KR20110075176A - Method of constructing a gravity simulation material and system for performing the method - Google Patents

Abstract

PURPOSE: A system for constructing a gravity simulation material and a method thereof are provided to construct gravity simulation data by combining virtual gravity data and actual gravity data. CONSTITUTION: An ideal gravity value estimator(100) estimates an ideal gravity value using topography data which is stored to a topography data storage unit(30). The ideal gravity value is used for compensating the difference between the gravity value and the measured value. An ideal gravity model generator(200) creates an ideal gravity model similar to an actual gravity value using an end matching algorithm and stores the created value to an ideal gravity model storage(40). The ideal gravity value model applies the estimated ideal gravity value to an ideal free air value.

Description

METHOOD OF CONSTRUCTING A GRAVITY SIMULATION MATERIAL AND SYSTEM FOR PERFORMING THE METHOD}

The present invention relates to a method for constructing gravity simulation data and a system for performing the same, and more particularly, to a method for constructing gravity simulation data for constructing a gravity simulation data reflecting reality and a system for performing the same.

In general, the geoid is a model of the earth that matches the average sea level of the ocean and the imaginary sea level that extends to the continents. In other words, geoid is a spatial information infrastructure that is the most engineering and scientific basis that provides more accurate height values as a vertical standard of a country, and is essential for geodynamic analysis, activation of indirect leveling using GPS, and tidal analysis.

Geoids are perpendicular to the direction of gravity due to gravity everywhere, and their shape is close to a flat ellipsoid. However, it is irregular in part because of the accumulation of material underground (unevenly lateral in the basement) and the elevation difference between the continents and the sea floor. Mathematically, geoid is an equipotential plane. In other words, the potential is constant in all geoids. The potential function shows the combined effect of gravity due to the Earth's mass and repulsive force due to the Earth's rotational centroid around the axis.

In particular, as the technology for determining the precise geodetic position by satellites has recently been developed, it is possible to calculate an accurate ellipse height, which needs to be efficiently converted into elevations that appear as contours on topographic maps or are used for construction work. It is widely highlighted that a precise geoid model must be built.

Here, the elevation is based on the geoid, which is one of the planes of equipotential potential. That is, accurate geoids in each region can effectively operate GPS technology in determining elevation. While the measurement accuracy of ellipsoids by GPS survey reaches a high precision of several centimeters or less, the calculation of the geoid required to determine the elevation is ideally difficult to be calculated from the gravitational data all over the earth. Therefore, many countries have developed a global gravitational field model that synthesizes the gravity measurement data and satellite data of each country to develop a precision geoid model with a few cm accuracy.

As such, the essential elements in the construction of precise geoid models are gravity observation data and terrain data with high precision and high distribution density. The precision and distribution density of gravity observation data directly affects the final geoid determination.

Previously, researches related to algorithms that can calculate geoid models based on available data have been conducted.

Therefore, the technical problem of the present invention is to focus on this point, the object of the present invention is to create a virtual gravity data based on the terrain data, merge the generated virtual gravity data and the actual gravity data to create a gravity simulation data reflecting reality It provides a way to build gravity simulation data to build.

Another object of the present invention is to provide a gravity simulation data construction system for performing the above-described gravity simulation data construction method.

In order to realize the object of the present invention, a gravity simulation data construction method according to an embodiment, gravity simulation for obtaining a gravity anomaly model approximating the actual gravity value by correcting the difference between the measured gravity value and the actual gravity value In the data construction method, (a) estimating the gravity outlier using a gravity anomaly formula including the isostasy theory in the terrain data, and (b) lowering the estimated gravity outlier from the terrain data with precise resolution. In order to combine the measured gravity outliers distributed at the resolution, the method includes generating the gravity anomaly model by combining the estimated gravity anomaly and the measured frayer outliers by applying an end-matching algorithm.

In an embodiment of the present invention, step (a) is a step of (a-1) applying different density values according to whether the target area corresponding to the terrain data is land or ocean, and (a-2) at a specific point Computing the potential value due to the terrain condensation of may generate a gravity outlier in consideration of the isostasis effect to generate a terrain-corrected gravity outlier. Here, the terrain-corrected gravity outliers,

(여기서, 지형자료는 Δx와 Δy의 간격을 갖는 j*k의 행렬이고, G는 뉴턴의 중력상수이며, ρ는 지형의 밀도이며, D는 3km임)에 의해 정의되고,

는

에 의해 정의되며,

및

각각은 지오이드를 평면으로 근사하였을 때의 공간 주파수로서, 아래의 수학식

(Where topography is a matrix of j * k with a space between Δx and Δy, G is Newton's gravity constant, ρ is the density of the terrain, and D is 3km),

Is

Is defined by

And

Each is a spatial frequency when the geoid is approximated in a plane, and the following equation

(여기서, l은 0부터 J-1이고, m은 0부터 K-1까지임)에 의해 정의될 수 있다.

Where l is 0 to J-1 and m is 0 to K-1.

