CN106125149B - The optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass determines method - Google Patents

Abstract

The invention relates to a method for determining the optimal burial depth of shallow high-resolution point quality in a point quality model, comprising: constructing a low-resolution layered residual point quality model by using the existing gravity model and gravity data of different resolutions; Gradient and precise position are measured, and depth inversion is carried out according to the measured data to determine the burial depth range of the point quality. Multiple burial depth values are selected with a certain step size, and the point quality model is calculated separately. The data of the non-grid midpoint is Restoration, compare with the actual measured value, calculate the restoration error, make a horizontal comparison of the restoration errors corresponding to the depths of all nodes, and determine the best burial depth of shallow high-resolution point quality corresponding to the minimum restoration error. The invention can more accurately obtain the burial depth of the shallow high-resolution point mass, and improve the accuracy of the layered point mass combination model approaching the gravitational force of near-ground space disturbance.

Description

Determination method of optimal burial depth of shallow high-resolution point quality in point quality model

technical field

The invention relates to the technical field of approaching the burial depth of a point mass in the earth's external disturbance gravitational force, in particular to a method for determining the optimal burial depth of a shallow high-resolution point mass in a point mass model.

Background technique

The point mass model method is a method developed to calculate the disturbance gravity of spacecraft. The advantage of this method is that the structure of the kernel function is simple, and it can avoid the singularity that occurs in the direct integral calculation of low-altitude orbit points. In addition, the point mass model can The superposition makes it more flexible to calculate the frequency band of the disturbance gravity field. In the research and application of the point mass model method, a key issue that needs to be dealt with is to select the burial depth of point masses with different resolutions. In the past, domestic studies on the selection of burial depth of point quality were mostly directly based on the existing theoretical conclusions, and the following empirical expression was also used when selecting the burial depth D of shallow high-resolution point quality:

D＝a _e ·θ

Where a and _e are the average radius of the earth's equator, and θ is the center angle of the earth corresponding to the grid (reflected as the grid resolution, in radians). From this, the burial depth corresponding to the commonly used grid is obtained, as shown in Figure 2 and Figure 3, the deep point quality refers to the point quality with a resolution of 1°×1°, 20′×20′, 5′×5′, The shallow point quality refers to the point quality with a resolution of 1′×1′. Since the shallow point mass is close to the surface, improper selection of its burial depth will lead to large errors in restoring the disturbed gravity in the near-surface space. "And Analysis" mainly studies the construction method of deeper point quality, solves the construction of medium and low resolution point quality models, but does not involve the construction and depth determination of shallow high resolution point quality models, and lacks the effect of shallow point quality However, it is impossible to effectively select the shallow high-resolution point quality burial depth. Therefore, there is an urgent need for a shallow high-resolution point-mass model construction and depth determination technology to improve the overall recovery effect of the disturbed gravitational field.

Contents of the invention

Aiming at the deficiencies of the prior art, the present invention provides a method for determining the optimal burial depth of the shallow high-resolution point quality in the point quality model, which can restore the gravitational disturbance on the ground and its surrounding space with higher precision compared with the prior art field.

According to the design scheme provided by the present invention, a method for determining the optimal burial depth of a shallow high-resolution point quality in a point quality model comprises the following steps:

Step 1. Construct a low-resolution layered residual point quality model based on the gravity anomaly data within the selected area;

Step 2. Perform vertical gravity gradient measurement and precise position measurement in the point mass model grid constructed in step 1, and calculate the gravity anomaly and disturbed gravity vertical gradient data of the midpoint of the shallow high-resolution point mass model grid;

Step 3. Depth inversion is performed on the shallow high-resolution gravity anomaly data and disturbed gravity vertical gradient data within the selected area to determine the point mass burial depth range;

Step 4. According to the point mass model constructed in step 1, according to the high-resolution gravity anomaly data and the perturbed gravity vertical gradient data of the midpoint of the shallow high-resolution point mass model grid obtained in step 2, the point mass Select multiple burial depth values within the burial depth range, calculate the point quality model one by one according to the burial depth values, and use the calculation results to restore the gravity anomaly data and disturbed gravity vertical gradient data of the non-grid midpoint within the selected area, and restore statistics Error, until the corresponding depths of all nodes within the point mass buried depth range, the point mass model calculations are completed one by one, and the point mass model recovery errors corresponding to the depths of all nodes are obtained;

Step 5. Comparing the restoration error of the obtained point quality model horizontally, and determining the depth corresponding to the minimum restoration error, which is the optimal burial depth of shallow high-resolution point quality.

