Sea-air magnetic measurement distance determination method considering magnetic anomaly space complexity

Abstract

The invention discloses a sea-air magnetic survey distance determination method considering magnetic anomaly space complexity, and belongs to the field of ocean geophysical data processing. According to the method, the magnetic survey line spacing is determined by using prior information and the complexity of calculation of a multi-feature fusion index model. A multi-attribute feature fusion model is designed to fuse a geomagnetic standard deviation, an average geomagnetic field, an accumulated gradient mean value, a kurtosis coefficient and a gradient standard deviation in combination with geomagnetic anomaly data characteristics, a magnetic field space complexity index is proposed, and sea area magnetic anomaly space distribution features are comprehensively evaluated. On the condition that the requirements of low-altitude and underwater geomagnetic navigation scenes for the spatial resolution and precision of the geomagnetic reference map are taken as the condition, the marine magnetic measurement line spacing required by construction of the geomagnetic reference map is estimated by combining aviation and shipborne high-resolution measured data; and reference is provided for offshore magnetic measurement technology design, geomagnetic matching navigation reference map construction and anti-submarine area magnetic background field construction.

Description

Technical Field

[0001] The invention belongs to the field of marine geophysical data processing, and in particular is a method for determining the sea-air magnetic survey distance taking into account the spatial complexity of magnetic anomalies. Background Art

[0002] Shipborne magnetic measurement, like marine gravity measurement and marine bathymetry, adopts the mode of survey line layout for planned measurement. Marine magnetic measurement can obtain the characteristic information of the earth's magnetic background field by shipborne or airborne means, but whether it is shipborne or airborne, it is necessary to determine the appropriate survey line spacing and survey line direction in the survey line layout. Reasonable survey line spacing and survey line direction are crucial to the overall mapping accuracy. In marine multi-beam bathymetry, the measurement coverage is generally divided according to the measurement level, and the survey line spacing is determined according to the required coverage. For marine magnetic measurement, the direction of the survey line is generally along the maximum direction of the gradient as much as possible, mostly along the direction perpendicular to the geological structure; the selection of survey line spacing should be as relaxed as possible under the premise of meeting the mapping accuracy, so as to improve work efficiency and reduce workload. In magnetic data acquisition, the determination of the magnetic measurement line spacing is generally also divided by the mapping scale. The measurement accuracy only requires the intersection difference, but there is no clear requirement for the final mapping accuracy. The determination of the survey line spacing in aeromagnetic survey also depends on the scale division, and its quality evaluation relies on the intersection discrepancy value to measure, and the final mapping quality is not evaluated. It relies on the scale of the mapping map to divide the survey line spacing, and the given intersection difference requirements are difficult to link with the error requirements of the benchmark map in actual applications, resulting in a large amount of marine magnetic data being difficult to play a practical application effect. The survey line planning in the above magnetic measurement specification requirements is difficult to effectively constrain the final mapping quality. Most of them adopt the single-beam water depth measurement mode. The obtained data still has room for improvement in the final management application and needs further improvement. Many scholars have proposed a more optimized survey line planning model for this purpose. Bian Gang et al. proposed a representative coefficient method to determine the survey line spacing of magnetic measurement, but the calculated representative coefficient did not consider the actual geomagnetic anomaly feature information and was difficult to prepare the geomagnetic benchmark map required for navigation; Bian Gang et al. also constructed a linear interpolation error propagation model to reasonably evaluate the survey line spacing, but it also did not consider the actual magnetic background field feature distribution, and its error propagation law was not consistent under different feature background fields. Cheng Fang et al. proposed an optimization model for the layout of survey line spacing in the field of water depth measurement, using the accuracy requirements of the interpolation relationship to determine the survey line spacing and evaluate it in combination with prior information. Xiao Fan et al. analyzed the impact of survey line spacing on gravity measurement accuracy and believed that the appropriate relaxation of survey line spacing has little effect on accuracy. In gravity measurement, Jin Shaohua et al. proposed to use the second-order derivative of gravity anomaly data to construct a linear error conduction model to estimate the survey line spacing, but for marine magnetism, it is necessary to consider the requirements of accuracy and resolution in actual navigation to select the appropriate survey line spacing.

