CN113466959A - Local gravity field modeling method and system based on ground gravity measurement data - Google Patents
Local gravity field modeling method and system based on ground gravity measurement data Download PDFInfo
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Abstract
The invention provides a local gravity field modeling method and a system based on ground gravity measurement data, wherein the method collects and preprocesses ground gravity observation data in a research area, determines the spatial resolution of a gravity field model and the maximum expansion order of the gravity field model, low-pass filters the preprocessed data, removes the part higher than the maximum expansion order in the ground gravity observation data to obtain the filtered gravity observation data in the research area, then determines the closed boundary of the research area, obtains an orthogonal basis function group and an optimal basis function number through calculation, obtains the expansion coefficient of a Slepian method through calculation to obtain a mathematical model describing the gravity field in the research area, and finally calculates the gravity field signal of any point in the research area according to the mathematical model of the gravity field. The invention solves the problem that the classical spherical harmonic method can not be applied in the local range of the spherical surface by constructing the orthogonal basis function in the research region.
Description
Technical Field
The invention relates to the technical field of local gravity field modeling, in particular to a local gravity field modeling method and system based on ground gravity measurement data.
Background
The earth gravity field is a basic physical field of the earth, reflects the distribution, motion and change of substances in the earth system, is an important constraint for researching the motion state and the dynamic mechanism of the substances in the earth system, and can provide important basic geophysical information for urgent problems of resources, environment, disasters and the like faced by human beings. The ground gravity measurement is the gravity observation carried out on the land, absolute gravimeters and relative gravimeters are adopted to be mixed and networked, and the change trend of the gravity field along with the time is obtained through periodic point-to-point repeated measurement, for example, the method is adopted by a ground gravity observation system taking a Chinese crust motion monitoring network as a leading factor. The ground gravity measurement has the advantages that the repeatability of an observation position is good, the distance from a field source is short, the attenuation amplitude of a gravity signal is small, the obtained gravity field signal contains more frequency bands, the high-frequency part is more accurate, and the data of the ground gravity observation is more suitable for analyzing regional and near-surface material motion and migration phenomena due to the characteristics of the ground gravity observation. However, the ground gravity observation is also easily restricted by factors such as geographical environment, economic cost and the like, so that: 1. areas which are difficult to measure exist, such as oceans, the two poles, deserts, jungles and the like, and data cannot realize global coverage; 2. the measurement points are difficult to realize uniform and dense spatial distribution and are sparse on the whole. The distribution diagram of the ground gravity measurement data which is sparse and uneven in the local range is shown in fig. 1. The range A marks a research area which is a closed area on the spherical surface; the black triangles in the range a mark gravity measurement points and are spatially non-uniformly distributed in the research range.
If data are measured in a certain range to recover a gravity field model of the region, the data only cover the region and are distributed unevenly, so that the requirements of the classical spherical harmonic analysis theory on the data cannot be met (the basis functions do not meet the orthogonality in the region), and a new theory and a new method are needed for obtaining the region gravity field model which optimally reflects the characteristics of the gravity field in a research range. Slepian local spectrum analysis method is firstly proposed by D.Slepian, aims to solve the problem of time domain and frequency domain energy concentration under the condition of one-dimensional continuity, and is continuously developed and introduced into the field of gravity field research. According to the Slepian method, signal energy can be concentrated in a research area through constructing orthogonal basis functions in the research area, and the Slepian method is suitable for expressing the change of a gravity field of an area scale. Other local gravity field recovery methods which are widely applied also comprise a least square configuration method, a spherical crown harmonic analysis method, a Mascon method, a radial basis function and the like.
Based on Slepian local spectral analysis theory, the invention provides a local gravity field modeling method and system by using ground gravity observation data aiming at core problems of determination of model resolution, selection of number of basis functions and the like.
Disclosure of Invention
The invention provides a local gravity field modeling method based on ground gravity measurement data, which aims at solving the problems that the ground actual gravity measurement data only covers the range of an area, the measuring points are difficult to realize the uniform spatial distribution, the classical spherical harmonic analysis theory is not applicable on the basis of the ground gravity measurement data and the like. The invention also relates to a local gravity field modeling system based on the ground gravity measurement data.
