CN113985490A - Method and device for performing surface gravity simulation by using terrain and crust density data - Google Patents
Method and device for performing surface gravity simulation by using terrain and crust density data Download PDFInfo
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Abstract
The invention belongs to the technical field of physical geodetic survey, and particularly relates to a method and a device for performing surface gravity simulation by using terrain and crust density data, wherein the method comprises the steps of determining the simulation range of the surface gravity data, and establishing a terrain and crust density database in the region by combining the terrain data and the crust density data; according to the database, calculating the terrain correction of the area under a certain resolution; calculating interlayer correction of the region under the same resolution according to the database; according to the database, calculating the balance correction of the area under the same resolution; according to the equilibrium theory, combining terrain correction, interlayer correction and equilibrium correction, the regional space gravity anomaly is constructed. The method utilizes the equilibrium theory and combines high-resolution topographic data and geophysical information (crustal layering and density) to fill blank space gravity data so as to improve the simulation precision.
Description
Technical Field
The invention belongs to the technical field of physical geodetic survey, and particularly relates to a method and a device for performing surface gravity simulation by using topographic and crust density data.
Background
Currently, gravity data padding in blank areas is generally divided into three methods, one is a model padding method, the other is a neighboring data interpolation method, and the other is an equilibrium theory padding method.
(1) Model filling method
The model filling method mainly utilizes the global gravitational field model to calculate the earth surface gravitational field data. The establishment and development of the ultra-high-order gravity field model improve the approximate precision of the global gravity field. However, this method has the following drawbacks: firstly, a position coefficient model is calculated under a sphere approximation condition, the earth is an irregular sphere, and the sphere approximation process has errors, so that the accuracy of the calculated earth surface gravity data is low; secondly, basic data of the structure bit coefficient model mainly come from data measured by a gravity satellite and ground surface measured data, the flight height of the gravity satellite is high, so that the basic data can only reflect low and medium frequency signals of earth gravity data, high frequency and ultrahigh frequency signals of the gravity satellite cannot be obtained by the gravity satellite method, and furthermore, the ground surface gravity data of the structure bit coefficient are extremely unevenly distributed, so that the ground surface gravity data calculated by the bit coefficient model has great system errors, and the overall calculation precision is poor;
(2) method of interpolation of adjacent data
The 'adjacent data interpolation method' obtains points in an interpolation radius according to mathematical interpolation models such as shepard models and Kriging models by searching gravity observation points in a certain radius. The method requires that the gravity points with certain resolution are measured in advance in the blank area of the gravity data, so that the manual workload is increased, the workload of filling the blank area gravity data is increased, and if the data distribution is sparse and the interpolation radius is usually far larger than the grid resolution, the method cannot be realized.
(3) Equilibrium theory filling method
The 'equilibrium theory filling method' is based on equilibrium theory and utilizes global high-resolution topographic data to simulate gravity data, but the method considers the density of the crust as constant density, and the approximation on the density term directly brings systematic errors of the simulated data.
Disclosure of Invention
Aiming at the defect of blank space filling of gravity data in the prior art, the invention provides a method and a device for performing surface gravity simulation by using terrain and crust density data, which are used for filling blank space gravity data by using a balance theory and combining high-resolution terrain data and geophysical information (crust layering and density) so as to improve simulation precision.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a method for performing surface gravity simulation by using terrain and crust density data, which comprises the following steps:
determining the simulation range of the earth surface gravity data, and establishing a terrain and crust density database of the region by combining terrain data and crust density data;
according to the database, calculating the terrain correction of the area under a certain resolution;
calculating interlayer correction of the region under the same resolution according to the database;
according to the database, calculating the balance correction of the area under the same resolution;
according to the equilibrium theory, combining terrain correction, interlayer correction and equilibrium correction, the regional space gravity anomaly is constructed.
Further, the CRUST density data come from a CRUST1.0 density model, and the model establishes the corresponding relation between the elevation and the density of each density layer of the CRUST.
Further, after the spatial gravity anomaly of the building region, the method further comprises the following steps:
and calculating the space gravity abnormal data of each discrete point by using a mathematical interpolation method based on the established space gravity abnormal data of the region under a certain resolution.