As mentioned above, Step 1 specifically includes the following steps:

Step 1.1. Calculate the average gravity anomaly data of each 1°×1° grid by using the low-order potential coefficient model Get residual observations: The 1°×1° point mass M ₁ is obtained as the first group point mass; step 1.2, using the potential coefficient model to calculate the average gravity anomaly of each 20′×20′ grid Calculate the average anomaly with 1°×1° point mass M ₁ Get residual observations:

, the 20′×20′ point mass M ₂ is obtained as the second group point mass;

Step 1.3. Calculate the average gravity anomaly for each 5′×5′ grid using the potential coefficient model Calculate the average anomaly with the first group and the second group of point masses respectively Get residual observations:

, the 5′×5′ point mass M ₃ is solved as the third group of point mass.

As mentioned above, in step 2, the gravity anomaly of each 1′×1′ grid midpoint is calculated using the potential coefficient model and the perturbed gravity vertical gradient

As mentioned above, step 4 specifically includes the following contents:

Step 4.1. Use the first group, the second group, and the third group of point masses to calculate the midpoint gravity anomaly of the shallow high-resolution point mass model grid and the perturbed gravity vertical gradient Get residual observations:

,

A vector is formed by combining two residual observations:

Step 4.2, according to the burial depth range determined in step 3, for the depth value of each node within the range, solve the system of equations according to the least square method to solve the point quality M4 corresponding to the burial depth of all nodes _;

Step _4.3 : Construct the point mass M4 corresponding to the burial depth of each node and the deep point mass to form a layered combination model, restore the gravity anomaly data and disturbed gravity vertical gradient data of non-grid midpoints within the selected area on the ground, and measure The actual observed value at the point is made a difference, and the recovery error is obtained and statistics are made.

As mentioned above, the formula for recovering the gravity anomaly data and disturbed gravity vertical gradient data of the non-grid midpoint within the selected area on the ground in step 4.3 is:

Among them, n _max and n _layer respectively represent the order of the low-order bit model and the number of layers of the residual point quality, R represents the radius of the sphere, represents the corresponding potential coefficient model, ρ represents the geocentric radius, Indicates the radius of the center of the sphere where the i-th ground gravity anomaly point is located, r _ij represents the distance between the i-th ground gravity anomaly point and the j-th point mass, K represents the mass number of the point, and M represents the mass of K points The vector of , a represents the radius of the earth's equator, and M _ij represents the quality of the jth point in the i-th layer.

Beneficial effects of the present invention:

The present invention uses the existing gravity model and gravity data of different resolutions in the research area to construct a low-resolution layered residual point quality model, and measures the vertical gravity gradient and precise position in the model grid, and performs depth inversion according to the measurement data. In order to determine the range of the point quality burial depth, select multiple burial depth values within the range with a certain step size, and perform point quality model calculations respectively, recover the data of non-grid midpoints, and compare them with the actual measured values. Statistical recovery error, horizontal comparison of the recovery errors corresponding to the depths of all nodes obtained, to determine the depth corresponding to the minimum recovery error, that is, the optimal burial depth of shallow high-resolution point quality, effectively reducing the traditional shallow depth based on empirical rules. The uncertainty of the burial depth of the high-resolution point mass in the layer can be obtained more accurately. The burial depth of the high-resolution point mass in the shallow layer can be more accurately obtained, and the accuracy of the layered point-mass combination model approaching the near-surface space disturbance gravity can be improved.

Description of drawings:

Figure 1 is a schematic diagram of the mass distribution of shallow high-resolution points;

Figure 2 is a schematic diagram of the depth structure of the low-resolution layered residual point quality model;

Figure 3 is a schematic diagram of the corresponding depth of the low-resolution layered residual point quality model grid;

Fig. 4 is a schematic flow sheet of the present invention;

Figure 5 is a comparison chart of the coordinates of the measuring points in the experimental area and their gravity anomalies and disturbed gravity vertical gradient observations;

Fig. 6 is a comparison diagram of gravity anomaly and disturbance gravity vertical gradient and burial depth;

Figure 7 is a schematic diagram of the error statistics results of all nodes compared horizontally;

Fig. 8 is a schematic diagram showing the comparison of the layered model results established by the present invention and transmission rules of thumb in the experimental area.

detailed description:

The present invention will be described in further detail below in conjunction with the accompanying drawings and technical solutions, and the implementation of the present invention will be described in detail through preferred embodiments, but the implementation of the present invention is not limited thereto.

