Review points of Geodesy

2022-05-15 07:27:30

Key points for review of fundamentals of Geodesy
Chapter one The introduction

1. The definition of Geodesy
Geodesy is at a certain time - In spatial reference system , The science of Surveying and mapping the earth and other planetary bodies . Its basic task is to measure and map the earth and monitor its changes , Provide human activities with spatial information about planetary bodies such as the earth .
2. The role of Geodesy （ Five , Briefly describe the specific role of one of them ）
① Geodesy plays an important guarantee role in the construction of national economy and social development ;
give an example ： The transportation 、 Resource development 、 Water conservancy and hydropower projects 、 Industrial enterprise construction 、 Topographic map is needed for urban planning 、 Basis of design and development , Topographic map is the basic information necessary for all economic construction planning and development . In order to make topographic maps, we must first set up a national and local Geodetic Control Network .
② Geodesy in disaster prevention 、 disaster reduction 、 Disaster relief and environmental monitoring 、 It plays a special role in evaluation and protection ;
give an example ： China, Japan and other countries have established intensive geodetic deformation monitoring systems in the seismic zone , utilize GPS Interference with fixed and flowing very long baselines 、 Laser satellite stations and other modern geodetic means for automatic and continuous monitoring .
③ Geodesy is an important guarantee for the development of space technology and national defense construction ;
give an example ： An electronic map of the war zone 、 Digital map 、 The accurate three-dimensional coordinates of the target and the digital image map of the regional scene depend on the direct or indirect participation of geodetic technology .
④ The position of Geodesy in contemporary geoscience research is becoming more and more important ;
⑤ Geodesy is the basic science of each branch of Surveying and mapping ;
3. The basic system of geodesy
Modern geodesy is mainly divided into the following three basic branches ： The geometric （ astronomical ） Geodesy 、 Physical geodesy 、 Space geodesy
4. The basic content of Geodesy
（1） Determine the shape of the earth and its external gravity field and its change with time , Establish a unified geodetic coordinate system , Study crustal deformation , Determine the polar shift and the topography of the ocean surface and its changes ;
（2） Study the shape and gravity field of the moon and planets in the solar system ;
（3） Establish and maintain a national and global astronomical geodetic level control network, precision leveling network and marine geodetic control network with high-tech level , Meet the needs of the national economy and national defense construction ;
（4） Research on instruments and methods to obtain high-precision measurement results ;
（5） Study the mathematical transformation of the projection of the earth's surface to ellipsoid or plane and related geodetic calculation ;
（6） Research scale 、 High precision and multi category terrain network 、 Data processing theory and method of space network and its joint network , Establishment and application of survey database, etc .
5. Claro's theorem ( Fundamentals of geodesy P8 and P73__3—123 type )
Content ： Suppose the earth is an ellipsoid composed of many homogeneous material layers with different densities . These ellipsoids are all level surfaces , And the density of each layer is reduced from the geocenter to the outer layer according to the Claro formula .
significance ： Firstly, it demonstrates the calculation formula of normal gravity , Just know the location of the point （ latitude ）, The normal point of gravity can be calculated according to this formula , If we use geometric geodetic method and astronomical method to measure and You can calculate the oblateness of the earth .

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Chapter two Time coordinate system

1. precession of the equinoxes 、 nutation 、 Pole shift
precession of the equinoxes ： Due to day 、 The influence of celestial bodies such as the moon , The earth's axis of rotation rotates slowly around the Yellow pole in space , Form an inverted cone , This movement is called precession . The precession moves the vernal equinox westward every year 50.3″.
nutation ： The orbit of the moon around the earth （ Baidao ） For the zodiac 5° Inclination , This makes the magnitude and direction of the torque generated by the lunar gravity constantly change , This leads to the superposition of the earth's rotation axis on the basis of precession （18.6 Year of ） Short period circular motion , This phenomenon is called nutation .
Pole shift ： The relative position change of the earth's rotation axis relative to the internal structure of the earth body , Cause the position of the pole on the earth's surface to change with time , This phenomenon is called pole shift .

