Method and system for magnetic source position estimation based on spatially normalized magnetic source strength

Abstract

The application is suitable for the field of geophysical magnetic exploration technology, and provides a magnetic source position estimation method and system based on space normalized magnetic source strength, which comprises the following steps: calculating the normalized magnetic source strength of each observation point according to a magnetic gradient tensor matrix, and determining the maximum value point of the normalized magnetic source strength on an observation plane and the plane coordinates thereof; selecting another observation point on the observation plane which is different from the maximum value point; and calculating the buried depth of the abnormal body and the structure index at the maximum value point according to the plane coordinates of the maximum value point and the other observation point, the normalized magnetic source strength and the vertical derivative thereof. The application only needs to use the observation point data at two different positions on the observation plane, and calculates the buried depth of the abnormal body and the structure index without the extension process; the method is simple to calculate, does not depend on strong prior information, and can quickly and stably realize accurate estimation of the magnetic source position and depth.

Description

Technical Field

[0001] This invention belongs to the field of geophysical magnetic exploration technology, and particularly relates to a method and system for estimating the location of magnetic sources based on spatially normalized magnetic source intensity. Background Technology

[0002] Magnetic source location inversion is an efficient method for interpreting magnetic anomalies. It typically does not rely on complex geological constraints or solving large systems of equations, and can quickly estimate the depth and geometric parameters of the magnetic source, thus proving its widespread and effective application in practice. However, in magnetic anomaly inversion, the total magnetization direction of a geological body is the vector sum of the directions of induced magnetization and remanent magnetization. The magnetic anomaly morphology of the same geological body at different latitudes will have significant differences. Under the influence of factors such as oblique magnetization, traditional magnetic anomaly-based inversion methods are prone to horizontal shifts in the magnetic source location and depth misestimation, which can lead to distorted interpretation conclusions in severe cases.

[0003] Against this backdrop, various methods for inverting magnetic source position parameters have been developed, including the Euler deconvolution method, the analytic signal method, and the local wavenumber method. In the past thirty years, gradient tensor data, due to its better spatial resolution and richer magnetic source information, has been widely used in the processing and interpretation of magnetic anomalies. The normalized magnetic source intensity, proposed based on the eigenvalues ​​of the magnetic gradient tensor, is completely independent of the magnetization direction in three dimensions. Even for complex magnetic sources, the normalized magnetic source intensity retains a weak sensitivity to the magnetization direction, exhibiting better properties than other transformation quantities. Therefore, it has become a common tool for interpreting magnetic anomalies in three dimensions.

[0004] Magnetic source location inversion based on normalized magnetic source intensity can accurately reconstruct the horizontal distribution and depth information of magnetic anomalies under oblique magnetization, and further obtain the geometric type of the anomaly. Magnetic source location inversion methods typically utilize the relationship between the transformation function and the anomaly's position parameters, combined with techniques such as the derivatives of the transformation function and data extension, to achieve the inversion of the anomaly without requiring prior information to construct an exponent.

[0005] However, existing methods for inverting the magnetic source location using normalized magnetic source intensity utilize the vertical gradient of the normalized magnetic source intensity and combine it with upward data extension to construct a ratio relationship with the magnetic source parameters. Although this method avoids solving complex equations, it requires simultaneous calculation of the higher-order vertical derivative and upward extension of the magnetic anomaly. The two independent data transformations will successively introduce noise amplification and signal loss. The cumulative effect reduces the final inversion accuracy, making the accuracy of the inversion results limited or more sensitive to noise. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for estimating the position of a magnetic source based on spatially normalized magnetic source intensity, in order to solve the problems mentioned in the background art.

[0007] This invention is implemented as follows: a magnetic source location estimation method based on spatially normalized magnetic source intensity, comprising the following steps:

[0008] Obtain magnetic anomaly data from each observation point in the target area and calculate the magnetic gradient tensor matrix.

[0009] The normalized magnetic source intensity at each observation point is calculated based on the magnetic gradient tensor matrix, and the maximum point of the normalized magnetic source intensity on the observation plane and its plane coordinates are determined.

[0010] Select another observation point on the observation plane that is different from the maximum point;

[0011] Based on the planar coordinates of the maximum point and another observation point, the normalized magnetic source intensity and its vertical derivative, the burial depth and structural index of the anomaly at the maximum point are calculated.

[0012] The location of the magnetic source in the target area is determined based on the planar coordinates of the maximum point, the burial depth of the anomaly, and the structural index.