Embodiment 1, referring to Figures 1 to 4, a method for determining the optimal burial depth of a shallow high-resolution point quality in a point quality model, comprising the following steps:

Step 1. Construct a low-resolution layered residual point quality model based on the gravity anomaly data within the selected area;

Step 2. Perform vertical gravity gradient measurement and precise position measurement in the point mass model grid constructed in step 1, and calculate the gravity anomaly and disturbed gravity vertical gradient data of the midpoint of the shallow high-resolution point mass model grid;

Step 3. Depth inversion is performed on the shallow high-resolution gravity anomaly data and disturbed gravity vertical gradient data within the selected area to determine the point mass burial depth range;

Step 4. According to the point mass model constructed in step 1, according to the high-resolution gravity anomaly data and the perturbed gravity vertical gradient data of the midpoint of the shallow high-resolution point mass model grid obtained in step 2, the point mass Select multiple burial depth values within the burial depth range, calculate the point quality model one by one according to the burial depth values, and use the calculation results to restore the gravity anomaly data and disturbed gravity vertical gradient data of the non-grid midpoint within the selected area, and restore statistics Error, until the corresponding depths of all nodes within the point mass buried depth range, the point mass model calculations are completed one by one, and the point mass model recovery errors corresponding to the depths of all nodes are obtained;

Step 5. Comparing the restoration error of the obtained point quality model horizontally, and determining the depth corresponding to the minimum restoration error, which is the optimal burial depth of shallow high-resolution point quality.

By constructing a low-resolution layered residual point mass model, and measuring the vertical gravity gradient and precise position in the model grid, and performing depth inversion according to the measurement data, the range of the point mass burial depth can be determined, with a certain step size in Select multiple burial depth values within the range, and calculate the point quality model separately, restore the data of the non-grid midpoint, compare it with the actual measurement value, calculate the restoration error, and restore the error of the corresponding depth of all nodes obtained Carry out horizontal comparison to determine the depth corresponding to the minimum recovery error, which is the optimal burial depth of shallow high-resolution point quality, which can effectively reduce the uncertainty of shallow high-resolution point quality burial depth obtained according to the traditional rule of thumb. Get more accurate burial depth at shallow high-resolution point-quality.

Embodiment 2, referring to Figures 1 to 8, a method for determining the optimal burial depth of a shallow high-resolution point quality in a point quality model, comprising the following steps:

Step 1. Construct a low-resolution layered residual point quality model based on the gravity anomaly data within the selected area, which specifically includes the following contents:

Step 1.1. Calculate the average gravity anomaly data of each 1°×1° grid by using the low-order potential coefficient model Get residual observations: The 1°×1° point mass M ₁ is obtained as the first group of point masses, in which the low-order potential coefficient model is selected as order 36, which is equivalent to the global average gravity anomaly of 5°×5°;

Step 1.2. Calculate the average gravity anomaly for each 20′×20′ grid using the potential coefficient model Calculate the average anomaly with 1°×1° point mass M ₁ Get residual observations:

, the 20′×20′ point mass M ₂ is obtained as the second group point mass;

Step 1.3. Calculate the average gravity anomaly for each 5′×5′ grid using the potential coefficient model Calculate the average anomaly with the first group and the second group of point masses respectively Get residual observations:

, the 5′×5′ point mass M ₃ is solved as the third group of point mass.

Step 2. Perform vertical gravity gradient measurement and precise position measurement in the point mass model grid constructed in step 1, and calculate the gravity anomaly and disturbed gravity vertical gradient data of points in the shallow high-resolution point mass model grid, specifically : Calculation of gravity anomalies at midpoints of each 1′×1′ grid using the potential coefficient model and the perturbed gravity vertical gradient Measure the gravity segment difference dg between two points in the vertical direction at the measuring point, and accurately measure the vertical height difference Δh between the two points, then use the formula Determine the gravity vertical gradient on the above observation point; according to the coordinates of the measurement point according to the formula Calculate the normal gravity vertical gradient, where B is the geodetic latitude of the measuring point; H is the geodetic height of the measuring point; further defined by gravity, according to the formula Calculate the disturbed gravity vertical gradient data on the measuring point.

