Magnetic field migration imaging method and device

Abstract

The invention relates to a magnetic field migration imaging method and device, and belongs to the technical field of exploration geophysics, and the method comprises the following steps: collecting any two components or component gradients of a magnetic field above a target body as observation magnetic field data; establishing a forward modeling algorithm of a magnetic field vector or a gradient thereof based on a given underground rock magnetic susceptibility or magnetization intensity parameter and a magnetic field integral equation; deriving an adjoint operator formula of any observation magnetic field based on a magnetic field vector forward modeling algorithm; deriving an adjoint magnetic field from an adjoint operator of the observation magnetic field; an underground space magnetic susceptibility distribution function is deduced through the accompanying magnetic field, and then migration imaging of a magnetic field vector is completed; according to the migration imaging principle of the magnetic field vector, a magnetic susceptibility space distribution function of the magnetic field gradient is deduced, and then migration imaging of the magnetic field gradient is completed. According to the invention, automatic migration imaging of two-dimensional magnetic field vector data is realized, and the method has strong anti-interference capability.

Description

Technical Field

[0001] The invention relates to a method and a device for magnetic field offset imaging, belonging to the technical field of exploration geophysics. Background Art

[0002] With the development of science and technology, people have developed many methods and technologies to study the magnetic susceptibility and spatial position distribution of underground targets through surface magnetic field data. In the early days, qualitative interpretation methods were mainly used, such as polarization, extension, boundary recognition, etc. Later, many potential field-based inversion algorithms such as two-dimensional and three-dimensional human-computer interactive fitting inversion and automatic inversion were developed. There are existing technologies that use damped least squares methods to solve generalized nonlinear inversion problems to obtain stable solutions. There are also existing technologies that use the selection method of generalized inverse matrices to iteratively invert two-dimensional magnetic anomalies, which can accurately obtain a finite number of combined plate models. With the development of computer technology, more new algorithms have emerged. Such as three-dimensional smooth regularized inversion, three-dimensional focused inversion, cluster-c mean focused inversion method, joint inversion method based on linear correlation constraints, and many three-dimensional potential field gradient inversion methods. The above two-dimensional and three-dimensional inversions are complex and time-consuming because they depend on prior models and constraints.

[0003] Migration imaging is a highly efficient data processing method that was developed earlier in seismic wave field imaging and electromagnetic field imaging. Mathematically speaking, migration is described by the effect of an adjoint operator on the observed data, where the adjoint operator is expressed as a reverse propagation function of the seismic or electromagnetic field. Based on the idea of ​​potential field migration, the present invention proposes a method and device for magnetic field migration imaging. Summary of the invention

[0004] The present invention provides a method and device for magnetic field offset imaging, which can realize automatic offset imaging of two-dimensional magnetic field vector data.

[0005] The technical solution adopted by the present invention to solve the technical problem is: In a first aspect, an embodiment of the present invention provides a method for magnetic field offset imaging, comprising the following steps: Step S1, collecting any two components or component gradients of the magnetic field above the target body as observed magnetic field data; Step S2, establishing a forward algorithm for the magnetic field vector or its gradient based on given underground rock magnetic susceptibility or magnetization intensity parameters and a magnetic field integral equation; Step S3, deriving the adjoint operator formula of any observed magnetic field based on the magnetic field vector forward algorithm; Step S4, deriving the adjoint magnetic field from the adjoint operator of the observed magnetic field; Step S5, deriving the underground space magnetic susceptibility distribution function from the accompanying magnetic field, and then completing the offset imaging of the magnetic field vector; Step S6, according to the offset imaging principle of the magnetic field vector, derive the magnetic susceptibility spatial distribution function of the magnetic field gradient, and then complete the offset imaging of the magnetic field gradient.

[0006] As a possible implementation of this embodiment, the forward algorithm for establishing the magnetic field vector or its gradient based on the given underground rock magnetic susceptibility or magnetization intensity parameter and the magnetic field integral equation includes: Assume that the complex form of the magnetization intensity satisfies: (1) in, is the magnetization intensity, the variable , is the x-direction component of the magnetization intensity, is the z-direction component of the magnetization intensity, is an imaginary unit, then the magnetic field intensity is defined in the complex plane as follows: (2) in, is the magnetic field strength, is the forward operator, ; (3) Among them, γ is the magnetic susceptibility, θ is the magnetization angle, H 0 is the geomagnetic field strength; Set the survey line on the ground , substituting equation (3) into equation (2), the magnetic field intensity on the measuring line satisfies: (4) For magnetic field gradient , and we get the following formula: (5) Where ζ is any point on the underground magnetic body: , ζ` is an arbitrary point on the ground: , ds is the area unit of underground magnetic body.

