A method for determining geoid gravity potential by combining gravity anomaly and sea level height

Abstract

The invention discloses a method for determining the geoid gravity potential by combining gravity anomaly and sea level height, comprising the following steps: 1. reading sea area gravity anomaly grid data and average sea level height grid data; 2. solving the geoid height of grid points; 3. calculating the disturbed gravity potential of grid points; 4. calculating the normal gravity potential of grid points; 5. calculating the actual gravity potential of grid points; 6. calculating the actual gravity average value of grid points; 7. calculating the vertical distance from the sea surface to the geoid at grid points; 8. calculating the geoid gravity potential of grid points; 9. determining the optimal estimated value of the geoid gravity potential of grid points. The invention makes full use of dense high-quality gravity anomaly data and average sea level height data of sea areas to jointly determine the geoid gravity potential of sea areas, avoids the link of using a priori gravity field model, simplifies the calculation process, improves the calculation accuracy, and provides a better idea for the autonomous determination of geoid gravity potential.

Description

Technical Field

[0001] The invention belongs to the technical field of physical geodesy, and in particular relates to a method for determining the gravity potential of the geoid by combining gravity anomaly and sea level height. Background Art

[0002] The geoid gravity potential W0 is an important physical property of the geoid. Using W0 as a definition of the global elevation datum will help establish, realize and maintain the global elevation datum, and play an important role in the unification and conversion of elevation datums in various regions. Studying W0 and its changes will also help analyze changes in geophysical characteristics on a global scale, such as crustal movement, sea level changes, post-glacial rebound, and related ecological environment, natural disasters and other issues. W0 is also adopted by the International Astronomical Union as a constant parameter for the realization of the relativistic atomic time scale.

[0003] The geoid gravity potential W0 value was determined to be 62636855.72m using the Topex / Poseidon altimetry satellite data from 1994 to 1996, the EGM96 gravity potential model, and the POCM4B sea surface topography model. 2 / s 2 The monthly variation of W0 during the three years from 1994 to 1996 was also analyzed. The W0 value was re-determined to be 62636856.0±0.5m using Topex / Poseidon altimetry satellite data from 1993 to 1998 and the EGM96 gravity potential model. 2 / s 2 Based on this value, the vertical deviations between the North American Height Datum (NAVD88), the Australian Height Datum (AHD), and the Finnish Height Datum (N60) and the geoid were obtained. The geoid gravity potential W0 value was determined to be 62636855.75±0.21m using the ellipsoidal harmonic gravity potential model and the GPS leveling data of the Baltic Sea region in 1990, 1993, and 1997. 2 / s 2 , the change rate of W0 is -0.0099m 2 / s 2 / year. The W0 value calculated by using EIGEN-CG03C, EGM96 gravity potential model and CLS01 mean sea surface model is 62636853.4m 2 / s 2 .

[0004] At present, international scholars generally use gravity potential models, mean sea level models and sea surface topography models to calculate the value of W0. However, gravity potential models (such as EGM2008 and EIGEN-6C4) have low resolution (up to 5 arc minutes) and have certain errors in the high frequency band. Using them to calculate the gravity potential of a point on the sea surface will also bring certain errors. At the same time, with the increase of the order of gravity potential models (greater than 2160 orders), the time to calculate the global sea gravity potential will also increase significantly. With the development of satellite altimetry technology and shipborne gravity measurement technology, the resolution and accuracy of sea gravity anomaly data are constantly improving. The currently published grid data has a maximum of 1 arc minute and an accuracy of 3-5mGal. Using these data in conjunction with the mean sea level model to calculate the gravity potential will further improve the calculation accuracy and the uniformity of data distribution, thereby improving the accuracy of W0. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for determining the geoid gravity potential by combining gravity anomaly and sea level height in view of the deficiencies in the above-mentioned prior art, so as to make full use of dense high-quality gravity anomaly data and average sea level height data in the sea area to jointly determine the geoid gravity potential in the sea area, avoid the link of using a priori gravity field model, simplify the calculation process, improve the calculation accuracy, provide a better idea for the autonomous determination of the geoid gravity potential, and facilitate popularization and use.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for determining the geoid gravity potential by combining gravity anomaly and sea level height, characterized in that the method comprises the following steps:

[0007] Step 1: read the sea area gravity anomaly grid data Δg(i) and the average sea level height grid data H(i), where i is the grid point number and i=1,2,...,N, and N is the total number of grid points;

[0008] Step 2: According to the Stokes theory formula Solve the geoid height N(i) of the i-th grid point, where R represents the average radius of the earth, j is a variable and j=1, 2, ..., i, λ represents the geodetic longitude of the grid point, represents the geodetic latitude of the grid point, ψ represents the spherical angular distance between the gravity anomaly data and the calculated grid point, and S(ψ) is the kernel function and