The technical scheme of the invention is as follows:
a local gravity field modeling method based on ground gravity measurement data is characterized by comprising the following steps:
the first step is as follows: collecting ground gravity observation data in a research area, and preprocessing the collected ground gravity observation data;
the second step is as follows: determining the position of an observation point according to collected and preprocessed ground gravity observation data, determining the spatial resolution of a gravity field model by testing the recovery capability of the gravity field change based on the distribution of the positions of the observation points in a research area, and further determining the maximum expansion order of the gravity field model;
the third step: performing low-pass filtering on the preprocessed ground gravity observation data, and filtering out the part of the ground gravity observation data, which is higher than the maximum expansion order, to obtain filtered gravity observation data in a research area, wherein the frequency band of a gravity field signal contained in the filtered gravity observation data is within the maximum expansion order;
the fourth step: determining a closed boundary of the research area, calculating an orthogonal basis function set according to the maximum expansion order determined in the second step, and calculating the optimal basis function quantity based on the orthogonal basis function set and the closed boundary;
the fifth step: and calculating the expansion coefficient of the Slepian method according to the filtered gravity observation data obtained in the third step and the orthogonal basis function set obtained in the fourth step, and obtaining a mathematical model of the gravity field in the research area based on the expansion coefficient of the Slepian method and the optimal basis function number determined in the fourth step.
Preferably, the method further comprises a sixth step of calculating a gravity field signal of any point in the study area according to the mathematical model of the gravity field obtained in the fifth step.
Preferably, after the mathematical model of the gravitational field is obtained in the fifth step, the expansion coefficient of the Slepian method is further converted into the expansion coefficient of the spherical harmonic method, and the gravitational field signal at any point in the study area is calculated based on the expansion coefficient of the spherical harmonic method.
Preferably, the pre-processing in the first step includes gross error detection and solid tide, air pressure and instrument height correction of the gravity data and completes gravity net adjustment.
Preferably, the EGM2008 ultra-high-order gravitational field model is used for the low-pass filtering in the third step.
A local gravity field modeling system based on ground gravity measurement data, comprising:
a first module: collecting ground gravity observation data in a research area, and preprocessing the collected ground gravity observation data;
a second module: determining the position of an observation point according to collected and preprocessed ground gravity observation data, determining the spatial resolution of a gravity field model by testing the recovery capability of the gravity field change based on the distribution of the positions of the observation points in a research area, and further determining the maximum expansion order of the gravity field model;
a third module: performing low-pass filtering on the preprocessed ground gravity observation data, and filtering out the part of the ground gravity observation data, which is higher than the maximum expansion order, to obtain filtered gravity observation data in a research area, wherein the frequency band of a gravity field signal contained in the filtered gravity observation data is within the maximum expansion order;
a fourth module: determining a closed boundary of a research area, calculating an orthogonal basis function set according to the determined maximum expansion order in the second module, and calculating the optimal basis function quantity based on the orthogonal basis function set and the closed boundary;
a fifth module: and calculating the expansion coefficient of the Slepian method according to the filtered gravity observation data obtained in the third module and the orthogonal basis function set obtained in the fourth module, and obtaining a mathematical expansion model of the gravity field in the research area based on the expansion coefficient of the Slepian method and the determined optimal basis function number in the fourth module.
Preferably, the device further comprises a sixth module, and the gravity field signal of any point in the research area is calculated according to the mathematical development model of the gravity field obtained in the fifth module.
Preferably, after the mathematical model of the gravity field is obtained in the fifth module, the expansion coefficient of the Slepian method may be further converted into the expansion coefficient of the spherical harmonic method, and the gravity field signal at any point in the study region is calculated based on the expansion coefficient of the spherical harmonic method.
Preferably, the pre-processing in the first module includes gross error detection and solids tide, air pressure and instrument height correction of the gravity data and completes gravity net adjustment.
Preferably, an EGM2008 ultra-high-order gravitational field model is used for simulation experiment during low-pass filtering in the third module.