[0007] As a possible implementation of this embodiment, the adjoint operator formula of any observed magnetic field is derived based on the magnetic field vector forward algorithm, including: Assuming that the measuring line is on L, the boundary of the magnetic body is Γ, the complex plane of Hilbert space is introduced: (6) Among them, H is the theoretical calculated magnetic field strength, f is the observed magnetic field, and D is the underground half space. Introduce the real plane M: (7) inη is the magnetization intensity, For any observation field The adjoint operator of the observation field is introduced , then: (8) Expand both sides of the equation and sort them out to get any observation field The adjoint operator of is: (9) Then the adjoint operator of magnetic field intensity is: (10) in, is the image magnetic field strength.

[0008] As a possible implementation of this embodiment, the step of deriving the accompanying magnetic field from the accompanying operator of the observed magnetic field includes: because is the mirror image of the magnetic body Γ in the lower half space, Is The resulting mirror field: = (11) say As the adjoint field, let P+ be located in the complex plane of the upper half space and P- be located in the negative half of the lower half space, separated by the x-axis. Consider any point Draw a circle with radius R. The part of the real axis x that occurs inside the circle will be The circle part P− will be represented by According to the Cauchy integral formula: (12) The closed contour The integral on the real axis is taken counterclockwise The integration of is from right to left; The limit of R→+Inf is The integral of the segment approaches 0, so formula (12) can be written as: (13) Derived from the above formula: (14) Further we get: (15) Considering formula (15) and formula (10), the accompanying magnetic field is obtained as: (16).

[0009] As a possible implementation of this embodiment, the method of deriving the underground space magnetic susceptibility distribution function from the accompanying magnetic field and then completing the offset imaging of the magnetic field vector includes: Depth Weighting Function Equal to the integrated sensitivity of the complex magnetic field intensity The prescription of: (17) (18) The magnetic susceptibility distribution satisfies the following formula: = = (19) in: ; ; = (20) Expanding the above formula, we can get the underground space magnetic susceptibility distribution function: (twenty one).

[0010] As a possible implementation of this embodiment, the magnetic susceptibility spatial distribution function of the magnetic field gradient is derived based on the offset imaging principle of the magnetic field vector, and then the offset imaging of the magnetic field gradient is completed, including: The magnetic field gradient is: = (twenty two) in, is the horizontal component of the magnetization The gradient field, is the vertical component of the magnetization intensity The gradient field of The adjoint operator of magnetic field gradient is: ; (twenty three) The magnetic field gradient field is accompanied by the field: (twenty four) The migration imaging of the magnetic field gradient is: (25).

[0011] As a possible implementation method of this embodiment, the principle of the magnetic field offset imaging is: taking the observation plane as a mirror, assuming that there is a virtual "mirror field source" in the upper half space, and the corresponding potential field is called a "mirror field", mathematically called an "offset field", and the offset field is extended downward. Since it is far away from the field source, the mathematical equation extended upward satisfies Dirichlet's first boundary value problem, and its solution is convergent and stable.

[0012] In a second aspect, an embodiment of the present invention provides a magnetic field offset imaging device, comprising: A magnetic field data acquisition module is used to acquire any two components or component gradients of the magnetic field above the target body as observed magnetic field data; A forward algorithm establishment module, used for establishing a forward algorithm of a magnetic field vector or its gradient based on given underground rock magnetic susceptibility or magnetization intensity parameters and a magnetic field integral equation; The adjoint operator derivation module is used to derive the adjoint operator formula of any observed magnetic field based on the magnetic field vector forward algorithm; An adjoint magnetic field derivation module is used to derive the adjoint magnetic field from the adjoint operator of the observed magnetic field; The magnetic field vector migration imaging module is used to derive the underground space magnetic susceptibility distribution function from the accompanying magnetic field, and then complete the migration imaging of the magnetic field vector; The magnetic field gradient migration imaging module is used to derive the magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, and then complete the migration imaging of the magnetic field gradient.

[0013] In a third aspect, an embodiment of the present invention provides an electronic device, comprising a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory through the bus, and the processor executes the machine-readable instructions to perform the steps of any of the above-mentioned magnetic field offset imaging methods.

[0014] In a fourth aspect, an embodiment of the present invention provides a storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of any of the above-mentioned magnetic field offset imaging methods are executed.