In an embodiment of the present invention, step (b) applies a low resolution triangular network by removing an optimized plane from the high resolution data corresponding to the terrain corrected gravity outlier based on the terrain corrected gravity outlier and the actual measured gravity outlier. And checking whether the high resolution data exists on the triangular network or the number is 3 or less, and if the high resolution data exists on the triangular network or the number is 3 or less, Generating a consistent high resolution gravitational abnormality model of the same order as the gravitational outlier measured from the terrain by applying a mathematical equation corresponding to the corrected gravitational outlier; and in the checking step, the high resolution data is outside the triangle network or If the number is more than 3, the terrain is applied by applying the equation corresponding to the second corrected gravity outlier. And generating a consistent high resolution gravitational outlier model of the same order as the gravitational outliers measured from. Here, the equation corresponding to the first corrected gravity outlier is

(여기서,

,

및

은 고해상도 데이터에 의해 만들어진 정규 격자상의 고해상도 데이터가 매핑된 평면의 방정식에서 x 및 y 각각에 대응하는 변수 및 상수)에 의해 정의될 수 있다.

(here,

,

And

May be defined by variables and constants corresponding to x and y respectively in the equation of the plane to which the high resolution data on the regular lattice generated by the high resolution data is mapped.

On the other hand, the equation corresponding to the second corrected gravity outlier is

,

및

은 고해상도 데이터에 의해 만들어진 정규 격자상의 고해상도 데이터가 매핑된 평면의 방정식에서 x 및 y 각각에 대응하는 변수 및 상수)에 의해 정의될 수 있다. (Where α, β and δ are variables and constants corresponding to x and y respectively in the equation of the plane of the triangle created by the low resolution data,

,

And

May be defined by variables and constants corresponding to x and y respectively in the equation of the plane to which the high resolution data on the regular lattice generated by the high resolution data is mapped.

In order to realize the above object of the present invention, a gravity simulation data building system according to an embodiment includes a gravity outlier estimation unit and a gravity abnormality model generation unit. The gravity outlier estimator estimates the gravity outlier using a gravity anomaly estimation formula including an isostasy theory in the terrain data stored in the terrain data storage to correct the difference between the measured gravity value and the actual gravity value. do. The gravity anomaly model generation unit generates a gravity anomaly model approximating the actual gravity value by applying an end-matching algorithm to apply the estimated gravity anomaly to the measured free air anomaly and stores it in the gravity anomaly model storage unit.

In an embodiment of the present invention, the gravity outlier estimating unit applies gravity to the terrain data reading module for reading the terrain data stored in the terrain data storage unit, and isostasis theory to the terrain data read by the terrain data reading module. An isostasis theory application module for estimating outliers, a target area determination module for determining whether a target area of the terrain data read by the terrain data reading module is a marine area or a land area, and the target area determination module If the terrain data is determined to be a marine area, the marine area density value application module applying a density value corresponding to the marine area, and if the terrain data is determined to be a land area by the target area determination module, the density corresponding to the land area. Land area density application module and a marine area density application module or land area density application Comprising a gravity outlier generating section that calculates the potential value due to terrain condensation at a specific point in the terrain data to which different density values are applied by the module, and generates a gravity-corrected terrain outlier considering the isostasi effect. can do.

The terrain-corrected gravity outlier,

(여기서, 지형자료는 Δx와 Δy의 간격을 갖는 j*k의 행렬이고, G는 뉴턴의 중력상수이며, ρ는 지형의 밀도이며, D는 3km임)에 의해 정의되고,

는 아래의 수학식

(Where topography is a matrix of j * k with a space between Δx and Δy, G is Newton's gravity constant, ρ is the density of the terrain, and D is 3km),

Is the following equation

에 의해 정의되며,

및

각각은 지오이드를 평면으 로 근사하였을 때의 공간 주파수로서, 아래의 수학식

Is defined by

And

Each is the spatial frequency when the geoid is approximated to the plane, and the following equation

(여기서, l은 0부터 J-1이고, m은 0부터 K-1까지임)에 의해 정의될 수 있다.

Where l is 0 to J-1 and m is 0 to K-1.

In an embodiment of the present invention, the gravity anomaly model generation unit may include a first storage module for storing the terrain-compensated high-resolution gravity outlier, a second storage module for storing the actually measured low-resolution gravity outlier, and the high resolution data. A gravitational outlier matching module for removing a planarized plane and applying the triangular network of low resolution gravitational outliers, and a high resolution for determining whether or not the high resolution data exists on the triangular network or within three areas defined by the triangular network If the data determination module and the high resolution data determination module check that the high resolution data exists on the triangular network or not more than three in the area defined by the triangular network, it corresponds to the first corrected gravity outlier. Apply the equation to the same order of gravity outlier A first gravity outlier application module for generating an inertial high resolution gravity anomaly model, and the high resolution data determination module causes the high resolution data not to exist on the triangle network or to exceed three in an area defined by the triangle network; A second gravity outlier application module for generating a consistent high resolution gravity anomaly model of the same order as the gravity outlier measured from the terrain by applying an equation corresponding to the second corrected gravity outlier if checked to be present. Can be. Here, the equation corresponding to the first corrected gravity outlier is

(여기서,

,

및

은 고해상도 데이터에 의해 만들어진 정규 격자상의 고해상도 데이터가 매핑된 평면의 방정식에서 x 및 y 각각에 대응하는 변수 및 상수)에 의해 정의될 수 있다.