2. Time system
Based on the earth's autobiographical motion, the stellar time （ST） And world time （UT）; Based on the earth's revolution, the almanac time （ET）, And further developed into the centroid mechanics of the solar system (TDB) And the mechanics of the earth's center of mass (TDT); Based on the motion characteristics of atoms in matter, the atomic time （TAI）.
When stars （ST）： Take the vernal equinox as the basic reference point , The time determined by the Sunday apparent movement at the vernal equinox , When it's called a star .
World time （UT）： Take the true sun as the basic reference point , The time determined by its Sunday apparent movement , When it is called the true sun ; Because the apparent velocity of the real sun is uneven , Therefore, the true solar time is not a uniform time scale , To this end, a virtual flat sun running evenly on the equator is introduced , Its speed is equal to the average speed of the annual motion of the true sun . The average solar time from midnight in Greenwich is called universal time .
In the almanac （ET）： Due to the uneven rotation speed of the earth , Resulting in uneven time measured with it .1958 In the first 10 the IAU decision , since 1960 The calendar time based on the earth's revolution has been used to measure time since , Replace universal time with almanac time system .
Atomic time （AT）： Under zero magnetic field , The transition radiation between two hyperfine energy levels in the ground state of cesium atom at sea level 192631770 The duration of the cycle is atomic hours and seconds , Specified as the time unit in the international system of units . The international time bureau compares 、 Integrating atomic clock data from all over the world 、 When the final atom is determined , When it is called the International Atomic （TAI）.
Coordinated universal time (UTC)： Atomic time is not directly related to the rotation of the earth , Due to the long-term trend of slowing down the rotation speed of the earth , The difference between atomic time and universal time will gradually become larger , In order to ensure the coordination of time and season , Easy for daily use , It is established that the unit of measurement is atomic time and second 、 The difference in time from the flat sun time is less than 0.9 Second time system , Call it universal coordinated time (UTC).
Satellite positioning system time （ understand ）：GPS The time system is based on the U.S. Navy observation laboratory USNO When an atom is maintained, it is called GPST, Regulations 1980 year 1 month 6 Japan 0 when GPS And UTC equal .

3. Geodetic datum
A rotating ellipsoid used to represent the shape of the earth （ A body formed by an ellipsoid rotating around its minor axis ）, Establishing geodetic datum is to determine the parameters and orientation of rotating ellipsoid （ The axis of rotation of the ellipsoid is parallel to the axis of rotation of the earth , The initial meridional plane of the ellipsoid is parallel to the initial meridional plane of the earth ） And positioning （ The relative relationship between the center of the rotating ellipsoid and the center of the earth ）.

4. Celestial sphere ： Centered on the center of mass of the earth , An imaginary sphere with a radius of infinity is called the celestial sphere ; Important points, lines and planes on the celestial sphere ：
The celestial axis and the celestial pole ： The straight line extending from the earth's rotation axis is the celestial axis ; The intersection of the celestial sphere and the celestial axis is called the celestial pole ;
The equatorial plane of the celestial sphere and the equator of the celestial sphere ： Through the plane perpendicular to the celestial axis of the earth's center of mass , Called the equatorial plane of the celestial sphere , The celestial sphere that intersects the equator is called the celestial sphere ;
The meridian plane and meridian circle of the celestial sphere ： A plane containing the celestial axis and passing through any point on the earth , Called the meridian of the celestial sphere ; The great circle that intersects the celestial sphere is called the celestial meridian circle ;
Time circle ： A half circle that intersects the celestial sphere through the plane of the celestial sphere ;
Ecliptic ： The great circle where the orbital plane of the earth's revolution intersects the celestial sphere , The angle between the ecliptic plane and the equatorial plane is called the Yellow equatorial angle ;
Huangji ： Through the center of the celestial sphere , And the intersection of the straight line perpendicular to the ecliptic and the celestial sphere ;
Spring equinox ： When the sun moves from the southern hemisphere of the celestial sphere to the northern hemisphere on the ecliptic , The intersection of the ecliptic and the celestial equator ;

5. Geodetic reference system
The coordinate reference system is divided into ： Celestial coordinate system and earth coordinate system
Celestial coordinate system ： It is used to study the positioning and motion of celestial bodies and man-made satellites .
The earth coordinate system ： Used to study the positioning and motion of objects on the earth , It is a coordinate system established with the rotating ellipsoid as the reference body , It is divided into geodetic coordinate system （ The longitude of the earth 、 Latitude of the earth 、 The earth is high ） And space rectangular coordinates （X、Y、Z） There are two forms ;
Elevation reference system ： The elevation system with geoid as the reference plane is called positive height The elevation system with quasi geoid as the reference surface is called normal height ; The normal height and positive height have the following relationship with the earth height ：
H=H normal +ζ H=H It's high +N

6. Ellipsoid positioning and orientation
Ellipsoid positioning : It refers to determining the position of the center of the ellipsoid , It can be divided into two categories ： Local positioning and geocentric positioning . Local positioning requires that the ellipsoid and geoid have the best coincidence in a certain range , There are no special requirements for the central position of the ellipsoid ; Geocentric positioning requires the best consistency between ellipsoid and geoid in the world , At the same time, the center of the ellipsoid is required to be consistent with or closest to the center of mass of the earth .
The orientation of the ellipsoid ： To determine the direction of the axis of rotation of an ellipsoid , Whether it's local positioning or geocentric positioning , Both should satisfy two parallel conditions, namely ： The minor axis of the ellipsoid is parallel to the earth's axis of rotation ; The earth starting meridian plane is parallel to the astronomical starting meridian plane .