[0015] The beneficial effects of the technical solution of the embodiment of the present invention are as follows: A method for magnetic field offset imaging of the technical solution of an embodiment of the present invention comprises the following steps: step S1, collecting basic data of observed magnetic field, wherein the basic data of observed magnetic field comprises rock magnetic susceptibility and magnetization intensity; step S2, based on given underground rock magnetic susceptibility or magnetization intensity parameters, assuming that any two orthogonal magnetic vectors or gradients constitute a complex plane, establishing a magnetic field vector and gradient forward algorithm by a magnetic field integral equation; step S3, deriving an adjoint operator formula of any observed magnetic field based on a magnetic field vector forward algorithm; step S4, deriving an adjoint magnetic field by the adjoint operator of the observed magnetic field; step S5, deriving an underground spatial magnetic susceptibility distribution function by the adjoint magnetic field, and obtaining an offset imaging formula of a magnetic field vector; step S6, deriving a magnetic susceptibility spatial distribution function of a magnetic field gradient according to the magnetic field vector offset imaging principle, and obtaining an offset imaging formula of a magnetic field gradient; step S7, performing magnetic field offset imaging by using the offset imaging formula of a magnetic field vector and the offset imaging formula of a magnetic field gradient. The present invention constructs a magnetic field intensity forward algorithm based on magnetic susceptibility and geomagnetic field intensity, and applies it to magnetic vector offset imaging, thereby providing more accurate magnetic field intensity information, improving the quality and anti-interference ability of magnetic vector offset imaging. At the same time, the introduction of magnetic field intensity accompanying operator, magnetic field intensity accompanying field, magnetic field gradient accompanying operator, magnetic field gradient accompanying field, etc., further enriches the content of magnetic field information and improves the utilization rate of information. In addition, the magnetic field intensity forward algorithm and application of the present invention have high real-time performance and accuracy, and can effectively cope with complex interference environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a flow chart of a method for magnetic field offset imaging according to an exemplary embodiment; Figure 2 is a schematic structural diagram of a magnetic field offset imaging device according to an exemplary embodiment; Figure 3 is a schematic diagram of a two-dimensional magnetic problem assuming a complex plane according to an exemplary embodiment; Figure 4 is a schematic diagram of a background field grid and a model grid according to an exemplary embodiment; Figure 5 is a schematic diagram of magnetic field vectors and their gradients calculated by forward modeling of a theoretical model on the surface according to an exemplary embodiment (wherein (a) is a schematic diagram of vertical Hz and horizontal Hx components of magnetic field intensity, and (b) is a schematic diagram of the gradients of vertical Hz and horizontal Hx components of magnetic field intensity); Figure 6 is a schematic diagram of defining an accompanying field according to an exemplary embodiment; Figure 7 is a schematic diagram of two magnetic bodies with the same buried depth (model 2) according to an exemplary embodiment; Figure 8 yes Figure 7 Schematic diagram of the forward simulated magnetic field and its gradient in the upper part of the middle model 2 (where (a) is a schematic diagram of the vertical and horizontal magnetic field component values ​​obtained through forward calculation, and (b) is a schematic diagram of the gradient values ​​of the vertical and horizontal magnetic field components obtained through forward calculation); Fig. 9 is a schematic diagram of magnetic field component offset imaging according to an exemplary embodiment; Fig.10 is a schematic diagram of magnetic field gradient migration imaging according to an exemplary embodiment; Fig.11 is a schematic diagram of measuring horizontal and vertical gradients of a magnetic field according to an exemplary embodiment; Fig.12 is a HXX curve diagram of a horizontal magnetic field gradient along the X direction according to an exemplary embodiment; Fig.13 The figure is a schematic diagram of measured magnetic field gradient data migration imaging according to an exemplary embodiment. DETAILED DESCRIPTION

[0017] In order to more clearly illustrate the technical features of the solution of the present invention, the present invention is described in detail below through specific implementation methods and in conjunction with the accompanying drawings.

[0018] like Figure 1 As shown, a method for magnetic field offset imaging provided by an embodiment of the present invention includes the following steps: Step S1, collecting any two components or component gradients of the magnetic field above the target body as observed magnetic field data; Step S2, establishing a forward algorithm for the magnetic field vector or its gradient based on given underground rock magnetic susceptibility or magnetization intensity parameters and a magnetic field integral equation; Step S3, deriving the adjoint operator formula of any observed magnetic field based on the magnetic field vector forward algorithm; Step S4, deriving the adjoint magnetic field from the adjoint operator of the observed magnetic field; Step S5, deriving the underground space magnetic susceptibility distribution function from the accompanying magnetic field, and then completing the offset imaging of the magnetic field vector; Step S6, according to the offset imaging principle of the magnetic field vector, derive the magnetic susceptibility spatial distribution function of the magnetic field gradient, and then complete the offset imaging of the magnetic field gradient.

[0019] As a possible implementation of this embodiment, the forward algorithm for establishing the magnetic field vector or its gradient based on the given underground rock magnetic susceptibility or magnetization intensity parameter and the magnetic field integral equation includes: Assume that the complex form of the magnetization intensity satisfies: (1) in, is the magnetization intensity, the variable , is the x-direction component of the magnetization intensity, is the z-direction component of the magnetization intensity, is an imaginary unit, then the magnetic field intensity is defined in the complex plane as follows: (2) in, is the magnetic field strength, is the forward operator, ; (3) Among them, γ is the magnetic susceptibility, θ is the magnetization angle, H 0 is the geomagnetic field strength; Set the survey line on the ground , substituting equation (3) into equation (2), the magnetic field intensity on the measuring line satisfies: (4) For magnetic field gradient , and we get the following formula: (5) Where ζ is any point on the underground magnetic body: , ζ` is an arbitrary point on the ground: , ds is the area unit of underground magnetic body.