[0003] At present, geomagnetic matching navigation technology mainly determines the location information by collecting magnetic field time series information on the route and comparing it with the pre-prepared high-precision geomagnetic reference map. Therefore, the construction accuracy of the geomagnetic reference map is directly related to the matching accuracy. Only by determining the appropriate survey line spacing and survey line direction can a geomagnetic reference map with high precision and high resolution in different matching scenarios be constructed. However, due to the particularity of the geophysical field, it is difficult to fill the large blank areas between the survey lines with the reference map construction algorithm alone. It is necessary to determine the survey line spacing that meets the objective physical laws before further using a reliable construction algorithm to reconstruct the geomagnetic reference map that meets the requirements of different matching scenarios. Different geomagnetic matching navigation scenarios have different resolution and accuracy requirements for the geomagnetic reference map, so the corresponding magnetic survey data survey line spacing requirements for the composition are also different. Since geomagnetic anomalies belong to the space physical field and have specific change laws, the relationship between the survey line spacing and the resolution and accuracy of the reference map can be established according to its change characteristics, and then the appropriate survey line spacing can be determined according to different application scenarios, or the data obtained by the current survey line interval can be reversed to see whether it meets the requirements, and then the supplementary survey information can be obtained. Geomagnetic anomaly data can be quantitatively described by a variety of characteristic indicators, such as geomagnetic standard deviation, average geomagnetic field, cumulative gradient mean, kurtosis coefficient and slope standard deviation. Different characteristic indicators contain characteristic information of different aspects of geomagnetic anomaly data. In order to accurately reflect the comprehensive characteristics of geomagnetic anomaly data, the present invention adopts a multi-feature fusion index model to fuse multi-attribute features, proposes a magnetic field space complexity index, and comprehensively evaluates the spatial distribution characteristics of marine magnetic anomalies. Based on the spatial resolution and accuracy requirements of geomagnetic reference maps in low-altitude and underwater geomagnetic navigation scenarios, the spacing between marine magnetic measurement lines required for the construction of geomagnetic reference maps is estimated in combination with aviation and shipborne high-resolution measured data, providing a reference for the design of marine magnetic measurement technology, the construction of geomagnetic reference maps and the construction of magnetic background fields in anti-submarine areas. Summary of the invention

[0004] The present invention aims to provide a method for determining the distance between sea and air magnetic surveys that takes into account the spatial complexity of magnetic anomalies. The invention aims to solve the problem that the traditional method does not fully consider the relationship between the resolution and accuracy of the result data map and the magnetic measurement distance, and uses prior information and the complexity of a multi-feature fusion index model to determine the magnetic survey line distance. In combination with the characteristics of geomagnetic anomaly data, a multi-attribute feature fusion model is designed to fuse the geomagnetic standard deviation, average geomagnetic field, cumulative gradient mean, peak coefficient and slope standard deviation, and a magnetic field spatial complexity index is proposed to comprehensively evaluate the spatial distribution characteristics of marine magnetic anomalies. Based on the spatial resolution and accuracy requirements of the geomagnetic reference map in low-altitude and underwater geomagnetic navigation scenes, the marine magnetic survey line distance required for the construction of the geomagnetic reference map is estimated in combination with aviation and shipborne high-resolution measured data, providing a reference for the design of marine magnetic measurement technology, the construction of geomagnetic matching navigation reference maps and the construction of magnetic background fields in anti-submarine areas.

[0005] The technical solution of the present invention:

[0006] The method for determining the sea-air magnetic survey spacing taking into account the spatial complexity of magnetic anomalies is as follows:

[0007] Step 1: First determine the required accuracy and resolution of the constructed result data, and select the existing high-resolution magnetic data for the corresponding scenario.

[0008] Step 2: Use the sliding sub-area module to calculate the geomagnetic standard deviation, mean geomagnetic field, cumulative gradient mean, kurtosis coefficient and slope standard deviation of each sub-area based on the selected high-resolution magnetic data.

[0009] Step 3: Multi-attribute fusion is performed on the characteristic indicators calculated for all sub-areas, and the final calculated value is the complexity index of the central coordinate point of the sub-area.

[0010] Step 4: Perform sparse modeling on each sub-area, analyze the corresponding changes in the resolution and accuracy of the constructed target data under different survey line spacings, and finally perform statistical modeling analysis: select the mean, median and 80th percentile respectively and use the least squares principle to fit the required magnetic survey line spacing to obtain the model curve.

[0011] Step 5: Calculate the complexity index using the prior data of the target area, and determine the model curve based on the corresponding magnetic survey line spacing obtained in step 4 to analyze the spacing distribution map of the target area to achieve the measurement accuracy and resolution.

[0012] Step 6: Use the spacing distribution map to reasonably determine the large-scale measurement partitions, and select smaller measurement line spacing values ​​in each partition to improve the overall accuracy index.