(here,

,

And

May be defined by variables and constants corresponding to x and y respectively in the equation of the plane to which the high resolution data on the regular lattice generated by the high resolution data is mapped.

On the other hand, the equation corresponding to the second corrected gravity outlier is

,

및

은 고해상도 데이터에 의해 만들어진 정규 격자상의 고해상도 데이터가 매핑된 평면의 방정식에서 x 및 y 각각에 대응하는 변수 및 상수)에 의해 정의될 수 있다.(Where α, β and δ are variables and constants corresponding to x and y respectively in the equation of the plane of the triangle created by the low resolution data,

,

And

May be defined by variables and constants corresponding to x and y respectively in the equation of the plane to which the high resolution data on the regular lattice generated by the high resolution data is mapped.

According to the method for constructing the gravity simulation data and the system for performing the same, the virtual gravity data is generated based on the terrain data and merged with the generated virtual gravity data and the actual gravity data, so that the gravity simulation data reflecting the reality can be constructed. have.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will now be described in more detail with reference to the accompanying drawings. As the inventive concept allows for various changes and numerous embodiments, particular embodiments will be illustrated in the drawings and described in detail in the text. However, this is not intended to limit the present invention to the specific disclosed form, it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention.

Like reference numerals are used for like elements in describing each drawing. In the accompanying drawings, the dimensions of the structures are shown in an enlarged scale than actual for clarity of the invention.

The terms first, second, etc. may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as the second component, and similarly, the second component may also be referred to as the first component. Singular expressions include plural expressions unless the context clearly indicates otherwise.

In this application, the terms "comprises", "having", and the like are used to specify that a feature, a number, a step, an operation, an element, a part or a combination thereof is described in the specification, But do not preclude the presence or addition of one or more other features, integers, steps, operations, components, parts, or combinations thereof.

Also, unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art, and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

In addition, in describing the present invention, when it is determined that the detailed description of the related well-known technology or configuration may make the gist of the present invention unclear, the detailed description thereof will be omitted. In addition, terms to be described below are terms defined in consideration of functions in the present invention, which may vary according to intention or custom of a user, an operator, or the like. Therefore, the definition should be based on the contents throughout this specification.

Then, prior to describing the present invention, the terms described in the present invention are briefly summarized as follows.

In general, the actual gravity cannot be compared with each other because the altitude, topography, and material distribution among the observation points are different. Therefore, to obtain a comparison value, the value must be corrected under the same physical condition, which is called gravity correction. There are three types of gravity correction, one of which is bool correction. The bouncy correction is a correction by removing the attraction force due to the material between the measuring point and the geoid surface affects gravity.

Calibrate to compare the gravity values observed at each point. The difference between the corrected observed gravity and the standard gravity is called gravity anomaly (ie corrected gravity-standard gravity). Here, the standard gravity is a gravity value calculated theoretically at each latitude, assuming that the earth is a geometric spheroid close to the geoid and the density distribution of the material inside the earth is constant in the horizontal direction. On the other hand, the correction gravity is the conversion of all necessary information into the gravity value on the reference plane through the correction.

The gravity anomaly generally has a small continental crust of '-' and a large ocean crust of '+'. The gravitational anomaly is close to zero at the coast, increases with a positive value toward the ocean floor in the ocean, and decreases with a negative value toward the highlands on the continent. This suggests that continental crusts are less dense and sea crusts are denser below sea level.

Gravity correction includes altitude correction, bouncy correction, terrain correction, and the like, and gravity correction includes altitude abnormality and boulder abnormality according to the degree of correction.

Gravity at the surface decreases with height at a rate of approximately 0.3 mGal for a height change of 1 meter. Therefore, the gravity value on the geoid plane can be obtained by adding the gravity value reduced due to the height of the observation site to the observed gravity value. This is called altitude correction.

After the altitude is corrected from the measured gravity value, the value obtained by subtracting the standard gravity is referred to as altitude or higher. Above this altitude, the influence of the attraction of the material between the gravimetric point and the geoid surface remains, so above the altitude in land areas it is usually positive, while in the sea area it is negative.

Altitude correction to the observed gravity values also retains the influence of the attraction by the material between the gravity measurement point and the geoid plane. This effect serves to increase gravity. Therefore, if the altitude correction is applied to the measured gravity value and the influence is subtracted, the gravity value without the substance above the geoid plane can be obtained. This correction is called boolean correction. The bouncy correction is corrected on the assumption that the material above the geoid plane is an infinite plate whose thickness is the distance between the observation point and the geoid plane, that is, the elevation of the viewpoint.

