CN110287620B - Spherical coordinate system density interface forward modeling method and system suitable for earth surface observation surface - Google Patents
Spherical coordinate system density interface forward modeling method and system suitable for earth surface observation surface Download PDFInfo
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Abstract
The invention discloses a spherical coordinate system density interface forward modeling method and system suitable for an earth surface observation surface, and belongs to the field of shell mantle density interface structure research. The method comprises the following steps: the method comprises a data reading step, a unit body dividing step, a subunit body dividing step, a unit body gravity abnormal value acquiring step and a density interface gravity abnormal grid data acquiring step. The method can reflect the gravity anomaly caused by the regional density interface and provide powerful technical support for high-precision inversion of regional and even global shell mantle interface structures.
Description
Technical Field
The invention belongs to the field of shell mantle density interface structure research, and particularly relates to a spherical coordinate system density interface forward modeling method and system suitable for a surface observation surface.
Background
When there is a density difference between two adjacent formations or strata, the interface between them is referred to as a density interface. When the underground density interface has transverse fluctuation, gravity anomaly can be caused on the surface observation surface, and conversely, the known gravity anomaly of the surface observation surface can be used for inverting and deducing the depth fluctuation condition of the underground density interface, thereby providing a deep basis for the deep structure and structure interpretation of the region. The density interface forward modeling is the theoretical basis of density interface inversion, and a high-precision forward modeling method provides powerful guarantee for inversion.
At present, many density interface forward modeling methods exist at home and abroad, the method is suitable for earth surface observation surfaces, and two main types of space domain forward modeling methods and frequency domain forward modeling methods exist in terms of calculation methods, but the space domain forward modeling methods and the frequency domain forward modeling methods belong to a Cartesian coordinate system, namely, the coordinates of the used model and the measuring point are plane coordinates. However, when the research area is large in area or even global scale, the actual surface observation surface is a curved surface, and the density interface forward modeling method of the conventional cartesian coordinate system is not applicable any more, and needs to adopt the density interface forward modeling method of the spherical coordinate system. Uieda & Barbosa (2017) researches a spherical coordinate system density interface inversion method, but the method is only suitable for high-altitude observation surfaces and is not suitable for ground surface observation surfaces. Therefore, the density interface forward modeling method of the spherical coordinate system suitable for the earth surface observation surface is developed, and the method has very important theoretical significance and application value.
By utilizing the spherical coordinate system density interface forward modeling method suitable for the earth surface observation surface, the gravity anomaly of the earth surface observation surface caused by the shell mantle density interface of regional or even global scale can be obtained, and powerful technical support is provided for regional deep structure and structural research and the like.
Disclosure of Invention
The invention provides a method and a system for forward modeling of a density interface of a spherical coordinate system suitable for a ground surface observation surface. By utilizing a density interface depth grid model and interface residual density of a geographic coordinate system (longitude and latitude), and performing high-precision forward calculation of a Gauss-Legendre integral algorithm of a spherical coordinate system, the gravity abnormal grid data of the earth surface observation surface caused by the density interface model can be obtained, so that the purposes of regional structure research, shell mantle interface structure analysis and the like of a research area are achieved. According to the technical scheme, the Tesseroid unit body subdivision scheme is adopted, forward accuracy can be greatly improved, meanwhile, subdivision is only carried out on a calculation area close to each observation point, Tesseroid grid fine subdivision is not needed to be carried out on the whole calculation space at the same time, and therefore on the basis of improving calculation accuracy, the calculation amount required by high-accuracy forward performance is greatly reduced, and the forward method is more practical.