[0013] Beneficial effects of the present invention: The layout of survey lines is a key content in the design of marine magnetic measurement technology, and reasonable survey line spacing plays a vital role in the accuracy and measurement efficiency of the constructed geomagnetic reference map. In view of the fact that the current marine magnetic survey line spacing is only determined by the scale, without considering the geomagnetic anomaly characteristics and the relationship between the spatial resolution and accuracy of the constructed magnetic anomaly map and the survey line spacing in actual needs, the present invention proposes a method for determining the survey line spacing by integrating feature complexity indicators, and determines the survey line spacing by constructing a conversion model of the magnetic background field feature distribution and the accuracy and spatial resolution of the result data, and verifies it in combination with the measured aviation and shipborne magnetic survey data. The results show that: by estimating the survey line spacing and composing the map by the present invention, under the premise of meeting the requirements of the actual application scenario for the accuracy and resolution of the geomagnetic reference map, 88.4% of the ship magnetic workload and 97.6% of the aerial survey workload can be saved in the magnetic survey area of ​​the example. The algorithm has three advantages: 1) Considering the distribution characteristics of magnetic anomalies, and using multiple feature index models to perform multi-attribute fusion to calculate the feature complexity index to determine the magnetic line spacing; 2) It has less reliance on the accuracy and resolution of prior information. The smaller value selected in a large range of line spacing can improve the overall measurement accuracy and reduce the problem of low accuracy of the prior data calculation complexity; 3) The line spacing can be determined according to the accuracy and resolution indicators required by the result data, constraining the measurement mode from the application end, greatly improving the measurement efficiency and the practicality of the final result data. The next research goal will be to further analyze the possibility of estimating line spacing using global and regional magnetic data sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the sliding sub-area.

[0015] Figure 2 Flowchart for determining the spacing between sea and air magnetic surveys taking into account the spatial complexity of magnetic anomalies.

[0016] Figure 3Statistical distribution of accuracy under different survey line spacings, where (a1) is the variation curve of complexity of -1.19 and survey line spacing of 1km, (a2) is the variation curve of complexity of -1.19 and survey line spacing of 3km, (a3) ​​is the variation curve of complexity of -1.19 and survey line spacing of 4.5km, (a4) is the variation curve of complexity of -1.19 and survey line spacing of 6km, (b1) is the variation curve of complexity of -0.29 and survey line spacing of 1km, (b2) is the variation curve of complexity of -0.29 and survey line spacing of 3km, (b3) is the variation curve of complexity of -0.29 and survey line spacing of 4.5km, (b4) is the variation curve of complexity of -0.29 and survey line spacing of 6km, (c1) is the variation curve of complexity of 0.61 and survey line spacing of 1km, (c2) is the variation curve of complexity of 0.61, The changing curve when the survey line spacing is 3km, (c3) is the changing curve with complexity of 0.61, when the survey line spacing is 4.5km, (c4) is the changing curve with complexity of 0.61, when the survey line spacing is 6km, (d1) is the changing curve with complexity of 1.51, when the survey line spacing is 1km, (d2) is the changing curve with complexity of 1.51, when the survey line spacing is 3km, (d3) is the changing curve with complexity of 1.51, when the survey line spacing is 4.5km, (d4) is the changing curve with complexity of 1.51, when the survey line spacing is 6km, (e1) is the changing curve with complexity of 2.42, when the survey line spacing is 1km, (e2) is the changing curve with complexity of 2.42, when the survey line spacing is 3km, (e3) is the changing curve with complexity of 2.42, when the survey line spacing is 4.5km, (e4) is the changing curve with complexity of 2.42, when the survey line spacing is 6km.

[0017] Figure 4 The accuracy change of ship magnetic data complexity under different statistical indicators, among which, (a1) is the 80% quantile change trend diagram, (a2) is the 80% quantile extracted contour point fitting least squares curve diagram when RMSE is 2nT, (b1) is the mean change trend diagram, (b2) is the mean when RMSE is 2nT extracted contour point fitting least squares curve diagram, (c1) is the median change trend diagram, (c2) is the median when RMSE is 2nT extracted contour point fitting least squares curve diagram.

[0018] Figure 5 Ship magnetic data indicator fusion curve.

[0019] Figure 6Statistical distribution of accuracy under different survey line spacings, where (a1) is the variation curve of complexity -1.63 and survey line spacing of 1km, (a2) is the variation curve of complexity -1.63 and survey line spacing of 3km, (a3) ​​is the variation curve of complexity -1.63 and survey line spacing of 5km, (a4) is the variation curve of complexity -1.63 and survey line spacing of 8km, (b1) is the variation curve of complexity -0.64 and survey line spacing of 1km, (b2) is the variation curve of complexity -0.64 and survey line spacing of 3km, (b3) is the variation curve of complexity -0.64 and survey line spacing of 5km, (b4) is the variation curve of complexity -0.64 and survey line spacing of 8km, (c1) is the variation curve of complexity 1.86 and survey line spacing of 1km, and (c2) is the variation curve of complexity 1.86 , the changing curve under the survey line spacing of 3km, (c3) is the changing curve under the survey line spacing of 5km with a complexity of 1.86, (c4) is the changing curve under the survey line spacing of 8km with a complexity of 1.86, (d1) is the changing curve under the survey line spacing of 1km with a complexity of 2.86, (d2) is the changing curve under the survey line spacing of 3km with a complexity of 2.86, (d3) is the changing curve under the survey line spacing of 5km with a complexity of 2.86, (d4) is the changing curve under the survey line spacing of 8km with a complexity of 2.86, (e1) is the changing curve under the survey line spacing of 1km with a complexity of 4.37, (e2) is the changing curve under the survey line spacing of 3km with a complexity of 4.37, (e3) is the changing curve under the survey line spacing of 5km with a complexity of 4.37, (e4) is the changing curve under the survey line spacing of 8km with a complexity of 4.37.

