A magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition

Abstract

The application discloses a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition. The method uses a detection platform composed of four magnetic flux gate sensors arranged in a cross shape to collect 12 component signals of the magnetic signal, obtains a magnetic induction intensity change matrix according to the differential signals between the sensors, obtains five independent magnetic gradient tensor elements based on the passivity and irrotationality of the magnetic field, performs wavelet packet decomposition and reconstruction on the five elements to realize band-pass filtering and remove noise and trend items, and then combines to obtain magnetic gradient tensor invariants. Variation mode extraction is performed on the tensor elements to obtain the expected mode of the tensor elements, the change of the magnetic induction intensity is projected onto the geomagnetic direction, six combined components are obtained according to the tensor invariants. Variation mode extraction is performed on the seven basis functions in the full magnetic gradient orthogonal basis decomposition method, then Schmidt orthogonalization and standardization processing are performed to obtain seven improved orthogonal basis functions. Then the six combined components projected onto the geomagnetic direction are decomposed by using the improved orthogonal basis functions to obtain six energy coefficients, the sum of squares of the energy coefficients is calculated, and the sum of squares is multiplied by the square of the tensor invariants to serve as a comprehensive anomaly evaluation index, and finally whether a magnetic anomaly exists in the to-be-detected signal is judged according to the comprehensive anomaly evaluation index. The method can still realize magnetic anomaly detection in an environment with extremely low signal-to-noise ratio.

Description

Technical Field

[0001] This invention relates to signal processing techniques such as variational mode extraction and orthogonal basis function decomposition, and belongs to the field of magnetic anomaly signal detection. Specifically, it relates to a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition. Background Technology

[0002] The Earth's magnetic field changes slowly in its spatial distribution. Ferromagnetic objects can alter the spatial distribution of the Earth's magnetic field, thus producing magnetic anomalies. Magnetic sensors can capture these anomaly signals, enabling the detection, location, and identification of magnetic targets. Because changes in the magnetic field are unaffected by non-ferromagnetic media such as soil and smoke, magnetic anomaly detection is widely used in geological exploration, unexploded ordnance detection, underwater detection, and regional intrusion detection.

[0003] Currently, the most widely used method in magnetic anomaly detection is the orthogonal basis function decomposition method based on the characteristics of the magnetic anomaly waveform, such as the full magnetic gradient orthogonal basis function detection method. When the signal-to-noise ratio of the signal to be detected is low, the signal first needs to be filtered and denoised. The denoising process may change the waveform characteristics of the original anomaly signal. When directly using theoretically orthogonal basis functions for decomposition, the imperfect matching between the basis functions and the magnetic anomaly waveform may result in a low signal-to-noise ratio of the output signal, leading to detection failure.

[0004] To address this problem, this invention discloses a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition. The method employs wavelet packet filtering and variational mode extraction (VME) algorithms for preprocessing the detection signal. Then, it uses the same VME algorithm with identical parameters to improve the seven basis functions in the full magnetic gradient decomposition method. Finally, by comprehensively utilizing the tensor invariants of the magnetic gradient signal, the signal-to-noise ratio of the output signal is effectively improved. This method can still determine the presence of magnetic anomalies in the detected signal even in environments with low magnetic signal-to-noise ratios. Summary of the Invention

[0005] The purpose of this invention is to provide a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition, thereby improving the signal-to-noise ratio of the detection output signal and enabling the detection of weak magnetic anomaly signals.

[0006] To achieve the above objectives, this invention provides a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition, comprising the following steps:

[0007] Step 1: Use four triaxial fluxgate sensors to form a cross-shaped detection platform with equal spacing. Simultaneously acquire 12 component signals from the four sensors in the x, y, and z axes. Calculate the differential signals between the four sensors to obtain five independent magnetic gradient signals G. xx G xy Gxz G yy G yz The calculation formula is as follows:

[0008]

[0009] In the formula, d represents the distance between the center points of two sensors on the same axis, and g S1x G represents the magnetic signal component of sensor S1 in the x-direction. S2y This represents the magnetic signal component of the S2 sensor in the y direction; other symbols follow the same pattern.

