# Review key points of basic geodesy

2022-05-15 07:28:46

《 Fundamentals of geodesy 》
1. Geodesy is through the establishment of a geodetic control network on a vast surface , Accurately determine the coordinates of geodetic control points , Study and determine the shape of the earth 、 The size and the theory of the earth's gravity field 、 The discipline of technology and method . Modern geodesy includes space 、 Physical and geometric geodesy
2. The three branches of modern geodesy are geometry ： Determine the shape and size of the earth and determine the geometric position of ground points . Physics ： Using physical methods （ Gravimetry ） Determine the shape of the earth and its external gravity field . Space ： The theory of space geodesy represented by artificial earth satellite and other space detectors 、 Technology and methods .
3. Geodesy is a branch of Surveying and mapping . The main task is to measure and map the earth and monitor its changes , Provide space information about the earth for human activities . Earth information is a subject . It is the foundation of all surveying and Mapping Science and technology .
4. The stage of human understanding of the earth, the stage of the earth's sphere , For the first time, the meridian arc length measurement method is used to estimate the earth's radius . This is the first time that human beings have applied the concept of radian measurement to estimate the size of the earth . The ellipsoidal phase of the earth , At this stage , After verifying Newton's law of universal gravitation and the theory that the earth is an ellipsoid , Begin to move towards the road of mature development , The achievements are mainly reflected in the following aspects ：1） Establishment of length unit 2） Least square method 3） The formation of ellipsoidal geodesy 4） Large scale expansion of radian measurement 5） Different earth ellipsoid parameters are calculated . This stage laid the foundation for physical geodesy .
Geoid stage , The development of geometric geodesy ：1） The layout of astronomical and geodetic network has made great progress ,2） Invar baseline ruler appeared and the development of physical geodesy 1） The theory of geodetic boundary value problem 2） A new ellipsoid parameter is proposed in the new era of modern geodesy Ranging by geomagnetic wave 、 The emergence of new measurement technologies represented by artificial earth satellite positioning system and its long baseline interferometry , Make geodetic positioning 、 Determine the earth parameters and gravity field , The basic surveying and mapping tasks such as building a digital earth are carried out with brand-new theories and methods . Due to the successful research and application of high-precision absolute gravimeter and relative gravimeter , Some countries have established their own high-precision gravity networks , Proposal and application of optimal design theory of geodetic control network and allocation method of least square method .
5. Modern geodetic technology and traditional methods ： Geometry and Physics . With the advent of man-made earth satellites , Satellite law came into being again .
6. The basic task of geodesy is the technical task : Accurately determine the position of the geodetic control point and its change with time, that is, its velocity field , Establish a precise Geodetic Control Network , As the control of mapping , Serve the national economic construction and national defense construction . Scientific mission : Determine the shape of the earth 、 Size and gravity field , Provide a mathematical model of the earth , Serve the earth and Its Related Sciences .
7. The function of geodesy is (1) It provides basic control for topographic mapping and large-scale engineering survey ;(2) Provide initial data for urban construction and mine engineering survey ;(3) Provide information for Earth Science Research ;(4) In disaster prevention 、 Role in disaster reduction and relief ; (5) The development of space technology is an important guarantee for national defense construction .
8. The research content of geodesy is geodesy 、 Ellipsometry 、 Astronomy, geodesy, gravity 、 Satellite geodesy 、 Inertial geodesy
9. The significance of refined geoid model is first , Geoid or quasi geoid is the elevation datum to obtain geospatial information . secondly ,GPS（ Global positioning system ） Technology combined with high-precision and high-resolution geoid model , It can replace the traditional water Huai measurement method to measure the positive height or normal height , True realization GPS Technology has the function of three-dimensional positioning in geometric and physical sense . Again , In the present day GPS Positioning the times , Refining regional geoid is as important as establishing a new generation of traditional national or regional elevation control network , It is also the main task of establishing modern elevation datum in a country or region , So as to meet the needs of national economic construction, the development of Surveying and Mapping Science and technology and relevant geoscience research . The final result of geoid refinement provides a regional elevation anomaly correction interpolation software .