Step 3. Depth inversion is performed on the shallow high-resolution gravity anomaly data and disturbed gravity vertical gradient data within the selected area to determine the point mass burial depth range. Specifically, it refers to: according to the potential field theory, a radius R, The gravity anomaly caused by any point in the outer space of a uniform sphere with a buried depth of D in the center and a residual density of κ is the same as that of a mass point where the remaining mass of the sphere M=4πR ³ κ/3 is all concentrated in the center of the sphere; if the sphere The projection point of the center on the ground is the coordinate origin, the z-axis is vertically downward, and the x-axis coincides with the selected measurement section, then the relationship between any point on the x-axis and the buried depth D is:

The relationship between the first derivative of the gravity anomaly (that is, the vertical gradient) at P(x,0) and the buried depth D is:

The burial depth D is inverted according to the gravity anomaly and the disturbed gravity vertical gradient, and the empirical rule of point mass burial depth is considered comprehensively to determine a burial depth interval as the point mass burial depth range used in the next step.

Step 4. According to the point mass model constructed in step 1, according to the high-resolution gravity anomaly data and the perturbed gravity vertical gradient data of the midpoint of the shallow high-resolution point mass model grid obtained in step 2, the point mass Select multiple burial depth values within the burial depth range, calculate the point quality model one by one according to the burial depth values, and use the calculation results to restore the gravity anomaly data and disturbed gravity vertical gradient data of the non-grid midpoint within the selected area, and restore statistics Error, until the corresponding depths of all nodes within the point mass buried depth range, the point mass model calculations are completed one by one, and the point mass model recovery errors corresponding to all nodes’ depths are obtained. The specific contents are as follows:

Step 4.1. Use the first group, the second group, and the third group of point masses to calculate the midpoint gravity anomaly of the shallow high-resolution point mass model grid and the perturbed gravity vertical gradient Get residual observations:

, a vector consisting of the union of two residual observations:

Step 4.2, according to the burial depth range determined in step 3, for the depth value of each node within the range, solve the system of equations according to the least square method to solve the point quality M4 corresponding to the burial depth of all nodes _;

Step _4.3 : Construct the point mass M4 corresponding to the burial depth of each node and the deep point mass to form a layered combination model, and restore the gravity anomaly data and Perturb the gravity vertical gradient data, make a difference with the actual observation value at the measuring point, obtain the restoration error and make statistics, among them, restore the gravity anomaly data at the middle point of the non-shallow high-resolution point quality model grid within the selected area of the ground And the formula for disturbing gravity vertical gradient data is:

Among them, n _max and n _layer respectively represent the order of the low-order bit model and the number of layers of the residual point quality, R represents the radius of the sphere, represents the corresponding potential coefficient model, ρ represents the geocentric radius, Indicates the radius of the center of the sphere where the i-th ground gravity anomaly point is located, r _ij represents the distance between the i-th ground gravity anomaly point and the j-th point mass, K represents the mass number of the point, and M represents the mass of K points The vector of , a represents the radius of the earth's equator, and M _ij represents the quality of the jth point in the i-th layer.

Step 5. Comparing the restoration error of the obtained point quality model horizontally, and determining the depth corresponding to the minimum restoration error, which is the optimal burial depth of shallow high-resolution point quality.

Among them, the calculation formulas used for gravity anomaly data and disturbed gravity vertical gradient data are as follows:

The formula for calculating the average gravity anomaly using the potential coefficient model:

in, is a set of fully normalized bit model coefficients;

The formula for calculating the average anomaly using point mass:

The formula for calculating the vertical gradient of the disturbance gravity using the potential coefficient model:

The formula for calculating the vertical gradient of perturbed gravity using point mass:

After selecting a low-order reference field to form a layered residual point mass model, the calculation formula for the vertical gradient of the perturbed gravity is:

Among them, n _max and n _layer represent the order of the low-order bit model and the number of layers of residual point quality, respectively.