Further, the integration zone σ is in the local plane coordinate system0The computational expression for the terrain correction using the prism integration method is as follows:
wherein, δ gTCTo calculate the terrain correction for point P, (x, y, z) are the flow point plane coordinates, G is the universal gravitation constant, h and hpRespectively flow point and calculated point elevation, hiThe elevation of each density layer of the crust, i is the number of the density layers of the crust, N +1 is the density layer of the elevation calculation surface corresponding to the calculation point,
the density value at the i-th layer (x, y) satisfies the formula N>1；
When N is equal to 1, the compound is,
when N is equal to 0, the compound is,
further, the calculation expression of the interlayer correction is as follows:
wherein, δ gCFor calculating the interlayer correction of the point P, M +1 is the density layer where the elevation starting surface corresponding to the calculation point is located,
the density value at the point is calculated for the ith layer.
Go toStep by step, the equilibrium correction uses an Airy-Heiskanen model which considers that the earth crust of constant density floats at a density of rhomThe mantle above the sea level or below the sea level, respectively, is compensated in the form of a "mountain root" or "inverted mountain root"; under the rectangular coordinate system of the local plane, the calculation expression of the equalization correction is as follows:
δgIC＝G△ρ
wherein, δ gICFor calculating the equilibrium correction of the point P, z2＝-T，z1And (T + T), wherein T is the depth of the equilibrium surface, T is the compensation depth, and Δ ρ is the density difference between the crust and mantle.
Further, according to the equilibrium theory, the gravity anomaly of the area space is constructed, and the equilibrium anomaly should meet the floating equilibrium theory, delta g I0, i.e. equalising gravity anomalies Δ gIThe following conditions should be satisfied:
△gair conditioner＝△gI-δgC-δgTC-δgIC
Wherein, Δ gAir conditionerIs a spatial gravity anomaly.
The invention also provides a device for simulating the gravity of the earth surface by using the density data of the terrain and the crust, which comprises:
the database establishing module is used for determining the simulation range of the earth surface gravity data and establishing a terrain and crust density database of the area by combining the terrain data and the crust density data;
the terrain correction calculation module is used for calculating the terrain correction of the area under a certain resolution according to the database;
the interlayer correction calculation module is used for calculating interlayer correction of the area under the same resolution according to the database;
the equilibrium correction calculation module is used for calculating the equilibrium correction of the region under the same resolution according to the database;
and the space gravity anomaly calculation module is used for constructing regional space gravity anomaly by combining terrain correction, interlayer correction and balance correction according to the balance theory.
Compared with the prior art, the invention has the following advantages:
in the traditional equilibrium theory filling method, the crust density is generally regarded as a constant 2.67g/m3The density of the earth mantle is 3.26g/m3The approximation of the density term directly brings systematic errors of simulation data; based on the above, the invention introduces the crust density term, namely, the crust density is regarded as a variable, and the change is closer to the actual crust density distribution. Theoretically, the accuracy of terrain correction, interlayer correction and equilibrium correction calculated according to the density distribution is higher, the method is closer to the reality of the earth, and the final calculation result is closer to the 'floating balance' theory, so that the simulation accuracy of the equilibrium theory filling method can be improved by introducing the changed crust density.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a method for surface gravity simulation using terrain and crust density data in accordance with an embodiment of the present invention;
FIG. 2 is a topographical view of an experimental area of an embodiment of the present invention;
FIG. 3 is a schematic representation of the CRUST1.0 global CRUST model of an embodiment of the present invention;
FIG. 4 is a plot of experimental regional terrain correction profiles for an embodiment of the present invention;
FIG. 5 is a graph of the experimental zone interlayer correction profile for an embodiment of the present invention;
FIG. 6 is a plot of the experimental zone equalization correction profile for an embodiment of the present invention;
FIG. 7 is a graph of spatial gravity anomaly distribution over an experimental area according to an embodiment of the present invention;
FIG. 8 is a point location profile for use in evaluating the accuracy of the method of the present invention according to an embodiment of the present invention;
FIG. 9 is a graphical representation of a CRUST1.0 density model distribution of an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
At present, global terrain models reach equivalent resolutions, such as TanDEM-X, SRTM series, ASTERGDEM and AW3D30, wherein the resolution of SRTM can reach 12m, and researches show that gravity anomaly and terrain show strong linear relation in medium-high frequency parts, so that the possibility of constructing local area high-resolution gravity anomaly by using equilibrium theory and terrain data is provided. Moreover, the global CRUST model CRUST1.0 contains abundant earth internal information, the resolution ratio reaches 1 degree, and the premise is provided for adding geophysical information (CRUST layering and density) in the process of constructing blank gravity data by utilizing a balanced model and topographic data.