[0010] Step 2: Process the five magnetic gradient signals G obtained in Step 1. xx G xy G xz G yy G yz Wavelet packet decomposition is performed, retaining the sub-band containing magnetic anomaly information, while clearing other sub-bands to zero. Reconstruction is then performed to obtain the magnetic gradient signal G' after removing noise and trend terms. xx G' xy G' xz G' yy G' yz ;

[0011] Step 3: Calculate the tensor invariant I using the five denoised magnetic gradient signals obtained in Step 2. The calculation formula is as follows:

[0012] I = G' xx G' xy +G' yy G' zz +G' xx G' zz -G' xy 2 -G' xz 2 -G' yz 2

[0013] Step 4: Process the five denoised magnetic gradient signals G' obtained in Step 2. xx G' xy G' xz G' yy G' yz Variational mode extraction (VME) was performed separately to obtain 5 desired modes B. xx B xy B xz B yy B yz ;

[0014] Step 5: Transpose the 5 desired modes obtained in Step 4, and project them onto the geomagnetic direction according to the magnetic angle relationship to obtain 6 projection elements S. Gxx S Gxy S Gxz S Gyy S Gyz S Gzz The calculation formula is as follows:

[0015]

[0016] In the formula, o, p, and q are the unit vectors of the geomagnetic field vector projected onto the x, y, and z axes, respectively, and the calculation formula is:

[0017] o=cos(I)cos(D)

[0018] p = cos(I)sin(D)

[0019] q = sin(I)

[0020] Where I and D are the geomagnetic field dip angle and deflection angle of the detection point, respectively;

[0021] Step 6: Improve the total magnetic gradient orthogonal basis function decomposition method using VME. The method is as follows: Use the VME parameters from Step 4 to improve the seven orthogonal basis functions h in the total magnetic gradient orthogonal basis function decomposition method. j Perform VME on (j=1~7) to obtain 7 desired modes. Then, perform Schmitt orthogonalization and normalization on the 7 desired modes to obtain 7 improved orthogonal basis functions f. j (j = 1 to 7);

[0022] Step 7: Utilize the 7 improved orthogonal basis functions f obtained in Step 6 j (j = 1 to 7), respectively for the 6 projection elements S obtained in step 5 Gxx S Gxy S Gxz S Gyy S Gyz S Gzz Orthogonal basis decomposition was performed, yielding 6 decomposition energy coefficients k. i (i = xx, xy, xz, yy, yz, zz), where the formula for orthogonal basis decomposition is:

[0023]

[0024] In the formula Where n is the number of sampling points, n = 1, 2, ..., N, v is the velocity of the magnetic target, and f is the velocity of the magnetic target. s Where CPA is the sampling frequency, and CPA is the shortest distance from the sensor to the magnetic target's trajectory.

[0025] Step 8: Calculate the 6 energy coefficients k obtained in Step 7. i The sum of squares of (i = xx, xy, xz, yy, yz, zz) is multiplied by the square of the tensor invariant I obtained in step 3 to obtain a magnetic anomaly assessment index E, the formula of which is:

[0026]

[0027] Step 9: Set a dynamic threshold based on the constant false alarm rate (CFAR) detection principle. When the magnetic anomaly assessment index E is greater than the threshold, it is determined that there is a magnetic anomaly in the signal to be tested; otherwise, it is determined that there is no magnetic anomaly in the signal to be tested.

[0028] In the above steps, the specific steps for obtaining the desired mode using the variational mode extraction (VME) method in steps 4 and 5 are as follows:

[0029] Step 4-1: Let f be the signal to be extracted. o (t) is derived from the desired mode f d (t) and residual signal f r (t) constitutes, i.e.: f o (t)=f d (t)+f r (t)

[0030] Step 4-2: Establish the combination of the quadratic penalty term and the Lagrange multipliers, and calculate the formula as follows:

[0031]

[0032] In the formula, λ is the Lagrange multiplier, ω is the frequency, α represents the balance parameter of the two penalty functions, and ω d Indicates the center frequency of the desired mode. f d The Fourier transform of (t), and other symbols are derived accordingly, where Here is the frequency response function of the filter:

[0033]

[0034] Step 4-3: Set the initial desired mode Initial expected center frequency The penalty parameter α, the convergence accuracy ε, the maximum number of iterations N, the update parameter τ of λ, and the number of iterations n is initialized to 1;

[0035] Step 4-4: Update the desired mode using the following formula:

[0036]

[0037] In the formula, This represents the updated expected mode. The expected mode before the update;

[0038] Step 4-5: Update the desired mode based on step 4-4 For center frequency The update is performed using the following formula:

[0039]

[0040] Step 4-6: Use the dual ascent method to process the Lagrange multipliers in step 4-2. Perform an update and increment the iteration count n by 1. The update formula is:

[0041]

[0042] Where τ is the update parameter set in step 4-3;

[0043] Step 4-7: Determine if the desired mode meets the accuracy requirements. If it does, or if the specified maximum number of iterations N is reached, proceed to step 4-8; otherwise, return to step 4-4 and repeat the iterations from step 4-4 to step 4-7. The criteria for determining whether the desired mode meets the accuracy requirements are as follows:

[0044]

[0045] In the formula, ε is the convergence accuracy set in step 4-3;

[0046] Step 4-8: Using the desired mode obtained in step 4-4 The desired mode f obtained at the end of VME d .

[0047] In the above steps, step 6, which involves improving the orthogonal basis function of the total magnetic gradient using VME, is as follows:

[0048] Step 6-1: Determine the seven basis functions h in the total magnetic gradient decomposition method. j Perform VME on (j = 1 to 7) to obtain 7 desired modes h' corresponding to 7 basis functions. j (j = 1 to 7), where the parameters used when performing VME are the same as those used in step 4;

[0049] Step 6-2: For the 7 desired modes h' obtained in Step 6-1 j (j=1~7) are subjected to Schmitt orthogonalization to obtain the orthogonalized basis functions f. j (j=1~7), the formula for Schmidt orthogonalization is:

[0050]

[0051] Step 6-3: Standardize the basis functions after orthogonalization in Step 6-2 to obtain the improved total magnetic gradient orthogonal basis functions f. j (j = 1 to 7), the standardized formula is:

[0052] Attached Figure Description

[0053] Figure 1 This is a flowchart of a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition.

[0054] Figure 2 This is a schematic diagram of the cross-shaped magnetic gradient tensor detection platform structure.

[0055] Figure 3 This is a schematic diagram showing the relationship between the detection platform and the magnetic target's trajectory during the detection process.

[0056] Figure 4 This is a waveform diagram of one of the independent gradient signals, where the dashed box indicates the time when the magnetic anomaly signal occurs.

[0057] Figure 5 This is a waveform diagram of the tensor invariant I obtained by combining gradient tensors.

[0058] Figure 6 These are waveforms of the seven improved orthogonal basis functions obtained after variational mode extraction.

[0059] Figure 7 This is the waveform diagram of the comprehensive abnormality index E. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific examples and the accompanying drawings. It should be noted that similar or identical parts are referred to by the same reference numerals in the drawings or description. Implementations not shown or described in the drawings are forms known to those skilled in the art. Furthermore, although this document provides examples of parameters containing specific values, it should be understood that the parameters need not be exactly equal to the corresponding values, but rather approximate the corresponding values ​​within acceptable error tolerances or design constraints. Therefore, the terminology used is illustrative and not intended to limit the scope of protection of this invention.

[0061] This invention discloses a magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition. The flowchart of this method is shown below. Figure 1 The method includes the following steps:

[0062] Step 1: Acquire the magnetic anomaly gradient tensor signal. (Using...) Figure 2 The detection platform shown consists of four fluxgate sensors arranged in a cross shape at equal intervals. It simultaneously acquires 12 component signals from the four sensors along the x, y, and z axes. The detection platform remains stationary, while the ferromagnetic object moves along a straight line. The positional relationship between the two is as follows: Figure 3 As shown; the differential signals between the four sensors are calculated, resulting in five independent gradient signals G. xx G xy G xz G yy G yz , Figure 4 This is the waveform of one of the independent gradient signals. The dashed box indicates the location of the magnetic anomaly signal. The calculation formulas for the five independent gradient signals are as follows:

[0063]

[0064] In the formula, d represents the distance between the center points of two sensors on the same axis, and g S1x G represents the magnetic signal component of sensor S1 in the x-direction. S2y This represents the magnetic signal component of the S2 sensor in the y direction; other symbols follow the same pattern.