[0020] As a possible implementation of this embodiment, the adjoint operator formula of any observed magnetic field is derived based on the magnetic field vector forward algorithm, including: Assuming that the measuring line is on L, the boundary of the magnetic body is Γ, the complex plane of Hilbert space is introduced: (6) Among them, H is the theoretical calculated magnetic field strength, f is the observed magnetic field, and D is the underground half space. Introduce the real plane M: (7) in η is the magnetization intensity, For any observation field The adjoint operator of the observation field is introduced , then: (8) Expand both sides of the equation and sort them out to get any observation field The adjoint operator of is: (9) Then the adjoint operator of magnetic field intensity is: (10) in, is the image magnetic field strength.

[0021] As a possible implementation of this embodiment, the step of deriving the accompanying magnetic field from the accompanying operator of the observed magnetic field includes: because is the mirror image of the magnetic body Γ in the lower half space, Is The resulting mirror field: = (11) say As the adjoint field, let P+ be located in the complex plane of the upper half space and P- be located in the negative half of the lower half space, separated by the x-axis. Consider any point Draw a circle with radius R. The part of the real axis x that occurs inside the circle will be The circle part P− will be represented by According to the Cauchy integral formula: (12) The closed contour The integral on the real axis is taken counterclockwise The integration of is from right to left; The limit of R→+Inf is The integral of the segment approaches 0, so formula (12) can be written as: (13) Derived from the above formula: (14) Further we get: (15) Considering formula (15) and formula (10), the accompanying magnetic field is obtained as: (16).

[0022] As a possible implementation of this embodiment, the method of deriving the underground space magnetic susceptibility distribution function from the accompanying magnetic field and then completing the offset imaging of the magnetic field vector includes: Depth Weighting Function Equal to the integrated sensitivity of the complex magnetic field intensity The prescription of: (17) (18) The magnetic susceptibility distribution satisfies the following formula: = = (19) in: ; ; = (20) Expanding the above formula, we can get the underground space magnetic susceptibility distribution function: (twenty one).

[0023] As a possible implementation of this embodiment, the magnetic susceptibility spatial distribution function of the magnetic field gradient is derived based on the offset imaging principle of the magnetic field vector, and then the offset imaging of the magnetic field gradient is completed, including: The magnetic field gradient is: = (twenty two) in, is the horizontal component of the magnetization The gradient field, is the vertical component of the magnetization intensity The gradient field of The adjoint operator of magnetic field gradient is: ; (twenty three) The magnetic field gradient field is accompanied by the field: (twenty four) The migration imaging of the magnetic field gradient is: (25).

[0024] As a possible implementation method of this embodiment, the principle of the magnetic field offset imaging is: taking the observation plane as a mirror, assuming that there is a virtual "mirror field source" in the upper half space, and the corresponding potential field is called a "mirror field", mathematically called an "offset field", and the offset field is extended downward. Since it is far away from the field source, the mathematical equation extended upward satisfies Dirichlet's first boundary value problem, and its solution is convergent and stable.

[0025] The present invention provides a magnetic field offset imaging algorithm with high computational efficiency, strong anti-noise capability and stable convergence.

[0026] like Figure 2 As shown, in a second aspect, an embodiment of the present invention provides a magnetic field offset imaging device, comprising: A magnetic field data acquisition module is used to acquire any two components or component gradients of the magnetic field above the target body as observed magnetic field data; A forward algorithm establishment module, used for establishing a forward algorithm of a magnetic field vector or its gradient based on given underground rock magnetic susceptibility or magnetization intensity parameters and a magnetic field integral equation; The adjoint operator derivation module is used to derive the adjoint operator formula of any observed magnetic field based on the magnetic field vector forward algorithm; An adjoint magnetic field derivation module is used to derive the adjoint magnetic field from the adjoint operator of the observed magnetic field; The magnetic field vector migration imaging module is used to derive the underground space magnetic susceptibility distribution function from the accompanying magnetic field, and then complete the migration imaging of the magnetic field vector; The magnetic field gradient migration imaging module is used to derive the magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, and then complete the migration imaging of the magnetic field gradient.

[0027] The magnetic field belongs to the potential field or conservative field. The essence of the migration imaging in the potential field is to determine the position of the field source by downward analytical extension. Its migration is a special form of the downward continuation of the potential field and its gradient. However, the mathematical equation of downward extension is an ill-posed problem, and its solution is unstable and easy to diverge. In order to overcome this problem, it is assumed that there is a virtual "mirror field source" in the upper half space with the observation plane as the mirror. The corresponding potential field is called the "mirror field", which is mathematically called the "offset field". The downward extension of the "offset field" means that it is far away from the "mirror field source". This migration process is actually an upward extension. Since the mathematical equation of upward extension satisfies the Dirichlet first boundary value problem, its solution is convergent and stable. Therefore, this assumption is correct and feasible. The offset field (mirror field) can be transformed from the measured field through the offset operator. The adjoint operator can be iterated multiple times, so that the iterative potential field migration is equivalent to the regularized inversion process, which is similar to the electromagnetic migration iteration.