The bouncy correction is corrected assuming that the material above the geoid plane is an infinite plate, but the actual terrain has ups and downs, so the bouncy correction is overcorrected as much as the influence of the ups and downs of the terrain. Terrain correction is to correct the difference between the infinite flat and the influence of the terrain ups and downs.

In addition, it is said that the observed gravity value is subtracted from the standard gravity after altitude correction, boolean correction, and terrain correction. As the Bouge anomaly does not include the influence of matter above the geoid plane, this suggests that there is a regional difference in the density distribution of underground constituents. So boogie ideals are the key to internal research. Bougain Anomaly is usually negative on land and positive on sea due to crustal balance. In other words, it will prove perceptual equilibrium.

Then, in the following, it will be described to create a virtual gravity data based on the topographical data, merge the generated virtual gravity data with the actual gravity data to build a gravity simulation data reflecting the reality.

In the present embodiment, the topographical data has been traditionally represented two-dimensionally by using topographical maps, etc., but recently, with the development of computers, the digital tereline model, which is a digital topographical data, has been improved due to the improvement of the allocation and processing capability of information storage media. As the need for Digital Terrain Model (DTM) emerges, various digital terrain data have been developed around the world, and its use is becoming common in many fields. The topographical data of Korea is officially managed by the National Geographic Information Institute under the Ministry of Construction and Transportation (Ministry of Land, Transport and Maritime Affairs). In response to recent social demands, the National Geographic Information Institute has published electronic maps based on topographic maps of various scales of Korea.

Gravity data is a measure of the small changes in gravity in the gravitational field of the earth's surface, and it can be used not only for mineral exploration by analyzing subterranean geometries and subterranean geometries, but also for geothermal systems and ocean tidal studies within the earth. to be. In other words, all objects have the property of moving to the center of the earth. In this phenomenon, the force acting on the object is gravity. The task of determining the shape of the earth from the basic flow that the value of gravity or direction of gravity varies with latitude is one of the main purposes of gravity measurement since Newton. Since the gravity value depends on the underground structure, the so-called gravity anomaly, which measures gravity and estimates the underground structure inversely from its geographical distribution, is a central problem of gravity.

Gravity exploration is a method of measuring the gravity of an irradiated area and estimating the density distribution structure underground from the measurement result. In the case where there is a rock with a high density underground, if the rock is the same depth and the depth is shallow, the greater gravity value is measured at the surface. On the contrary, when there are cavities in the basement, the gravity value measured at the surface becomes small. Therefore, gravity exploration measures the change of gravity and is used for exploration of underground geological structures and underground resources.

1 is a block diagram illustrating a gravity simulation data construction system according to the present invention.

Referring to FIG. 1, the gravity simulation data building system 10 according to the present invention includes a gravity outlier estimator 100 and a gravity abnormality model generator 200. Although the gravity simulation data building system 10 is shown as a separate system from the user computer 20, this is logically separated for convenience of description but not separated in hardware. That is, the gravity simulation data building system 10 may be programmed in a computer-readable recording medium to be accessed by the user computer 20.

The gravity outlier estimator 100 estimates the gravity outlier using the terrain data stored in the terrain data storage unit 30 to correct the difference between the estimated gravity value and the actual gravity value, and estimates the estimated gravity outlier. Provided to the gravity abnormality model generation unit 200. The terrain data may include Shuttle Radar Topography Mission (SRTM) data. The world's first Digital Elevation Models (DEMs), called Shuttle Radar Topography Missions (SRTMs), are available at 90m * 90m intervals. Altitude attribute value is stored.

The gravity anomaly model generation unit 200 generates a gravity anomaly model that approximates the actual gravity value by applying an end-matching algorithm in order to apply the estimated gravity anomaly to the estimated free air outlier. Save to 40). That is, the gravity anomaly model generation unit 200 generates a gravity anomaly model of the same order as the measured gravity anomaly by combining the estimated gravity anomaly and the measured Freyer anomaly using an end-matching algorithm.

FIG. 2 is a block diagram illustrating a gravity outlier estimation unit shown in FIG. 1.

Referring to FIG. 2, the gravity outlier estimator 100 includes an isostasi application unit 110 and a gravity outlier generation unit 120.

The isostasi application unit 110 is a topographical data reading module 111, isostasi theory theory module 112, target area determination module 113, marine area density application module 114 and land area density value Application module 115 is included.

The terrain data reading module 111 reads the terrain data stored in the terrain data storage unit 30.

The isostasis theory application module 112 applies isostasis theory to the terrain data read by the terrain data reading module to estimate the gravity outlier.

The target area determination module 113 determines whether the target area of the terrain data read by the terrain data reading module is a corresponding area or a land area.

The marine area density application module 114 applies the marine area density value when the terrain data is determined to be a marine area by the target area determination module.

The land area density application module 115 applies the land area density value when the terrain data is determined to be the land area by the target area determination module.

The gravity outlier generating unit 120 includes a discrete Fourier application module 122.