[0013] Furthermore, the formula for calculating the normalized magnetic source strength is as follows:

[0014] ;

[0015] In the formula, μ is the normalized magnetic source intensity; , , Let be the three eigenvalues ​​of the magnetic gradient tensor matrix, and we have: ; q is the distance from the observation point to the magnetic source point; n is the geometric factor; q is the construction exponent at the maximum point; C m It is a constant.

[0016] Furthermore, the steps for determining the maximum point of the normalized magnetic source intensity on the observation plane and its planar coordinates specifically include:

[0017] Let the horizontal position of the magnetic source point be taken as the maximum point, and its plane coordinates be (x0, y0); let the normalized magnetic source intensity reach its maximum value above the magnetic source point, then we have: , Then when the observation plane is At that time, the normalized magnetic source intensity at the maximum point is:

[0018] ;

[0019] In the formula, z0 is the depth of the anomalous body at the maximum point, i.e., the depth of the magnetic source point.

[0020] Furthermore, the step of calculating the burial depth and structural index of the anomaly at the maximum point based on the planar coordinates of the maximum point and another observation point, the normalized magnetic source intensity, and its vertical derivative specifically includes:

[0021] Calculate the ratio C of the normalized magnetic source intensity and its vertical derivative at the maximum point. o ;

[0022] Calculate the ratio C of the normalized magnetic source intensity and its vertical derivative at another observation point. p ;

[0023] Based on the planar coordinates of the maximum point and another observation point, determine the offset of the other observation point relative to the maximum point in the x and y directions on the observation plane. , ;

[0024] According to the ratio C o C p Establish the relationship between the burial depth z0 and the offset of the anomaly body. , Relationship;

[0025] Based on the aforementioned relationship, the burial depth and structural index of the anomaly at the maximum point are calculated.

[0026] Furthermore, the ratio C o C p The calculation formula is as follows:

[0027] ;

[0028] ;

[0029] In the formula, n is the construction exponent at the maximum point.

[0030] Furthermore, the burial depth z0 of the anomaly is related to the offset. , The relation is:

[0031] ;

[0032] In the formula, s is the ratio C p Ratio C o The ratio between them.

[0033] Furthermore, the formula for calculating the construction index at the maximum point is as follows:

[0034] .

[0035] Another object of the present invention is to provide a magnetic source position estimation system based on spatially normalized magnetic source intensity, for implementing the above-mentioned magnetic source position estimation method based on spatially normalized magnetic source intensity, comprising:

[0036] The data acquisition unit is used to acquire magnetic anomaly data from each observation point in the target area and calculate the magnetic gradient tensor matrix.

[0037] The maximum point determination unit is used to calculate the normalized magnetic source intensity of each observation point based on the magnetic gradient tensor matrix, and to determine the maximum point of the normalized magnetic source intensity on the observation plane and its plane coordinates.

[0038] The observation point selection unit is used to select another observation point on the observation plane that is different from the maximum point;

[0039] The magnetic source parameter calculation unit is used to calculate the burial depth and structural index of the anomaly at the maximum point based on the planar coordinates of the maximum point and another observation point, the normalized magnetic source intensity and its vertical derivative.

[0040] The magnetic source location determination unit is used to determine the magnetic source location of the target area based on the planar coordinates of the maximum point and the burial depth and structural index of the anomaly.

[0041] The magnetic source location estimation method based on spatially normalized magnetic source intensity provided by this invention only requires data from two observation points at different locations on the observation plane to calculate the burial depth and structural index of the anomaly without the need for an extension process. This method is simple to calculate, does not rely on strong prior information, and can quickly and stably achieve accurate estimation of the magnetic source location and depth. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the magnetic source location estimation method based on spatially normalized magnetic source intensity provided in an embodiment of the present invention.

[0043] Figure 2 This is a schematic diagram of the plane coordinates of the maximum point and another observation point.

[0044] Figure 3The following are diagrams illustrating the effect of estimating the magnetic source location using the method provided in this embodiment of the invention: (a) a magnetic anomaly map of the combined model containing noise; (b) a normalized magnetic source intensity map after denoising by extending the point spacing by 2 times; (c) a depth result map (s=1.2) of the horizontal magnetic source location estimation method based on the ratio of the normalized magnetic source intensity to its vertical derivative; and (d) a structural index result map (s=1.2) of the horizontal magnetic source location estimation method based on the ratio of the normalized magnetic source intensity to its vertical derivative. In the diagrams, ①, ②, ③, and ④ represent the four geological models preset in the experiment. The models are: ① a sphere model with a radius of 500m, a burial depth of 1000m, and a structural index of 3; ② a prism model with a burial depth of 500m and a structural index of 0; ③ a plate-like model with a burial depth of 500m and a structural index of 1; ④ a dike model with a burial depth of 800m and a structural index of 1. X and Y are the Cartesian coordinates in the model experiment. The X-axis generally represents due east, and the Y-axis generally represents due north. The different colored points in the figure represent the geological bodies whose depth and structural index meet the range shown in the legend. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0046] In one embodiment of the present invention, a magnetic source location estimation method based on spatially normalized magnetic source intensity is provided. This method can be applied to the inversion of magnetic anomaly source locations and can solve problems such as the offset of inversion results under oblique magnetization and the low accuracy of methods based on normalized magnetic source intensity. Specifically, as shown... Figure 1 As shown, the method includes the following steps:

[0047] S1. Obtain magnetic anomaly data from each observation point in the target area and calculate the magnetic gradient tensor matrix.

[0048] S2. Calculate the normalized magnetic source intensity at each observation point based on the magnetic gradient tensor matrix, and determine the maximum point of the normalized magnetic source intensity on the observation plane and its plane coordinates.

[0049] S3. Select another observation point on the observation plane that is different from the maximum point;

[0050] S4. Based on the plane coordinates of the maximum point and another observation point, the normalized magnetic source intensity and its vertical derivative, the burial depth and structural index of the anomaly at the maximum point are calculated.

[0051] S5. Determine the location of the magnetic source in the target area based on the planar coordinates of the maximum point, the burial depth of the anomaly, and the structural index.

[0052] In practical applications, the normalized magnetic source strength (NSS) is a rotational invariant derived from the magnetic gradient tensor matrix of a magnetic dipole. The magnetic gradient tensor matrix contains the first derivative of the magnetic field. For a general magnetic body, its magnetic field can be expressed as:

[0053] ;

[0054] In the formula, It is the magnetic field vector; It is a constant in the International System of Units (SI); It is a magnetic scalar potential; and These are the position vectors of the observation point and the magnetic source point, respectively; To obtain the gradient operator for the magnetic source point position vector; Let V be the magnetization vector of the magnetic body; V be the total volume of the magnetic body; then the magnetic gradient tensor matrix is... It can be represented as:

[0055] ;

[0056] The above magnetic gradient tensor matrix B is a real symmetric matrix. xx B xy B xz They are magnetic field vectors The derivatives of the x-component in the x, y, and z directions; B yx B yy B yz They are magnetic field vectors The derivatives of the y-component in the x, y, and z directions; B zx B zy B zz They are magnetic field vectors The derivatives of the z-component in the x, y, and z directions; through We can obtain its three corresponding eigenvalues. , , The details are as follows:

[0057] First, based on the data in the magnetic gradient tensor matrix, the three tensor invariants I0, I1, and I2 of this matrix can be calculated:

[0058] ;

[0059] ;

[0060] ;

[0061] The characteristic equation for the three eigenvalues ​​can be obtained through the three tensor invariants:

[0062] ;

[0063] Solving this equation yields the three eigenvalues ​​of the magnetic gradient tensor matrix:

[0064] ;

[0065] ;

[0066] ;

[0067] In the formula: , .

[0068] Based on the above magnetic gradient tensor matrix For any magnetic body, the formula for calculating its normalized magnetic source strength is:

[0069] ;

[0070] In the formula, μ is the normalized magnetic source intensity; , , Let be the three eigenvalues ​​of the magnetic gradient tensor matrix, and we have: ; is the distance from the observation point to the magnetic source point; q is the geometric factor; n is the structural index at the maximum point, used to reflect the geological body type; C m It is a constant.

[0071] Let the horizontal position of the magnetic source point be taken as the maximum point, and its plane coordinates be (x0, y0); let the normalized magnetic source intensity reach its maximum value above the magnetic source point, then we have: , Then when the observation plane is At that time, the normalized magnetic source intensity at the maximum point is:

[0072] ;

[0073] Taking the vertical derivative of the normalized magnetic source intensity at the maximum point, its expression with respect to the magnetic source parameters is as follows:

[0074] ;

[0075] In the formula, z0 is the depth of the anomalous body at the maximum point, i.e., the depth of the magnetic source point; n is the structural index at the maximum point.

[0076] The existing method combines the normalized magnetic source intensity and its vertical derivative with upward continuation to estimate the burial depth and structural index of the anomalous body (magnetic body). The calculation formula is as follows:

[0077] ;

[0078] ;

[0079] In the formula, C o C is the ratio of the normalized magnetic source intensity to its vertical derivative. h The ratio of the normalized magnetic source intensity to its vertical derivative after extending upwards to a certain height is given; h is the extension height. Existing methods suffer from low estimation accuracy; therefore, this invention improves upon this.