[0028] Therefore, the present invention proposes a magnetic field offset imaging algorithm, the principle of which is: taking the observation plane as a mirror, assuming that there is a virtual "mirror field source" in the upper half space, and the corresponding potential field is called a "mirror field", mathematically called an "offset field", and the offset field is extended downward. Since it is far away from the field source, it is actually extended upward. Since the mathematical equation of the upward extension satisfies Dirichlet's first boundary value problem, the solution of the equation is convergent and stable.

[0029] After obtaining the basic data of the on-site magnetic field, the specific implementation process of magnetic field offset imaging is as follows.

[0030] First, construct the forward operator of the magnetic vector or its gradient.

[0031] Based on the given underground rock magnetic susceptibility or magnetization intensity parameters, such as Figure 3As shown, assuming that any two orthogonal magnetic vectors or gradients form a complex plane, the magnetic field vector and gradient forward algorithm are established by the magnetic field integral equation.

[0032] Assume that the complex form of the magnetization intensity satisfies the following formula: (1) in: is the magnetization intensity, the variable , is the x-direction component of the magnetization intensity, is the z-direction component of the magnetization intensity, is an imaginary unit, then the magnetic field intensity is defined in the complex plane as follows: (2) in, is the forward operator,

[0033] (3) Where γ is the magnetic susceptibility, H 0 is the geomagnetic field strength. Set the measuring line to be on the ground , substituting equation (3) into equation (2), the magnetic field intensity on the measuring line satisfies: (4) For magnetic field gradient , and we get the following formula: (5) Where ζ is an arbitrary point on the underground magnetic body: ,ζ` is any point on the ground, According to formulas (4) and (5), the two-dimensional magnetic field distribution can be calculated, as Figure 4 and Figure 5 shown.

[0034] Figure 4 The solid line grid is the background field grid. The calculation area is from -2050m to +2050m in the X direction, with a step length of 100m, and from -50m to -1050m in the Z direction, with a step length of 100m. The dashed line is the model grid. The model area is from -1100m to +1100m in the X direction, with a step length of 100m, and from 0 to -1000m in the Z direction, with a step length of 100m. The gray-filled grid represents the position and size of the magnetic body. The magnetic body is 100m long in the x direction and 200m long in the depth direction. The top burial depth is -400m, the center is located at x=50m, the magnetic susceptibility is 0.4, and the magnetic susceptibility of other units is 0. Calculate the horizontal component of the total magnetic field generated by the magnetic body at the ground (Z=0) , vertical component , and its gradient field and .

[0035] Figure 5 is the forward calculation result, where (a) is the vertical Hz and horizontal Hx components of the magnetic field intensity, and its abnormal parts are mainly distributed between -550m and +450m, while the magnetic field gradient anomaly is concentrated between -500m and +400m, as shown in (b). From the forward modeling results, the magnetic field gradient anomaly range is narrower, close to the horizontal position of the magnetic body. Comparing the forward modeling results of model 2 with model 1, as the top burial depth of the magnetic body increases, the magnetic anomaly amplitude decreases and the lateral range becomes wider, which means that it is more difficult to determine the location of the magnetic body.

[0036] Second, derive the adjoint operator of any observed magnetic field.

[0037] Based on the magnetic field vector forward algorithm, the specific process of deriving the adjoint operator formula of any observed magnetic field is as follows: Assuming that the measuring line is on L, the boundary of the magnetic body is Γ, the complex plane of Hilbert space is introduced: (6) Among them, H is the theoretical calculated magnetic field strength, f is the observed magnetic field, and D is the underground half space. Introduce the real plane M: (7) in η is the magnetization intensity, For any observation field The adjoint operator of the observation field is introduced ; (8) According to the above calculation rules, expand both sides of the equation and sort them out to get any observation field The adjoint operator of is: (9) Then the adjoint operator of magnetic field intensity is: (10) in, is the image magnetic field strength.

[0038] Third, the companion magnetic field is derived from the companion operator of the observed magnetic field.

[0039] because is the mirror image of the magnetic body Γ in the lower half space, Is The resulting mirror field: = (11) say For the accompanying field, Figure 6 As shown, let P+ be located in the complex plane of the upper half space and P- be located in the negative half of the lower half space, separated by the x-axis. Consider any point Draw a circle with radius R. The part of the real axis x that occurs inside the circle will be The circle part P− will be represented by ; According to the Cauchy integral formula: (12) Among them, the closed contour The integral over is taken in the counterclockwise direction. In particular, for the real axis segment The integral is from right to left. Now let's look at the limit of R→+Inf. The integral of the segment approaches 0, and formula (12) can be written as: (13) Derived from the above formula: (14) Further we get: (15) Considering formula (15) and formula (10), we get the accompanying magnetic field: (16).

[0040] Fourth, the magnetic susceptibility distribution function of the underground space is derived from the accompanying magnetic field.

[0041] is the integrated sensitivity of the complex magnetic field intensity, is the depth weighting function, equal The prescription of: (17) (18) The magnetic susceptibility distribution satisfies the following formula: = = (19) in, , , = (20) Expanding the above formula, we can get the underground space magnetic susceptibility distribution function: (twenty one).