[0009] γ i represents the normal gravity of the ith grid point and represents the geodetic latitude of the ith grid point, γ0 represents the normal gravity of the reference ellipsoid and γ e represents the normal gravity at the equator and γ e The value is 9.7803253349ms -2 ;

[0010] Step 3: According to formula T i =N(i)·γ i , calculate the disturbed gravity potential T of the i-th grid point i ;

[0011] Step 4: According to the formula Calculate the normal gravity potential U of the i-th grid point i , where GM is a constant and GM = 3986005 × 10 8 m 3 s -2 , r represents the distance from the center of the sea grid to the center of the earth and a represents the semi-major axis of the reference ellipsoid and a=6378137m, E2=2F-F 2 , F represents the reference ellipsoid flattening and F = 0.00335281068118, C 20 is the first normal gravitational potential coefficient and C 20 =-0.001092, C 40 is the second normal gravitational potential coefficient and C 40 =0.00000237, C 60 is the third normal gravitational potential coefficient and C 60 =-0.00000000608347, represents the Legendre function, n is the number of iterations, Φ i represents the centrifugal force potential of the grid points and ω is the angular velocity of the Earth’s rotation;

[0012] Step 5: According to formula W i =U i +T i , calculate the actual gravity potential W of the i-th grid point i ;

[0013] Step 6: According to the formula Calculate the actual average gravity of i grid points Where G represents the gravitational constant and its value is 6.67259×10 -11 m 3 kg -1 s -2 , ρ represents the density of seawater and the value of ρ is 1.03 g / cm 3 ;

[0014] Step 7: Calculate the vertical distance h(i) from the sea surface to the geoid at the i-th grid point according to the formula h(i)=H(i)-N(i);

[0015] Step 8: According to the formula Calculate the geoid gravity potential W of the i-th grid point 0i ;

[0016] Step 9: According to the formula Determine the best estimate of the geoid gravity potential at grid points Among them, P pi is the weight of the i-th grid point.

[0017] The beneficial effect of the present invention is that it makes full use of dense high-quality gravity anomaly data and average sea level height data in the sea area to jointly determine the geoid gravity potential of the sea area, avoids the use of a priori gravity field model, simplifies the calculation process, improves the calculation accuracy, and provides a better idea for the autonomous determination of the geoid gravity potential, which is convenient for promotion and use.

[0018] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The figure is a flowchart of the method of the present invention.

[0020] Figure 2 This is a grayscale diagram of the gravity data distribution of DTU10 in this embodiment.

[0021] Figure 3 This is a grayscale diagram of the average sea level height data distribution of DTU10 in this embodiment.

[0022] Figure 4 This is a grayscale schematic diagram of the sea area gravity potential calculated in this embodiment minus the value 62636800. DETAILED DESCRIPTION

[0023] like Figures 1 to 4 As shown, a method for determining the geoid gravity potential by combining gravity anomaly and sea level height of the present invention comprises the following steps:

[0024] Step 1: read the sea area gravity anomaly grid data Δg(i) and the average sea level height grid data H(i), where i is the grid point number and i=1,2,...,N, and N is the total number of grid points;

[0025] Step 2: According to the Stokes theory formula Solve the geoid height N(i) of the i-th grid point, where R represents the average radius of the earth, j is a variable and j=1, 2, ..., i, λ represents the geodetic longitude of the grid point, represents the geodetic latitude of the grid point, ψ represents the spherical angular distance between the gravity anomaly data and the calculated grid point, and S(ψ) is the kernel function and

[0026] γ i represents the normal gravity of the ith grid point and represents the geodetic latitude of the ith grid point, γ0 represents the normal gravity of the reference ellipsoid and γ e represents the normal gravity at the equator and γ e The value is 9.7803253349ms -2 ;

[0027] Step 3: According to formula T i =N(i)·γ i , calculate the disturbed gravity potential T of the i-th grid point i ;

[0028] Step 4: According to the formula Calculate the normal gravity potential U of the i-th grid point i , where GM is a constant and GM = 3986005 × 10 8 m 3 s -2 , r represents the distance from the center of the sea grid to the center of the earth and a represents the semi-major axis of the reference ellipsoid and a=6378137m, E2=2F-F 2 , F represents the reference ellipsoid flattening and F = 0.00335281068118, C 20 is the first normal gravitational potential coefficient and C 20 =-0.001092, C 40 is the second normal gravitational potential coefficient and C 40 =0.00000237, C 60 is the third normal gravitational potential coefficient and C 60 =-0.00000000608347, represents the Legendre function, n is the number of iterations, Φ i represents the centrifugal force potential of the grid points and ω is the angular velocity of the Earth’s rotation;