As shown in fig. 1, a method for performing surface gravity simulation using terrain and crust density data of this embodiment includes the following steps:
and S101, determining the simulation range of the earth surface gravity data, and establishing a terrain and crust density database of the area by combining high-precision terrain data and crust density data.
Preferably, the CRUST density data is from CRUST1.0 DensityDegree model (as shown in FIG. 9), hi(i-1 … 9) and ρi(i-1 … 9) shows the elevation and density of each density layer of the crust, respectively, with a planar resolution of 1 °.
Step S102, according to the database in step S101, calculating the terrain correction of the area under a certain resolution, and integrating the area sigma in the local plane coordinate system during the calculation of the local terrain correction0The computational expression for the terrain correction using the prism integration method is as follows:
wherein, δ gTCTo calculate the terrain correction for point P, (x, y, z) are the flow point plane coordinates, G is the universal gravitation constant, h and hpRespectively flow point and calculated point elevation, hiThe elevation of each density layer of the crust, i is the number of the density layers of the crust, N +1 is the density layer of the elevation calculation surface corresponding to the calculation point,
the density value at the i-th layer (x, y) satisfies the formula N>1。
When N is equal to 1, the compound is,
when N is equal to 0, the compound is,
step S103, calculating the interlayer correction of the area at the same resolution according to the database in step S101, where the calculation expression of the interlayer correction is as follows:
wherein, δ gCFor the interlayer correction of the calculation point P, M +1 is the density layer where the elevation starting surface corresponding to the calculation point is located, rhoi PThe density value at the point is calculated for the ith layer.
Step S104, calculating the balance correction of the area under the same resolution according to the database in the step S101, wherein the balance correction adopts an Airy-Heiskanen model which is relatively consistent with the actual balance state of the earth, and the theory considers that the earth crust with constant density floats on the earth with the density of rhomThe mantle above the sea level or below the sea level, respectively, is compensated in the form of a "mountain root" or "inverted mountain root"; under the rectangular coordinate system of the local plane, the calculation expression of the equalization correction is as follows:
δgIC＝G△ρ
wherein, δ gICFor calculating the equilibrium correction of the point P, z2＝-T，z1And (T + T), wherein T is the depth of the equilibrium surface, T is the compensation depth, and Δ ρ is the density difference between the crust and mantle.
Step S105, according to the equilibrium theory, combining the terrain correction, the interlayer correction and the equilibrium correction calculated in the steps S102-S104 to construct regional space gravity anomaly, wherein the equilibrium anomaly should meet the floating equilibrium theory, delta g I0, i.e. equalising gravity anomalies Δ gIThe following conditions should be satisfied:
△gair conditioner＝△gI-δgC-δgTC-δgIC
Wherein, Δ gAir conditionerIs a spatial gravity anomaly.
Step S106, based on the spatial gravity anomaly data at a certain resolution in the region established in step S105, calculating the spatial gravity anomaly data at each discrete point by using a mathematical interpolation method.
The following is a specific example for a better understanding of the invention.
Step S201, determining the simulation range of the earth surface gravity data, and establishing a terrain and crust density database of the area by combining the terrain data and the crust density data.
(1) Topographic data.
The experimental area is distributed in the Madbeli plateau in the southeast part of Africa. The experimental area is selected to be an area of 6 degrees multiplied by 6 degrees, the regional distribution range is 20 degrees to 26 degrees from east longitude and 28 degrees to 34 degrees from south latitude, the topographic data of 1 'multiplied by 1' published by Etopo1 is adopted in the example, the Etopo1 is topographic elevation data developed by NGDC (national geophysical data center), the elevation information statistics is shown in table 1, the average height value of the altitude of the experimental area is about 1000m, the mean square error is 320m, the topographic change of the experimental area is severe, the gravitational field signal is complex, and the topographic map of the experimental area is shown in fig. 2.
TABLE 1 statistical table of elevation information
(2) Crust density data.