[0020] Figure 7 The accuracy change of aeromagnetic data complexity under different statistical indicators, where (a1) is the 80% quantile change trend diagram, (a2) is the 80% quantile extracted contour point fitting least squares curve diagram when the RMSE is 1nT, (b1) is the mean change trend diagram, (b2) is the mean when the RMSE is 1nT extracted contour point fitting least squares curve diagram, (c1) is the median change trend diagram, (c2) is the median when the RMSE is 1nT extracted contour point fitting least squares curve diagram.

[0021] Figure 8 Aeromagnetic data indicator fusion curve.

[0022] Fig. 9 Original ship measurement data and complexity calculation results, where (a) is the complexity calculation result of the area, and (b) is the distribution of original ship magnetic data.

[0023] Fig.10Original aerial survey data and complexity calculation results, where (a) is the distribution of original aeromagnetic data and (b) is the complexity calculation result of the area.

[0024] Fig.11 Schematic diagram of survey line spacing estimation, where (a) is the distribution of survey line spacing assessment for ship magnetic data, and (b) is the distribution of survey line spacing assessment for aeromagnetic data. DETAILED DESCRIPTION

[0025] The technical solution of the present invention will be further described below in conjunction with specific embodiments and drawings.

[0026] 1. Selection of model data

[0027] Combining the actual measurement background and application background, taking the ship-surveyed water surface data to construct a spatial grid geomagnetic reference map with 500m resolution and RMSE=2nT indicator and the aerial survey data to construct a geomagnetic reference map with 50m resolution and 1nT indicator as examples, the relationships between the complexity indicators and the measurement accuracy and survey line spacing in the two scenarios are established respectively.

[0028] The experimental data selected are ship survey data of a certain sea area in 2008, with an original survey line interval of 500m and an area size of 50km×60km. First, the multi-faceted function method with high composition accuracy is used to interpolate the survey line magnetic anomaly data after various corrections into 500m grid data; the aerial survey experimental data are aeromagnetic survey data at an altitude of 300m in a certain sea area, with an original survey line interval of 50m and an area size of 52km×53km. Taking the grid resolution requirement of the aerial background field data as 50m and the RMSE as 1nT as an example, the original survey line data is interpolated into 50m resolution grid data using the multi-faceted function method in the same way as the ship magnetic data.

[0029] 2. Construction of complexity index model

[0030] The complexity index is calculated for the selected two resolutions, accuracy indexes and scene data respectively. The calculation method of the complexity index model is as follows:

[0031] In order to accurately describe the characteristic information of magnetic anomaly, the present invention adopts the sliding sub-area method to calculate the fusion feature complexity index. The sliding sub-area extraction method is to extract the geomagnetic anomaly map data in the corresponding coordinate area by setting a sub-area of ​​a certain size through translation. The change degree of two adjacent sliding sub-areas is small and the overlap rate is high. The step size of each sliding can control the change degree and overlap rate of adjacent sub-areas. The smaller the step size, the more detailed the data feature description. The sliding sub-area moving path is as follows: Figure 1As shown, there are two sliding modes: left and right translation and downward translation, which can be understood as a convolution-like mode to calculate the fusion feature index. In order to more accurately reflect the magnetic anomaly characteristics, the sub-area size should not be too large; but it should not be too small, otherwise it will be difficult to estimate the spacing between survey lines with lower complexity and the amount of calculation will be high. In order to explore the higher-precision measurement of the spacing between aerial and surface magnetic anomaly survey lines, the spacing between survey lines is generally less than 10km. Therefore, the present invention selects a sliding sub-area size of 15km×15km for calculation. In order to maximize the degree of refinement of the magnetic anomaly feature characterization, the sliding step size is set to a grid point length each time. Figure 1 Schematic diagram of the sliding sub-area extraction mode.

[0032] In order to analyze the modeling capabilities of different modeling methods under different geomagnetic complexities, five geomagnetic characteristic parameters, namely, geomagnetic standard deviation, mean geomagnetic field, cumulative gradient mean, peak coefficient and slope standard deviation, were selected and fused into a complexity index by feature fusion. The calculation formulas for the five geomagnetic characteristic parameters are as follows:

[0033] The geomagnetic standard deviation can be used to analyze the discreteness and fluctuation of the geomagnetic anomaly field. The larger the calculated value, the more drastic the change of the geomagnetic anomaly field and the more obvious the magnetic field characteristics. The calculation formula is as follows:

[0034]

[0035] In the above formula, σ is the geomagnetic standard deviation of the area, M represents the number of horizontal grid points in the geomagnetic anomaly map, N represents the number of vertical grid points in the geomagnetic anomaly map, f(i, j) represents the geomagnetic anomaly value at the grid point (i, j), and formula (2) represents the mean value of the geomagnetic anomaly field.

