A method for inverting seabed topography from gravity data in a wide ocean area based on Gaussian surface estimation

Abstract

This invention discloses a method for inverting seabed topography based on Gaussian surface estimation using gravity data from a wide sea area. The method includes the following steps: 1. Acquiring gridded gravity data from a wide sea area; 2. In each small region, solving for the first set of characteristic parameters using the known gravity data according to a Gaussian surface function model and the least squares principle; 3. Reading prior seabed topography grid data from the wide sea area; 4. In each small region, solving for the second set of characteristic parameters using the prior seabed topography data according to a Gaussian surface function model and the least squares principle; 5. Solving for the estimated seabed topography in a local small region; 6. Repeating steps 2 to 5 multiple times until all small regions are calculated, outputting the seabed topography for all areas of the wide sea area. This invention fully utilizes the correlation between marine gravity data and seabed topography, mapping the characteristic parameters of the gravity data to the seabed topography, and obtaining the estimated seabed topography through error iteration based on a prior seabed topography model.

Description

Technical Field

[0001] This invention belongs to the field of seafloor topography inversion technology, specifically relating to a method for inverting seafloor topography based on gravity data from a wide sea area using Gaussian surface estimation. Background Technology

[0002] The determination of seabed topography in vast global ocean areas currently primarily employs shipborne single-beam and multi-beam measurements, as well as satellite altimetry inversion techniques. Sea depth in narrow channels, nearshore areas, and tidal flats is generally determined using shipborne multi-beam, satellite-borne laser bathymetry, airborne laser bathymetry, and multispectral inversion techniques. Currently, shipborne multi-beam measurements offer the highest accuracy and have become the primary method for high-precision seabed topography mapping. However, limitations imposed by measurement platforms and the objective marine environment make it difficult to achieve uniform global coverage. Ocean satellite altimetry, through multi-satellite flyby and synthetic aperture altimeter techniques, can acquire disturbed gravity data with a resolution as high as 1′ globally within approximately 2.5 years, enabling the inversion of seabed topography at a corresponding resolution.

[0003] In methods for inverting seabed topography in wide sea areas, current approaches widely utilize gravity anomaly data obtained from satellite altimetry to invert seabed topography using gravity geology methods, analytical methods, frequency domain methods, and least squares collocation methods. These methods generally employ linearization followed by calculation of first-order terms. Some scholars have also considered the influence of higher-order terms and constructed nonlinear quadratic correlation models, using limited known shipborne water depth / gravity data to invert seabed topography. However, the problem of low accuracy in seabed topography models still exists. Summary of the Invention

[0004] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a method for inverting seabed topography from gravity data in a wide sea area based on Gaussian surface estimation. This method divides a local sea area into several small regions, each composed of 6×6 original gravity grid data. The latitude and longitude corresponding to the peak values ​​and the amplitude of peak value variation in each small region are obtained by solving a Gaussian surface function. These parameters are then combined with a prior seabed topography model to iteratively solve for new seabed topography information in the corresponding region. Considering the strong stochastic correlation between sea area gravity data and seabed topography, a sea area gravity characteristic model can be constructed using a Gaussian surface function. Then, based on the prior seabed topography model, the seabed topography of the corresponding region can be iteratively solved, facilitating widespread application.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for inverting seabed topography based on gravity data of a wide sea area using Gaussian surface estimation, characterized in that the method includes the following steps:

[0006] Step 1: Obtain grid gravity data in a wide sea area to form a δg(i) sequence. Divide the data into multiple small regions from north to south and from west to east. Each small region contains 6×6 grids, and the size of each grid is 1'×1'. Here, i is the small region number and i takes the values ​​1, 2, ..., n, where n is the total number of small regions.

[0007] Step 2: In each small region, using known gravity data, apply the Gaussian surface function model. The five first set of characteristic parameters G are obtained by solving using the least squares principle. T,i Gx T,i Gy T,i C Gx,i C Gy,i ;

[0008] Among them, G T,i Gx represents the peak value of the gravitational field in a small local region. T,i Gy represents the longitude information corresponding to the peak gravity field in a local small region. T,i C represents the latitude information corresponding to the peak gravity field in a local small region. Gx,i C represents the magnitude of the change in the gravitational field along the longitude direction within a small local area. Gy,i X represents the magnitude of the change in the gravitational field along the latitudinal direction within a small local area. i Y represents the longitude information corresponding to the gravity field variables in a local small region. i This indicates the latitude information corresponding to the gravity field variables within a small local region.

