniently applied to the discretization of the complex ferromagnetic binary with magnetic susceptibility distribution and the relief topography situation by finely describing the complex ferromagnetic binary by utilizing the rectangular unit with the advantages of simplicity, flexibility and the like.
The method can be efficiently and accurately applied to calculating the magnetic field of the strong-magnetism binary body with larger magnetic susceptibility, thereby improving the precision of fine inversion and interpretation by utilizing magnetic field data, and can be also applied to weak-magnetism binary body.
Because the number of the model weighting coefficients and the number of the observation point weighting coefficients are the same as the number of the two-dimensional rectangular model, the invention has the advantage of occupying less memory of a computer when large-scale exploration of the ferromagnetic binary body is carried out.
In addition, the invention can accurately calculate the ferromagnetic binary magnetic field with any given observation height, including the above-ground and below-ground areas.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating a two-dimensional rectangular model in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a two-dimensional model with a circular cross section according to an embodiment of the present invention;
FIG. 4 is a numerical solution of z-component of an anomalous magnetic field in accordance with an embodiment of the invention;
FIG. 5 is a resolution of z-component analysis of an anomalous magnetic field in accordance with an embodiment of the invention;
FIG. 6 is a graph of absolute error of z-component of an anomalous magnetic field in accordance with an embodiment of the invention;
the symbols in the drawings are as follows:
bz: the z component of the abnormal magnetic field is represented by nT;
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.
In one embodiment of the present invention, a method for exploration of ferromagnetic binary is provided, comprising:
s1: setting an underground target area, a spreading range of a ferromagnetic secondary body, magnetic susceptibility distribution data of the ferromagnetic secondary body, ground observation height and horizontal observation point coordinates;
s2: calculating the magnetic field of the ferromagnetic secondary body of the underground target area according to the underground target area, the spreading range of the ferromagnetic secondary body and the magnetic susceptibility distribution data of the ferromagnetic secondary body;
s3: calculating the magnetic field of the ferromagnetic binary body at the position of the horizontal observation point according to the ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic binary body of the underground target area;
s4: judging that the magnetic field of the ferromagnetic binary body at the calculated horizontal observation point is the same as the magnetic field of the ferromagnetic binary body at the horizontal observation point measured by an instrument, and if the magnetic fields are the same, taking the magnetic susceptibility distribution data of the ferromagnetic binary body as the actual magnetic susceptibility distribution data of the ferromagnetic binary body to be used for exploring the ferromagnetic binary body.
Referring to fig. 1, a flowchart of a method for exploration of ferromagnetic binary according to an embodiment of the present invention is shown.
In an embodiment of the present invention, in S2, calculating a magnetic field of the ferromagnetic binary in the underground target area according to the underground target area, the spread range of the ferromagnetic binary, and the magnetic susceptibility distribution data of the ferromagnetic binary, includes:
(a) And establishing an initial two-dimensional rectangular model according to the underground target area and the spreading range of the ferromagnetic binary.
(b) And uniformly dividing the spreading range of the initial ferromagnetic binary body into a plurality of unit rectangles.
And selecting any point in the space as a coordinate origin, establishing a two-dimensional rectangular coordinate system Oxz, and determining the initial position of the initial two-dimensional rectangular model in the x and z directions.
The initial two-dimensional rectangular model is then uniformly divided into regular unit rectangles using a series of lines parallel to the x, z axes, the geometric center coordinates of the unit rectangles being (x i ,z j ) The dimensions in the x and z directions are Δx and Δz, respectively, where the x and z directions are split at equal intervals. The number of unit rectangles divided in the x and z directions of the initial two-dimensional rectangular model is N x And N z 。
(c) And assigning a value to the magnetic susceptibility of each unit rectangle according to the magnetic susceptibility distribution data of the ferromagnetic binary body to obtain a target two-dimensional rectangular model corresponding to the initial ferromagnetic binary body.
In each unit rectangle, the magnetic susceptibility is constant, so that the unit rectangle center (x i ,z j ) The magnetic susceptibility at that point represents the magnetic susceptibility of the entire cell rectangle.