[0036] The average geomagnetic field value is used to measure the overall magnetic anomaly mean of the geomagnetic anomaly field. The calculation formula is shown in formula (2).

[0037] The cumulative gradient mean is used to reflect the average gradient change of the geomagnetic anomaly field, which can reveal the overall slope change of the geomagnetic anomaly field. The larger the value, the more drastic the anomaly field change in the area and the more obvious the characteristics. The calculation formula is as follows:

[0038]

[0039] In the above formula, T x (i, j) represents the lateral gradient at the grid point (i, j), T y (i, j) represents the magnitude of the longitudinal gradient at the grid point (i, j), and T is the required cumulative gradient mean.

[0040] The kurtosis coefficient is used to reflect the distribution of geomagnetic anomaly values. If the distribution of anomalies is more concentrated, the calculated kurtosis coefficient value will be larger, and the characteristic distribution of geomagnetic anomaly will be less obvious. The calculation formula is as follows:

[0041]

[0042] In the above formula, C e is the calculated kurtosis coefficient.

[0043] The slope standard deviation can be used to reflect the lateral and longitudinal change rates of a certain point in the geomagnetic anomaly field. The calculation formula is as follows:

[0044]

[0045] In the above formula, S x (i, j) is the lateral change rate of the geomagnetic reference map at point (i, j), S y (i,j) is the longitudinal rate of change at point (i,j).

[0046] The principle of principal component analysis multi-feature index fusion calculation is as follows:

[0047] The data of the geomagnetic anomaly map are extracted by sliding sub-areas of a certain size to calculate the geomagnetic characteristic parameters respectively. Assuming that there are m sub-areas extracted in the region and n types of geomagnetic characteristic parameters (5 types in the present invention), the evaluation matrix is:

[0048]

[0049] Where: x ij Represents the evaluation value of the i-th convolution module on the j-th geomagnetic characteristic parameter.

[0050] The calculated geomagnetic characteristic indicators are processed in the same trend. Since the value of the peak coefficient is inversely proportional to the situation reflecting the geomagnetic characteristics, it is taken as a negative number for the same trend processing. In order to eliminate the inconsistency of the numerical scales calculated for different geomagnetic characteristic parameters, the magnetic characteristic parameters of each region are normalized. The calculation formula is:

[0051]

[0052] Where: x' j Represents x j The value after trending, x j represents the evaluation value of the jth geomagnetic characteristic parameter, that is, a column of the matrix X. The evaluation matrix after normalization is:

[0053] Z=[z ij ] m×n (i=1,2,…,m; j=1,2,…,n) (10)

[0054] R=[r kj ] n×n (k,j=1,2,…,n) (11)

[0055] In the formula, z ij Represents x ij The normalized values ​​are used to calculate the correlation matrix R of the evaluation matrix Z using formula (11). In the above formula, And there is r jj =1, r kj =r jk .

[0056] The correlation matrix R is used to calculate the characteristic roots, eigenvectors and contribution rates. The characteristic equation is as follows: (12)

[0058] |λI-R|=0

[0059] Where λ is all the characteristic roots and I is the unit matrix.

[0060] Arrange all the calculated characteristic roots in descending order, and let a characteristic root be λ g (g=1,2…,n), using [λ g IR]L g = 0 to obtain the eigenvector L corresponding to the eigenvalue g . Where λ g The size of L represents the comprehensive evaluation size of the magnetic characteristic parameters of each place. g Z j =[z 1j ,z 2j ,…,z mj ] T The coefficients of each component in the new coordinate system, where Z j is a column of Z. Using the calculated λ g Calculate the variance contribution rate of the magnetic characteristic parameters of each region and set it as α g , the calculation formula is:

[0061]

[0062] The variance contribution rate is used to calculate the complexity of each sliding sub-area. The calculation formula is as follows:

[0063]

[0064] Where, T ig is the weighted sum of different geomagnetic features, L gj represents the coefficients of different geomagnetic characteristic parameters. The complexity of the calculation of the i-th sliding sub-area is T i .

[0065] The calculated complexity index integrates five geomagnetic anomaly characteristic index information, and uses sliding extraction to further finely characterize the distribution of magnetic background field characteristics. From the perspective of practical applications, geomagnetic matching navigation usually requires a high resolution of the geomagnetic reference map and certain requirements for the accuracy of the overall reference map. Therefore, when conducting magnetic measurements, the spacing between survey lines should be planned in combination with the actual application scenarios and magnetic map requirements. The flowchart of this method is given as follows: Figure 2 .