According to a first aspect of the present invention, there is provided a method for forward modeling a density interface of a spherical coordinate system suitable for a ground surface observation surface, the method being based on a depth grid model of the density interface of the geographic coordinate system and an interface residual density, and obtaining gravity anomaly grid data of the ground surface observation surface by performing high-precision forward computation of a gaussian-legendre integral algorithm of the spherical coordinate system on the basis of the depth grid model and the interface residual density, the method comprising:
step 1: reading in data, namely reading in a density interface depth grid model and interface residual density of a geographic latitude and longitude coordinate system known in a research area;
step 2: a unit body dividing step, namely dividing a material layer between an earth surface observation surface and a density interface into a plurality of Tesseroid unit body combinations and arranging according to the grid rule of a density interface depth grid model;
and step 3: a subunit body dividing step, namely dividing each Tessenoid unit body in the calculation area close to the observation point into a plurality of Tessenoid subunit body combinations again;
and 4, step 4: a unit body gravity abnormal value obtaining step, wherein the gravity abnormal values of all Tessenoid subunit bodies in each Tessenoid unit body at each observation point of the earth surface observation surface are obtained and summed, and then the gravity abnormal value of each Tessenoid unit body at each observation point is obtained;
and 5: and a density interface gravity anomaly grid data acquisition step, namely summing the gravity anomaly values of all Tesseroid unit bodies at any observation point to finally obtain the gravity anomaly grid data of the earth surface observation surface caused by the density interface model.
Further, in the step 2, the densities of the Tesseroid unit bodies are equal, the sizes of the Tesseroid unit bodies in the longitude and latitude directions are consistent with the grids of the density interface depth grid model, the top surface is a ground surface observation surface, and the bottom surface is a density interface.
Further, in the step 3, a specific manner of subdividing each tesseoid unit body in the calculation region close to the observation point into a plurality of tesseoid subunit body combinations is as follows:
for a certain observation point P, if the geometric position relation between the observation point P and the center of the Tesseroid unit body grid does not satisfy the judgment formula, the grid needs to be finely divided:
wherein d is the distance from the observation point to the center of the Tesseroid grid;
Lλthe lengths of the Tesseroid unit bodies in the longitude and latitude directions are respectively; high precision forward result and D valueIn this regard, D is a positive scalar quantity called the distance-to-size ratio, and is generally greater than or equal to 1.
Through the judgment formula, the method realizes subdivision only aiming at the calculation area close to each observation point, does not need to finely subdivide Tesseroid grids in the whole calculation space, and thus can greatly reduce forward calculation amount on the basis of improving calculation precision.
Further, in the step 4, a gravity abnormal value of each observation point of each tesseoid subunit body on the ground surface observation surface in each tesseoid subunit body is calculated by a gaussian-legendre integral algorithm of a spherical coordinate system with high precision.
Further, a specific formula for calculating the gravity abnormal value of all the Tesseroid subunit bodies in each Tesseroid unit body at each observation point of the earth surface observation surface by using a spherical coordinate system Gauss-Legendre integral algorithm in a high-precision forward modeling manner is as follows:
wherein Δ g is an abnormal value of gravity; g is a universal gravitation constant, G is 6.67 multiplied by 10-11N·m2/kg2(ii) a Δ ρ is the residual density of the study area in kg/m3(ii) a In the spherical coordinate system, the observation point coordinates are
The coordinate ranges of the elongation, latitude and radial direction of the Tesseroid unit body are (lambda)1,λ2)，
(r1,r2) And the center point coordinates thereof are
nλ,
The number of measuring points in the longitude direction and the latitude direction respectively; l is the distance from the observation point to the center point of the Tesseroid unit body, and the unit is m; psi represents the spherical angle from the observation point to the center point of the Tesseroid cell body, and the unit is degree; omegaiAnd ωjRespectively, gaussian-legendre coefficients related to longitude and latitude.