[0065] Step 2: Apply magnetic gradient tensor signal G xx G xy G xz G yy G yz Preprocessing is performed. Wavelet packet decomposition is used to decompose the tensor signal into 10 layers, resulting in 1024 sub-bands. After frequency rearrangement, sub-bands from layer 3 to layer 32 are selected for reconstruction to obtain the magnetic gradient signal G', which contains no trend term and high-frequency background noise. xx G' xy G' xz G' yy G' yz ;

[0066] Step 3: Calculate the tensor invariant I using the five denoised magnetic gradient signals obtained in Step 2. The calculation formula is as follows:

[0067] I = G' xx G' xy +G' yy G' zz +G' xx G' zz -G' xy 2 -G' xz 2 -G' yz2

[0068] Step 4: Process the five denoised magnetic gradient signals G' obtained in Step 2. xx G' xy G' xz G' yy G' yz Variational mode extraction (VME) was performed separately to obtain 5 desired modes B. xx B xy B xz B yy B yz The specific steps are as follows:

[0069] Step 4-1: Let the magnetic gradient signal to be extracted be f. o (t), derived from the desired mode f d (t) and residual signal f r (t)

[0070] Composition, namely:

[0071] f o (t)=f d (t)+f r (t)

[0072] Step 4-2: Establish the combination of the quadratic penalty term and the Lagrange multipliers, and calculate the formula as follows:

[0073]

[0074] In the formula, λ is the Lagrange multiplier, ω is the frequency, α represents the balance parameter of the two penalty functions, and ω d Indicates the center frequency of the desired mode. f d The Fourier transform of (t), and other symbols are derived accordingly, where Let be the frequency response function of the filter, i.e.:

[0075]

[0076] Step 4-3: Set the initial desired mode The initial desired center frequency is 0. The value is 0, the penalty parameter α is 700000, the convergence accuracy ε is 1.0E-5, the maximum number of iterations N is 1000, the update parameter τ of λ is 1.0E-6, and the number of iterations n is initialized to 1;

[0077] Step 4-4: Update the desired mode using the following formula:

[0078]

[0079] In the formula, This represents the updated expected mode. The expected mode before the update;

[0080] Step 4-5: Based on the updated desired mode obtained in Step 4-4 For center frequency The update is performed using the following formula:

[0081]

[0082] Step 4-6: Use the dual ascent method to process the Lagrange multipliers in step 4-2. Perform an update and increment the iteration count n by 1. The update formula is:

[0083]

[0084] Where τ is the update parameter set in step 4-3;

[0085] Step 4-7: Determine if the desired mode meets the accuracy requirements. If it does, or if the specified maximum number of iterations N is reached, proceed to step 4-8; otherwise, return to step 4-4 and repeat the iterations from step 4-4 to step 4-7. The criteria for determining whether the desired mode meets the accuracy requirements are as follows:

[0086]

[0087] In the formula, ε is the convergence accuracy set in step 4-3;

[0088] Step 4-8: Using the desired mode obtained in step 4-4 The desired mode f obtained at the end of VME d With G' xx Taking the signal as an example, if the accuracy requirement is met when the number of iterations n is 2^22, then we take... As the final desired mode B xx .

[0089] Step 5: Transpose the 5 desired modes obtained in Step 4, and project them onto the geomagnetic direction according to the magnetic angle relationship to obtain 6 projection elements S. Gxx S Gxy S Gxz S Gyy S Gyz S Gzz The calculation formula is as follows:

[0090]

[0091] In the formula, o, p, and q are the unit vectors of the geomagnetic field vector projected onto the x, y, and z axes, respectively, and the calculation formula is:

[0092] o=cos(I)cos(D)

[0093] p = cos(I)sin(D)

[0094] q = sin(I)

[0095] Where I and D are the geomagnetic field dip angle and deflection angle of the detection point, respectively;

[0096] Step 6: Improve the orthogonal basis functions of the total magnetic gradient using VME to obtain 7 improved standard orthogonal basis functions f. j (j = 1~7), the specific steps of the improved method are as follows:

[0097] Step 6-1: Using the VME parameters from Step 4, perform the analysis on the seven basis functions h in the total magnetic gradient decomposition method. j (j=1~7) Perform VME processing to obtain the expected modes h' of the basis functions. j (j = 1 to 7), of which 7 basis functions h j The formula for (j = 1 to 7) is:

[0098]

[0099] In the formula Where n is the number of sampling points, n = 1, 2, ..., N, v is the velocity of the magnetic target, and f is the velocity of the magnetic target. s Where CPA is the sampling frequency, and CPA is the shortest distance from the sensor to the magnetic target's trajectory.