In the present embodiment, the isostar application unit 110 is a topographical data reading module 111, isostar theory theory application module 112, target area determination module 113, marine area density value application module 114 And it was described that separated by the land area density application module 115, which is logically separated, not separated by hardware.

Then, a description of the terrain data-based gravity anomaly simulation by the gravity anomaly estimation unit 100 will be described.

The first step in the process of merging the estimated gravity outlier from the elevation of terrain data (H) and the actual measured free-air gravity outlier is to establish a theoretical relationship between the estimated gravity outlier and the actual measured free-air gravity outlier.

The Bouguer outlier ΔgB (P) at a point P on the ground surface may be defined as in Equation 1 below.

Where G is Newton's gravitational constant, ρ is the terrain density, and c is the terrain correction calculated by the difference between the assumption of a boogie board around the measurement point and the actual terrain.

In Equation 1, ignoring the constant (c), the linear relationship between the elevation (H) and the unduly outlier (ΔgB (P)) becomes apparent.

Assuming that the region-wide boolean outlier Δg (P) is a long wavelength signal or a specific constant, ie, B = ΔgB, the following equation is established.

Where B = ΔgB, G is Newton's gravity constant, and ρ is the density of the terrain.

The second method for estimating the correlation between elevation (H) and gravitational outliers is to use the Isostasy theory. Isostasis theory is a theory based on the feature that the terrain is trying to achieve mechanical equilibrium with time. Gravity anomaly ΔgI (P) estimated by isostasis theory may be defined as in Equation 3 below.

Here, C (P) is information corresponding to the influence of gravity according to all masses on the top of the geoid, and A (P) is information corresponding to the correction effect calculated based on the isostasi theory.

If C (P) is removed, the space on the geoid becomes uniform, and the effect of the terrain is expressed as the rate of change in the negative direction with respect to the gravity potential of the terrain mass, as shown in Equation 4 below.

)이다. Where σQ is the unit sphere in the integral region and SPQ 'is the distance between the P point and the Q point in the mass (

)to be.

A (P) refers to the attraction caused by the mass added to make the mantle homogeneous below the compensation depth. Using the Airy-Isostasy (Airy-Isostasy) model, this effect is expressed by Equation 5 below by the difference in density between the crust and the mantle beneath it.

Where ρ is the density of the crust and ρm is the density of the mantle.

3 is a conceptual diagram for explaining an Airy-Isostasy model.

As shown in FIG. 3, according to the Airy-Isostatashi model, it is assumed that the terrain floats in balance on the mantle according to the buoyancy principle.

As shown in FIG. 3, the density ρH of the compensation depth is defined by Equation 6 below.

Where H 'is the depth of the root relative to the depth of compensation.

Similarly, in oceans, the water is less dense than the crust, so the mantle penetrates into the crust and becomes in equilibrium. In summary, Equation 6 may be defined as Equation 7 below.

Where B is the depth to the bottom of the sea, B 'is the height away from the mantle root, and ρw is the density of the seawater.

If the tectonic balance correction is applied perfectly, the isostatic anomaly is eliminated since the pre-air gravitational outlier Δg (P) is a value due to the density and the tectonic balance compensation value compared to the terrain. In general, since the perceptual balance abnormality is very small when? GI (P)? 0, the pre-air gravity abnormality value Δg (P) of Equation 3 may be expressed as Equation 8 below.

Here, C (P) is information corresponding to the influence of gravity according to all masses on the top of the geoid, and A (P) is information corresponding to the correction effect calculated based on the isostasi theory.

Therefore, it can be judged that the pre-air gravitational outlier Δg (P) is calculated from the attraction caused by the mass of the terrain whose density is ρ present on the geoid and the mass present below the compensation depth.

Assuming that the mass existing under the compensation depth is negative, the following equation (9) is given.

In Equation 9, the right side may be defined through various assumptions.

One of them is to condense the terrain onto the geoid with Helmert condensation, and the effect of gravity is calculated from a two-dimensional mass layer with a given density at points on the geoid, as shown in Equation 10 below. .

In a similar way, the effect of gravity in the oceans that exist beneath the terrain can be modeled by forming layers on the geoid. This means a lack of density in the ocean compared to the earth's crust. Density in the two-layer is a negative value, can be defined as shown in Equation 11 below.

On the other hand, the potential (V) due to the condensation of the terrain at a point (P) that is not the geoid phase is shown in Equation 12 below.

Here, S is the distance between one point P and the integration point, Q∈land refers to satisfying the conditions of the land area, and Q∈ocean refers to satisfying the conditions of the marine area.

Potential (V) and its variation is a continuous value as long as point (P) is above the geoid. In addition, Equation 12 for the fixed height of a point P is expressed as a convolution between the elevation H and the inverse of the distance s.

By the average approximation equation, the distance s is defined as in Equation 13 below.

Where (x ', y') is the local coordinate on the geoid.

In the case of z> 0, if the convolution theory is applied to explain the Fourier transform with respect to the potential, the following equation (14) is used.