The type of ellipsoid :
Reference ellipsoid : With definite parameters ( Long radius a Flattening rate α), After local positioning and orientation , The earth ellipsoid that best fits the geoid of a certain area ;
Total earth ellipsoid : In addition to satisfying the geocentric positioning and double parallel conditions , When determining the parameters of the ellipsoid, it can make it the earth's ellipsoid which is the closest to the earth in the world ;

1. Geostationary coordinate system （ The earth coordinate system ）：
The earth fixed coordinate system is also called the earth coordinate system , It is a coordinate system fixed on the earth and rotating with the earth . The earth fixed coordinate system is divided into the reference center earth fixed coordinate system and the earth center earth fixed coordinate system ： A coordinate system based on a reference ellipsoid , It is firmly connected with the earth and moves synchronously with the earth , A coordinate system with the center of the reference ellipsoid as the origin , It's called the metacentric geostationary coordinate system .
A coordinate system based on the total earth ellipsoid . It is firmly connected with the earth and moves synchronously with the earth , A coordinate system with the center of the earth as the origin , Also known as the geocentric earth fixed coordinate system .

2. Old and new Beijing 54 The relationship of coordinate system
Old and new Beijing 54 The coordinate system adopts krasovsky ellipsoid parameters ;
They are all in the geocentric coordinate system ;
The positioning of the two is similar , But the orientation is different ;
New Beijing 54 The coordinate system is used in old Beijing 54 Xi'an coordinate system 80 The transition coordinate system established by coordinate system transformation .

3. Coordinate conversion rotation parameters
For existing rotations 、 The coordinate conversion of two spatial rectangular coordinate systems of translation and scaling exists 3 Two translation parameters and 3 Two rotation parameters and 1 A scale change parameter , total 7 Parameters .

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7. Satellite leveling can solve at least the following problems ：
（1） The height of the world's great ocean surface is measured in a unified system all over the world , So as to comprehensively study the Ocean Topography and regularly refine the parameters of the earth's external gravity field ;
（2） The radial component of the origin of the coordinate system to the center of mass of the earth in the satellite leveling equation is determined with centimeter accuracy ;
（3） Find out the parameters of the ellipsoid closest to the geoid in the world ;
（4） Can quickly study geoid , That is to determine the change in the distribution of the earth's mass in its body 、 The rapid change of geoid curvature and elevation caused by submarine earthquake ;
（5） Compare the satellite predicted altitude with its observed altitude , With these large amounts of statistical data, we can evaluate and improve the accuracy of satellite prediction ;
（6） Using satellite leveling data, the geodynamic shape parameters and their changes caused by the change of earth mass distribution can be determined reliably .

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3. The horizontal direction of ground observation is reduced to ellipsoid
Two basic requirements for reducing the horizontal direction of ground observation to ellipsoid ：① Based on the normal of the ellipsoid ;② The ground observation elements are transformed into the corresponding elements of the geodesic on the ellipsoid .
Reduce the horizontal direction to the ellipsoid , Including correction of vertical deviation 、 Elevation difference correction and section difference correction , It is customary to call these three corrections three difference corrections .
Ground length reduction ：1. Reduction of baseline ruler distance 2. Reduction of electromagnetic wave ranging

1. Earth theme solution
It is known that P1 Geodetic coordinates of points （L1,B1）,P1 to P2 The length of the earth line S And its large local potential angle A12, Calculation P2 Geodetic coordinates of points （L2,B2） And ground wire S stay P2 The inverse potential angle of the point A21, This kind of problem is called the positive solution of the Earth Theme ;
It is known that P1 and P2 Geodetic coordinates of points （L1,B1）(L2,B2), Calculation P1 To P2 The length of the earth line S And its positive and negative azimuth A12 and A21, This kind of problem is called Earth Theme inverse solution .

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Solving steps of geodetic subject based on Bezier geodetic projection ：（P131）
(1) Calculate the corresponding value of the sphere according to the known value on the ellipsoid , That is to realize the transition from ellipsoid to sphere ;
(2) Solving geodetic problems on a sphere ;
(3) Calculate the corresponding value on the ellipsoid according to the value obtained on the sphere , That is to realize the transition from a sphere to an ellipsoid . The fifth chapter Basic techniques and methods of geodesy

1. Layout principle of national plane geodetic control network
（1） The geodetic control network shall be arranged in grades 、 Step by step control ;
（2） The geodetic control network shall have sufficient accuracy ;
（3） The geodetic control network should have a certain density ;
（4） The geodetic control network shall have unified technical specifications and requirements .
2. Layout principle of national elevation control network
（1） From high to low 、 Step by step control ;
（2） The distribution of benchmarks shall meet a certain density ;
（3） The leveling reaches sufficient accuracy ;
（4） The first-class leveling network shall be retested regularly .