According to a second aspect of the present invention, there is provided a spherical coordinate system density interface forward modeling system suitable for a ground surface observation surface, the system being based on the spherical coordinate system density interface forward modeling method according to any one of the above aspects, the system comprising:
the data reading component is used for reading the density interface depth grid model and the interface residual density of the geographic latitude and longitude coordinate system in the known research area;
the unit body subdivision component is used for subdividing a material layer between the earth surface observation surface and the density interface into a plurality of Tesseroid unit body combinations and arranging the Tesseroid unit bodies according to the grid rule of the density interface depth grid model;
the subunit body splitting component is used for splitting each Tessenoid unit body in the calculation area close to the observation point into a plurality of Tessenoid subunit body combinations again;
the unit body gravity abnormal value acquisition component is used for acquiring the gravity abnormal values of all Tesserioid subunit bodies in each Tesserioid unit body at each observation point of the earth surface observation surface and summing the gravity abnormal values so as to obtain the gravity abnormal value of each Tesserioid unit body at each observation point;
and the density interface gravity anomaly grid data acquisition component is used for summing the gravity anomaly values of all Tesseroid unit bodies at any observation point to finally obtain the surface observation surface gravity anomaly grid data caused by the density interface model.
Furthermore, the Tesseroid unit bodies have equal density, the size in the longitude and latitude directions is consistent with the grid of the density interface depth grid model, the top surface is a ground surface observation surface, and the bottom surface is a density interface.
Further, the specific way of subdividing each tesseoid unit cell in the calculation region close to the observation point into a plurality of tesseoid subunit combinations is as follows:
for a certain observation point P, if the geometric position relation between the observation point P and the center of the Tesseroid unit body grid does not satisfy the judgment formula, the grid needs to be finely divided:
wherein d is the distance from the observation point to the center of the Tesseroid grid;
Lλthe lengths of the Tesseroid unit bodies in the longitude and latitude directions are respectively; the forward result of high accuracy is related to the selection of the value of D, which is a positive scalar called the distance-to-size ratio, and is generally greater than or equal to 1.
Furthermore, a spherical coordinate system Gaussian-Legendre integral algorithm is used for calculating the gravity abnormal value of all Tesseroid subunit bodies in each Tesseroid unit body at each observation point of the ground surface observation surface in a high-precision forward mode.
Further, a specific formula for calculating the gravity abnormal value of all the Tesseroid subunit bodies in each Tesseroid unit body at each observation point of the earth surface observation surface by using a spherical coordinate system Gauss-Legendre integral algorithm in a high-precision forward modeling manner is as follows:
wherein Δ g is an abnormal value of gravity; g is a universal gravitation constant, G is 6.67 multiplied by 10-11N·m2/kg2(ii) a Δ ρ is the residual density of the study area in kg/m3(ii) a In the spherical coordinate system, the observation point coordinates are
The coordinate range of the elongation, latitude and radial direction of the Tesseroid unit cell is (lambda)1,λ2)，
(r1,r2) And the center point coordinates thereof are
nλ,
The number of measuring points in the longitude direction and the latitude direction respectively; l is the distance from the observation point to the center point of the Tesseroid unit body, and the unit is m; psi represents the spherical angle from the observation point to the center point of the Tesseroid cell body, and the unit is degree; omegaiAnd ωjRespectively, gaussian-legendre coefficients related to longitude and latitude.
The invention has the following beneficial effects
1) The invention realizes a forward modeling method and program development of a density interface of a spherical coordinate system suitable for a surface observation surface.
2) The method combines the Tesseroid unit body subdivision scheme, greatly improves forward accuracy, reduces the calculated amount required by high-accuracy forward to a certain extent, and ensures that the forward method has higher practicability.
Drawings
FIG. 1 is a flow chart of a density interface forward modeling method of a spherical coordinate system suitable for a ground surface observation surface.
FIG. 2 is a geographic coordinate system density interface depth grid model.
Fig. 3 is the gravity anomaly grid data of the earth surface observation surface in the embodiment 1 of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. On the contrary, the invention is intended to cover alternatives, modifications, equivalents and alternatives which may be included within the spirit and scope of the invention as defined by the appended claims.
Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. It will be apparent to one skilled in the art that the present invention may be practiced without these specific details.