The invention has the beneficial effects that:
the invention provides a local gravity field modeling method based on ground gravity measurement data, which comprises the steps of preprocessing the collected ground gravity observation data after collecting the ground gravity observation data in a research area, testing the restoring capacity of the position distribution of observation points in the research area to gravity field change before starting modeling to determine the spatial resolution of a gravity field model, further determining the maximum expansion order of the gravity field model, carrying out low-pass filtering on the preprocessed ground gravity observation data before modeling, filtering out the part of the ground gravity observation data, which is higher than the maximum expansion order, improving the model resolving precision, determining the closed boundary of the research area, calculating an orthogonal basis function group according to the determined maximum expansion order, calculating the optimal basis function number based on the orthogonal basis function group and the closed boundary, and calculating the Slepian method according to the obtained filtered ground gravity observation data and the obtained orthogonal basis function group And obtaining a mathematical expansion model for describing the gravity field in the research area based on the expansion coefficient of the Slepian method and the determined optimal basis function number, and finally calculating the gravity field signal of any point in the research area according to the mathematical model of the gravity field. According to the invention, through constructing the orthogonal basis functions in the research region, the spectrum energy is effectively concentrated in the research region, the problem that the classical spherical harmonic method cannot be applied in the local range of the spherical surface is solved, and meanwhile, the same-order classical spherical harmonic expansion can be approached by using fewer basis functions, so that the number of unknowns required to be solved during modeling is far less than that of the classical spherical harmonic method, the calculation time is greatly shortened, errors caused by grid-screening and other treatments on sparse observation data are avoided, and the obtained model result is stable and reliable. In addition, the optimal expansion order and the number of basis functions can be automatically determined through an optimal criterion during modeling, the automation degree of model calculation is improved, and compared with a conventional spatial interpolation method, the algorithm provided by the invention can avoid the overfitting phenomenon of interpolation, can obtain the expansion of ground observation data in a frequency domain, is beneficial to extracting the gravity change signal of a specific frequency band in the ground observation data, and can better analyze the time-space association between the gravity change signal and the researched physical phenomenon, thereby obtaining a more thorough analysis result.
The invention also relates to a local gravity field modeling system based on ground gravity measurement data, which corresponds to the local gravity field modeling method based on ground gravity measurement data and can be understood as a system for realizing the local gravity field modeling method based on ground gravity measurement data, the system preprocesses the collected ground gravity observation data through the mutual cooperative work of five modules which are executed in sequence, tests the restoring capability of gravity field change based on the position distribution of observation points in a research area before the modeling is started to determine the spatial resolution of a gravity field model so as to determine the maximum expansion order of the gravity field model, low-pass filters the preprocessed ground gravity observation data before the modeling, filters off the part higher than the maximum expansion order in the ground gravity observation data, and improves the resolving precision of the model, obtaining filtered gravity observation data in a research area, then determining a closed boundary of the research area, calculating an orthogonal basis function group according to a determined maximum expansion order, calculating an optimal basis function number based on the orthogonal basis function group and the closed boundary, calculating an expansion coefficient of a Slepian method according to the obtained filtered ground gravity observation data and the obtained orthogonal basis function group, obtaining a mathematical expansion model describing a gravity field in the research area based on the expansion coefficient of the Slepian method and the determined optimal basis function number, and finally calculating a gravity field signal of any point in the research area according to the mathematical model of the gravity field. The system can obtain a reliable gravity field model result and can accurately reflect the motion and the spatial and temporal evolution process of the substances in the earth system.
Drawings
Fig. 1 is a schematic diagram of sparse and uneven ground gravity measurement data distribution in a local range.
Fig. 2 is a flowchart of the local gravity field modeling method based on the ground gravity measurement data according to the present invention.
Fig. 3 is a working schematic diagram of the local gravity field modeling system based on the ground gravity measurement data according to the present invention.
Detailed Description
For a clearer understanding of the contents of the present invention, reference will be made to the accompanying drawings and examples.