CRUST1.0 is a global three-dimensional earth CRUST model with a resolution of 1 ° × 1 °, and the CRUST1.0 model divides the world into 1 ° × 1 ° networks, totaling 64800 cells. The crust of the earth is divided into 9 layers by the model, and the first layer to the ninth layer are respectively as follows: water layer, ice layer, upper deposition layer, middle deposition layer, lower deposition layer, upper crust, middle crust, lower crust, and mantle. The water depth data as well as the terrain data in the model were from Etopo1, and the parameters of the mantle were from the LLNL-G3Dv3 model. In the experiment, the crustal depth and density information of the experimental area need to be extracted from the global crustal model. In the experimental area of 6 degrees multiplied by 6 degrees, a total of 36 multiplied by 9 density terms are included, wherein the maximum value of the average density of the crust is 2390kgm-3Minimum value of 2080kgm-3. The actual average density value is different from the normal density. The CRUST1.0 global crustal model is shown in FIG. 3.
In step S202, the terrain correction value is calculated from the data in step S201 by using the terrain correction formula in step S102, and the regional terrain correction profile is shown in fig. 4.
TABLE 2 terrain correction value statistics table
In step S203, the interlayer correction value is calculated by the interlayer correction formula in step S103 according to the data in step S201, and the regional interlayer correction distribution map is shown in fig. 5.
TABLE 3 statistical table of inter-layer correction values
In step S204, the equalization correction value is calculated by using the equalization correction formula in step S104 based on the data in step S201, and the local equalization correction distribution map is shown in fig. 6.
TABLE 4 statistical table of equilibrium correction values
In step S205, the spatial gravity anomaly of the region is calculated by using the data calculated in steps S202 to S204 and combining the spatial gravity anomaly formula in step S105, and the distribution map of the spatial gravity anomaly of the region is shown in fig. 7.
Step S206, based on the spatial gravity anomaly data at a certain resolution in the region established in step S205, calculates the spatial gravity anomaly data at each discrete point by using a mathematical interpolation method.
And performing precision evaluation on the data in the step S205, wherein the actually measured gravity data for checking is extracted from the "GRAVCD-africa" data set, and includes 1789 actually measured spatial gravity anomaly data in the area, the statistics of the gravity anomaly data are shown in table 5, and the point location distribution diagram is shown in fig. 8.
TABLE 5 statistical table of abnormal gravity values
By using the Kriging interpolation method, the gravity abnormal value of each discrete point in fig. 8 is obtained by combining the gridded spatial gravity abnormal value in the region with a certain resolution calculated by the invention, and is compared with the real value of each point, and the comparison results are obtained as shown in tables 6 and 7:
TABLE 6 statistics table for blank area filling difference value by traditional equilibrium theory filling method
TABLE 7 statistical table of filling difference values of blank area according to the present invention
The results of the comparative experiment show that: the average value of the filling difference values of the gravity data of the variable density blank area is-35.3848 mGal, and the average value of the filling difference values of the gravity data of the constant density blank area is-51.3602 mGal, and the mean square deviations of the filling difference values and the constant density blank area are equivalent. This shows that, compared with the constant density item, the density item added has smaller system difference, and is more beneficial to filling the blank gravity data. Therefore, the system difference of the blank area gravity data filling by using the CRUST1.0 model is smaller, the average value is obviously superior to that of blank area filling by using the constant density, the effect of gravity data filling by using the method is better, and the method better meets the actual requirement.
Corresponding to the above method for performing surface gravity simulation by using terrain and crust density data, the present embodiment further provides an apparatus for performing surface gravity simulation by using terrain and crust density data, comprising:
the database establishing module is used for determining the simulation range of the earth surface gravity data and establishing a terrain and crust density database of the area by combining the terrain data and the crust density data;
the terrain correction calculation module is used for calculating the terrain correction of the area under a certain resolution according to the database;
the interlayer correction calculation module is used for calculating interlayer correction of the area under the same resolution according to the database;
the equilibrium correction calculation module is used for calculating the equilibrium correction of the region under the same resolution according to the database;
and the space gravity anomaly calculation module is used for constructing regional space gravity anomaly by combining terrain correction, interlayer correction and balance correction according to the balance theory.