In order to verify the effect of the present invention, the present invention will be further described below in conjunction with specific examples:

According to the above steps, make full use of the existing gravity field model with a high degree of agreement with the gravity data in China and the gravity data of different resolutions in the study area to establish a layered point quality model in the study area; use the high-precision CG-5 The relative gravimeter and GRS RTK equipment carry out the vertical gravity gradient measurement and precise position measurement of the observation point, and obtain the vertical gravity gradient information of the midpoint of the 1′×1′ grid and a certain amount of internal points within the selected range; according to the principle, a point The vertical gravity gradient is equal to the sum of the normal gravity vertical gradient and the disturbed gravity vertical gradient of the point. By calculating the normal gravity vertical gradient of the measuring point, the disturbed gravity vertical gradient on the measuring point can be determined; according to the height of the selected range in the research area The resolution gravity anomaly and the disturbed gravity vertical gradient information obtained above are used to invert the underground density anomaly depth at the same time, and the rule of thumb for estimating the point mass burial depth is to determine the interval of the point mass burial depth; Step size, set multiple depth values, solve the 1′×1′ or higher resolution point quality model according to each depth value, and then use the solved point quality model to restore the non-grid within the selected range of the center of the research area The gravity anomaly at the midpoint and the vertical gradient of the disturbance gravity are used to statistically analyze the restoration error; the statistical results of the restoration error of the layered point quality model at each depth are compared comprehensively, and the best buried depth is selected according to the smallest error.

The observation experiment area was selected near Songshan Mountain in Zhengzhou, the size of which is 8km×8km, the longitude of the upper left corner is 113°38′, and the latitude is 34°46′. In the experimental area, 16 points were evenly distributed and measured. The coordinates of these measuring points and their gravity anomalies and disturbed gravity vertical gradient observation values are shown in Figure 5; according to the experimental area, four resolutions were established according to Figure 1 (resolution from low to the point mass models whose heights are 1°×1°, 20′×20′, 5′×5′, 1′×1′), sort out the gravity data in these areas with different ranges and resolutions, and establish resolution Low-order point-mass combination model with rate up to 5′×5′. Combining the gravity anomaly data in the 1′×1′ area and the disturbed gravity vertical gradient of the above-mentioned measuring points, respectively using the relationship between the gravity anomaly and the disturbed gravity vertical gradient and the buried depth to determine the burial depths D ₁ and D ₂ of the corresponding particles, and Calculate the average depth D=(D ₁ +D ₂ )/2, as shown in Figure 6, the buried depth interval is established as (1300m, 2400m) in combination with the empirical rule of point mass buried depth; multiple depths are set within the buried depth interval At each node, the low-order point mass model is combined with the ground 1′×1′ residual gravity anomaly and disturbed gravity vertical gradient data at each node depth to solve the high-resolution point mass model on the ground, and use the solved complete point mass model to restore the above The vertical gradient of the disturbed gravity at 16 points is compared with the measured value to obtain the error statistical result (with ∑(v _calculation -v _quantity ) ² as the index, where v _calculation is the calculated recovery value, and the v _quantity is the measured value); horizontal comparison From the statistical results of errors on all nodes, select the result with the smallest error and determine its corresponding burial depth. According to Figure 7, the statistical results in the second column in the figure can determine the best burial depth of 1′×1′ point quality About 1900 meters.

In various literatures on the gravitational calculation of the external disturbance of the earth, it is a very meaningful method to use the layered point mass model for approximation. However, when determining the burial depth of the shallow point mass, almost all methods use this Invent the aforementioned rule of thumb, that is to say, the rule of thumb is the current traditional practice for determining the mass depth of shallow points. In order to illustrate the advantages of the present invention with respect to traditional rules of thumb, the following process is used here for comparison:

Select benchmark reference data for comparison reference: airborne gravity measurement data of 10 points at a height of about 1500 meters above the experimental area (which has been processed into gravity anomalies); establish a four-layer point mass model of the experimental area, in which the shallow point mass The burial depth is determined according to empirical rules, and then the gravity anomaly of the datum reference point is recovered by using the established layered point mass combination model, and the difference is made with the measured value; a four-layer point mass model of the experimental area is established, and the point mass model of the shallow layer is The depth of burial is determined according to the method proposed by the present invention, and then the gravity anomaly of the benchmark reference point is restored by using the layered point mass combination model established, and the difference is made with the measured value; the above-mentioned poor results are analyzed, as shown in Figure 8 , the unit in the figure is 10 ^-5 ms ^-2 , according to the poor comparison results in the figure, the error of recovering the measured data using the layered point quality model established by the present invention is obviously smaller than that of the layered model established according to the rule of thumb result.