[0042] Fifth, based on the magnetic field vector offset imaging principle, the magnetic susceptibility spatial distribution function of the magnetic field gradient is derived.

[0043] According to the same method principle, the migration imaging correlation function based on the magnetic field vector gradient can be obtained: 1) Magnetic field gradient: = (twenty two) 2) Magnetic field gradient adjoint operator: (twenty three) 3) Magnetic field gradient field accompanied by field: (twenty four) 4) Magnetic field gradient migration imaging (magnetic susceptibility spatial distribution function): (25).

[0044] 6. Testing and verification of magnetic field offset imaging.

[0045] 1) Forward data testing of theoretical models.

[0046] Theoretical models such as Figure 7 As shown: the top burial depth of the two magnetic bodies is 400m, the horizontal distance is 1800m, the magnetic susceptibility is 0.4, the length along the x direction is 100m, and the length along the depth direction is about 200m. The center of the left magnetic body is located at x=-950m, and the center of the right magnetic body is located at x=+950m.

[0047] After forward calculation, the vertical and horizontal magnetic field component values, namely Hz and Hx, are obtained, such as Figure 8 As shown in (a), the gradient values ​​of the vertical and horizontal magnetic field components, namely Hzx and Hxx, are Figure 8 As shown in (b), it can be seen that although the two magnetic bodies are far apart, the two components of the magnetic field are still affected to a certain extent, such as the poor symmetry of the Hz anomaly and the Hx anomaly minimum value being greater than the maximum value.

[0048] The above magnetic field component data are migrated and imaged, and the results are as follows: Fig. 9 and Fig.10 As shown. Fig. 9 As shown in the figure, in the magnetic field migration imaging, the maximum value of the underground unit magnetic susceptibility is 0.15, which is smaller than the theoretical value of 0.4 in the model, and the center positions of its two magnetic bodies are consistent with the center positions of the magnetic bodies in the model; Fig.10As shown in the figure, the magnetic field gradient migration imaging corresponds to the position of the magnetic body more accurately, and the maximum magnetic susceptibility of the unit magnetic body is 0.1, which is consistent with the position of the model magnetic body, but the magnetic susceptibility is smaller. At the same time, it can be observed that the inversion result of the magnetic field gradient is more convergent than the inversion result of the magnetic field.

[0049] 2) Physical experiment data migration imaging test.

[0050] In order to further verify the adaptability of the migration imaging algorithm to the measured data, a 5×5×5cm 3 The iron block is actually observed, such as Fig.11 As shown, the survey line is east-west, 3.0m long, 0.1m apart, 0.3m above the ground, 0.6m apart from the probes, and the magnetic field gradient value is defined as probe 1 minus probe 2. When the horizontal gradient Hxx is observed, Fig. 9 The two probes on the left are placed horizontally. When observing the vertical gradient Hzx, Fig.11 The two probes on the right side of the center are placed vertically.

[0051] In order to eliminate some errors, each measuring point was observed three times and the average value was taken as the final value to form the magnetic field gradient curve, such as Fig.12 Horizontal magnetic field gradient H xx There is a maximum value and a minimum value. When the magnetic probe is far away from the target, H xx The magnetic field gradient varies between -27 and -40nT / m. When the first probe is close to the iron block, the magnetic field gradient increases, with a maximum value of 206.37nT / m. When the iron block is located at the center of the two probes, the horizontal magnetic field gradient is close to 0nT. When the second probe passes the iron block, the magnetic field gradient reaches a minimum value of -283.97nT / m. The reason for the large difference in the two extreme values ​​may be the inconsistency of the sensitivity of the two probes. Another reason may be the distance error between the probe and the iron block during the measurement process. After all, the probe is only 0.3m away from the iron block.

[0052] In vertical magnetic field observation, the magnetic field gradient at both ends of the measuring line H zx The value is between -40 and -110nT / m. When the probe passes over the iron block, a minimum value of -267.97 appears. The two sides of the anomaly are basically symmetrical. In addition, the observed data on the right side of the measurement line jumps greatly, indicating that the external interference is large. The ratio of noise to minimum value is about 27.7%.

[0053] According to the principle of offset imaging, the mirror field and its corresponding original field have their own characteristics. xx With the original H xx Equal, but with H zxare opposite numbers to each other. Through the mirror field, we can obtain the adjoint operator and then obtain the magnetic susceptibility distribution map. By performing migration imaging on the measured data, the results are as follows: Fig.13 As shown, the target body is clearly imaged, with a maximum magnetic susceptibility of about 0.05, and its center position is basically consistent with the lateral position of the magnetic body, between 1.4-1.6m; the top burial depth of the offset imaging target body is 0.5m, while the top burial depth of the model is 0.3m, which has a certain error, indicating that this method has poor resolution in the depth direction. Fig.12 It can be seen that the right side of the vertical magnetic field Hzx curve is interfered by strong noise, but the offset imaging is still possible, which shows that this algorithm has strong anti-noise ability.