(d) And calculating according to the target two-dimensional rectangular model to obtain a model weighting coefficient.
Wherein: the region where the target two-dimensional rectangular model is located, namely, the region where the magnetic field of the underground target region ferromagnetic binary is located coincides with the magnetic field observation point region of the underground target region ferromagnetic binary, and the center of each unit rectangle is simultaneously used as the observation point of the magnetic field observation point region of the underground target region ferromagnetic binary, (x) i ,z j ) And (xi) m ,ζ n ) Respectively representing the central coordinates of unit rectangles in the target two-dimensional rectangular model and the observation point coordinates of the magnetic field observation point region of the strong magnetic binary body of the underground target region, i=1, 2, …, N x ，j＝1,2,…,N z ，m＝1,2,…,N x ，n＝1,2,…,N z ，N x And N z The number of unit rectangles divided in the x and z directions of the two-dimensional rectangular model, and Δx and Δz are the sizes of the unit rectangles in the x and z directions of the two-dimensional rectangular model, respectively, arctan represents an arctangent operation, and ln represents a logarithmic operation.
(e) Calculating the earth main magnetic field H at the center of each unit rectangle in the target two-dimensional rectangular model according to the earth main magnetic field model b (x i ,z j )；
(f) Taking the main magnetic field of the earth at the center of each unit rectangle as the initial magnetic field value H (0) (x i ,z j )；
H (0) (x i ,z j )＝H b (x i ,z j ) (3)
The spatial domain magnetization M (x i ,z j ) The method comprises the following steps:
M(x i ,z j )＝χ(x i ,z j )H (0) (x i ,z j ) (4)
(g) Calculated according to the target two-dimensional rectangular model, the initial value of the magnetic field and the model weighting coefficientTo the space domain abnormal magnetic field H a (x i ,z j )；
Wherein: m is m x (ξ m ,ζ n ) And m z (ξ m ,ζ n ) Respectively represent (xi) m ,ζ n ) The spatial domain magnetization M (x i ,z j ) Is the x-component and z-component of (2), M (x i ,z j )＝χ(x i ,z j )H (0) (x i ,z j )，H (0) (x i ,z j )＝H b (x i ,z j )，H b (x i ,z j ) Is the earth's main magnetic field at the center of the cell rectangle.
(h) Calculating to obtain a total magnetic field according to the magnetic field initial value and the space domain abnormal magnetic field;
H (1) (x i ,z j )＝H a (x i ,z j )+H b (x i ,z j ) (7)
(i) Setting an iteration convergence condition:
wherein ε 0 Is of desired numerical accuracy.
Judging whether the total magnetic field meets an iteration convergence condition, if the total magnetic field meets the iteration convergence condition, taking the total magnetic field as a magnetic field of a strong magnetic binary body of an underground target area, and 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 (g) to (i) until the given iteration convergence condition is met.
In S3 of an embodiment of the present invention: according to the ground observation height, the horizontal observation point coordinates and the magnetic field of the strong magnetic binary in the underground target area, the magnetic field of the strong magnetic binary at the position of the horizontal observation point is calculated, and the method comprises the following steps:
(3.1) calculating an observation point weighting coefficient ω (X) for observing the high magnetic field p -ξ m ,Z 0 -ζ n )：
Wherein: omega x (X p -ξ m ,Z 0 -ζ n ) And omega z (X p -ξ m ,Z 0 -ζ n ) Respectively representing the weighting coefficients of the observation points for calculating the observation height magnetic field, (xi) m ,ζ n ) Representing the center coordinates of a small rectangle, m=1, 2, …, N x ，n＝1,2,…,N z Where N is x And N z The number of small rectangles in the x and Z directions of the two-dimensional rectangular model, respectively, Δx and Δz are the dimensions of the small rectangles in the x and Z directions, respectively, arctan represents the arctan operation, ln represents the logarithmic operation, and Z 0 Indicating the observed height, X p Represents the coordinates of the horizontal observation points, p=1, 2, …, N 0 ，N 0 The number of observation points is represented, and here, the horizontal observation point coordinate interval is Δx.