The invention relates to a local gravity field modeling method based on ground gravity measurement data, which can also be called as a local gravity field modeling method based on sparse ground gravity measurement data, and the flow of the local gravity field modeling method is shown in figure 2, and the method comprises the following steps: the first step is as follows: collecting ground gravity observation data in a research area, and preprocessing the collected ground gravity observation data; the second step is as follows: determining the position of an observation point according to collected and preprocessed ground gravity observation data, determining the spatial resolution of a gravity field model by testing the recovery capability of the gravity field change based on the distribution of the positions of the observation points in a research area, and further determining the maximum expansion order of the gravity field model; the third step: low-pass filtering the preprocessed ground gravity observation data, and filtering out the part of the ground gravity observation data which is higher than the maximum expansion order to obtain the gravity observation data after filtering in the research area, wherein the gravity field signal frequency band contained in the gravity observation data after filtering is within the maximum expansion order; the fourth step: determining a closed boundary of the research area, calculating an orthogonal basis function set according to the maximum expansion order determined in the second step, and calculating the optimal basis function quantity based on the orthogonal basis function set and the closed boundary; the fifth step: calculating an expansion coefficient of the Slepian method according to the filtered gravity observation data obtained in the third step and the orthogonal basis function set obtained in the fourth step, and obtaining a mathematical expansion model of the gravity field in the research area based on the expansion coefficient of the Slepian method and the optimal basis function number determined in the fourth step; preferably, the sixth step: and calculating the gravity field signal of any point in the research area according to the mathematical model of the gravity field. The local gravity field modeling method based on the ground gravity measurement data can effectively concentrate the frequency spectrum energy in a research area as much as possible, the number of unknowns required to be solved during modeling is far less than that of a classical spherical harmonic method, the calculation time is greatly shortened, grid formation and other preprocessing processes are not required in practical application, sparse ground gravity observation data with uneven spatial distribution can be directly expanded, errors caused by grid formation and other processing on the sparse observation data are avoided, and the obtained model result is stable and reliable. Meanwhile, the modeling method can approximate the same-order classical spherical harmonic expansion by using a small number of basis functions, and the number of unknowns required to be solved is about one percent of the same-order classical spherical harmonic expansion generally. When the number of observed data is limited (more than the number of solved unknowns), the modeling method of the invention can still obtain stable and reliable model results.
The following describes each step of the local gravity field modeling method based on the ground gravity measurement data in detail.
The method comprises the following steps of firstly, collecting and preprocessing ground gravity observation data: and collecting ground gravity observation data in the research area, and preprocessing the collected ground gravity observation data. Preferably, the preprocessing includes gross error detection and various corrections, such as solid tide, air pressure and instrument high corrections to the gravity data, and gravity net adjustment is performed.
A second step of testing the spatial resolution of the data: and determining the position of an observation point according to the collected ground gravity observation data, and determining the spatial resolution of the gravity field model by testing the recovery capability of the gravity field change based on the position distribution of the observation point in the research area, thereby determining the maximum expansion order of the gravity field model.
Since the positions of the gravity observation points in the study region are sparsely distributed and uneven (non-uniform grids), the spatial resolution of the gravity field model cannot be directly determined based on the criteria such as the sampling theorem, before the modeling is started, the positions of the observation points are determined according to the collected ground gravity observation data, and then the spatial resolution of the gravity field model is determined by testing the recovery capability of the gravity field change based on the positions of the observation points in the study region, so as to determine the maximum expansion order L of the gravity field model.
A third step of removing the high order part of the observation data: and performing low-pass filtering on the preprocessed ground gravity observation data, and filtering out the part of the ground gravity observation data higher than the maximum expansion order to obtain the gravity observation data after filtering in the research area, wherein the frequency band of a gravity field signal contained in the gravity observation data after filtering is within the maximum expansion order.
The ground gravity observation data includes a signal (full band) from 0 to ∞ order, and when modeling the gravity field, the signal cannot be expanded to ∞ order, and can be truncated to only a certain maximum order, that is, the maximum order determined in the second stepAnd the large expansion order L is recorded as L-order (L & lt & infinity), and if the ground gravity data is directly used for modeling the L-order gravity field, the part of the data higher than the L-order can generate leakage to a low-order coefficient in the resolving process, so that the resolving precision of the model is influenced. In order to weaken the influence, the part higher than the L order in the ground gravity observation data needs to be removed before modeling, and the process filters the part higher than the L order in the ground gravity observation data by low-pass filtering the ground gravity observation data preprocessed in the first step to obtain the filtered gravity observation data in the research area, and records the gravity observation data as the gravity observation data which is recorded in the research area
(i.e., removing the high-order portion of the ground gravity observation data, when only a few values are present, i.e., 1, 2obs，NobsTotal number of observation points), and the gravity observation data includes a gravity field signal frequency band within the maximum expansion order. Preferably, the EGM2008 ultra-high order gravity field model is used as the known field for low pass filtering, and then the part of the known gravity field higher than the L order is removed by combining the position distribution of the actual ground observation point. Furthermore, filter parameters are required to be adjusted before the low-pass filter is used, the L-order result of the known field and the filtered result are compared, the minimum residual error between the L-order result and the filtered result is the optimal low-pass filter, and after the optimal low-pass filter is determined, the ground gravity observation data are filtered, and the part, higher than the L-order, in the data are removed.