[0054] The present invention has carried out research on the offset imaging algorithm by numerical simulation and physical experiment, built multiple model examples to verify the effect of two-dimensional magnetic field and its gradient offset imaging, optimized the grid division, and set different noise data to test the robustness of the program algorithm. The measured magnetic field data was obtained through physical experiments, and the test algorithm has a stable and reliable effect.

[0055] The present invention realizes automatic offset imaging of two-dimensional magnetic field vector data and has strong anti-interference ability.

[0056] An electronic device provided by an embodiment of the present invention includes a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the device is running, the processor communicates with the memory through the bus, and the processor executes the machine-readable instructions to perform steps of any of the above-mentioned magnetic field offset imaging methods.

[0057] Specifically, the above-mentioned memory and processor can be general-purpose memory and processor, which are not specifically limited here. When the processor runs the computer program stored in the memory, the above-mentioned magnetic field offset imaging method can be executed.

[0058] Those skilled in the art will appreciate that the structure of the electronic device does not limit the electronic device and may include more or fewer components than shown in the figure, or combine or split certain components, or arrange the components differently.

[0059] In some embodiments, the electronic device may also include a touch screen that can be used to display a graphical user interface (e.g., a startup interface of an application) and receive user operations on the graphical user interface (e.g., startup operations on an application). The specific touch screen may include a display panel and a touch panel. The display panel may be configured in the form of LCD (Liquid Crystal Display), OLED (Organic Light-Emitting Diode), etc. The touch panel may collect the user's contact or non-contact operations on or near it, and generate pre-set operation instructions, for example, the user uses any suitable object such as a finger, stylus, or accessories on or near the touch panel. In addition, the touch panel may include two parts: a touch detection device and a touch controller. The touch detection device detects the user's touch position and posture, detects the signal brought by the touch operation, and transmits the signal to the touch controller; the touch controller receives the touch information from the touch detection device, converts it into information that the processor can process, and then sends it to the processor, and can receive and execute commands from the processor. In addition, the touch panel can be implemented by various types such as resistive, capacitive, infrared and surface acoustic wave, and any technology developed in the future can also be used to implement the touch panel. Further, the touch panel can cover the display panel, and the user can operate on or near the touch panel covered on the display panel according to the graphical user interface displayed on the display panel. After the touch panel detects the operation on or near it, it is transmitted to the processor to determine the user input, and then the processor provides corresponding visual output on the display panel in response to the user input. In addition, the touch panel and the display panel can be implemented as two independent components or integrated.

[0060] Corresponding to the method for starting the above-mentioned application, an embodiment of the present invention further provides a storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of any of the above-mentioned magnetic field offset imaging methods are executed.

[0061] The application startup device provided in the embodiment of the present application can be specific hardware on the device or software or firmware installed on the device. The device provided in the embodiment of the present application, its implementation principle and the technical effect produced are the same as those in the aforementioned method embodiment. For the sake of brief description, the parts not mentioned in the device embodiment can refer to the corresponding contents in the aforementioned method embodiment. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, devices and units described above can all refer to the corresponding processes in the aforementioned method embodiment, and will not be repeated here.

[0062] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0063] In the embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of modules is only a logical function division. There may be other division methods in actual implementation. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0064] The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed on multiple network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0065] In addition, each functional module in the embodiments provided in the present application may be integrated into one processing module, or each module may exist physically separately, or two or more modules may be integrated into one module.

[0066] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0067] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0068] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for magnetic field offset imaging, It is characterized in that The steps include: Step S1, collecting any two components or component gradients of the magnetic field above the target body as observed magnetic field data; Step S2, establishing a forward algorithm for the magnetic field vector or its gradient based on given underground rock magnetic susceptibility or magnetization intensity parameters and a magnetic field integral equation; Step S3, deriving the adjoint operator formula of any observed magnetic field based on the magnetic field vector forward algorithm; Step S4, deriving the adjoint magnetic field from the adjoint operator of the observed magnetic field; Step S5, deriving the underground space magnetic susceptibility distribution function from the accompanying magnetic field, and then completing the offset imaging of the magnetic field vector; Step S6, according to the offset imaging principle of the magnetic field vector, derive the magnetic susceptibility spatial distribution function of the magnetic field gradient, and then complete the offset imaging of the magnetic field gradient.

2. The method for magnetic field offset imaging according to claim 1, It is characterized in that The forward algorithm for establishing a magnetic field vector or its gradient based on a given underground rock magnetic susceptibility or magnetization intensity parameter and a magnetic field integral equation comprises: Assume that the complex form of the magnetization intensity satisfies: （1） in, is the magnetization intensity, the variable , is the x-direction component of the magnetization intensity, is the z-direction component of the magnetization intensity, is an imaginary unit, then the magnetic field intensity is defined in the complex plane as follows: （2） in, is the magnetic field strength, is the forward operator, ; （3） Among them, γ is the magnetic susceptibility, θ is the magnetization angle, H 0 is the strength of the Earth's magnetic field; Set the line on the ground , substituting equation (3) into equation (2), the magnetic field intensity on the measuring line satisfies: （4） For magnetic field gradient , and we get the following formula: （5） Where ζ is any point on the underground magnetic body: , ζ` is an arbitrary point on the ground: , ds is the area unit of underground magnetic body.