[0009] Step 3: Read the prior seabed topographic grid data in a wide sea area to form H s (i) Sequence;

[0010] Step 4: In each small region, using prior seabed topography data, apply the Gaussian surface function model. The five second set of characteristic parameters H are obtained by solving using the least squares principle. T,i Hx T,i Hy T,i C Hx,i C Hy,i ;

[0011] Where H T,i Hx represents the peak value of the seabed topography within a small local area. T,i Hy represents the longitude information corresponding to the peak value of the seabed topography within a local small region. T,i C represents the latitude information corresponding to the peak value of the seabed topography within a local small area. Hx,i C represents the magnitude of seafloor topography variation along the longitude direction within a small local area. Hy,i The x represents the magnitude of latitudinal seafloor topography variation within a small local area. iThis shows the longitude information corresponding to each seabed topographic variable, y i This represents the latitude information corresponding to each seabed topography variable;

[0012] Step 5, according to Solving for local small-area estimation of seabed topography H est-i When estimating seabed topography H in a small area est-i and prior seabed topography data H s When the root mean square error between (i) is less than 0.5 times the prior seabed topography error, the loop solution ends and the estimated seabed topography of a small area is output.

[0013] Among them, H T,i,new C represents the peak value of the seafloor topography to be estimated. Hx,i-new This represents the magnitude of the change in seafloor topography along the longitude direction within the small area to be estimated, and C Hx,i-new =scale·C Gx,i C Hy,i-new This represents the magnitude of the latitudinal seafloor topography variation within the small region to be estimated, and C Hy,i-new =scale·C Gy,i Scale is a scaling factor;

[0014] Step 6: Repeat steps 2 to 5 multiple times to calculate all small areas and output the seabed topography of all areas in the wide sea area.

[0015] The above-mentioned method for inverting seabed topography based on Gaussian surface estimation of gravity data in a wide sea area is characterized by: in step one, grid gravity data is obtained by reading satellite altimetry inversion methods.

[0016] The above-mentioned method for inverting seabed topography based on Gaussian surface estimation of gravity data in a wide sea area is characterized in that: in step two, the gravity field includes gravity anomalies and disturbed gravity.

[0017] The above-mentioned method for inverting seabed topography from gravity data in a wide sea area based on Gaussian surface estimation is characterized in that: in step five, the peak value H of the seabed topography to be estimated is... T,i,new In (H) T,i -500, H T,i Cycles within the range of +500; the scale factor cycles within the range of (-0.1, 0.1).

[0018] The beneficial effects of this invention are that, starting from marine gravity data and the related characteristics of seabed topography, the parameters of the marine gravity characteristic model are solved using Gaussian surface functions. Based on a prior seabed topography model, a new seabed topography grid model is obtained through iterative solving. The local marine area is divided into several small regions, each composed of 6×6 original gravity grid data. The latitude and longitude corresponding to the peak values ​​and the peak value variation range of each small region are obtained through Gaussian surface functions. These parameters are then used in conjunction with the prior seabed topography model to iteratively solve for new seabed topography information in the corresponding region. Considering the strong stochastic correlation between marine gravity data and seabed topography, a marine gravity characteristic model can be constructed using Gaussian surface functions, and then the seabed topography of the corresponding region can be iteratively solved based on the prior seabed topography model, facilitating widespread application.

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention.

[0021] Figure 2 This is a grayscale diagram illustrating the 1′ resolution gravity data obtained by inverting the altimetry data from the Saral satellite in this embodiment.

[0022] Figure 3 This is a grayscale diagram illustrating the seabed topography data estimated in this embodiment. Detailed Implementation

[0023] like Figures 1 to 3 As shown, the method for inverting seabed topography based on Gaussian surface estimation of gravity data in a wide sea area according to the present invention includes the following steps:

[0024] Step 1: Obtain grid gravity data in a wide sea area to form a δg(i) sequence. Divide the data into multiple small regions from north to south and from west to east. Each small region contains 6×6 grids, and the size of each grid is 1'×1'. Here, i is the small region number and i takes the values ​​1, 2, ..., n, where n is the total number of small regions.