(3.2) calculating the magnetic field H of the ferromagnetic binary at the position of the horizontal observation point a (X p ,Z 0 ) Its two components in the x-direction and in the z-direction are as follows:
in the step (g) of the step S2, a two-dimensional discrete convolution fast algorithm is adopted to calculate the abnormal magnetic field H in the spatial domain a (x i ,z j ) Is defined by two components H ax (x i ,z j ) And H az (x i ,z j ) Comprising:
(1) The weighting coefficient omega (x 1 -ξ m ,z 1 -ζ n ) Arranged in a matrix t, denoted as
In the formula (13), the matrix element t m,n And a weighting coefficient omega (x 1 -ξ m ,z 1 -ζ n ) There is a relationship
t m,n ＝ω(x 1 -ξ m ,z 1 -ζ n ) (14)
(2) Zero padding and expanding matrix t into matrix
Matrix is formedDivided into four block matrices, denoted as
The block matrix is interchanged to obtain a matrix c ext
(3) The magnetization component m (ζ) m ,ζ n ) Where m=1, 2, …, N x ，n＝1,2,…,N z Arranged in a matrix g, matrix elements g m,n In relation to magnetization
g m,n ＝m(ξ m ,η n ) (18)
Zero padding and expanding the matrix g into the matrix g ext
In the formula (19), the amino acid sequence of the compound,represents N x ×N z A zero matrix;
(4) Calculation ofWherein fft2 () represents a two-dimensional fast fourier transform;
(5) Calculation ofWherein "..x" denotes a corresponding element multiplication operation;
(6) Calculation ofWhere ifft2 () represents the two-dimensional inverse fast fourier transform;
(7) Extracting matrix f ext Is N the first of (2) x Front N of line z And the columns form a matrix f, namely a two-dimensional discrete convolution result. When ω and m in the calculation of f are ω given by the formulas (5) and (6), respectively x ，ω z ，m x ，m z And then four two-dimensional discrete convolutions can be obtained:
in the step (3.2) of the step S3, a one-dimensional discrete convolution fast algorithm is adopted to repeatedly call N z Secondly, two components of an abnormal magnetic field of the horizontal observation point ferromagnetic binary are calculated: the method comprises the following steps:
(1) For a given n, the weighting coefficient ω (X p -ξ m ,Z 0 -ζ n ) Arranged as a vector t, denoted as
t＝[t 0 ,t 1 ,t 2 ,…,t M-1 ,t M-1 ,t M-2 ,…,t -2 ,t -1 ] T (20)
In the formula, matrix element t m And a weighting coefficient omega (X p -ξ m ,Z 0 -ζ n ) There is a relationship
t m ＝ω(X 1 -ξ m ,Z 0 -ζ n ) (21)
(2) The magnetization value m (ζ) of the nth layer m ,ζ n )(m＝1,2,…,N x ) Arranged as a vector g, vector element g m In relation to magnetization value
g m ＝m(ξ m ,ζ n ) (22)
Zero padding vector g to vector g ext
In the method, in the process of the invention,represents N p X 1 zero vector;
(3) Calculation of
Wherein fft () represents one-dimensional fast fourier transform;
(4) Calculation of
Wherein "..x" denotes a corresponding element multiplication operation;
(5) Calculation of
Where ifft () represents one-dimensional inverse fast fourier transform;
(6) Extracting matrix f ext Is N the first of (2) p The row elements form a vector f, namely a one-dimensional discrete convolution calculation result. When ω and m in the calculation of f are ω given by the formulas (11) and (12), respectively x ，ω z ，m x ，m z And then four one-dimensional discrete convolutions can be obtained:
the effect of the method for exploration of ferromagnetic binary provided by the above embodiment of the present invention is examined as follows.