[0029] Step 5: According to formula Wi =U i +T i , calculate the actual gravity potential W of the i-th grid point i ;

[0030] Step 6: According to the formula Calculate the actual average gravity of i grid points Where G represents the gravitational constant and its value is 6.67259×10 -11 m 3 kg -1 s -2 , ρ represents the density of seawater and the value of ρ is 1.03 g / cm 3 ;

[0031] Step 7: Calculate the vertical distance h(i) from the sea surface to the geoid at the i-th grid point according to the formula h(i)=H(i)-N(i);

[0032] Step 8: According to the formula Calculate the geoid gravity potential W of the i-th grid point 0i ;

[0033] Step 9: According to the formula Determine the best estimate of the geoid gravity potential at grid points Among them, P pi is the weight of the i-th grid point.

[0034] When used in the present invention, the ocean gravity data and average sea level height data adopt the DTU10 series grid data released by the Danish National Space Center. The data covers the entire ocean area with a resolution of 1′. The data is calculated using the altimetry data of 8 altimetry satellites for 12 years (1993-2004). The distribution of gravity data and average sea level height data is shown in Figure 2 and Figure 3 .

[0035] In the calculation, the density of seawater is taken as 1.03 g / cm 3 The reference ellipsoid used is WGS84 ellipsoid. Considering that the polar regions are ice areas and Antarctica, the calculation range is determined to be the sea area between 80 degrees north and south latitude. Finally, the geoid gravity potential value with a resolution of 1' in the global sea area is calculated. Figure 4 (Minus the constant value of 62636800). Remove the values ​​greater than 3 times the mean error and use the least squares adjustment (weighting the observations equally) to obtain the value of the sea area geoid gravity potential W0 = 62636857.28 ± 0.32m 2 / s 2 .

[0036] The present invention makes full use of dense high-quality gravity anomaly data and average sea level height data in the sea area to jointly determine the sea area geoid gravity potential, avoids the use of a priori gravity field model, simplifies the calculation process, improves calculation accuracy, provides a better idea for the autonomous determination of geoid gravity potential, and is easy to promote and use.

[0037] 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 still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for determining the geoid gravity potential by combining gravity anomaly and sea level height, characterized in that: The method comprises the following steps: Step 1: read the sea area gravity anomaly grid data Δg(i) and the average sea level height grid data H(i), where i is the grid point number and i=1,2,...,N, and N is the total number of grid points; Step 2: According to the Stokes theory formula Solve the geoid height N(i) of the i-th grid point, where R represents the average radius of the earth, j is a variable and j=1, 2, ..., i, λ represents the geodetic longitude of the grid point, represents the geodetic latitude of the grid point, ψ represents the spherical angular distance between the gravity anomaly data and the calculated grid point, and S(ψ) is the kernel function and γ i represents the normal gravity of the ith grid point and represents the geodetic latitude of the ith grid point, γ0 represents the normal gravity of the reference ellipsoid and γ e represents the normal gravity at the equator and γ e The value is 9.7803253349ms -2 ; Step 3: According to formula T i =N(i)·γ i , calculate the disturbed gravity potential T of the i-th grid point i ; Step 4: According to the formula Calculate the normal gravity potential U of the i-th grid point i , where GM is a constant and GM = 3986005 × 10 8 m 3 s -2 , r represents the distance from the center of the sea grid to the center of the earth and a represents the semi-major axis of the reference ellipsoid and a=6378137m, E2=2F-F 2 , F represents the reference ellipsoid flattening and F = 0.00335281068118, C 20 is the first normal gravitational potential coefficient and C 20 =-0.001092, C 40 is the second normal gravitational potential coefficient and C 40 =0.00000237, C 60 is the third normal gravitational potential coefficient and C 60 =-0.00000000608347, represents the Legendre function, n is the number of iterations, Φ i represents the centrifugal force potential of the grid points and ω is the angular velocity of the Earth’s rotation; Step 5: According to formula W i =U i +T i , calculate the actual gravity potential W of the i-th grid point i ; Step 6: According to the formula Calculate the actual average gravity of i grid points Where G represents the gravitational constant and its value is 6.67259×10 -11 m 3 kg -1 s -2 , ρ represents the density of seawater and the value of ρ is 1.03 g / cm 3 ; Step 7: Calculate the vertical distance h(i) from the sea surface to the geoid at the i-th grid point according to the formula h(i)=H(i)-N(i); Step 8: According to the formula Calculate the geoid gravity potential W of the i-th grid point 0i ; Step 9: According to the formula Determine the best estimate of the geoid gravity potential at grid points Among them, P pi is the weight of the i-th grid point.

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