일 때, μ, ν는 지오이드를 평면으로 근사하였을 때의 공간 주파수이다.here,

Is the spatial frequency when the geoid is approximated in a plane.

로 가정) 때문에 발생하는 중력에 대한 푸리에변환은 아래의 수학식 15와 같으며, 위의 관계는 수학식 3에서 고려된 바와 같이 선형이다. As a result, the mass layer (

The Fourier transform for gravity caused by the equation is as shown in Equation 15 below, and the relationship is linear as considered in Equation 3.

If the model includes the perceptual balance correction according to the Airy theory for the topographic layer, the other layer can be identified by the value at the compensation depth.

의

밀도에 대한 보정의 깊이가 응축된다. 밀도이며, 이것은 레벨 D 아래의 맨틀의 밀도와 확정된 깊이 H’에 대한 밀도에서의 부족량을 의미한다. 또한, 해양지역에서는 In land areas these layers

of

The depth of correction for the density is condensed. Density, which means the deficiency in the density of the mantle below level D and the density for a defined depth H '. In marine areas,

와

밀도를 갖는 이상층(anomalous layer)을 포함함으로 인한 지형과 지각균형 보상값 때문에 발생하는 전체 포텐셜의 푸리에변환은 지표면층의 값으로 근사하면 아래의 수학식 16과 같이 정의될 수 있다. In land and sea

Wow

The Fourier transform of the entire potential caused by the terrain and the crustal equilibrium compensation value due to the inclusion of an anomalous layer having a density can be defined as Equation 16 below when approximated to the surface layer value.

From this, the Fourier transform corresponding to the gravity error may be defined as in Equation 17 below.

That is, the gravity outlier at the level z> 0 is defined by Equation 18 below.

In general, the perceptual balance correction amount factor for D = 30 km, which is a compensation surface depth, is expressed by Equation 19. If the gravity value estimated from the terrain with a resolution more than D / 2 = 15 km, the correction amount can be ignored.

For the practical application of Equation 18 above, applying the Discrete Fourier Transform defined by Brigham can yield a gravitational outlier as shown in Equation 20 below.

Here, the topographic data is a matrix of j * k with a space between Δx and Δy, G is Newton's gravity constant, ρ is the density of the terrain, and D is 3km. The unit of gravity outlier calculated by Equation 20 is mGal.

는 아래의 수학식 21에 의해 정의될 수 있다. In Equation 20,

May be defined by Equation 21 below.

각각은 지오이드를 평면으로 근사하였을 때의 공간 주파수로서, 아래의 수학식 22에 의해 정의될 수 있다. 및 In Equation 21,

Each is a spatial frequency when the geoid is approximated in a plane, and may be defined by Equation 22 below. And

Where l is from 0 to J-1 and m is from 0 to K-1.

In other words, Equation 20 is a process of calculating gravity anomaly from the elevation of terrain data, and is an estimated gravity outlier model by applying the theory of isostasy.

FIG. 4 is a block diagram illustrating a gravity abnormality model generation unit shown in FIG. 1.

Referring to FIG. 4, the gravity abnormality model generating unit 200 includes a first storage module 210, a second storage module 220, a gravity abnormality matching module 230, a high resolution data determination module 240, and a first gravity. The outlier applying module 250 and the second gravity outlier applying module 260 are included.

The first storage module 210 stores the terrain-corrected high-resolution gravity outlier data (or Fine Resolution-data) provided by the gravity outlier estimation unit 100.

The second storage module 220 stores the actual measured low resolution gravitational outlier data (or CR (Coarse Resolution) -data).

The gravity outlier matching module 230 removes the optimized plane from the high resolution data and applies a triangular network of the low resolution gravity outliers.

The high resolution data determination module 240 determines whether or not the high resolution data exists on the triangular net or less than three in an area defined by the triangular net.

If the first gravity outlier application module 250 is checked by the high resolution data determination module that the high resolution data exists on the triangular network or is present in three or less areas within the area defined by the triangular network, the first correction is performed. Applying the equation corresponding to the gravity outliers generated by the generated gravity data based on the terrain data corrected by the actual gravity data to provide to the gravity abnormality model storage unit 40 (shown in Figure 1).

The second gravity outlier application module 260 checks that the high resolution data is not present on the triangle network or is more than three in the area defined by the triangle network by the high resolution data determination module. Applying a mathematical equation corresponding to the corrected gravity outliers to generate a simulation gravity data based on the terrain data corrected by the actual gravity data to the gravity abnormality model storage unit 40.

In the present embodiment, the gravity abnormality model generation unit 200 applies the first storage module 210, the second storage module 220, the gravity outlier matching module 230, the high resolution data determination module 240, and the first gravity outlier. Although the separation into the module 250 and the second gravity outlier application module 260 has been described, this is logically separated and not separated into hardware.

Next, the two-dimensional end-matching between the actual gravity abnormality and the terrain-based gravity abnormality by the gravity abnormality model generation unit 200 will be described.