10. Celestial sphere ： Take the earth's centroid as loyalty , An imaginary sphere with a radius of infinity is called the celestial sphere . Ecliptic ： The average orbit of the earth around the sun . The equator ： Draw a plane at right angles to the earth's axis through the center of the earth , An imaginary circle corresponding to the polar distance of the earth appears on the earth's surface . Baidao ： The orbit of the moon around the earth . precession of the equinoxes ： The earth rotates on its axis , It can be seen as a huge gyro rotation , Due to the influence of celestial bodies such as the sun and moon , Similar to the precession of a rotating gyro in a gravity field , The earth's axis of rotation rotates slowly around the Yellow pole in space , Form an inverted cone , The rotation period is 26000 year . nutation ： Because the white Tao has an appointment with the zodiac 5 Inclination of degrees , 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 Short period circular motion in , The amplitude is 9.21 second . Pole shift ： The motion of the earth's instantaneous rotation axis relative to the earth's inertial axis . angular velocity ： The angular velocity of the earth's body rotating from west to East about the axis of rotation passing through its center of mass . Linear velocity ： When the earth rotates , The speed at any point on the ground surface . Spring equinox ： The point where the sun passes through the celestial equator from south to north along the ecliptic . Celestial pole ： Through the center of the celestial sphere 、 Two points where a straight line parallel to the earth's rotation axis intersects the celestial sphere . Huangji ： The distance between the celestial sphere and the angle of the ecliptic is 90 Two points of degrees . Time circle ： Centered on the earth , The great circle made by the celestial pole and celestial body . Meridian plane ： A plane containing the axis of rotation of an ellipsoid . Meridian circle ： The section between the meridian of the celestial sphere and the celestial sphere . Yellow and red angles ： The angle between the ecliptic plane and the equatorial plane . use g Express . Huang Jing nutation ： The amount of movement of the vernal equinox on the ecliptic caused by the nutation of the sun and moon . The amount of change in the angle of intersection of yellow and red caused by the nutation of the sun and moon .
11. Kepler's three laws, orbital law ： Each planet orbits the sun in its own elliptical orbit , The sun is in a focal point of the ellipse . The law of area ： In equal time , The area swept by the line between the sun and the moving planet is equal . Periodic law ： The square of each planet's revolution period around the sun is directly proportional to the cube of the semimajor axis of their elliptical orbit .
12. Instantaneous polar celestial coordinate system ： The origin is at the center of mass of the earth ,z The axis points to the direction of instantaneous earth rotation ,x The axis points to the instantaneous vernal equinox ,y The axis is oriented according to the right-hand coordinate system . Celestial coordinate system ： Choose an epoch time , The nutation value at this moment is deducted from the direction of the earth's rotation axis and the vernal equinox as z Axis and x Axis pointing ,y The axis is oriented according to the right-hand coordinate system , The origin of the coordinate system is the same as the celestial coordinate system . Agreement celestial coordinate system ： Choose a moment as the standard epoch , And put the instantaneous rotation axis of the earth at this moment （ Point to the north pole ） The direction from hedisin to the instantaneous vernal equinox , After instantaneous precession and nutation correction , Respectively as z Axis and x Direction of axis .
Instantaneous polar earth coordinate system ： The origin is at the center of mass of the earth ,z The axis points in the direction of the instantaneous earth's rotation axis ,x The axis points to the intersection of the instantaneous equatorial plane and the meridian plane containing the instantaneous earth rotation axis and the equatorial reference point of the average observatory ,y The axis forms the orientation of the right-hand coordinate system . Protocol earth coordinate system ：WGS-84 The origin of the coordinate system is at the center of mass of the earth ,Z Axis pointing BIH1984.0 Defined agreement earth pole （CTP） Direction ,X Axis pointing BIH1984.0 Zero degree meridian and CTP The intersection of the equator ,Y Axis and Z、X The axis forms the right-hand coordinate system .
13. Geodetic reference system is a set of geometric and physical parameters to determine the earth's ellipsoid . Reference frame ： A geodetic datum is established by a rotating ellipse representing the earth's form , Is to determine the parameters of the rotating ellipsoid and its orientation and positioning .
14. Geodetic rectangular coordinates ： origin O Coincide with the center of mass of the earth ,Z The axis points to the north pole of the earth ,X The axis points to the intersection of the earth's equatorial plane and the Greenwich meridian ,Y The axis is in the equatorial plane with XOZ Form a right-hand coordinate system . Geodetic coordinates ： The center of the earth's ellipsoid coincides with the earth's center of mass , The minor axis of the ellipsoid coincides with the earth's rotation axis . The position of the space point is expressed as （L,B,H）.
15. A geodetic coordinate system whose origin is the geometric center of a reference ellipsoid . Usually divided into ： Centroid space rectangular coordinate system and centroid geodetic coordinate system . Geocentric coordinate a space rectangular coordinate system established with the center of mass of the earth as the origin , Or the geodetic coordinate system established with the earth's ellipsoid whose center of mass coincides with the earth's center of mass as the datum plane . A coordinate system that points to Cartesian coordinates . Take the station as the origin , Use a fixed , affirmatory , Use the prepared base to point, observe and measure , Generally used for construction engineering .
16.ITRF： International Earth reference framework ITRS: International Earth reference system .CTRS： Protocol earth reference system .WGS84: Is for GPS The coordinate system used by GPS .PZ90:GOLNASS Earth reference system .CGCS2000:2000 China Geodetic coordinate system .JGD2000: The geodetic coordinate system of Japan .