Thus, it is further verified that compared with the traditional method, the present invention has the following advantages: when determining the burial depth of the shallow point mass, a new type of observation data is used, that is, the observation data of the vertical gradient of the disturbance gravity, so its modeling The external known gravitational field information used in the process is more comprehensive; when the layered point mass model established by the invention is used to restore the earth's external gravitational field, the accuracy of the result is higher than that of the layered point mass model established by using traditional empirical rules.

The present invention is not limited to the specific embodiments described above, and those skilled in the art can also make various changes accordingly, but any changes that are equivalent or similar to the present invention should be covered within the scope of the claims of the present invention.

Claims (5)

1. A method for determining the optimal burial depth of shallow high-resolution point quality in a point quality model, characterized in that: comprising the steps: Step 1. Construct a low-resolution layered residual point quality model based on the gravity anomaly data within the selected area; Step 2. Perform vertical gravity gradient measurement and precise position measurement in the point mass model grid constructed in step 1, and calculate the gravity anomaly and disturbed gravity vertical gradient data of the midpoint of the shallow high-resolution point mass model grid; Step 3. Depth inversion is performed on the shallow high-resolution gravity anomaly data and disturbed gravity vertical gradient data within the selected area to determine the point mass burial depth range; Step 4. According to the point mass model constructed in step 1, according to the high-resolution gravity anomaly data and the perturbed gravity vertical gradient data of the midpoint of the shallow high-resolution point mass model grid obtained in step 2, the point mass Select multiple burial depth values within the burial depth range, calculate the point quality model one by one according to the burial depth values, and use the calculation results to restore the gravity anomaly data and disturbed gravity vertical gradient data of the non-grid midpoint within the selected area, and restore statistics Error, until the corresponding depths of all nodes within the point mass buried depth range, the point mass model calculations are completed one by one, and the point mass model recovery errors corresponding to the depths of all nodes are obtained; Step 5. Comparing the restoration error of the obtained point quality model horizontally, and determining the depth corresponding to the minimum restoration error, which is the optimal burial depth of shallow high-resolution point quality. 2. in the point quality model according to claim 1, the method for determining the optimum burial depth of shallow high-resolution point quality is characterized in that: step 1 specifically comprises the following steps: Step 1.1. Calculate the average gravity anomaly data of each 1°×1° grid by using the low-order potential coefficient model Get residual observations: The 1°×1° point mass M ₁ is solved as the first group of point mass; Step 1.2. Calculate the average gravity anomaly for each 20′×20′ grid using the potential coefficient model Calculate the average anomaly with 1°×1° point mass M ₁ Get residual observations: <mrow><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>20</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>20</mn><mo>&amp;prime;</mo></msup></mrow><mi>e</mi></msubsup><mo>=</mo><msub><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>20</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>20</mn><mo>&amp;prime;</mo></msup></mrow></msub><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>20</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>20</mn><mo>&amp;prime;</mo></msup></mrow><mi>S</mi></msubsup><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>20</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>20</mn><mo>&amp;prime;</mo></msup></mrow><msub><mi>M</mi><mn>1</mn></msub></msubsup></mrow> , The 20′×20′ point mass M ₂ is solved as the second group point mass; Step 1.3. Calculate the average gravity anomaly for each 5′×5′ grid using the potential coefficient model Calculate the average anomaly with the first group and the second group of point masses respectively Get residual observations: <mrow><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>5</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>5</mn><mo>&amp;prime;</mo></msup></mrow><mi>e</mi></msubsup><mo>=</mo><msub><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>5</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>5</mn><mo>&amp;prime;</mo></msup></mrow></msub><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>5</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>5</mn><mo>&amp;prime;</mo></msup></mrow><mi>S</mi></msubsup><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>5</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>5</mn><mo>&amp;prime;</mo></msup></mrow><msub><mi>M</mi><mn>1</mn></msub></msubsup><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>5</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>5</mn><mo>&amp;prime;</mo></msup></mrow><msub><mi>M</mi><mn>2</mn></msub></msubsup></mrow> , The 