In an embodiment of the present invention, an end-matching algorithm is used in this embodiment in order to match the estimated gravity outliers estimated from the terrain data with precise resolution and the measured free air gravity outliers distributed at low resolution.

First, divide a given low resolution data network into triangles. For example, Deluanary triangulation is an optimal algorithm that maximizes the minimum value of each truncated triangle. The higher resolution data can then be adjusted to fit the triangle's vertices.

6 is a conceptual diagram illustrating an end-matching algorithm for explaining the construction of gravity simulation data according to the present invention.

Referring to Figure 6, the triangles created by the resolution data and the high resolution data on the regular grid are adjusted to the optimal plane by the triangle vertices that contain them. First, assuming the equation of the plane can be defined as shown in Equation 23 below.

Where z is gravity anomaly and (x, y) is the plane coordinate.

에 대해 평면으로 조정하고, 산출된 추정치는

와 같다. If there is a gravitational outlier simulated from the geocoordinate of n> 3 in the triangle, then the outlier

With respect to the

Same as

On the other hand, if the high-resolution data on the regular grid is expressed in a matrix, the following equation (25).

We can remove the plane defined by Equation (25) from the terrain data-based gravity outliers, and add the plane containing the vertices of the actual gravity data by the given equation.

은 실제 삼각망에 매핑된 저해상도의 중력 이상치 집합 데이터이고,

는 고해상도 데이터에서 평면을 제거하기 위한 변수이고,

은 지형 자료 기반의 중력 이상치 집합 데이터이다. here,

Is a low resolution set of gravity outliers mapped to a real triangle network,

Is a variable for removing planes from high resolution data,

Is a set of gravity outlier data based on terrain data.

은 세 꼭지점에서 실제 중력자료의 값을 가진다. ACR is the same as A in Equation 26, but at the vertices of the triangle

Has the actual gravity data at three vertices.

Therefore, as shown in Equation 27 below, the terrain-based simulation gravity data corrected by the actual gravity data can be generated.

In equation 27, if n = 0, no calculation is performed.

On the other hand, if n is 1, 2, 3 or terrain-based gravity data in a straight line in the triangle, it is defined as in Equation 28 below.

In this way, a high resolution gravitational anomaly model of the same order as the gravitational anomalies measured from the terrain can be generated.

Although described above with reference to the embodiments, those skilled in the art can be variously modified and changed within the scope of the invention without departing from the spirit and scope of the invention described in the claims below. I can understand.

As described above, according to the present invention, it is possible to obtain high-precision height information by using a state-of-the-art GPS technology by constructing a precision geoid, thereby improving the method of acquiring spatial information more efficiently.

In addition, the construction of the geoid according to the present invention determines the gravitational field of the wide area, for example, the gravitational field of the Republic of Korea can be used as a basic data for studying the crustal movement, underground resource exploration, changes in sea level. In particular, the gravity data according to the present invention is to provide a precise gravity value required for the operation of aircraft, missiles, submarines, etc. can be usefully applied to the defense field.

1 is a block diagram illustrating a gravity simulation data construction system according to the present invention.

FIG. 2 is a block diagram illustrating a gravity outlier estimation unit shown in FIG. 1.

3 is a conceptual diagram for explaining an Airy-Isostasy model.

FIG. 4 is a block diagram illustrating a gravity abnormality model generation unit shown in FIG. 1.

5 is a conceptual diagram illustrating an end-matching algorithm for explaining the construction of gravity simulation data according to the present invention.

<Description of the symbols for the main parts of the drawings>

10: gravity simulation data building system 20: user computer

30: terrain data storage 40: gravity abnormal model storage

100: gravity outlier estimation unit 200: gravity failure model generation unit

110: isostar application unit 120: gravity outlier generating unit

111: terrain data reading module 112: isostasis theory application module

113: target area determination module 114: marine area density application module

115: land area density application module 122: discrete Fourier application module

210: first storage module 220: second storage module

230: gravity outlier matching module 240: high resolution data determination module

250: first gravity outlier application module 260: second gravity outlier application module

Claims (12)

In the gravity simulation data construction method to obtain the gravity anomaly model approximating the actual gravity value by correcting the difference between the measured gravity value and the actual gravity value, (a) estimating gravity outliers using gravity anomaly estimation formulas including isostasy theory in the topographical data; And (b) Combine the estimated gravity anomaly with the measured frayer anomalies by applying an end-matching algorithm to combine the estimated gravity anomalies from the precise resolution terrain data with the low-resolution distribution. Gravity simulation data building method comprising the steps of generating. The method of claim 1, wherein step (a) (a-1) applying different density values according to whether the target area corresponding to the topographical data is land or ocean; And (a-2) generating a gravity outlier considering the isostasi effect by calculating the potential value due to terrain condensation at a specific point, and generating a terrain-corrected gravity outlier. Way. The method of claim 2, wherein the terrain-corrected gravity outliers,