17. Reference ellipsoid : Approximate the shape and size of the earth , And the relative position between them is determined . location ： Locate the center of the ellipsoid . The reference ellipsoid is the datum plane for measurement and calculation , The normal of ellipsoid is the datum line of measurement and calculation . in addition , The level is the datum for field observation , The plumb line is the datum line for field observation . directional ： Determine the direction of the coordinate axis of the space rectangular coordinate system with the center of the ellipsoid as the origin , That is to determine the direction of the minor axis of the ellipsoid and the starting meridian of the great earth . A little positioning ： The astronomical longitude and latitude and astronomical azimuth measured at the geodetic origin are regarded as geodetic longitude and latitude and large local potential angle , The positive height at the geodetic origin （ Normal high ） As the earth is high . Multipoint positioning ： List the radian measurement equations at multiple astronomical sites , Through adjustment calculation ξ、η、Ν, So as to complete the positioning of the ellipsoid .
18. The geodetic origin is also called the geodetic datum point , It's the national geographic coordinates —— Starting point and datum point of longitude and latitude . The geodetic origin is an artificially defined point . China's geodetic origin is 1975 Year begins , In beihongliu village, Yongle Town, Jingyang County, Shaanxi Province .
19. The geodetic coordinate system is determined by the geodetic latitude 、 The coordinate system composed of geodetic longitude and geodetic height . Based on the plumb line , Astronomical coordinate is a coordinate system composed of astronomical latitude and astronomical longitude, which is called .
20.BJ1954 Parameters ： Long half axis a=6378245m, Oblateness ： alpha =1：298.3.GDZ80 Parameters ：6378140m,1：298.257.CGCS2000 Parameters :6378137,1:298.257222101.
21. The four parameters are the transformation of different coordinate systems in the same ellipsoid ：X translation ,Y translation , Rotation angle and scale . Seven parameters ：X translation ,Y translation ,X translation ,X Rotation axis ,Y Rotation axis ,Z Rotation axis , Zoom ratio .
22. Time system （1） Stellar time is a time system with the vernal equinox as the reference point . Spring equinox （ Or any star other than the sun ） The time interval between two consecutive passes through the meridian circle of the station is one stellar day .（2） When the sun is flat, the sun is flat （ The sun moving at an average speed ） Time system for reference point . The time interval between two consecutive passes of the flat sun through the meridian circle of the station is a flat sun day . The average solar time is called civil time from midnight .（3） Universal time is Greenwich mean solar time （ From midnight ）. Due to the instability of the earth's rotation , stay UT Add pole shift correction to get UT1.UT1 Plus the seasonal variation of the earth's rotation speed, it is UT2. In longitude 15° The meridian of multiples of Ln The civil time defined by the location is called area time Tn.Tn=UT+n,n Area code .（4） Almanac time and mechanics time are from 1960 Since, the calendar era based on the earth's revolution began to replace world time . The second length of almanac time is specified as 1900 year 1 month 1 Japan 12 The length of the whole regression year 1/31556925.9747, The beginning of the epoch 1900 year 1 month 1 Japan 12 when . The centroid mechanics of the solar system （TDB） When the earth's center of mass mechanics （TDT）.（5） Atomic time is based on the period of atomic motion in matter （ Such as cesium atom 133 Energy level radiation oscillation frequency 9192631170 A week is a second ）. In Mechanics TDT The measurement of has been realized by atomic clock , Because of their different starting points .（6） Coordinated world world time defined in atomic time seconds .(7) GPS The system time is seconds long IAT, The starting point of time is 1980 year 1 month 6 Japan UTC 0 when , Don't jump seconds after startup , Continuous running time system . Important to remember the formula ：GPS when = Atomic time IAT-19s TDT=IAT+32.184s8. Star day ： One year equals 366.2422 It's usually a sunny day ： One year equals 365.2422 When the sun is flat =366.2422/365.2422 When stars =（1+0.002737909） When stars 9. punctual ： Save the correct time and give the time ： Use accurate radio signal to broadcast time and signal time comparison ： The punctual instrument receives the radio time signal and compares it with its time （ It's commonly known as "on the watch" ）
23. Common coordinate system ： Celestial coordinate system, earth coordinate system, astronomical coordinate system, geodetic coordinate system, space geodetic rectangular coordinate system, geocentric coordinate system, station centric coordinate system Gauss plane rectangular coordinate system
24. site ： A basic form of material existence , With energy 、 Momentum and mass , Can transfer the interaction between objects . field of gravity ： Space under the action of earth gravity . In this space , Each point has a unique gravity vector corresponding to it . Gravitational field ： Is a field that describes a particle's gravitational attraction in space . Vector field ： For example, the attributes of each point in a space can be represented by a vector , So this field is a vector field .
25. gravity ： The resultant force of the earth's gravity and the earth's centrifugal force on a unit particle . Unit: cm / Second square , It's called GA for short （GAL), One thousandth is milligamma . Gravity ： The force of attraction between substances according to Newton's law of universal gravitation . Determined by the shape of the earth and its internal mass distribution . Centrifugal force ： The force of a particle leaving the center of rotation due to its rotation around the earth's rotation axis . Its size is determined by the mass of particles , The earth's rotational velocity , The radius of the parallel circle where the particle is located jointly determines . Normal gravity ： The gravitational field produced by a normal ellipsoid . Gravity anomaly ： The difference between the normal value of gravity on the geoid and the normal value of gravity on the geoid .