[0080] Specifically, in a preferred embodiment of the present invention, the step of calculating the burial depth and structural index of the anomalous body at the maximum point based on the planar coordinates of the maximum point and another observation point, the normalized magnetic source intensity, and its vertical derivative specifically includes:

[0081] Calculate the ratio C of the normalized magnetic source intensity and its vertical derivative at the maximum point. o ;

[0082] Calculate the ratio C of the normalized magnetic source intensity and its vertical derivative at another observation point. p ;

[0083] Based on the planar coordinates of the maximum point and another observation point, determine the offset of the other observation point relative to the maximum point in the x and y directions on the observation plane. , ;

[0084] According to the ratio C o C p Establish the relationship between the burial depth z0 and the offset of the anomaly body. , Relationship;

[0085] Based on the aforementioned relationship, the burial depth and structural index of the anomaly at the maximum point are calculated.

[0086] In practical applications, such as Figure 2 As shown, another observation point is selected outside the normalized magnetic source intensity maximum (i.e., the maximum point) on the observation plane, such that: , Then the ratio C o C p The calculation formula is as follows:

[0087] ;

[0088] ;

[0089] The ratio C o Cp Combining the calculation formulas, we have:

[0090] ;

[0091] The formula for calculating z0 is:

[0092] ;

[0093] In the formula, s is the ratio C p Ratio C o The ratio between them, that is:

[0094] ;

[0095] Where s is a real number greater than 1; substituting it into the above formula for calculating z0, we can obtain the relationship between the burial depth z0 of the anomaly and the offset. , The relation is:

[0096] ;

[0097] Furthermore, the formula for calculating the construction exponent at the maximum point is as follows:

[0098] .

[0099] By the burial depth z0 of the anomaly and the offset , The value of z0 can be obtained from the relation, which is the depth corresponding to the maximum point (i.e., the magnetic source point). Combined with the planar coordinates of the maximum point, the planar position and depth of the magnetic source point can be determined, thus completing the estimation of the magnetic source position. In addition, n is the construction index at the maximum point, which can reflect the geometric characteristics of the anomalous body at the magnetic source position.

[0100] Example 1: Using the method provided in the above embodiments of the present invention, four different underground geological body models were calculated: a plate model, a prism model, a dike model, and a sphere model. The inversion results are as follows: Figure 3As shown in the figure, the method provided in this embodiment of the invention accurately obtains the boundary depth and structural index of the model body. For the sphere model, the depth point is in the red interval, close to a burial depth of 1000m, and the structural index is also in the red interval, greater than 1.5, consistent with the theoretical range. For the prism model, the depth interval is in the green and black intervals, close to a burial depth of 500m, and the structural index is concentrated in the black interval, close to 0, consistent with the theoretical range. For the plate-like model, the depth and structural index intervals are concentrated in the black and yellow intervals, respectively, close to a burial depth of 500m and a structural index of 1, both consistent with the theoretical range. For the dike model, the depth and structural index intervals are mostly concentrated in the yellow interval, close to a burial depth of 800m and a structural index of 1, consistent with the theoretical range. Due to the influence of noise, there is a certain error in the calculation, causing the calculation of some points to deviate from the theoretical value of the model. For points with sharp geometric inflections (such as the corners of the plate-like model), the calculation is relatively unstable, but all are within an acceptable error range and do not affect the practical applicability of the method.

[0101] In summary, the method provided by the embodiments of the present invention can more accurately calculate the burial depth and structural index of magnetic anomalies without being affected by oblique magnetization in practical applications. This method can accurately delineate the distribution target area of ​​magnetic bodies, thereby assisting in mineral resource exploration.

[0102] In another embodiment of the present invention, a magnetic source position estimation system based on spatially normalized magnetic source intensity is also provided, for implementing the above-described magnetic source position estimation method based on spatially normalized magnetic source intensity, specifically including:

[0103] The data acquisition unit is used to acquire magnetic anomaly data from each observation point in the target area and calculate the magnetic gradient tensor matrix.

[0104] The maximum point determination unit is used to calculate the normalized magnetic source intensity of each observation point based on the magnetic gradient tensor matrix, and to determine the maximum point of the normalized magnetic source intensity on the observation plane and its plane coordinates.

[0105] The observation point selection unit is used to select another observation point on the observation plane that is different from the maximum point;

[0106] The magnetic source parameter calculation unit is used to calculate the burial depth and structural index of the anomaly at the maximum point based on the planar coordinates of the maximum point and another observation point, the normalized magnetic source intensity and its vertical derivative.