[0025] Step 2: In each small region, using known gravity data, apply the Gaussian surface function model. The five first set of characteristic parameters G are obtained by solving using the least squares principle. T,i Gx T,i Gy T,i C Gx,i C Gy,i ;

[0026] Among them, G T,i Gx represents the peak value of the gravitational field in a small local region. T,iGy represents the longitude information corresponding to the peak gravity field in a local small region. T,i C represents the latitude information corresponding to the peak gravity field in a local small region. Gx,i C represents the magnitude of the change in the gravitational field along the longitude direction within a small local area. Gy,i X represents the magnitude of the change in the gravitational field along the latitudinal direction within a small local area. i Y represents the longitude information corresponding to the gravity field variables in a local small region. i This indicates the latitude information corresponding to the gravity field variables within a small local region.

[0027] Step 3: Read the prior seabed topographic grid data in a wide sea area to form H s (i) Sequence;

[0028] Step 4: In each small region, using prior seabed topography data, apply the Gaussian surface function model. The five second set of characteristic parameters H are obtained by solving using the least squares principle. T,i Hx T,i Hy T,i C Hx,i C Hy,i ;

[0029] Where H T,i Hx represents the peak value of the seabed topography within a small local area. T,i Hy represents the longitude information corresponding to the peak value of the seabed topography within a local small region. T,i C represents the latitude information corresponding to the peak value of the seabed topography within a local small area. Hx,i C represents the magnitude of seafloor topography variation along the longitude direction within a small local area. Hy,i The x represents the magnitude of latitudinal seafloor topography variation within a small local area. i This shows the longitude information corresponding to each seabed topographic variable, y i This represents the latitude information corresponding to each seabed topography variable;

[0030] Step 5, according to Solving for local small-area estimation of seabed topography H est-i When estimating seabed topography H in a small area est-i and prior seabed topography data H s When the root mean square error between (i) is less than 0.5 times the prior seabed topography error, the loop solution ends and the estimated seabed topography of a small area is output.

[0031] Among them, H T,i,new C represents the peak value of the seafloor topography to be estimated. Hx,i-new This represents the magnitude of the change in seafloor topography along the longitude direction within the small area to be estimated, and C Hx,i-new =scale·C Gx,i CHy,i-new This represents the magnitude of the latitudinal seafloor topography variation within the small region to be estimated, and C Hy,i-new =scale·C Gy,i Scale is a scaling factor;

[0032] Step 6: Repeat steps 2 to 5 multiple times to calculate all small areas and output the seabed topography of all areas in the wide sea area.

[0033] It should be noted that, starting from marine gravity data and seabed topography characteristics, the parameters of the marine gravity characteristic model are solved using Gaussian surface functions. Based on a prior seabed topography model, a new seabed topography grid model is obtained through iterative solving. The local marine area is divided into several small regions, each composed of 6×6 original gravity grid data. The latitude and longitude corresponding to the peak values ​​in each small region are obtained using Gaussian surface functions, along with the peak value variation range. These parameters are then used in conjunction with the prior seabed topography model to iteratively solve for new seabed topography information for the corresponding regions. This process takes into account the relationship between marine gravity data and seabed topography. There is a strong stochastic correlation between them. Therefore, a marine gravity feature model can be constructed using Gaussian surface functions. Then, based on the prior seabed topography model, the seabed topography of the corresponding area can be iteratively solved. By making full use of the correlation between marine gravity data and seabed topography, the feature parameters of gravity data are mapped to the seabed topography. Based on the prior seabed topography model, the estimated seabed topography is obtained through error iteration. The obtained seabed topography is an improvement and refinement of the original prior seabed topography model without relying on shipborne water depth data. Moreover, the denser the gravity data, the better the estimation effect.

[0034] In this embodiment, in step one, grid gravity data is obtained by reading satellite altimetry inversion.

[0035] In this embodiment, in step two, the gravity field includes gravity anomalies and disturbed gravity.

[0036] In this embodiment, in step five, the peak value H of the seabed topography to be estimated is... T,i,new In (H) T,i -500, H T,i Cycles within the range of +500; the scale factor cycles within the range of (-0.1, 0.1).