25. The potential function is a corresponding quantity function that can be found for the conservative force , The partial derivative of this function on each coordinate axis is equal to the component of the force on the corresponding coordinate axis . Gravitational potential is the work done by moving a unit particle from infinity to that point . The normal gravitational potential is a simple function 、 The auxiliary gravitational potential of the approximate value of the earth's gravitational potential that can be calculated directly without involving the earth's shape and density . The disturbance potential is the difference between the earth's normal gravity potential and the earth's gravity potential . Gravitational potential is gravitational potential V And centrifugal force Q The sum of the .W=f∫dm/r+ω2/2(x2+y2)
27. Harmonic functions ： The gravitational potential is a harmonic function , It satisfies the Laplace operator . The second derivative operator of centrifugal force potential △Q, △Q=2w2, So the centrifugal force potential function is not a harmonic function . The sum of the second derivative of the gravitational potential , External points ：△W=△V+△Q=2w2 On the inside , Give... Without proof ：△W=△V+△Q=-4∏fδ+2w2(δ- Bulk density ), Because they are not equal to 0, Therefore, the gravitational potential is not a harmonic function .
28. Studying the meaning of gravity potential can easily get a cluster of surfaces , It's called the gravitational equipotential surface . The normal gravitational potential is a simple function , The auxiliary gravitational potential of the approximate value of the earth's gravitational potential that can be calculated directly without involving the earth's shape and density . When you know the normal gravitational potential , Try to figure out the difference between it and the earth's gravitational potential , Then we can find the difference between the geoid and the known shape , Finally, solve the problems of the earth's gravitational potential and the shape of the earth .
29. Geoid is when the ocean is assumed to be in static equilibrium , Extend it below the continent and maintain a closed level that surrounds the whole earth orthogonal to the plumb line everywhere . characteristic ： The direction of gravity changes irregularly : The reason is that the surface is uneven 、 The distribution of material density in the crust is uneven
30. Total earth ellipsoid ： From a global perspective , We must seek one that is closest to the whole earth 、 The closest ellipsoid , This ellipsoid is also called total earth ellipsoid or average ellipsoid . The total earth ellipsoid satisfies the following conditions ：（1） The mass of the ellipsoid is equal to the mass of the earth , The rotational angular velocities of the two are equal .（2） The volume of the ellipsoid is equal to that of the earth , The sum of squares of the difference between its surface and geoid is the smallest .（3） The center of the ellipsoid coincides with the center of the earth , The minor axis of the ellipsoid coincides with the earth's horizontal rotation axis , The earth's starting meridian plane is parallel to the astronomical starting meridian plane . The height difference between geoid and ellipsoid at a certain point is called geoid gap , use N Express . Normal ellipsoid ： The normal shape of geoid is ellipsoid . Laplace point ： Geoastronomy mainly studies the methods of astronomical measurement , The theoretical and practical problems of determining the geographical coordinates and azimuth of the earth's surface . A point at which the azimuth is measured simultaneously at a large astronomical site . Earth elements ： The geodetic longitude of a point on an ellipsoid L, Latitude of the earth B, The length of the earth wire between two points S Extremely positive 、 Anti large local potential angle A12、A21, Commonly known as the earth element . Correction of vertical deviation direction ： The correction that should be added when the horizontal direction value of the ground observation based on the vertical line is reduced to the direction value based on the normal line is defined as the vertical deviation correction . Elevation difference direction correction ： When making horizontal observation , If the aiming point is higher than a certain height of the ellipsoid , Then the collimation plane cannot pass through the intersection of the normal of the collimation point and the ellipsoid , The correction of the resulting direction deviation is called elevation difference correction . Section difference direction correction ： The correction that should be added to change the normal arc cutting direction into the direction of the earth wire is called the section difference correction .

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33. Characteristics of Gaussian projection ：（1） Gaussian projection is a kind of orthomorphic projection , The angles before and after projection are equal .（2） The central meridian is projected into a straight line , And the length remains the same . The farther away from the central meridian , The greater the bend after projection , The greater the length deformation .（3） The ellipsoid is curved to the central meridian after the projection of other meridians except the central meridian , And converge to the poles , Symmetrical to the central meridian, the equator .（4） A latitude circle symmetrical to the equator on an ellipsoid , A curve that remains symmetrical after projection , It is perpendicular to the projection curve of the meridian and concave to the two poles .
34. Parameters of the earth's normal gravity field Corresponding to the actual earth 4 There are two basic parameters, the gravitational constant fM With spherical harmonic coefficient J2, Equatorial radius of the earth ag The rotation angle of the earth ω As the normal ellipsoid of the earth （ Level ellipsoid ） The basic parameters of , They are also called Earth geodetic datum constants .