[0100] Step 6-2: Perform Schmitt orthogonalization on the 7 desired modes obtained in Step 6-1 to obtain the orthogonalized basis functions f. j (j=1~7), the formula for Schmidt orthogonalization is:

[0101]

[0102] Step 6-3: Standardize the basis functions after orthogonalization in Step 6-2 to obtain the improved total magnetic gradient orthogonal basis functions f. j (j = 1 to 7), the standardized formula is:

[0103]

[0104] Finally, the improved orthogonal basis functions are obtained, such as Figure 6 As shown.

[0105] Step 7: Utilize the 7 improved orthogonal basis functions f obtained in Step 6j (j = 1 to 7), respectively for the 6 projection elements S obtained in step 5 Gxx S Gxy S Gxz S Gyy S Gyz S Gzz Orthogonal basis decomposition was performed, yielding 6 decomposition energy coefficients k. i (i = xx, xy, xz, yy, yz, zz), the formula for orthogonal basis decomposition is:

[0106]

[0107] Step 8: Calculate the 6 energy coefficients k obtained in Step 7. i The sum of squares of (i = xx, xy, xz, yy, yz, zz) is multiplied by the square of the tensor invariant I obtained in step 3 to obtain a magnetic anomaly assessment index E, such as... Figure 7 As shown, the calculation formula is:

[0108]

[0109] Step 9: Set a dynamic threshold based on the constant false alarm rate (CFAR) detection principle. When the magnetic anomaly assessment index E is greater than the threshold, it is determined that there is a magnetic anomaly in the signal to be tested; otherwise, it is determined that there is no magnetic anomaly in the signal to be tested.

[0110] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description, and it is impossible to exhaustively list all possible implementations here. Any modifications, equivalent substitutions, and improvements made within the technical concept and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition, characterized in that, Includes the following steps: Step 1: Use four triaxial fluxgate sensors to form a cross-shaped detection platform with equal spacing. Simultaneously acquire 12 component signals from the four sensors in the x, y, and z axes. Calculate the differential signals between the four sensors to obtain five independent magnetic gradient signals G. xx G xy G xz G yy G yz The calculation formula is as follows: In the formula, d represents the distance between the center points of two sensors on the same axis, and g S1x G represents the magnetic signal component of sensor S1 in the x-direction. S2y This represents the magnetic signal component of the S2 sensor in the y direction; other symbols follow the same pattern. Step 2: Process the five magnetic gradient signals G obtained in Step 1. xx G xy G xz G yy G yz Wavelet packet decomposition is performed, retaining the sub-band containing magnetic anomaly information, while clearing other sub-bands to zero. Reconstruction is then performed to obtain the magnetic gradient signal G' after removing noise and trend terms. xx G' xy G' xz G' yy G' yz ; Step 3: Calculate the second-order tensor invariant I2 using the five denoised magnetic gradient signals obtained in Step 2. The calculation formula is as follows: I2=G' xx G' xy +G' yy G' zz +G' xx G' zz -G' xy 2 -G' xz 2 -G' yz 2 Step 4: Process the five denoised magnetic gradient signals G' obtained in Step 2. xx G' xy G' xz G' yy G' yz VME variational mode extraction was performed separately to obtain 5 desired modes B. xx B xy B xz B yy B yz ; Step 5: Transpose the 5 desired modes obtained in Step 4, and project them onto the geomagnetic direction according to the magnetic angle relationship to obtain 6 projection elements S. Gxx S Gxy S Gxz S Gyy S Gyz S Gzz The calculation formula is as follows: In the formula, o, p, and q are the unit vectors of the geomagnetic field vector projected onto the x, y, and z axes, respectively, and the calculation formula is: o=cos(I)cos(D) p = cos(I)sin(D) q = sin(I) Where I and D are the geomagnetic field dip angle and deflection angle of the detection point, respectively; Step 6: Improve the total magnetic gradient orthogonal basis function decomposition method using VME. The method is as follows: Use the VME parameters from Step 4 to improve the seven orthogonal basis functions h in the total magnetic gradient orthogonal basis function decomposition method. j For j = 1 to 7, VME is performed to obtain 7 desired modes. Then, the 7 desired modes are subjected to Schmitt orthogonalization and normalization to obtain 7 improved orthogonal basis functions f. j j = 1 to 7; Step 7: Utilize the 7 improved orthogonal basis functions f obtained in Step 6 j For the 6 projection elements S obtained in step 5 respectively Gxx S Gxy S Gxz S Gyy S Gyz S Gzz Orthogonal basis decomposition was performed, yielding 6 decomposition energy coefficients k. i Let i = x, xy, xz, yy, yz, zz, where the formula for orthogonal basis decomposition is: In the formula Where n is the number of sampling points, n = 1, 2, ..., N, v is the velocity of the magnetic target, and f is the velocity of the magnetic target. s Where CPA is the sampling frequency, and CPA is the shortest distance from the sensor to the magnetic target's trajectory. Step 8: Calculate the 6 energy coefficients k obtained in Step 7. i The sum of squares of the variables is multiplied by the square of the second-order tensor invariant I2 obtained in step 3 to obtain a magnetic anomaly assessment index E, which is calculated using the following formula: Step 9: Based on the constant false alarm rate (CFAR) detection principle, set a dynamic threshold. When the magnetic anomaly assessment index E is greater than the threshold, determine that there is a magnetic anomaly in the signal to be tested; otherwise, determine that there is no magnetic anomaly in the signal to be tested.