[0107] The magnetic source location determination unit is used to determine the magnetic source location of the target area based on the planar coordinates of the maximum point and the burial depth and structural index of the anomaly.

[0108] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods.

[0109] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A magnetic source position estimation method based on spatially normalized magnetic source intensity, characterized in that, Includes the following steps: Obtain magnetic anomaly data from each observation point in the target area and calculate the magnetic gradient tensor matrix. The normalized magnetic source intensity at each observation point is calculated based on the magnetic gradient tensor matrix, and the maximum point of the normalized magnetic source intensity on the observation plane and its plane coordinates are determined. Select another observation point on the observation plane that is different from the maximum point; Based on the planar coordinates of the maximum point and another observation point, the normalized magnetic source intensity and its vertical derivative, the burial depth and structural index of the anomaly at the maximum point are calculated. The location of the magnetic source in the target area is determined based on the planar coordinates of the maximum point, the burial depth of the anomaly, and the structural index.

2. The magnetic source position estimation method based on spatially normalized magnetic source intensity according to claim 1, characterized in that, The formula for calculating the normalized magnetic source strength is: ； In the formula, μ is the normalized magnetic source intensity; , , Let be the three eigenvalues ​​of the magnetic gradient tensor matrix, and we have: ; q is the distance from the observation point to the magnetic source point; n is the geometric factor; q is the construction exponent at the maximum point; C m It is a constant.

3. The magnetic source position estimation method based on spatially normalized magnetic source intensity according to claim 2, characterized in that, The steps for determining the maximum point of the normalized magnetic source intensity on the observation plane and its planar coordinates specifically include: Let the horizontal position of the magnetic source point be taken as the maximum point, and its plane coordinates be (x0, y0); let the normalized magnetic source intensity reach its maximum value above the magnetic source point, then we have: , Then when the observation plane is At that time, the normalized magnetic source intensity at the maximum point is: ； In the formula, z0 is the depth of the anomalous body at the maximum point, i.e., the depth of the magnetic source point.

4. The magnetic source position estimation method based on spatially normalized magnetic source intensity according to claim 3, characterized in that, The steps for calculating the burial depth and structural index of the anomaly at the maximum point based on the planar coordinates of the maximum point and another observation point, the normalized magnetic source intensity, and its vertical derivative specifically include: Calculate the ratio C of the normalized magnetic source intensity and its vertical derivative at the maximum point. o ; Calculate the ratio C of the normalized magnetic source intensity and its vertical derivative at another observation point. p ; Based on the planar coordinates of the maximum point and another observation point, determine the offset of the other observation point relative to the maximum point in the x and y directions on the observation plane. , ; According to the ratio C o C p Establish the relationship between the burial depth z0 and the offset of the anomaly body. , Relationship; Based on the aforementioned relationship, the burial depth and structural index of the anomaly at the maximum point are calculated.

5. The magnetic source position estimation method based on spatially normalized magnetic source intensity according to claim 4, characterized in that, Ratio C o C p The calculation formula is as follows: ； ； In the formula, n is the construction exponent at the maximum point.

6. The magnetic source position estimation method based on spatially normalized magnetic source intensity according to claim 5, characterized in that, Anomaly burial depth z0 and offset , The relation is: ； In the formula, s is the ratio C p Ratio C o The ratio between them.

7. The magnetic source position estimation method based on spatially normalized magnetic source intensity according to claim 5, characterized in that, The formula for calculating the construction index at the maximum point is as follows: 。 8. A magnetic source position estimation system based on spatially normalized magnetic source intensity, used to implement the magnetic source position estimation method based on spatially normalized magnetic source intensity as described in any one of claims 1-7, characterized in that, include: The data acquisition unit is used to acquire magnetic anomaly data from each observation point in the target area and calculate the magnetic gradient tensor matrix. The maximum point determination unit is used to calculate the normalized magnetic source intensity of each observation point based on the magnetic gradient tensor matrix, and to determine the maximum point of the normalized magnetic source intensity on the observation plane and its plane coordinates. The observation point selection unit is used to select another observation point on the observation plane that is different from the maximum point; The magnetic source parameter calculation unit is used to calculate the burial depth and structural index of the anomaly at the maximum point based on the planar coordinates of the maximum point and another observation point, the normalized magnetic source intensity and its vertical derivative. The magnetic source location determination unit is used to determine the magnetic source location of the target area based on the planar coordinates of the maximum point and the burial depth and structural index of the anomaly.

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