35. The essence of leveling : Leveling is actually carried out along the level , The height difference between two points is the difference between two levels of two points .(2) The characteristic that the levels are not parallel to each other is called the non parallelism of the level, which is also called the gravitational equipotential surface . Potential energy difference between two levels △w=gh At two different latitudes A、B At two o'clock ：-△w=gAhA=gBhB Due to different latitudes g Different , namely gA≠gB, therefore hA≠hB.
36. Elevation system ：（1） Positive altitude system —— Elevation system with geoid as elevation datum . It's high —— The distance from the point along the actual gravity line to the geoid (2) Normal high system —— Elevation system based on quasi geoid . The quasi geoid is the corresponding point cut down along the plumb line according to the normal height of each point on the ground , Connect many of these points into a continuous surface .(3) Geodetic system ： Elevation system based on ellipsoid . The earth is high H： The distance from the ground point along the normal to the ellipsoid . Normal high ： The distance from the ground point along the normal gravity line to the quasi geoid . The force height system, that is to say, the r(m,A) Use latitude 45 Normal gravity of degrees r45 Degree instead of , The force height at one point is the latitude of the level 45 Normal height at degrees .
37. Measurement method of vertical deviation ： Absolute vertical deviation ： The angle formed by the vertical line and the normal of the total earth ellipsoid . Relative vertical deviation ： The angle formed by the perpendicular and the normal of the reference ellipsoid .(1) Determination of vertical deviation by Astrogeodetic method (2) Gravity measurement method , The essence is to use the gravity anomaly on the geoid and the earth ellipsoid to calculate the vertical deviation on the geoid according to the Stokes method .（3） Comprehensive astronomical geodetic gravity measurement method .(4) GPS measuring method
38. Method for determining geoid difference ： Earth gravity field model method ; Stokes method ; Satellite altimetry ;GPS Elevation fitting method and least square collocation method . A method of determining the shape and size of the earth ： Astrogeodetic method 、 Gravity measurement method 、 Space geodetic method .
39. National geodetic control network and its function (1) Provide precise control for topographic mapping ① Limit mapping error accumulation , Ensure mapping accuracy ; ② Unified coordinate system , Ensure the splicing of adjacent drawings ; ③ Provide the plane coordinates of the point , Ensure that the plane survey . (2) To study the shape of the earth 、 Provide information on size and other scientific issues (3) Provide information for national defense construction and space technology
40. National horizontal control network （1） measuring method :① Triangulation ② Precision Traverse Survey ③ Trilateral measurement ④ Edge and angle CO measurement （2） Layout principle :① Grading network , Step by step control ② Maintain the necessary accuracy ③ It should have a certain density ④ There should be uniform specifications （3） Why take triangulation as the main method of national horizontal control network ？ answer ： Because the triangular points are arranged into a network , Large control area , Conducive to root encryption ; The measurement of edge length is mainly the measurement of edge length , The operation is more convenient , At the same time, due to the use of precise angle measurement 、 Ranging instrument , So the observation angle 、 The side length can achieve high accuracy ; When calculating the office adjustment , There are many geometric conditions , High point accuracy .
41. National elevation control network （1） Mission ：① Elevation control of topographic mapping and engineering survey ② Vertical crustal deformation 、 Data provided by scientific research such as the change of average sea surface .（2） The principle of network layout ： Adopt geometric leveling method , From high to low 、 Whole to part , Grading network 、 Step by step control 、 Encrypt in sequence . Elevation systems at all levels are unified 、 The accuracy is the same 、 Even density . National leveling is divided into one 、 Two 、 3、 ... and 、 Four wait .
42. Leveling origin 1）1956 The elevation of Qingdao leveling origin of the Yellow Sea mean sea level is 72.298m （2）1985 National elevation datum 1952-1979 Annual total 27 Annual average sea surface . The elevation of Qingdao leveling origin is 72.2604m. Visible ratio 1956 The average sea level is higher 0.0286m
43. Country GPS network ： Set up nationwide GPS The main purpose of the network is to focus on , These include ： Monitor and study crustal deformation and block movement ; Check and strengthen the astronomical and geodetic networks in various regions , Establish a unified high-precision geodetic datum ; Establish geocentric reference system , Accurately determine the conversion parameters between the parametric coordinate system and the geocentric coordinate system ; Refined geoid and so on , However, the establishment and retest of these national networks can become a new generation of high-precision geocentric reference system in China 、 The basis of monitoring and studying crustal movement .