[0037] In implementing this invention, the test area was selected as the South China Sea, with the area defined as 10°N-12.4°N and 111.4°E-112.9°E, and an average sea depth of 3800 meters. The marine gravity data used was 1′ resolution gravity data obtained by inverting altimetry data from the Saral satellite, such as... Figure 2As shown, the prior seabed topography model adopted was the ETOPO-1 water depth model published by the National Center for Environmental Information (NCEI). The ship-measured water depth verification data came from the Ministry of Natural Resources. During the calculation, the test area was divided into 24×15 regions according to a 6×6 grid and iterated repeatedly. The estimated seabed topography obtained after the calculation is as follows: Figure 3 As shown.

[0038] Through the accuracy check of the shipborne data, the estimated mean square error of the seabed topography is 139.61 meters, which is 5 meters higher than the accuracy of the ETOPO-1 water depth model. The specific results are shown in Table 1.

[0039] Table 1. Statistical precision (m) for estimating seabed topography

[0040] Maximum value Minimum Mean of difference Mean squared deviation 758.76 -941.61 -6.61 139.61

[0041] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technical essence of the present invention shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for inverting seabed topography from gravity data over a wide sea area based on Gaussian surface estimation, characterized in that, The method includes the following steps: Step 1: Acquire grid gravity data in a wide sea area to form... The sequence divides the data into multiple small regions from north to south and west to east. Each small region contains 6×6 grids, and the size of each grid is [missing information]. ,in, Number the small area and Let 1, 2, ..., n be the total number of sub-regions; Step 2: In each small region, using known gravity data, apply the Gaussian surface function model. The five first set of characteristic parameters were obtained by solving using the least squares principle. , , , , ; in, This represents the peak value of the gravitational field within a small local region. This indicates the longitude information corresponding to the peak gravity field in a local small region. This indicates the latitude information corresponding to the peak gravity field within a small local region. This indicates the magnitude of the change in the gravitational field along the longitude direction within a small local area. It represents the magnitude of the latitudinal gravitational field variation within a small local area. This represents the longitude information corresponding to the gravity field variables within a small local region. This indicates the latitude information corresponding to the gravity field variables within a small local region. Step 3: Read the prior seabed topographic grid data in a wide sea area to form... sequence; Step 4: In each small region, using prior seabed topography data, apply the Gaussian surface function model. The five second set of characteristic parameters were obtained by solving using the least squares principle. , , , , ; Where, This represents the peak value of the seabed topography within a small local area. This indicates the longitude information corresponding to the peak value of the seabed topography within a local small region. This indicates the latitude information corresponding to the peak value of the seabed topography within a local small region. This indicates the magnitude of changes in seabed topography along the longitude direction within a small, localized area. This indicates the magnitude of latitudinal seabed topography variation within a small local area. This displays the longitude information corresponding to each seabed topographic variable. This represents the latitude information corresponding to each seabed topography variable; Step 5, according to Solve for local small-area estimation of seabed topography When estimating seabed topography in a small area and prior seabed topography data When the root mean square error between the two is less than 0.5 times the prior seabed topography error, the loop solution ends and the estimated seabed topography of a small area is output. in, The peak value of the seabed topography to be estimated; This represents the magnitude of the change in seafloor topography along the longitude direction within the small area to be estimated, and , This represents the magnitude of the latitudinal seafloor topography variation within the small region to be estimated, and , It is a scaling factor; Step 6: Repeat steps 2 to 5 multiple times to calculate all small areas and output the seabed topography of all areas in the wide sea area.

2. The method for inverting seabed topography from gravity data in a wide sea area based on Gaussian surface estimation according to claim 1, characterized in that: In step one, grid gravity data is obtained through satellite altimetry inversion.

3. The method for inverting seabed topography from gravity data in a wide sea area based on Gaussian surface estimation as described in claim 1, characterized in that: In step two, the gravity field includes gravity anomalies and disturbed gravity.

4. The method for inverting seabed topography from gravity data in a wide sea area based on Gaussian surface estimation according to claim 1, characterized in that: In step five, the peak value of the seabed topography to be estimated is... exist Loop within range; Scale factor Cycle within the range of (-0.1, 0.1).

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