5'×5' point mass M ₃ is obtained as the third group of point mass. 3. The method for determining the optimal burial depth of shallow high-resolution point quality in the point quality model according to claim 1, characterized in that: in the step 2, the bit coefficient model is used to calculate each 1'×1' grid gravity anomaly at midpoint and the perturbed gravity vertical gradient 4. the shallow layer high-resolution point quality optimal burial depth determination method in the point quality model according to claim 2, is characterized in that: described step 4 specifically comprises the following content: Step 4.1. Use the first group, the second group, and the third group of point masses to calculate the midpoint gravity anomaly of the shallow high-resolution point mass model grid and the perturbed gravity vertical gradient Get residual observations: <mrow><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><mi>e</mi></msubsup><mo>=</mo><msub><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow></msub><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><mi>S</mi></msubsup><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><msub><mi>M</mi><mn>1</mn></msub></msubsup><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><msub><mi>M</mi><mn>2</mn></msub></msubsup><mo>-</mo><msubsup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><msub><mi>M</mi><mn>3</mn></msub></msubsup></mrow> <mrow><msubsup><mover><mrow><mi>&amp;delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><mi>&amp;rho;</mi><mi>&amp;rho;</mi><mrow><mo>(</mo><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><mo>)</mo></mrow></mrow><mi>e</mi></msubsup><mo>=</mo><msub><mover><mrow><mi>&amp;delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><mi>&amp;rho;</mi><mi>&amp;rho;</mi><mrow><mo>(</mo><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><mo>)</mo></mrow></mrow></msub><mo>-</mo><msubsup><mover><mrow><mi>&amp;delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><mi>&amp;rho;</mi><mi>&amp;rho;</mi><mrow><mo>(</mo><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><mo>)</mo></mrow></mrow><mi>S</mi></msubsup><mo>-</mo><msubsup><mover><mrow><mi>&amp;delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><mi>&amp;rho;</mi><mi>&amp;rho;</mi><mrow><mo>(</mo><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><mo>)</mo></mrow></mrow><msub><mi>M</mi><mn>1</mn></msub></msubsup><mo>-</mo><msubsup><mover><mrow><mi>&amp;delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><mi>&amp;rho;</mi><mi>&amp;rho;</mi><mrow><mo>(</mo><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><mo>)</mo></mrow></mrow><msub><mi>M</mi><mn>2</mn></msub></msubsup><mo>=</mo><msubsup><mover><mrow><mi>&amp;delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mrow><mi>&amp;rho;</mi><mi>&amp;rho;</mi><mrow><mo>(</mo><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow><mo>)</mo></mrow></mrow><msub><mi>M</mi><mn>3</mn></msub></msubsup></mrow> , A vector is formed by combining two residual observations: <mrow><mi>G</mi><mo>=</mo><mfenced open = "[" close = "]"><mtable><mtr><mtd><mrow><msub><msup><mover><mrow><mi>&amp;Delta;</mi><mi>g</mi></mrow><mo>&amp;OverBar;</mo></mover><mi>e</mi></msup><mrow><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup></mrow></msub></mrow></mtd></mtr><mtr><mtd><mrow><msubsup><mi>&amp;delta;g</mi><mrow><mi>&amp;rho;</mi><mi>&amp;rho;</mi><mrow><mo>(</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>&amp;times;</mo><msup><mn>1</mn><mo>&amp;prime;</mo></msup><mo>)</mo></mrow></mrow><mi>e</mi></msubsup></mrow></mtd></mtr></mtable></mfenced><mo>;</mo></mrow> Step 4.2, according to the burial depth range determined in step 3, for the depth value of each node within the range, solve the system of equations according to the least square method to solve the point quality M4 corresponding to the burial depth of all nodes _; Step _4.3 : Construct the point mass M4 corresponding to the burial depth of each node and the deep point mass to form a layered combination model, and restore the gravity anomaly data and Perturb the gravity vertical gradient data, and make a difference with the actual observation value at the measuring point to obtain the recovery error and make statistics. 5. The method for determining the optimal burial depth of shallow high-resolution point quality in the point quality model according to claim 4, characterized in that: in the step 4.3, the non-shallow high-resolution point within the selected area on the ground is recovered The formulas of gravity anomaly data and disturbed gravity vertical gradient data at the midpoint of the mass model grid are: Among them, n _max and n _layer respectively represent the order of the low-order bit model and the number of layers of the residual point quality, R represents the radius of the sphere, represents the corresponding potential coefficient model, ρ represents the geocentric radius, Indicates the radius of the center of the sphere where the i-th ground gravity anomaly point is located, r _ij represents the distance between the i-th ground gravity anomaly point and the j-th point mass, K represents the mass number of the point, and M represents the mass of K points The vector of , a represents the radius of the earth's equator, and M _ij represents the quality of the jth point in the i-th layer.