44. Engineering plane control network ：1. classification ： Mapping control network 、 Construction control network 、 Deformation monitoring network 2. The principle of network layout ：① Grading network , Step by step control ② Have enough accuracy ③ Have enough density ④ There should be a unified specification 3. The network layout scheme has triangular network 、 Trilateral network 、 Traverse network 、GPS Net, etc . Practical application , The primary control network is based on GPS The layout of the network is the main form , The secondary encryption network has GPS network 、 Wire network and other forms . The grade and density of the primary network of the engineering control network , It is generally determined according to the survey area and the needs of engineering tasks .4. characteristic ① Compared with the corresponding level of national triangulation , Its average side length is significantly shortened .② There are many levels and classifications of engineering survey control network .③ Each level of control network can be used as the primary control network of the survey area .④ 3、 ... and 、 The starting edge of the fourth-order triangulation , The primary network and encryption network are treated separately .5. Technical design steps ① Data collection ② Field survey ③ The design on the drawing ④ Write the technical design of control network ⑤ Hand in the information
45. Main steps of leveling and elevation control network layout ： Design on the leveling network diagram 、 Field selection 、 Mark stone embedding 、 Field observation 、 Adjustment calculation and preparation of result table .
46. Angle observation error analysis （1） Error caused by external conditions ① The change of atmospheric density and atmospheric transparency affect the stability and clarity of target imaging ② The non-uniformity of atmospheric density produces systematic horizontal refraction for directional observation . ③ The phase difference of the collimation target caused by sunlight .④ The instrument stability caused by temperature change is reversed , Periodically over time .（2） Instrument error ① Collimation axis error . The collimation axis is not perpendicular to the horizontal axis . Turn left 、 The influence of the right wheel on the observation direction is equal , The symbols are opposite . Elimination method ： Take the left side of the tray 、 The middle number of the right reading of the dial can eliminate the influence of the collimation axis error ② Horizontal axis tilt error , The horizontal axis is not perpendicular to the vertical axis . Turn left 、 The influence of the right wheel on the observation direction is equal , The symbols are opposite . Vertical angle with observation target α of . Elimination method ： Take the left side of the tray 、 The middle number of the right reading of the disc can eliminate the influence of the tilt error of the horizontal axis ③ Vertical axis tilt error . The vertical axis itself deviates from the plumb line , I.e. not vertical . The influence on the observation direction does not change with the rotation of the collimator ; It is related to the vertical angle and azimuth of the observation target 、 Right fetching in the disk cannot eliminate ; When observing , Bubbles must not deviate from one grid ; Reset the instrument between measurement and return ; Observe the vertical angle of the target >3° when , Calculate the vertical axis tilt correction according to the number of bubble deviation cells .④ Mechanical transmission error of the instrument .（3） Observation error ① Collimation error . It has something to do with people's eyes and external conditions .② Reading error . It mainly depends on the coincidence error of diameter division , The second is the reading error of micrometer . Take multiple survey returns and multiple collimation target observation ; Take the method of overlapping readings twice
47. Absolute gravimetry : Is to directly measure the absolute gravity value of the ground point with a gravity instrument . Relative gravity measurement : Is to use a gravity instrument to measure the gravity difference between two points on the ground , The largest difference in gravity on the earth's surface is about 5000 On the order of milligamma . Gravimetry classification ： Terrestrial gravimetry 、 Marine gravimetry and aviation （ Or aerospace ） Gravimetry . Satellite gravimetry . Gravity field measurement method ： One is to use gravimeter to observe the gravity on the earth's surface , Second, satellite altimetry in marine areas , Third, the earth's gravity field model is obtained by satellite orbit tracking analysis
48. The ellipsoid indicates that the earth must solve 2 problem ：① Selection of ellipsoid parameters ② Determine the relative position of the ellipsoid and the earth , That is, the positioning of the ellipsoid .
Ellipsoid positioning fixes the relevant positions of the ellipsoid with certain parameters and the earth , Determine the specific position of the datum plane for surveying and calculation and the starting data of geodesy . Location condition ：① The minor axis of the ellipsoid is parallel to the earth's rotation axis of a specified epoch ② The starting geodesic meridional plane is parallel to the starting astronomical meridional plane ③ Within a certain area , Ellipsoid and geoid （ Or geoid ） Most closely
49. Ground wire ： The shortest curve between two points on a surface . Geometric features ：① The included angle between the geodesic and the relative normal section is δ=△/3.
② The length difference between the geodesic and the relative normal section is very small ,600km The difference between the two is only 0.007mm.③ At two o 'clock Q1 And Q2 On the same meridian or equator , Then the geodesic line and the meridian circle 、 The equator coincides . Geodetic clarau equation ：r·sinA=C(C Is a constant ) namely ： For a large earth wire on the ellipsoid , The product of the radius of the parallel circle at each point and the sine of the azimuth of the geodesic at that point is a constant . constant C Also called geodetic constant
50. Geodetic problem solving (1) Positive solution of geodetic problem —— It is known that P1 Point geodetic coordinates （B1,L1）、P1P2 The earth line is long S And large local potential angle A1, Deduce P2 Point geodetic coordinates （B2,L2） And large local potential angle A2.(2) Inverse solution of geodetic problem —— It is known that P1P2 Geodetic coordinates of two points （B1,L1）、（B2,L2） Reverse calculation P1P2 The length of the earth line S And large local potential angle A1、A2. Solution method
(1) According to the calculated distance, it is divided into short distance （<400km)、 middle distance （400～1000km) And long distance （1000～2000km) The solution of the problem .