In order to illustrate the efficiency and accuracy of the method for exploring a ferromagnetic binary object provided by the above embodiment of the present invention applied to calculating a complex binary object abnormal magnetic field with any geometric shape and any susceptibility distribution, a binary object model with a circular cross section as shown in fig. 3 is designed, and the specific details are as follows:
the two-dimensional rectangular model is internally provided with a ferromagnetic binary body with a circular section, and the range of the two-dimensional rectangular model is as follows: the x direction is from-1000 m to 1000m, and the z direction is from 0m to 1000m (the z axis is positive downwards); the space coordinate of the center of the circle of the ferromagnetic secondary body with the circular section is (0 m,500 m), and the radius is 400m; the magnetic susceptibility is 5SI; target area earth ownerThe magnetic field is 50000nT and the magnetic dip angle is 90 degrees. Dividing the two-dimensional rectangular model into 1000 times 1000 small rectangles with the same size, wherein the observation height is Z 0 -100m, horizontal observation points from-1000 m to 1000m, and the calculated point number is 1000. The expected relative root mean square error magnitude |ε 0 |＝10 -3 ％。
The method for exploring the ferromagnetic binary provided by the embodiment of the invention is realized by Matlab language, and the configuration of the operation platform is as follows: the CPU is i7-8750H, the main frequency is 2.20GHZ, and the memory is 8GB. For a 1000 x 1000 model, the method for exploration of ferromagnetic binaries according to the above embodiment of the present invention takes about 1.5 seconds for one iteration, and the relative root mean square error converges to 10 -3 % require 8 iterations, and thus can have a higher efficiency. The numerical solution and the analytical solution for the z-component of the high anomaly magnetic field are observed to be identical from a morphological point of view as shown in fig. 4 and 5. The numerical accuracy of the embodiment of the present invention is measured using the absolute error of the numerical solution and the analytical solution, as shown in fig. 6, the maximum absolute error is 4.99nT, the minimum absolute error is 0.002nT, and the absolute error average value is 2.14nT.
The embodiment of the invention also provides a ferromagnetic binary exploration system, which comprises: 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 perform the exploration of ferromagnetic binaries as described in 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 (7)
1. The exploration method of the ferromagnetic binary body is characterized by comprising the following steps:
setting an underground target area, a spreading range of a ferromagnetic secondary body, magnetic susceptibility distribution data of the ferromagnetic secondary body, ground observation height and horizontal observation point coordinates;
according to the distribution range of the underground target area and the ferromagnetic secondary body and the magnetic susceptibility distribution data of the ferromagnetic secondary body, calculating the magnetic field of the ferromagnetic secondary body of the underground target area, comprising:
(a) Establishing an initial two-dimensional rectangular model according to the underground target area and the spreading range of the ferromagnetic binary;
(b) Uniformly dividing the spreading range of the initial ferromagnetic binary body into a plurality of unit rectangles;
(c) Assigning a value to the magnetic susceptibility of each unit rectangle according to the magnetic susceptibility distribution data of the ferromagnetic binary body to obtain a target two-dimensional rectangular model corresponding to the initial ferromagnetic binary body;
(d) Calculating according to the target two-dimensional rectangular model to obtain a model weighting coefficient;
model weighting coefficient ω (x) 1 -ξ m ,z 1 -ζ n ) Including omega x (x i -ξ m ,z j -ζ n ) And omega z (x i -ξ m ,z j -ζ n ) Two components are respectively:
wherein: the region where the target two-dimensional rectangular model is located, namely, the region where the magnetic field of the underground target region ferromagnetic binary is located coincides with the magnetic field observation point region of the underground target region ferromagnetic binary, and the center of each unit rectangle is simultaneously used as the observation point of the magnetic field observation point region of the underground target region ferromagnetic binary, (x) i ,z j ) And (xi) m ,ζ n ) Respectively representing central coordinates of unit rectangles in a two-dimensional rectangular model of the target and strong magnetism of an underground target areaObservation point coordinates of the magnetic field observation point region of the sex-secondary body, i=1, 2, …, N x ，j＝1,2,…,N z ，m＝1,2,…,N x ，n＝1,2,…,N z ，N x And N z The method comprises the steps of dividing the two-dimensional rectangular model into the number of unit rectangles in the x and z directions respectively, wherein Deltax and Deltaz are the sizes of the unit rectangles in the x and z directions of the two-dimensional rectangular model respectively, arctan represents arctangent operation, and ln represents logarithmic operation;