3. The method for magnetic field offset imaging according to claim 2, It is characterized in that The adjoint operator formula of any observed magnetic field is derived based on the magnetic field vector forward algorithm, including: Assuming that the measuring line is on L, the boundary of the magnetic body is Γ, the complex plane of Hilbert space is introduced: （6） Among them, H is the theoretical calculated magnetic field strength, f is the observed magnetic field, and D is the underground half space. Introduce the real plane M: （7） in η is the magnetization intensity, For any observation field The adjoint operator of the observation field is introduced , then: （8） Expand both sides of the equation and sort them out to get any observation field The adjoint operator of is: （9） Then the adjoint operator of magnetic field intensity is: （10） in, is the mirror magnetic field strength.

4. The method for magnetic field offset imaging according to claim 3, It is characterized in that The method of deriving the adjoint magnetic field from the adjoint operator of the observed magnetic field comprises: because is the mirror image of the magnetic body Γ in the lower half space, Is The resulting mirror field: = （11） say As the adjoint field, let P+ be located in the complex plane of the upper half space and P- be located in the negative half of the lower half space, separated by the x-axis. Consider any point Draw a circle with radius R. The part of the real axis x that occurs inside the circle will be The circle part P− will be represented by According to the Cauchy integral formula: （12） The closed contour The integral on the real axis is taken counterclockwise The integration of is from right to left; The limit of R→+Inf is The integral of the segment approaches 0, so formula (12) can be written as: （13） Derived from the above formula: （14） Further we get: （15） Considering formula (15) and formula (10), the accompanying magnetic field is obtained as: （16）。 5. The method for magnetic field offset imaging according to claim 4, It is characterized in that The method of deriving the underground space magnetic susceptibility distribution function from the accompanying magnetic field and then completing the offset imaging of the magnetic field vector includes: Depth Weighting Function Equal to the integrated sensitivity of the complex magnetic field intensity The prescription of: （17） （18） The magnetic susceptibility distribution satisfies the following formula: = = （19） in: ; ; = （20） Expanding the above formula, we can get the underground space magnetic susceptibility distribution function: （21）。 6. The method for magnetic field offset imaging according to claim 5, It is characterized in that The method of deriving the magnetic susceptibility spatial distribution function of the magnetic field gradient based on the offset imaging principle of the magnetic field vector, and then completing the offset imaging of the magnetic field gradient, includes: The magnetic field gradient is: = （22） in, is the horizontal component of the magnetization The gradient field, is the vertical component of the magnetization intensity The gradient field of The adjoint operator of magnetic field gradient is: ； （23） The magnetic field gradient field is accompanied by the field: （24） The migration imaging of the magnetic field gradient is: （25）。 7. The method for magnetic field offset imaging according to any one of claims 1 to 6, It is characterized in that The principle of magnetic field offset imaging is: taking the observation plane as a mirror, assuming that there is a virtual "mirror field source" in the upper half space, and the corresponding potential field is called the "mirror field", mathematically called the "offset field", and the offset field is extended downward. Since it is far away from the field source, the mathematical equation extended upward satisfies the Dirichlet first boundary value problem, and the solution of the equation is convergent and stable.

8. A magnetic field offset imaging device, It is characterized in that include: A magnetic field data acquisition module is used to acquire any two components or component gradients of the magnetic field above the target body as observed magnetic field data; A forward algorithm establishment module, used for establishing a forward algorithm of a magnetic field vector or its gradient based on given underground rock magnetic susceptibility or magnetization intensity parameters and a magnetic field integral equation; The adjoint operator derivation module is used to derive the adjoint operator formula of any observed magnetic field based on the magnetic field vector forward algorithm; An adjoint magnetic field derivation module is used to derive the adjoint magnetic field from the adjoint operator of the observed magnetic field; The magnetic field vector migration imaging module is used to derive the underground space magnetic susceptibility distribution function from the accompanying magnetic field, and then complete the migration imaging of the magnetic field vector; The magnetic field gradient migration imaging module is used to derive the magnetic susceptibility spatial distribution function of the magnetic field gradient according to the migration imaging principle of the magnetic field vector, and then complete the migration imaging of the magnetic field gradient.

9. An electronic device, It is characterized in that It includes a processor, a memory and a bus, the memory stores machine-readable instructions executable by the processor, when the electronic device is running, the processor and the memory communicate through the bus, and the processor executes the machine-readable instructions to perform the steps of the method for magnetic field offset imaging as described in any one of claims 1-7.

10. A storage medium, It is characterized in that The storage medium stores a computer program, which, when executed by a processor, executes the steps of the method for magnetic field offset imaging as described in any one of claims 1 to 7.

Images