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The earth's gravity field is a basic physical event that reflects the spatial distribution, movement and change of the earth's materials, and restricts the earth and adjacent space, which is not only a physical field, but also one of the earth's inherent physical characteristics. On the surface, the coverage of the ocean reaches 70% of the earth's surface area, so the marine gravity field constitutes a key part of the earth's gravity field, which has become an important research topic in the study of earth science, and also provides non-negligible research value for improving the earth's gravity field.
Nowadays, marine gravity field plays an important application value in seafloor depth prediction, plate tectonic and lithospheric structure research, submarine volcanic research, oil exploration, polar ice sheet monitoring, inertial navigation field, global climate and dynamic monitoring of sea level change.
Development of satellite altimetry technology
In the 70s of the 19th century, NASA first proposed the idea of using altimetry technology to reflect marine geoid information. However, due to the limited level of development in the field of aviation in the early stage, it was not until the 70s of the 20th century, after the rapid development of satellite altimetry as a new technology, altimetry technology began to be applied to the acquisition of accurate sea surface height in a wide sea area.
In 1971, NASA launched the first experimental satellite Skalab carrying an altimeter, so the mode of carrying an altimeter on an altimeter satellite was officially opened. In 1975, NASA launched GEOS-3, the first sea surface topography satellite dedicated to sea surface altitude determination, which effectively solved the complex sea surface topography problem in the vast sea area. As shown in the figure, due to the rapid development of satellite altimetry technology, the number of altimetry satellites has also changed greatly, especially in Western countries with strong aerospace strength, the number of altimetry satellites accounts for more than 80%, up to now, according to statistics, the number of altimetry satellites is nearly 20.
Satellite altimetry technology inverts the progress of marine gravity field
At present, there are two main series of global ocean gravity field models in the world: the SS series model constructed by the Scripps Oceanographic Institution in the United States; The KMS-DNSC-DTU series model constructed by the Danish University of Science and Technology. Generally, the quality of the marine gravity field model inverted by altimetry technology is mainly determined by two factors: its accuracy and spatial resolution, and the factors affecting these two aspects are mainly determined by the following five aspects: satellite measurement accuracy; Density of satellite trajectory coverage; Various orbit fixing technologies; Correlation error filtering processing technology; Introduced correlation correction model accuracy.
Due to the rapid development of aeronautical space technology, the gradual accumulation of altimetry satellite data, the gradual improvement of orbit accuracy, the increasingly perfect data processing technology, the introduction of high-order and high-precision gravity field models and sea surface topography models, etc., the spatial resolution and accuracy of marine gravity field models have gradually improved, so their application in oceanography, geophysics, geodesy, geodynamics and other fields has good prospects.
Principle of satellite altimetry
The principle of satellite altimetry technology is mainly to use the pulse signal transmitted by the radar altimeter mounted on the altimetry satellite to reflect to the receiving antenna to determine the time required, and then use the speed of light propagation in the air to calculate the distance value from the satellite to the reflection point of the sea surface. The specific schematic diagram is shown in the figure.
Selection of reference tracks
Since collinear processing is to calculate a lot of trajectory data into a single trajectory, this trajectory is the reference trajectory. First of all, we need to obtain a reference trajectory with better altimetry data on the trajectory, because obtaining a better reference trajectory is more conducive to calculating the sea surface height. At present, the orbital parameter method and the measured data method are often used for the selection of the reference trajectory, and the orbital parameter method refers to the orbital parameters set by the altimetry satellite to first calculate the position of the normal point in the orbit of the satellite subsatellite, and then obtain the set theoretical reference position.
However, the theoretical calculation of the reference trajectory is more complicated and there are many trajectories, and more trajectories are not sure whether they are in the ocean, which will further increase the complexity and difficulty of further determining the actual reference trajectory, and will also obtain a smoother satellite orbit, resulting in many problems that the actual noise cannot be reflected. Relatively speaking, the measured data method is relatively simple, that is, the data of all periods are usually summarized, and a trajectory with a more uniform distribution of trajectory data and a large distribution of data volume is selected as a reference trajectory, but there will be obvious result randomness and the result will change with the change of the external environment.
Obtain the sea surface height value at the normal point of the reference trajectory
After obtaining the reference trajectory in the experimental area, it is necessary to further obtain the sea surface height value at the normal point of the reference trajectory. At present, there are two main calculation methods for obtaining normal points: straight line fitting method; Distance-weighted average method. Among them, the straight-line fitting method is to use the fitting method to fit the collinear data, and the sea surface height at the normal point on the reference trajectory is obtained after averaging the fitted data.
However, the distance-weighted average method selects the value of a certain number of points with similar normal point size on the non-reference trajectory and attributes it to the normal point of the reference trajectory, and then weights the calculated data to obtain the sea level high data value of the normal point on the reference trajectory. Compared with the straight-line fitting method, the distance-weighted average method participates in the calculation of more data, which can more approximate the actual value of the normal point on the trajectory, and can avoid accidental error to a large extent, so it is more conducive to the acquisition of high sea surface values.
Experimental data from altimetry satellites
With the rapid development of space technology, altimetry satellites are increasing, which provides enough data sources for altimetry technology to invert the marine gravity field. Because the accuracy and resolution of the ocean gravity field are not only related to the amount of data of altimetry satellites, but also inseparable from the data type of altimetry satellites. The specific data types are shown in the following table. For example, during the period from May 2012~June 2013, when the Jason-1 altimetry satellite was about to stop operating, the spatial distribution became denser by changing from an equatorial distance of 315 km to 7 km, which had a significant impact on inverting the ocean gravity field with high accuracy and high spatial resolution.
The above table shows the two data modes generated by the altimetry satellite Jason-1, and the different orbital spacing of different modes also leads to changes in period, and the specific trajectory distribution is shown in the figure.