2. The magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition as described in claim 1, characterized in that, The steps in steps 4 and 5 described above for obtaining the desired mode using the VME variational mode extraction method are as follows: Step 4-1: Let f be the signal to be extracted. o (t) is derived from the desired mode f d (t) and residual signal f r (t) composition, that is: f o (t)=f d (t)+f r (t) Step 4-2: Establish the combination of the quadratic penalty term and the Lagrange multipliers, and calculate the formula as follows: In the formula, λ is the Lagrange multiplier, ω is the frequency, α represents the balance parameter of the two penalty functions, and ω d Indicates the center frequency of the desired mode. f d The Fourier transform of (t), and other symbols are derived accordingly, where Here is the frequency response function of the filter: Step 4-3: Set the initial desired mode Initial expected center frequency The penalty parameter α, the convergence accuracy ε, the maximum number of iterations N, the update parameter τ of λ, and the number of iterations n is initialized to 1; Step 4-4: Update the desired mode using the following formula: In the formula, This represents the updated expected mode. The expected mode before the update; Step 4-5: Update the desired mode based on step 4-4 For center frequency The update is performed using the following formula: Step 4-6: Use the dual ascent method to process the Lagrange multipliers in step 4-2. Perform an update and increment the iteration count n by 1. The update formula is: Where τ is the update parameter set in step 4-3; Step 4-7: Determine if the desired mode meets the accuracy requirements. If it does, or if the specified maximum number of iterations N is reached, proceed to step 4-8; otherwise, return to step 4-4 and repeat the iterations from step 4-4 to step 4-7. The criteria for determining whether the desired mode meets the accuracy requirements are as follows: In the formula, ε is the convergence accuracy set in step 4-3; Step 4-8: Using the desired mode obtained in step 4-4 The desired mode f obtained at the end of VME d .

3. The magnetic anomaly detection method based on tensor invariants and improved orthogonal basis function decomposition as described in claim 1, characterized in that, The step described in step 6, which involves improving the orthogonal basis function of the total magnetic gradient using VME, is as follows: Step 6-1: Determine the seven basis functions h in the total magnetic gradient decomposition method. j For j = 1 to 7, perform VME to obtain 7 desired modes h' corresponding to 7 basis functions. j , j = 1 to 7, where the parameters used when performing VME are the same as those used in step 4; Step 6-2: For the 7 desired modes h obtained in Step 6-1 ' j Performing Schmidt orthogonalization, we obtain the orthogonalized basis functions f. j ', j = 1~7, the formula for Schmidt orthogonalization is: Step 6-3: Standardize the basis functions after orthogonalization in Step 6-2 using the following formula: This leads to the improved orthogonal basis function f of the total magnetic gradient. j .

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