[0066] 3. Determine the model curve based on the measurement line spacing

[0067] In order to analyze how the composition accuracy changes with the survey line spacing under the same complexity, the survey line thinning method is first used to obtain the composition data under different survey line spacings. Secondly, the data of different survey line intervals are restored to 500m grid interval data using the multifaceted function method, and the accuracy is evaluated and the RMSE is calculated respectively with the original data. Then, a total of 6643 sub-area data in the area are extracted by sliding sub-areas, and all sub-areas are thinned out and the composition accuracy after thinning is calculated. Finally, by analyzing the accuracy changes of 6643 sub-area data with the change of survey line spacing under different complexities, the survey line spacing required for the 500m grid resolution 2nT accuracy index requirements of ship magnetic surface magnetic data under different complexities is obtained. The figure below only selects all sub-areas to construct composition data with survey line spacings of 1km, 3km, 4.5km and 6km under 5 complexities. The statistical distribution corresponding to the calculation accuracy is shown as follows Figure 3 shown.

[0068] like Figure 3 As shown, the figure above selects the accuracy distribution of each sub-area under different survey line spacings within 5 complexity intervals. The complexity interval length is set to 0.5, and the complexity marked in the figure is the upper limit of the interval. It can be seen that the accuracy distribution under different conditions is more in line with the normal distribution. Under the same complexity and survey line spacing, the statistical distribution of accuracy is more concentrated. It can be seen that the calculated complexity can better reflect the accuracy performance of magnetic anomaly data under different survey line spacings. In order to more accurately reflect the correspondence of complexity to composition accuracy and survey line spacing, the present invention divides 6643 sub-areas into multiple complexity intervals according to the calculated complexity, and the complexity interval length is set to 0.5. The composition RMSE values ​​of sub-areas under the same complexity interval at different survey line spacings are statistically calculated, and the 80% quantile, mean and median are used to reflect the accuracy of different survey line spacings under the same complexity interval. The distribution trend diagrams of complexity, survey line spacing and accuracy under the three statistical indicators are obtained, and the corresponding change curves are given by the least squares fitting method for the mean, median and 80% quantile corresponding to different survey line spacings under the same complexity interval.

[0069] Depend on Figure 4 visible, Figure 4 (a1) Figure 4 (b1) and Figure 4 (c1) in the figure is a trend chart of the accuracy change of the complexity calculated by three statistical indicators and the distance between measuring lines, where the marked red line is the 2nT indicator curve. Figure 4 (a2) Figure 4 (b2) and Figure 4 (c2) in the figure is the extracted contour point and the least square fitting curve with an RMSE value of 2nT. It can be seen that the similarity between the three is high. In order to comprehensively reflect the advantages of the three statistical indicators, the least square fitting method is also used to fuse the three indicators as a reference for the spacing of ship magnetic data survey lines. The fusion curve is shown in Figure 5 .

[0070] Depend on Figure 5 As shown in the figure, the three statistical indicators can be integrated through least squares fitting to obtain the corresponding curve of the complexity of ship-measured magnetic anomaly data and the spacing between survey lines under the 500m grid resolution and RMSE value of 2nT.

[0071] The aerial survey experimental data is the aeromagnetic data of a certain sea area at an altitude of 300m, with the original survey line interval of 50m and the area size of 52km×53km. Taking the grid resolution requirement of the aerial background field data as 50m and the RMSE of 1nT as an example, the original survey line data is interpolated into 50m resolution grid data using the multifaceted function method in the same way as the ship magnetic data, and the sub-area data of different areas are extracted by sliding the sub-area method, and the proposed model is used to calculate the fusion feature complexity value of each sub-area, and it is used as the complexity value of the grid center point of the sub-area. The size of the selected sliding sub-area is also set to 15km×15km. Due to the high resolution of the aerial survey data, the sliding sub-area slides one grid spacing each time, so a total of 555660 sub-area data are calculated for statistical calculations. The statistical method and calculation method are consistent with the ship survey data. The accuracy changes of 555660 sub-area data under different complexities with the change of survey line spacing are analyzed to obtain the survey line spacing required for the 1nT accuracy index requirement of 50m grid resolution of aeromagnetic magnetic data under different complexities. The figure below shows the composition data of all sub-areas constructed at 1km, 3km, 5km and 8km survey line spacing under the 5 selected complexities. The statistical distribution corresponding to the calculation accuracy is shown below. Figure 7 .