(Where topography is a matrix of j * k with a space between Δx and Δy, G is Newton's gravity constant, ρ is the density of the terrain, and D is 3km),

Is the following equation

Is defined by

And

Each is a spatial frequency when the geoid is approximated in a plane, and the following equation

(Where l is 0 to J-1 and m is 0 to K-1). The method of claim 1, wherein step (b) comprises: (b-1) applying a low resolution triangle network by removing an optimized plane from the high resolution data corresponding to the terrain corrected gravity outlier based on the terrain corrected gravity outlier and the actual measured gravity outlier; (b-2) checking whether the high resolution data exists on a triangular network or the number is three or less; (b-3) In the checking step, when the high resolution data exists on the triangular network or the number is checked to be 3 or less, the gravitational outlier measured from the terrain by applying the equation corresponding to the first corrected gravitational outlier and Generating a consistent high resolution gravity anomaly model of the same order; And (b-4) In the checking step, if the high resolution data exists outside the triangular network or the number is checked more than three, the same as the gravity outlier measured from the terrain by applying the equation corresponding to the second corrected gravity outlier And generating a consistent, high resolution gravitational anomaly of orders. The equation corresponding to the first corrected gravity outlier is

(here,

,

And

Is a variable and constant corresponding to each of x and y in the equation of a plane to which high resolution data on a regular lattice generated by the high resolution data is mapped. The equation corresponding to the second corrected gravity outlier is

(Where α, β and δ are variables and constants corresponding to x and y respectively in the equation of the plane of the triangle created by the low resolution data,

,

And

Is a variable and constant corresponding to each of x and y in the equation of a plane to which high resolution data on a regular lattice created by the high resolution data is mapped. In order to compensate for the difference between the measured gravity value and the actual gravity value, the gravity outlier estimator estimates the gravity outlier by using the gravity anomaly formula including isostasy theory in the terrain data stored in the terrain data storage. ; And In order to apply the estimated gravity anomaly to the measured free air anomaly, a gravity anomaly model generator which generates a gravity anomaly approximating the actual gravity value and stores it in the gravity anomaly model storage through the application of an end-matching algorithm Gravity simulation data building system. The method of claim 7, wherein the gravity outlier estimation unit, A terrain data reading module for reading terrain data stored in the terrain data storage unit; An isostasis theory application module for estimating gravity outliers by applying isostasis theory to the terrain data read by the terrain data reading module; A target area determination module for determining whether a target area of the terrain data read by the terrain data reading module is a corresponding area or a land area; A marine area density value application module for applying a density value corresponding to the marine area when the terrain data is determined to be a marine area by the target area determination module; A land area density application module for applying a density value corresponding to a land area if the terrain data is determined as the land area by the target area determination module; And Calculate the potential outlier considering the isostasi effect by calculating the potential value due to terrain condensation at a specific point in the terrain data to which different density values are applied by the marine area density application module or the land area density application module. Gravity outlier generation unit comprising a gravity outlier generating unit for generating a terrain-corrected gravity outlier. The method of claim 8, wherein the terrain-corrected gravity outlier,

(Where topography is a matrix of j * k with a space between Δx and Δy, G is Newton's gravity constant, ρ is the density of the terrain, and D is 3km),

Is the following equation

Is defined by

And

Each is a spatial frequency when the geoid is approximated in a plane, and the following equation

(Where l is 0 to J-1 and m is 0 to K-1). The method of claim 7, wherein the gravity abnormality model generation unit, A first storage module for storing the terrain-compensated high resolution gravity outlier; A second storage module that stores the actual measured low resolution gravity outlier; A gravity outlier matching module for removing the optimized plane from the high resolution data and applying a triangular network of the low resolution gravity outliers; A high resolution data determination module for determining whether the high resolution data exists on the triangular network or less than three in the area defined by the triangular network; If it is checked by the high resolution data determination module that the high resolution data is present on the triangular network or not more than three in the area defined by the triangular network, the equation corresponding to the first corrected gravity outlier is applied. A first gravity outlier application module for generating a consistent high resolution gravity outlier model of the same order as the gravity outliers measured from the terrain; And If it is checked by the high resolution data determination module that the high resolution data does not exist on the triangular network or exists more than three in the area defined by the triangular network, the equation corresponding to the second corrected gravity outlier is applied. And a second gravity outlier application module for generating a consistent high resolution gravity outlier model of the same order as the gravity outlier measured from the terrain. 11. The method of claim 10, wherein the equation corresponding to the first corrected gravity outlier is

(here,

,

And

And a variable and a constant corresponding to each of x and y in the equation of the plane to which the high resolution data on the regular lattice generated by the high resolution data are mapped. 11. The method of claim 10, wherein the equation corresponding to the second corrected gravity outlier is

(Where α, β and δ are variables and constants corresponding to x and y respectively in the equation of the plane of the triangle created by the low resolution data,

,

And

And a variable and a constant corresponding to each of x and y in the equation of the plane to which the high resolution data on the regular lattice generated by the high resolution data are mapped.

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