(2) direct method —— Directly solve the geodetic dimension of the control point 、 Geodetic longitude difference between large local potential angle and adjacent starting point . Indirect solution —— First find the earth meridian difference 、 Latitude difference and earth azimuth difference , And then find the geodetic coordinates of the control points
51. Derivation steps of Gaussian mean argument positive solution formula ：（1）、 Menstrual aberration l、 Latitude difference b、 Azimuth difference a yes S Function of , So it can be developed into S Taylor series （ Average arguments in S/2 The exhibition is S Power series of ）.（2）、 Introduce the average latitude and average azimuth of the two ends of the geodesic line , take dL/dS With Bm、Am Expand according to Taylor series .（3）、 Calculating the coefficients of Taylor series according to the differential equation of geodesic line .（4）、 Substitute the coefficient into the average argument formula .（5）、 because B2、A2 Unknown ,Bm、Am The exact value is unknown , Can be obtained by successive approach method . Usually three times . The derivation steps of the inverse solution formula of Gaussian average argument ：（1）、 The latitude difference between two points is known b、 Menstrual aberration l And mean latitude Bm, export SsinAm and ScosAm, seek a″.（2）、 from SsinAm、ScosAm and a Calculation S and A1、A2.
52. Map projection is to project an element on an ellipsoid （ Including coordinates 、 length 、 Direction ） Project onto a plane according to certain mathematical rules .
Projection distortion ： Angular deformation 、 Length deformation and area deformation . Projection length ratio —— Infinitesimal line segments on the projection plane ds And the actual length of the line segment on the ellipsoid dS The ratio of the , With m Express ,m=ds/dS. Length deformation —— v= m-1 Deformation index ： Projection length ratio in the main direction a and b It's called deformation index . if a=b, Is isometric projection , The length ratio does not change with the direction after projection . if ab=1, Equal area projection .
53. Map projection classification isometric projection ： The angle remains unchanged after projection , Keep the graphics similar in a small range . Equal area projection ： For some thematic maps , The projected area remains unchanged . Plane projection ： The projection plane is tangent to the ellipsoid at a certain point , Establish functional relationship according to mathematical projection .
Conical projection ： The conical surface is tangent to the ellipsoid in a certain latitude circle or cut by two latitude circles , According to mathematical projection . Cylindrical projection ： A cylinder or ellipse is tangent to the ellipsoid at the equator or on a meridional plane , Project by number . Orthaxial projection ： The central axis of the cylindrical surface coincides with the minor axis of the ellipsoid , The cylindrical surface is tangent to the equator . Transverse projection ： The central axis of the cylindrical surface coincides with the long axis of the ellipsoid , The cylindrical surface is tangent to a meridional circle .
Oblique projection ： The central axis of the cylindrical surface and the length of the ellipsoid 、 The minor axes do not coincide , Between the two
54. Conformal projection properties (1) At any point , Projection length ratio m Is a constant , It doesn't change with the direction , Only related to the point position .(2) The angle is not deformed after projection . It is also called conformal mapping or conformal projection . The condition is that it holds on a small scale . The deduction steps are ：(1) Starting from the length ratio expression Find out m2 And dx2,dy2 and dB2,dl2 Relational ;(2) Introduction of equivalent latitude q, take x、y The table is q、l Function of ;(3) Yes x=f1（q,l）,y=f2（q,l） Take the total differential , Introduce symbols E、F、G;(4) According to the length ratio m And direction A irrelevant ,a=b, have to E=G;(5) from E=G、F=0 The main conditions .
55. Gaussian projection condition （1） The angle will not deform after projection , Meet the requirements of conformal projection ;（2） The projection of the central meridian is a straight line ;（3） The length of the central meridian remains unchanged after projection , Its projection length ratio is equal to 1. Gaussian projection calculation includes Gaussian projection coordinate calculation 、 Calculation of convergence angle of plane meridian 、 Direction correction calculation 、 Distance correction calculation . characteristic :1) The central meridian is projected as a straight line , And the length remains the same .2) Except for the central meridian , The projection of other meridians is a curve concave to the central meridian , And take the central meridian as the axis of symmetry . There is length deformation after projection .3) The equatorial line is projected as a straight line , But there is length deformation .4) The rest of the latitude except the equator , After projection, it is a curve convex to the equator , And take the equator as the axis of symmetry .5) The longitude and latitude remain orthogonal after projection . 6) All length deformed segments , The length deformation ratio is greater than l.7) The farther away from the central meridian , The greater the length deformation .
56… Coordinate zone change calculation ：（1） When two adjacent projection zones are located at the edge of the control zone , In order to carry out adjustment calculation in the same area , The coordinates of the starting point of the control network must be converted into the same projection zone .（2） When mapping or surveying works are carried out in the area near the zonal meridian , It is often necessary to use the control results in another area , therefore , It is also necessary to convert the coordinates of these points into the same area .（3） When mapping on a large scale , Especially in engineering survey, in order to limit the projection deformation, it is often required to adopt 3° belt 、1.5° With or without projection , The results of national control points are usually only 6° With coordinates , And then there is 6° Belt and 3° belt （ or 1.5° belt 、 Any band ） Mutual coordinate conversion between .