According to the method, the earth surface gravity data simulation is carried out by utilizing the equilibrium theory, the published global high-resolution topographic data and the published crust density data according to the strong correlation between the gravity data high-frequency part and the topographic data, namely, the regional space gravity anomaly (namely gravity data) is simulated, so that the cost of the earth surface manual measurement is reduced.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Finally, it is to be noted that: the above description is only a preferred embodiment of the present invention, and is only used to illustrate the technical solutions of the present invention, and not to limit the protection scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (8)
1. A method for surface gravity simulation by using terrain and crust density data is characterized by comprising the following steps:
determining the simulation range of the earth surface gravity data, and establishing a terrain and crust density database of the region by combining terrain data and crust density data;
according to the database, calculating the terrain correction of the area under a certain resolution;
calculating interlayer correction of the region under the same resolution according to the database;
according to the database, calculating the balance correction of the area under the same resolution;
according to the equilibrium theory, combining terrain correction, interlayer correction and equilibrium correction, the regional space gravity anomaly is constructed.
2. The method for surface gravity simulation using terrain and CRUST density data as defined in claim 1 wherein the CRUST density data is from a CRUST1.0 density model that establishes a correspondence between elevation and density of each density layer of the CRUST.
3. A method for surface gravity simulation using terrain and crust density data as set forth in claim 1, further comprising, after constructing the regional spatial gravity anomaly:
and calculating the space gravity abnormal data of each discrete point by using a mathematical interpolation method based on the established space gravity abnormal data of the region under a certain resolution.
4. The method for surface gravity simulation using terrain and crust density data as set forth in claim 2, wherein the integration zone σ is in a local planar coordinate system0The computational expression for the terrain correction using the prism integration method is as follows:
wherein, δ gTCTo calculate the terrain correction for point P, (x, y, z) are the flow point plane coordinates, G is the universal gravitation constant, h and hpAre respectively asFlow points and calculated point elevation, hiThe elevation of each density layer of the crust, i is the number of the density layers of the crust, N +1 is the density layer of the elevation calculation surface corresponding to the calculation point,
the density value at the i-th layer (x, y) satisfies the formula N>1；
When N is equal to 1, the compound is,
when N is equal to 0, the compound is,
5. the method for surface gravity simulation using terrain and crust density data as set forth in claim 4, wherein the computational expression for the interlayer correction is as follows:
wherein, δ gCFor calculating the interlayer correction of the point P, M +1 is the density layer where the elevation starting surface corresponding to the calculation point is located,
the density value at the point is calculated for the ith layer.
6. The method of surface gravity simulation using terrain and crust density data as set forth in claim 5, wherein said equilibrium correction uses an Airy-Heiskanen model that considers the constant density crust floating at a density of ρmOn the mantle and is kept in balance, partly above sea level or lowThe part below the equilibrium surface of the sea level is compensated in the form of a "mountain root" or a "reverse mountain root" respectively; under the rectangular coordinate system of the local plane, the calculation expression of the equalization correction is as follows:
δgIC＝G△ρ
wherein, δ gICFor calculating the equilibrium correction of the point P, z2＝-T，z1And (T + T), wherein T is the depth of the equilibrium surface, T is the compensation depth, and Δ ρ is the density difference between the crust and mantle.
7. The method of claim 6, wherein the regional space gravity anomaly is constructed according to a balance theory, wherein the balance anomaly satisfies a floating balance theory, Δ gI0, i.e. equalising gravity anomalies Δ gIThe following conditions should be satisfied:
△gair conditioner＝△gI-δgC-δgTC-δgIC
Wherein, Δ gAir conditionerIs a spatial gravity anomaly.
8. An apparatus for surface gravity simulation using terrain and crust density data, comprising:
the database establishing module is used for determining the simulation range of the earth surface gravity data and establishing a terrain and crust density database of the area by combining the terrain data and the crust density data;
the terrain correction calculation module is used for calculating the terrain correction of the area under a certain resolution according to the database;
the interlayer correction calculation module is used for calculating interlayer correction of the area under the same resolution according to the database;
the equilibrium correction calculation module is used for calculating the equilibrium correction of the region under the same resolution according to the database;
and the space gravity anomaly calculation module is used for constructing regional space gravity anomaly by combining terrain correction, interlayer correction and balance correction according to the balance theory.
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