The sphere coordinate system density interface forward modeling method technology suitable for the earth surface observation surface is one of the hotspots and development trends of the current regional shell mantle density interface structure research, is used for obtaining earth surface observation surface gravity abnormal grid data caused by a density interface model, and is beneficial to regional or even global shell mantle density interface structure analysis, regional structure research and the like. The implementation takes a density interface depth grid model of a geographic coordinate system as an example, and adopts a density interface forward modeling method of a spherical coordinate system suitable for a ground surface observation surface, as shown in fig. 1, which is performed in sequence. The method comprises the following steps:
(1) reading in a known geographic coordinate system (longitude and latitude) density interface depth grid model and interface residual density in a research area;
(2) dividing a material layer between a ground surface observation surface and a density interface into a plurality of Tesseroid unit bodies for combination and arranging according to a model grid rule, wherein the Tesseroid unit bodies have equal density, the size in the longitude and latitude direction is consistent with that of the model grid, the top surface is the ground surface observation surface, and the bottom surface is the density interface;
(3) subdividing each Tesseroid unit body into a plurality of Tesseroid subunit body combinations;
(4) calculating the gravity abnormal values of all the subunit bodies in each Tessenoid unit body at each measuring point of the earth surface observation surface in a high-precision forward modeling manner by using a Gauss-Legendre integral algorithm of a spherical coordinate system, and summing the gravity abnormal values to obtain the gravity abnormal values of the Tessenoid unit body at each measuring point;
(5) and summing the gravity abnormal values of all Tesseroid unit bodies at any measuring point to finally obtain the gravity abnormal grid data of the earth surface observation surface caused by the density interface model.
In the step (3), the formula for subdividing each Tesseroid unit body in the specific scheme is as follows:
wherein d is the distance from the observation point to the center of the Tesseroid grid;
Lλthe lengths of the Tesseroid unit bodies in the longitude and latitude directions are respectively; the forward result of high accuracy is related to the selection of the value of D, which is a positive scalar called the distance-to-size ratio, and is generally greater than or equal to 1. For any observation point P, if the geometric position relation between the measurement point and the center of the Tesseroid grid does not satisfy the judgment formula, the grid needs to be finely divided, that is, only a calculation area close to the observation point needs to be divided, and the Tesseroid grid does not need to be finely divided in the whole calculation space, so that the forward calculation amount can be greatly reduced on the basis of improving the calculation precision.
In the step (4), for a single tesseloid subunit, the high-precision forward calculation formula of the gaussian-legendre integral algorithm of the spherical coordinate system is specifically as follows:
wherein Δ g is an abnormal value of gravity; g is a universal gravitation constant, G is 6.67 multiplied by 10-11N·m2/kg2(ii) a Δ ρ is the residual density of the study area in kg/m3(ii) a In the spherical coordinate system, the observation point coordinates are
The coordinate ranges of the elongation, latitude and radial direction of the Tesseroid unit body are (lambda)1,λ2)，
(r1,r2) And the center point coordinates thereof are
nλ,
The number of measuring points in the longitude direction and the latitude direction respectively; l is the distance from the observation point to the center point of the Tesseroid unit body, and the unit is m; psi represents the spherical angle from the observation point to the center point of the Tesseroid cell body, and the unit is degree; omegaiAnd ωjRespectively, gaussian-legendre coefficients related to longitude and latitude.
The invention is further described with reference to the following figures and specific examples, which are not intended to be limiting. The following are preferred embodiments of the present invention:
example 1
In the method of the embodiment, a spherical coordinate system density interface forward modeling method suitable for the earth surface observation surface is adopted, and is used for obtaining earth surface observation surface gravity anomaly grid data caused by a density interface model, so that regional and even global shell mantle density interface structure analysis, regional structure research and the like are facilitated.