[0072] like Figure 6As shown in the figure above, the composition accuracy of each sub-area of ​​the aerial survey data in 5 complexity intervals varies with the change of the survey line spacing. The complexity interval length is set to 0.5, and the complexity marked in the figure above is the upper limit of the interval. It can be seen that the accuracy distribution of aerial survey data has the statistical characteristics of normal distribution, just like ship survey data. Therefore, representative accuracy can be selected in each complexity interval to represent the composition accuracy of the complexity of the interval, providing an accuracy basis for the subsequent selection of survey line spacing. A total of 555,660 sub-areas were extracted from the aeromagnetic data, and the 555,660 sub-areas were divided into multiple complexity intervals according to the calculated complexity, and the complexity interval length was set to 0.5. In each complexity interval, the 80% quantile, mean and median are used to select the representative accuracy under different survey line spacing in the interval. The distribution trend diagram of complexity, survey line spacing and accuracy under three statistical indicators can be obtained, and the 1nT accuracy index curve is extracted for least squares fitting. The survey line spacing that meets the 50m resolution 1nT accuracy index under different complexities is obtained by fitting the curve, which provides a reference for the selection of survey line spacing for measurement.

[0073] Depend on Figure 7 visible, Figure 7 (a1) Figure 7 (b1) and Figure 7 (c1) in the figure is a trend chart of the accuracy change of the complexity and the measurement line spacing calculated by three statistical indicators, where the marked red line is the accuracy curve with an RMSE of 1nT. Figure 7 (a2) Figure 7 (b2) and Figure 7 (c2) is the contour extraction point with RMSE of 1nT and the least square fitting curve. The three indicators are also fused by the least square fitting method as the reference basis for the survey line spacing of the final aerial survey data. The fusion curve is as follows:

[0074] Depend on Figure 8 As shown in the figure, the three statistical indicators are integrated through least squares fitting to obtain the corresponding curve of the complexity of the aerial survey magnetic anomaly data and the survey line spacing under the index of 50m composition grid resolution and RMSE value of 1nT. The survey line spacing can be estimated based on this curve.

[0075] 4. Example calculation of measuring line spacing determined by prior data

[0076] The line spacing estimation model in the same scenario can be applied to the magnetic data collection in this scenario. The complexity calculation requires the use of prior magnetic field data of the sea area. The complexity value calculated by the present invention relies on the data or data set with larger line spacing to estimate. In the absence of data, global or regional magnetic anomaly data sets can be used, such as MAMEA data set, EMAG2 data set, etc. In order to verify the rationality of using fusion feature complexity to estimate the spacing of magnetic anomaly survey lines, measured marine magnetic data with smaller line spacing are selected for verification. The selected ship survey data and aerial survey data are used to estimate the line spacing. The original ship survey line spacing is thinned to 10km and the original aerial survey line spacing is thinned to 10km through the method of line thinning. The surface magnetic RMSE is 2nT with a resolution of 500m, and the aerial magnetic RSME is 1nT with a resolution of 50m through supplementary measurement. The complexity of the area is calculated from the thinned data as follows: Fig. 9 and Fig.10 , and the following survey line spacing planning is obtained through the relationship between complexity and survey line spacing Fig.11 .

[0077] The survey line spacing in the measurement area should be kept consistent as much as possible, so the above area is divided into zones, and the required accuracy requirements are guaranteed with the minimum survey line spacing within the zones. Fig.11 The longitudinal distances of 30km and 10km in the image are divided into three areas: upper, middle and lower. The survey line spacings of 10km, 3km and 10km are used for composition respectively. The aerial survey area is directly composed with the minimum estimated spacing of 2.5km. The composition data are compared with the measured data, and the results are shown in Table 1.

[0078] Table 1 Accuracy statistics of estimated survey line spacing using ship survey and aerial survey data

[0079]

[0080] From the data in Table 1, it can be seen that the composition based on the survey line spacing estimated by complexity can meet the accuracy index requirements in different scenarios. In the ship survey data, different partitions can meet the accuracy requirements of the set 500m resolution 2nT. Compared with the accuracy of the measured high resolution, the whole area mapping can also meet the preset indicators, and the overall workload is saved by 88.4% compared with the original data. The same is true for the aerial survey data. By selecting the minimum survey line spacing of 2.5km for composition, the accuracy of its resolution at 50m is only 0.41nT, which is 59% higher than the preset 1nT accuracy index, and the workload is saved by more than 97.6%, and there is still room for further reduction.