As shown in the figure, the first phase of the Jason-1 altimetry satellite, Phase 1, is too spaced compared to the GM data trajectories of the final stage, which indicates that the data in the last stage area is densely distributed. Therefore, this paper mainly processes GM type data, and inverts the marine gravity field for local sea areas of 2°×2° (region 1: longitude 112°E~114°E, latitude 12°N~14°N, region 2: longitude 124°E~126°E, latitude 24°N~26°N).
Perpendicular deviation
At present, since there is no suitable model for external testing of perpendicular deviation, EGM2008 is usually used for testing, and the figure is a reference diagram of the residual perpendicular deviation component of 2′×2′ obtained with EGM2008 as the reference field.
Examination between inversion results and ocean gravity field models
In order to prove the correctness of the results of the research results in the selected area, this paper conducts external and internal checks on the marine gravity field acquired in the study area. Among them, the internal inspection is mainly for the work of various global ocean gravity field models, and the external inspection is mainly to compare the inversion results with the ship survey data.
This paper selects the DTU17 in the DTU series of the Andersen team of the internationally recognized Danish University of Science and Technology and the SSV28.1 marine gravity field model of the SS series of the Sandwell team of the American Institute of Oceanology, which summarizes satellite altimetry data, ship survey data, earth gravity field data, aeronautical gravity field data, etc., and the marine gravity field model in the study area is shown in the figure below. For the selection of ship survey data, the global ocean gravity dataset provided by the United States (NGDC) is mainly used.
Research on the theory and method of traditional encryption reconstruction of marine gravity reference map
Since the highest spatial resolution of the reference map of the ocean gravity reference map inverted by satellite altimetry technology is 1′×1′, which greatly limits the application of the marine gravity reference map for seabed resource exploration, underwater navigation and other fields, it is necessary to interpolate and reconstruct the inverted gravity reference map to obtain the gravity reference map with limited accuracy loss but higher spatial resolution. The following table shows the results of several commonly used interpolation reconstruction methods for interpolation reconstruction experiments.
The statistical results in the table below show that traditional kriging has better results than several other interpolation reconstruction methods. However, the traditional kriging interpolation method still has a large accuracy loss in the interpolation reconstruction process of ocean gravity reference map, so this paper will improve on the traditional kriging interpolation method and propose a method with less accuracy loss while increasing spatial resolution.
Based on the new three-dimensional correction method of mean sea level
With the improvement of spatial positioning technology, the research and application fields of altimetry technology have been further expanded and deepened, and it has been able to provide a geoid with a unified elevation datum and high precision and high spatial resolution for the ocean area. The indirect application of satellite altimetry technology is to invert the ocean gravity field, by first obtaining the average sea level height value (that is, removing the value of the sea surface topography), and then combining the geoid transformation gravity field formula to obtain the marine gravity field. The figure is a diagram of the relationship between the geoid and mean sea level.
Verification of the mean sea level three-dimensional correction method
In order to further verify the effectiveness and reliability of the new three-dimensional mean sea level correction method based on generalized index model, this paper performs encryption reconstruction experiments on a variety of ocean gravity reference maps with different spatial resolutions, such as 4′×4′ encryption for 2′×2′ and 1′×1′, 3′×3′ encryption to 1′×1′, 2′×2′ encryption to 1′×1′, etc.
First, the selected area was experimented with traditional kriging two-dimensional interpolation, and the obtained ocean gravity reference map is shown in Figure 5-6. At the same time, the error approximation at the 3D grid point corresponding to the figure below. By comparing the four maps (a), (b), (c) and (d) in the figure, it is found that there are many regional differences (such as northwest region and other individual regions) in the ocean gravity reference map after encrypted reconstruction of data with different starting spatial resolution.
Then, the error approximation plots (a), (b), (c), and (d) at the three-dimensional grid points in the comparison plot can be obtained, and the approximation error gradually decreases as the spatial resolution of the original data increases. For example, the error approximation range of Figure (a) is about -30~15mGal, and the error approximation range of Figure (d) is about -5~3mGal.
summary
The satellite altimetry data are preprocessed by collinear processing method, and then the weighted intersection adjustment method is used to carry out comprehensive adjustment processing, which can improve the accuracy of sea level height at the intersection. The experimental results show that the rms at the intersection can be reduced from 6.24 cm to 4.63 cm by this method.
On the basis of satellite altimetry data, processing and weighted adjustment, the inversion of marine gravity field in local areas of the South China Sea was completed, and the spatial resolution of 2′×2′ perpendicular deviation and gravity anomaly reference maps of the two regions were obtained. Compared with the reference gravity field EGM2008, the root mean square error is less than 2 arcseconds, and it is better than 1 arcsecond in the vast sea.
For the acquired ocean gravity field, by comparing with the ship survey data, the accuracy of region 1 reached 4.7482 mGal, and the accuracy of region 2 was 4.8437 mGal, both better than 5 mGal. Therefore, the regional marine gravity field can provide some reference gravity data for the insufficient marine gravity data of continental ships.
Various research on the encryption reconstruction of ocean gravity anomaly datum maps is carried out, and a new encryption reconstruction method based on the traditional kriging interpolation algorithm is proposed. The 4′×4′, 3′×3′ and 2′×2′ ocean gravity anomaly datum maps were encrypted to 1′×1′ ocean gravity anomaly datum maps as an example, and the improved three-dimensional correction method of mean sea level was experimentally verified, and the accuracy of the traditional kriging two-dimensional interpolation method was improved by 62.25%, 140.92% and 104.93%, respectively.
Therefore, the high-precision and high-spatial resolution gravity reference map for underwater gravity matching navigation requirements has important research significance.