The method comprises the following steps: reading in the density field of the known geographic coordinate system (longitude and latitude) of the research areaThe surface depth grid model (fig. 2) and the interface residual density Δ ρ ═ 0.3g/cm3；
Step two: dividing a material layer between a ground surface observation surface and a density interface into a plurality of Tesseroid unit bodies for combination and arranging according to a model grid rule, wherein the Tesseroid unit bodies have equal density, the size in the longitude and latitude direction is consistent with that of the model grid, the top surface is the ground surface observation surface, and the bottom surface is the density interface;
step three: subdividing each Tesseroid unit body into a plurality of Tesseroid subunit body combinations;
step four: calculating the gravity abnormal values of all the subunit bodies in each Tessenoid unit body at each measuring point of the earth surface observation surface in a high-precision forward modeling manner by using a Gauss-Legendre integral algorithm of a spherical coordinate system, and summing the gravity abnormal values to obtain the gravity abnormal values of the Tessenoid unit body at each measuring point;
step five: and summing the gravity abnormal values of all Tesseroid unit bodies at any measuring point to finally obtain the gravity abnormal grid data of the earth surface observation surface caused by the density interface model (figure 3). The spherical coordinate system density interface forward modeling method suitable for the earth surface observation surface can be used for obtaining earth surface observation surface gravity anomaly grid data caused by a density interface model in an area, and is beneficial to shell mantle density interface structure analysis, area structure research and the like in an area or even a global scale.
The above-described embodiment is only one of the preferred embodiments of the present invention, and general changes and substitutions by those skilled in the art within the technical scope of the present invention are included in the protection scope of the present invention.
Claims (8)
1. A spherical coordinate system density interface forward modeling method suitable for a ground surface observation surface is characterized by comprising the following steps:
a data reading step: reading in a density interface depth grid model and interface residual density of a geographic latitude and longitude coordinate system known in a research area;
a unit body dividing step: dividing a material layer between a ground surface observation surface and a density interface into a plurality of Tesseroid unit body combinations and arranging according to the grid rule of the density interface depth grid model;
a subunit body subdivision step: each Tessenoid unit body is divided into a plurality of Tessenoid subunit body combinations again;
acquiring a unit body gravity abnormal value: acquiring and summing the gravity abnormal values of all the Tessenoid subunit bodies in each Tessenoid unit body at each observation point of the earth surface observation surface, and further acquiring the gravity abnormal value of each Tessenoid unit body at each observation point;
acquiring density interface gravity anomaly grid data: summing the gravity abnormal values of all Tesseroid unit bodies at any observation point to finally obtain the gravity abnormal grid data of the earth surface observation surface caused by the density interface depth grid model;
in the unit body gravity abnormal value obtaining step, the gravity abnormal values of all Tesserioid subunit bodies in each Tesserioid unit body at each observation point of the earth surface observation surface are calculated by a Gauss-Legendre integral algorithm of a spherical coordinate system in a high-precision forward modeling manner;
the specific formula for calculating the gravity abnormal value of each observation point of each Tessenoid subunit on the surface observation surface in a high-precision forward manner by using a spherical coordinate system Gauss-Legendre integral algorithm is as follows:
wherein Δ g is an abnormal value of gravity; g is a universal gravitation constant, G is 6.67 multiplied by 10-11N·m2/kg2(ii) a Δ ρ is the residual density of the study area in kg/m3(ii) a In the spherical coordinate system, the observation point coordinates are
The coordinate ranges of the elongation, latitude and radial direction of the Tesseroid unit body are (lambda)1,λ2)，
(r1,r2) And the center point coordinates thereof are
nλ,
The number of measuring points in the longitude direction and the latitude direction respectively; l is the distance from the observation point to the center point of the Tesseroid unit body, and the unit is m; psi represents the spherical angle from the observation point to the center point of the Tesseroid cell body, and the unit is degree; omegaiAnd ωjRespectively, gaussian-legendre coefficients associated with longitude and latitude.
2. The spherical coordinate system density interface forward modeling method as claimed in claim 1, wherein in the unit body dividing step, the Tesseroid unit bodies have equal density, the size of the Tesseroid unit bodies in the longitude and latitude directions is consistent with the grid of the density interface depth grid model, the top surface is the earth surface observation surface, and the bottom surface is the density interface.