And a fourth step of optimizing the number of basis functions: and determining a closed boundary of the research area, calculating an orthogonal basis function set according to the maximum expansion order determined in the second step, and calculating the optimal basis function number based on the orthogonal basis function set and the closed boundary.
After the spatial resolution of the model and the maximum expansion order L of the model are determined, the number of basis functions of the local gravity field modeling is optimized. First, the closed boundary of the study area (denoted by R and simultaneously the whole sphere by Ω) is determined, and then the set of orthogonal basis functions is calculated according to the maximum expansion order L determined in the second step, as follows:
in the above formula, the first and second carbon atoms are,
is the spherical coordinate of the observation point, theta is the weft remainders (theta is more than or equal to 0 and less than or equal to pi),
is longitude
L, m are respectively the order and the number of times of expansion, L is the highest order,
is a classical surface spherical harmonic function, slmIs the Slepian coefficient, and is the Slepian coefficient,
for the set of orthogonal basis functions, the energy is maximized within the region of interest by the expression:
in the above formula, the first and second carbon atoms are,
has orthogonal characteristics in the whole sphere and in the research area, and has (L +1)2Actually, only a small number of basis functions are completely concentrated inside a research area, most of the basis functions are concentrated outside the research area (influence on gravity change in the research area is small), the calculation amount and the required storage space in the resolving process can be greatly reduced by optimizing the number of the basis functions and extracting the basis functions concentrated inside the research area, and meanwhile, the stability of the resolving process and the accuracy of the restored model result are ensured, and the optimal number of the basis functions is calculated according to the following formula:
in the formula, λαIs determined based on the closed boundary and the set of orthogonal basis functions in equation (2).
Step five, resolving model parameters: and calculating the expansion coefficient of the Slepian method according to the filtered gravity observation data obtained in the third step and the orthogonal basis function set obtained in the fourth step, and obtaining a mathematical expansion model of the gravity field in the research area based on the expansion coefficient of the Slepian method and the optimal basis function number determined in the fourth step.
Wherein L-order gravitational field signals in the region of interest
The expression of (a) is shown as:
in the formula, L-order gravitational field signal
From the third step, the set of orthogonal basis functions at the ground observation point is determined
Determined by the fourth step, determine
And
then, the expansion coefficient v of Slepian method can be solved according to the least square methodα(i.e., model parameters), it should be noted that the gravity field signal obtained in the third step
(i.e. earth gravity observation data with the high order part removed, only several values, i ═ 1, 2, …, Nobs，NobsTotal number of observation points), the number N of which ground gravity observation needs to be ensuredobsIs greater than the optimal number of basis functions NoptOtherwise, the solution process is underdetermined.
Based on the expansion coefficient of the Slepian method and the optimal basis function number determined in the fourth step, obtaining the optimal approximation result of the gravity field in the research area (namely obtaining a gravity field mathematical expansion model), and calculating according to the following formula:
preferably, the method further comprises a sixth step of calculating a gravity field signal at any point in the study area according to the mathematical model of the gravity field obtained in the fifth step.
After a mathematical model describing the gravitational field in the research area is obtained, any point in the research area can be calculated according to the formula (5)
Gravity field signal of
Preferably, after the mathematical model of the gravitational field is obtained in the fifth step, the expansion coefficient of the Slepian method is converted into the expansion coefficient of the classical spherical harmonic method, and the gravitational field signal at any point in the study region is calculated based on the expansion coefficient of the spherical harmonic method.
The expansion coefficient of the classical spherical harmonic method is calculated according to the following formula:
v is to beαExpansion coefficient C converted into classical spherical harmonic methodlmFor the purpose of facilitating the use of the inventionFamily, get ClmThen, the user can calculate any point in the research area according to the classical spherical harmonic formula
G of (A)LCalculated according to the following formula:
wherein L and m are respectively the order and the number of times of expansion, L is the highest order,
is a classical surface spherical harmonic function.
The gravity field signals obtained in the formula (5) and the formula (7) are described
The corresponding maximum expansion order is L order.