Claims

1. A method for determining the distance between sea and air magnetic surveys taking into account the spatial complexity of magnetic anomalies, characterized in that: Here are the steps: Step 1: First, determine the required accuracy and resolution of the constructed result data, and select the existing high-resolution magnetic data for the corresponding scene; Step 2: Using the sliding sub-area module to calculate the characteristic indicators of each sub-area for the selected high-resolution magnetic data, the characteristic indicators include geomagnetic standard deviation, average geomagnetic field, cumulative gradient mean, kurtosis coefficient and slope standard deviation; Step 3: Multi-attribute fusion is performed on the characteristic indicators calculated for all sub-areas, and the final calculated value is the complexity index of the central coordinate point of the sub-area; Step 4: Perform sparse modeling on each sub-area, analyze the corresponding changes in the resolution and accuracy of the constructed target data under different survey line spacings, and finally perform statistical modeling analysis: select the mean, median and 80th percentile respectively and use the least squares principle to fit the required magnetic survey line spacing to obtain the model curve; Step 5, using the prior data of the target area to calculate the complexity index, and determining the model curve according to the corresponding magnetic line spacing obtained in step 4 to analyze the spacing distribution map of the target area to achieve the measurement accuracy and resolution; Step 6: Use the spacing distribution map to reasonably determine the large-scale measurement partitions, and select smaller measurement line spacing values ​​in each partition to improve the overall accuracy index.

2. The method for determining the sea-air magnetic survey distance taking into account the spatial complexity of magnetic anomalies according to claim 1 is characterized in that: The calculation formula of geomagnetic standard deviation is as follows: In the above formula, σ is the geomagnetic standard deviation of the area, M represents the number of horizontal grid points of the geomagnetic anomaly map, N represents the number of vertical grid points of the geomagnetic anomaly map, f(i, j) represents the geomagnetic anomaly value at the grid point (i, j), and formula (2) represents the mean value of the geomagnetic anomaly field; The calculation formula of the average geomagnetic field is shown in formula (2); The calculation formula of the cumulative gradient mean is as follows: In the above formula, T x (i, j) represents the lateral gradient at the grid point (i, j), T y (i, j) represents the longitudinal gradient at the grid point (i, j), and T is the required cumulative gradient mean; The calculation formula of the kurtosis coefficient is as follows: The formula for calculating the slope standard deviation is as follows: S x (i,j)=[f(i+1,j+1)+f(i,j+1)+f(i-1,j+1)- (6) f(i+1,j-1)-f(i,j-1)-f(i-1,j-1)] / 6 S y (i,j)=[f(i+1,j+1)+f(i+1,j)+f(i+1,j-1)- (7) f(i-1,j+1)-f(i-1,j)-f(i-1,j-1)] / 6 In the above formula, S x (i, j) is the lateral change rate of the geomagnetic reference map at point (i, j), S y (i,j) is the longitudinal rate of change at point (i,j).

3. The method for determining the sea-air magnetic survey distance taking into account the spatial complexity of magnetic anomalies according to claim 1 is characterized in that: The multi-attribute fusion described adopts the principal component analysis multi-feature index fusion method, and the calculation principle is as follows: By setting a certain size of sliding sub-area to slide and extract the data of geomagnetic anomaly map, the geomagnetic characteristic parameters are calculated respectively. Assuming that there are m sub-areas extracted in this area and n geomagnetic characteristic parameters, the evaluation matrix is: Where: x ij Represents the evaluation value of the i-th convolution module on the j-th geomagnetic characteristic parameter; The calculated geomagnetic characteristic indicators are processed with the same trend. Since the value of the peak coefficient is inversely proportional to the situation reflecting the geomagnetic characteristics, it is taken as a negative number for the same trend processing; in order to eliminate the inconsistency of the numerical scales calculated for different geomagnetic characteristic parameters, the magnetic characteristic parameters of each region are normalized, and the calculation formula is: Where: x' j Represents x j The value after trending, x j represents the evaluation value of the jth geomagnetic characteristic parameter, that is, a column of the matrix X. The evaluation matrix after normalization is: Z=[z ij ] m×n ,i=1,2,…,m;j=1,2,…,n (10) R=[r kj ] n×n ;k,j=1,2,…,n (11) In the formula, z ij Represents x ij The normalized values ​​are used to calculate the correlation matrix R of the evaluation matrix Z using formula (11); in the above formula, And there is r jj =1, r kj =r jk ; The correlation matrix R is used to calculate the characteristic roots, eigenvectors and contribution rates. The characteristic equation is as follows: (12) |λI-R|=0 Where λ is all the characteristic roots, I is the unit matrix; Arrange all the calculated characteristic roots in descending order, and let a certain characteristic root be λ g , g=1,2…,n, using [λ g IR]L g = 0 to obtain the eigenvector L corresponding to the eigenvalue g ; where λ g The size of L represents the comprehensive evaluation size of the magnetic characteristic parameters of each place. g Z j =[z 1j ,z 2j ,…,z mj ] T The coefficients of each component in the new coordinate system, where Z j is a column of Z; use the calculated λ g Calculate the variance contribution rate of the magnetic characteristic parameters of each region and set it as α g , the calculation formula is: The variance contribution rate is used to calculate the complexity of each sliding sub-area. The calculation formula is as follows: Where, T ig is the weighted sum of different geomagnetic features, L gj represents the coefficients of different geomagnetic characteristic parameters. The complexity of the calculation of the i-th sliding sub-area is T i .

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