57. Several cases of Gaussian projection band changing ：(1) 6° With coordinates → adjacent 6° With coordinates ;(2) 6° With coordinates →3° With coordinates ;(3) 3° With coordinates → adjacent 3° With coordinates ;(4) 6° Bring or 3° With coordinates → Calculation steps with arbitrary coordinates ： First project the coordinates of a point into a known plane （x1, y1）, The geodetic coordinates on the ellipsoid are obtained according to the inverse calculation formula of Gaussian projection coordinates （B, L）; Then, according to the latitude and the longitude of the central meridian of the projection zone to be converted L0, Calculate the longitude difference of the point in the new projection zone l, Then calculate the Gauss plane coordinates of the point in the new projection zone according to the Gauss projection coordinate forward calculation formula （x2, y2）.UTM The projection belongs to the horizontal axis equiangular cutting elliptic cylinder projection , Gauss Kruger projection is a horizontal axis equiangular tangent elliptic cylinder projection , Lambert projection is a conic projection of orthomorphic axis
58. The purpose of the budget estimate is ：(1） Systematically check the quality of field observation results , Control the quality ;（2） Convert the observation results on the ground to the Gaussian plane , Check according to the geometric conditions of the control network , Prepare data for adjustment calculation . step : ① Angle centering correction ② Height difference calculation ③ Change the slant margin 、 Centering correction and correction converted to Gaussian plane ④ Calculate the closing error of traverse azimuth condition and ring condition ⑤ Calculate the mean square error of traverse angle measurement ⑥ Calculate the error in traverse ranging ⑦ Calculate the relative closure error of the conductor
59.GPS Field inspection of observation results （1） Check the synchronous side observation data in each period ：① Data rejection rate ② Synchronous observation loop check （2） Check of asynchronous side observation data in different periods ① Retest baseline check ② Asynchronous observation loop inspection
60. The necessary starting data of traverse network is 3 individual ： The vertical of a point 、 Abscissa and the coordinate azimuth of an edge . A traverse network without redundant starting data is called a free traverse network , A network with redundant starting data is called an attached traverse network
61.M、N、R Three curvature radius relationships ： A point on an ellipsoid M、N、R Are measured inward along the normal from this point , They are usually unequal in length , From the comparison of their respective calculation formulas, we can see that their relationship is N>R>M, They are equal only at the poles , And are equal to the radius of polar curvature c, namely N90=R90=M90=c.
62. The spherical angle super assumes that the earth's ellipsoid is a sphere , On the sphere, there is a geodesic line east of the axis meridian AB, Of course, it must be a big arc . We know , A quadrilateral on a sphere ABED The sum of the inner angles of is equal to 360°+ε,ε Is the spherical angle of a quadrilateral .
63. Bessel projection condition （1） The geodesic projection of the ellipsoid onto the sphere is a large arc ;（2） The azimuth of the corresponding points on the geodetic line and the large arc is equal ;（3） The latitude of any point on the sphere is equal to the normalized latitude of the corresponding point on the ellipsoid . step ：1） According to the known value on the ellipsoid, the corresponding value of the sphere , That is, the process of realizing the ellipsoid .2） Solving geodetic problems on a sphere .3） According to the value obtained on the sphere and the corresponding value on the ellipsoid, the transition of the ellipsoid is realized .
64. Directional observation method ： In one survey loop, all directions to be observed on the survey station shall be observed one by one , Read on the level dial , Obtain the observed values in all directions , The horizontal angle measured by the direction observation method is in the middle of one measurement , In the first half of the survey, it is required to turn forward the collimation department to collimate with the target , The second half of the test return requires the reverse collimation department to collimate with the target . Group observation method ： Divide the imaging situation in roughly the same direction into a group , Each group contains approximately the same number of directions . Observation is that both groups should jointly measure two common directions , One of the best is the common zero direction , In order to strengthen the connection between the two groups . Full combined observation angle method ： Put the station in all directions , Take two directions at any time to form a single angle for observation , Until all possible single angles are observed with the same number of measurement rounds .

1. It is known that the elevation anomaly in an area is

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,A、B At two o'clock 1985 The elevation under the national elevation datum system
3. It is known that the meridional component and the maounitary component of the vertical deviation of a survey station are ：
5. The latitude of a point is 36°11’20", The geodetic orientation of this point is 42°17’30"
10. Calculation 30°10’10" The meridian arc length of the point
11. Try to explain the geodesic line on the ellipsoid by using the geodetic line klelau theorem
12． Combined with the concept of gravity potential and the calculation formula of gravity component
13． The total station was used to observe the edge of the ground AB Horizontal value and distance of
15． Try to derive the klelau square of the earth wire from the differential equation of the earth wire
16. What is multivalued in geometric leveling