The present invention also relates to a local gravity field modeling system based on ground gravity measurement data, which corresponds to the above-mentioned local gravity field modeling method based on ground gravity measurement data, and can be understood as a system for implementing the local gravity field modeling method based on ground gravity measurement data, and as shown in fig. 3, the system is a working schematic diagram of the system, and the system includes:
a first module: collecting ground gravity observation data in a research area, and preprocessing the collected ground gravity observation data; preferably, the pre-processing includes gross error detection and high-level corrections of the absolute gravity data for solid tide, air pressure and instrumentation, and completes gravity net adjustment.
A second module: determining the position of an observation point according to collected and preprocessed ground gravity observation data, determining the spatial resolution of a gravity field model by testing the recovery capability of the gravity field change based on the distribution of the positions of the observation points in a research area, and further determining the maximum expansion order of the gravity field model;
a third module: low-pass filtering the preprocessed ground gravity observation data, and filtering out the part of the ground gravity observation data higher than the maximum expansion order to obtain the filtered gravity observation data in the research area; preferably, an EGM2008 ultra-high-order gravity field model is adopted for testing during low-pass filtering, further, filter parameters are required to be adjusted before low-pass filtering, the result of the known field maximum expansion order and the result after filtering are compared, the minimum residual error between the two results is the optimal low-pass filter, after the optimal low-pass filter is determined, ground gravity observation data are filtered, and the part of the data higher than the maximum expansion order is removed.
A fourth module: determining a closed boundary of a research area, calculating an orthogonal basis function set according to the determined maximum expansion order in the second module, and calculating the optimal basis function quantity based on the orthogonal basis function set and the closed boundary;
a fifth module: and calculating the expansion coefficient of the Slepian method according to the filtered gravity observation data obtained in the third module and the orthogonal basis function set obtained in the fourth module, and obtaining a mathematical model of the gravity field in the research area based on the expansion coefficient of the Slepian method and the determined optimal basis function number in the fourth module. Preferably, after the mathematical model of the gravity field is obtained, the expansion coefficient of the Slepian method is converted into the expansion coefficient of the spherical harmonic method, and the gravity field signal of any point in the research area is calculated based on the expansion coefficient of the spherical harmonic method.
Preferably, the device further comprises a sixth module, and the gravity field signal of any point in the study area is calculated according to the mathematical model of the gravity field obtained in the fifth module.
The invention provides a local gravity field modeling method and system based on ground gravity measurement data. By constructing orthogonal basis functions in a research region, spectrum energy is effectively concentrated in the research region, the problem that a classical spherical harmonic method cannot be applied in a spherical local range is solved, and the same-order classical spherical harmonic expansion can be approximated by fewer basis functions, so that the number of unknowns required to be solved during modeling is far less than that of the classical spherical harmonic method, the calculation time is greatly shortened, errors caused by grid-networking and other processing of sparse observation data are avoided, and the obtained model result is stable and reliable. Meanwhile, the optimal expansion order and the number of basis functions can be automatically determined through an optimal criterion during modeling, the automation degree of model calculation is improved, and compared with a conventional spatial interpolation method, the algorithm provided by the invention can avoid the phenomenon of overfitting of interpolation, can obtain the expansion of ground observation data in a frequency domain, is beneficial to extracting the gravity change signal of a specific frequency band in the ground observation data, and can better analyze the time-space association between the gravity change signal and the researched physical phenomenon, thereby obtaining a more thorough analysis result.
The gravity observation data obtained by the actual ground gravity network is very complex, the point location spatial distribution of the data may be very uneven, or systematic errors which are difficult to eliminate may still be contained in the data after various corrections are completed. Point position distribution directly influences resolving of model parameters and influences reliability of a gravity field modeling result; systematic errors can be transmitted to a final model result along with a resolving process, and deviation is caused to a resolving result. Whether the point location distribution is reasonable can be judged by the second step of the invention; whereas systematic deviations need to be verified by other independent gravity observations. The best possible conditions for use of the invention: the point location distribution of the ground observation data is reasonable, the observation of the ground gravity observation data is accurate, and no obvious system error exists. At the moment, the local gravity field modeling method based on the ground gravity measurement data can obtain a reliable gravity field model result, and more accurately reflects the material motion and the time-space evolution process in the earth system.
It should be noted that the above-mentioned embodiments enable a person skilled in the art to more fully understand the invention, without restricting it in any way. Therefore, although the present invention has been described in detail with reference to the drawings and examples, it will be understood by those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention.