(e) Calculating an earth main magnetic field at the center of each unit rectangle in the target two-dimensional rectangle model according to the earth main magnetic field model;
(f) Taking the main magnetic field of the earth at the center of each unit rectangle as the magnetic field initial value;
(g) Calculating to obtain a space domain abnormal magnetic field according to the target two-dimensional rectangular model, the magnetic field initial value and the model weighting coefficient;
abnormal magnetic field H in space domain a (x i ,z j ) Is composed of two components in the x-direction and in the z-direction, as follows:
wherein: m is m x (ξ m ,ζ n ) And m z (ξ m ,ζ n ) Respectively represent (xi) m ,ζ n ) The spatial domain magnetization M (x i ,z j ) Is the x-component and z-component of (2), M (x i ,z j )＝χ(x i ,z j )H (0) (x i ,z j )，H (0) (x i ,z j )＝H b (x i ,z j )，H b (x i ,z j ) Is the earth's main magnetic field at the center of the cell rectangle;
(h) Calculating to obtain a total magnetic field according to the magnetic field initial value and the space domain abnormal magnetic field;
(i) Setting an iteration convergence condition, judging whether the total magnetic field meets the iteration convergence condition, taking the total magnetic field as a magnetic field of a strong magnetic binary body of an underground target area if the total magnetic field meets the iteration convergence condition, taking the total magnetic field as the magnetic field initial value if the total magnetic field does not meet a given iteration convergence condition, and repeatedly executing the steps (g) to (i) until the given iteration convergence condition is met;
calculating the magnetic field of the ferromagnetic binary body at the position of the horizontal observation point according to the ground observation height, the horizontal observation point coordinates and the magnetic field of the ferromagnetic binary body of the underground target area;
judging that the magnetic field of the ferromagnetic binary body at the calculated horizontal observation point is the same as the magnetic field of the ferromagnetic binary body at the horizontal observation point measured by an instrument, and if the magnetic fields are the same, taking the magnetic susceptibility distribution data of the ferromagnetic binary body as the actual magnetic susceptibility distribution data of the ferromagnetic binary body to be used for exploring the ferromagnetic binary body.
2. The method of claim 1, wherein in step (g), a two-dimensional discrete convolution fast algorithm is used to calculate the spatially anomalous magnetic field H a (x i ,z j ) Is defined by two components H ax (x i ,z j ) And H az (x i ,z j )。
3. The method of claim 2, wherein in step (H), the total magnetic field H (1) (x i ,z j )＝H a (x i ,z j )+H b (x i ,z j )。
4. A method of ferromagnetic binary exploration according to claim 3, wherein the iterative convergence conditions set in step (i) are:
wherein ε 0 Is of desired numerical accuracy.
5. The method for exploration of ferromagnetic dichotomies according to claim 1 or 2 or 3 or 4, wherein calculating the magnetic field of the ferromagnetic dichotomies at the position of the horizontal observation point comprises:
calculating the observation point weighting coefficient omega (X) p -ξ m ,Z 0 -ζ n )：
Wherein: omega x (X p -ξ m ,Z 0 -ζ n ) And omega z (X p -ξ m ,Z 0 -ζ n ) Two components of the observation point weighting coefficient respectively representing the observation height magnetic field, Z 0 Indicating the observed height, X p Representing coordinates of a horizontal observation point, p=1 , 2,…,N 0 ，N 0 The number of observation points is represented, and the coordinate interval of the horizontal observation points is deltax;
calculating the magnetic field H of the ferromagnetic binary body at the position of the horizontal observation point a (X p ,Z 0 ) Its two components in the x-direction and in the z-direction are as follows:
6. according to claimThe method for exploring the ferromagnetic binary body is characterized in that a one-dimensional discrete convolution fast algorithm is adopted to repeatedly call N z Secondly, calculating the magnetic field H of the ferromagnetic binary body at the position of the horizontal observation point a (X p ,Z 0 ) Its two components in the x-direction and in the z-direction.
7. A system for the exploration of ferromagnetic binaries 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 exploration method of ferromagnetic binaries according to claim 1.
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