3. The spherical coordinate system density interface forward modeling method of claim 1, wherein in the subunit body splitting step, each Tesseroid unit body is split again into a plurality of Tesseroid subunit body combinations in a specific manner:
for a certain observation point P, if the geometric position relation between the observation point P and the center of the Tesseroid unit body grid does not satisfy the following judgment formula, the grid needs to be finely divided:
wherein d is the distance from the observation point to the center of the Tesseroid grid;
Lλthe lengths of the Tesseroid unit bodies in the longitude and latitude directions are respectively; the high precision forward result is related to the selection of a value of D, D is a positive scalar quantity called a distance-size ratio, and the value of D is more than or equal to 1.
4. A spherical coordinate system density interface forward modeling system suitable for a ground surface observation surface, the system being based on the spherical coordinate system density interface forward modeling method according to any one of the preceding claims 1 to 3, the system comprising:
the data reading component is used for reading the density interface depth grid model and the interface residual density of the geographic latitude and longitude coordinate system in the known research area;
the unit body subdivision component is used for subdividing a material layer between the earth surface observation surface and the density interface into a plurality of Tesseroid unit body combinations and arranging the Tesseroid unit bodies according to the grid rule of the density interface depth grid model;
the subunit body splitting component is used for splitting each Tesseroid unit body in the calculation area close to the observation point into a plurality of Tesseroid subunit body combinations again;
the unit body gravity abnormal value acquisition component is used for acquiring the gravity abnormal values of all the Tesseroid subunit bodies in each Tesseroid unit body at each observation point of the earth surface observation surface and summing the gravity abnormal values so as to obtain the gravity abnormal value of each Tesseroid unit body at each observation point;
and the density interface gravity anomaly grid data acquisition component is used for summing the gravity anomaly values of all Tesseroid unit bodies at any observation point to finally obtain the surface observation surface gravity anomaly grid data caused by the density interface depth grid model.
5. The spherical coordinate system density interface forward modeling system of claim 4, wherein the Tesseroid units have equal density, the size in the longitude and latitude direction is consistent with the grid of the density interface depth grid model, the top surface is the ground surface observation surface, and the bottom surface is the density interface.
6. The spherical coordinate system density interface forward modeling system of claim 4, wherein each Tesseroid unit cell in the calculation region near the observation point is subdivided into a plurality of Tesseroid subunit cell combinations in a manner that:
aiming at a certain observation point P, if the geometric position relation between the observation point P and the center of the Tesseroid unit body grid does not satisfy the following judgment formula, the grid needs to be finely divided:
wherein d is the distance from the observation point to the center of the Tesseroid grid;
Lλthe lengths of the Tesseroid unit bodies in the longitude and latitude directions are respectively; the high precision forward result is related to the selection of a value of D, D is a positive scalar quantity called a distance-size ratio, and the value of D is more than or equal to 1.
7. The spherical coordinate system density interface forward modeling system according to claim 4, wherein a Gaussian-Legendre integral algorithm of the spherical coordinate system is used to calculate the gravity outlier of all Tesseroid subunits in each Tesseroid unit at each observation point on the surface observation surface with high precision.
8. The spherical coordinate system density interface forward modeling system of claim 7, wherein the spherical coordinate system gaussian-legendre integral algorithm is used for calculating the gravity abnormal value of each observation point of each tesseoid subunit on the surface observation surface in a high-precision forward modeling manner, and the specific formula of the gravity abnormal value of each observation point of each tesseoid subunit inside each tesseferoid subunit is as follows:
wherein Δ g is an abnormal value of gravity; g is a universal gravitation constant, G is 6.67 multiplied by 10-11N·m2/kg2(ii) a Δ ρ is the residual density of the study area in kg/m3(ii) a In the spherical coordinate system, the observation point coordinates are
The coordinate ranges of the elongation, latitude and radial direction of the Tesseroid unit body are (lambda)1,λ2)，
(r1,r2) And the center point coordinates thereof are
nλ,
The number of measuring points in the longitude direction and the latitude direction respectively; l is the distance from the observation point to the center point of the Tesseroid unit body, and the unit is m; psi represents the spherical angle from the observation point to the center point of the Tesseroid cell body, and the unit is degree; omegaiAnd ωjRespectively, gaussian-legendre coefficients related to longitude and latitude.
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