Claims (10)
1. A local gravity field modeling method based on ground gravity measurement data is characterized by comprising the following steps:
the first step is as follows: collecting ground gravity observation data in a research area, and preprocessing the collected ground gravity observation data;
the second step is as follows: determining the position of an observation point according to collected and preprocessed ground gravity observation data, determining the spatial resolution of a gravity field model by testing the recovery capability of the gravity field change based on the distribution of the positions of the observation points in a research area, and further determining the maximum expansion order of the gravity field model;
the third step: performing low-pass filtering on the preprocessed ground gravity observation data, and filtering out the part of the ground gravity observation data, which is higher than the maximum expansion order, to obtain filtered gravity observation data in a research area, wherein the frequency band of a gravity field signal contained in the filtered gravity observation data is within the maximum expansion order;
the fourth step: determining a closed boundary of the research area, calculating an orthogonal basis function set according to the maximum expansion order determined in the second step, and calculating the optimal basis function quantity based on the orthogonal basis function set and the closed boundary;
the fifth step: and calculating the expansion coefficient of the Slepian method according to the filtered gravity observation data obtained in the third step and the orthogonal basis function set obtained in the fourth step, and obtaining a mathematical model of the gravity field in the research area based on the expansion coefficient of the Slepian method and the optimal basis function number determined in the fourth step.
2. The method according to claim 1, further comprising a sixth step of calculating a gravity field signal at any point in the area of interest based on the mathematical model of the gravity field obtained in the fifth step.
3. The local gravitational field modeling method based on ground gravity measurement data according to claim 1, characterized in that after the mathematical model of the gravitational field is obtained in the fifth step, the expansion coefficient of the Slepian method is further converted into the expansion coefficient of a spherical harmonic method, and the gravitational field signal at any point in the study area is calculated based on the expansion coefficient of the spherical harmonic method.
4. The method according to claim 1, wherein the preprocessing in the first step comprises gross error detection and solid tide, air pressure and instrument height correction of gravity data, and gravity net adjustment is performed.
5. The method according to claim 1, wherein the EGM2008 ultra-high order gravity field model is used for the low pass filtering in the third step.
6. A local gravity field modeling system based on ground gravity measurement data, comprising:
a first module: collecting ground gravity observation data in a research area, and preprocessing the collected ground gravity observation data;
a second module: determining the position of an observation point according to collected and preprocessed ground gravity observation data, determining the spatial resolution of a gravity field model by testing the recovery capability of the gravity field change based on the distribution of the positions of the observation points in a research area, and further determining the maximum expansion order of the gravity field model;
a third module: performing low-pass filtering on the preprocessed ground gravity observation data, and filtering out the part of the ground gravity observation data, which is higher than the maximum expansion order, to obtain filtered gravity observation data in a research area, wherein the frequency band of a gravity field signal contained in the filtered gravity observation data is within the maximum expansion order;
a fourth module: determining a closed boundary of a research area, calculating an orthogonal basis function set according to the determined maximum expansion order in the second module, and calculating the optimal basis function quantity based on the orthogonal basis function set and the closed boundary;
a fifth module: and calculating the expansion coefficient of the Slepian method according to the filtered gravity observation data obtained in the third module and the orthogonal basis function set obtained in the fourth module, and obtaining a mathematical expansion model of the gravity field in the research area based on the expansion coefficient of the Slepian method and the determined optimal basis function number in the fourth module.
7. The ground gravity measurement data-based local gravitational field modeling system according to claim 6, further comprising a sixth module for calculating a gravitational field signal at any point in the area of interest based on a mathematical expansion model of the gravitational field obtained in said fifth module.
8. The ground gravity measurement data-based local gravitational field modeling system according to claim 6, wherein after obtaining the mathematical model of the gravitational field in the fifth module, the fifth module is further configured to convert the expansion coefficient of the Slepian method into the expansion coefficient of a spherical harmonic method, and calculate the gravitational field signal at any point in the study area based on the expansion coefficient of the spherical harmonic method.
9. The system of claim 6, wherein the preprocessing in the first module comprises gross error detection and solid tide, barometric pressure and instrument height correction of gravity data and gravity net adjustment.
10. The ground-based gravity measurement data based local gravity field modeling system according to claim 6, wherein EGM2008 ultra high order gravity field model is used for simulation experiment during low pass filtering in the third module.
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