13大地水准面和参考椭球

1、Unit 13 Geoid and Reference Ellipsoid （大地水准面和参考椭球）The Earth?s physical surface is a reality upon which the survey ing observati ons are made and points are located.（地球物理表面【或者说，地球自然表面】 是一个实体，测量 工作【observation观测】 在其上进行，点位在其上进行定位。）However, due to its variable topographic surface and overall shape, it c

2、annot be defined mathematically and so position cannot be computed on its surfaceC然而，由于【due to】 它的起伏不定的【variable可变的、不定的，这里按中文习惯译为起伏不定的】地形 表面和总的【overall】形状，它不能被数学的定义，因此点位也不能在其上进行计算。） It is for this reason that in surveys of limited extent, the Earth is treated as flat and plane trigo no metry used to

3、 define positi on.（正是因为这个原因，在有限范围内的测量中，地 球被当成平的，并用平面三角学【trigo no metry三角学】来确定位置。）If the area un der con sideratio n is of limited exte nt, orthog onal projecti on of this area onto a plane surface may result in negligible distortion女口果在考虑中的【un der con sideration 在考虑中的】 区域是有限范围的，该区域在一个平面【 pla ne surf

4、ace】 上 的正交投影【ortho gonal projectio n】 导致的【直译为导致，可以意译为：其结果】 是可以忽略的【negligible 可以忽略的】 变形【distortion】）Plane surveying techniques could be used to capture field data and plane trigonometry used to compute position.（平面测量技术可以被用来获取外业数据，平面三角学用来 计算位置坐标）However, if the area extended to a large area beyond lim

5、itation and treated as a flat surface the effect of the Earth?s curvature will produce unacceptabldistortion.（然而，如果该区 域延伸【extend】为一个大的区域超过了限度，把它当成一个平面，地球的曲率影响【effect】 将产生不可被接收的【unacceptabld 变形）It can also be clearly seen that the use of a plane surface as a reference datum for the elevations of poin

6、ts is totally unacceptable.（同样可以明显的【clearly】 看至U, 用平面 作点的高程的参考基准是完全【totally完全地】不可被接受的【不可以的】 。Therefore, to represent horizontal positions and elevations on maps and charts, we need a mathematical model of the Earth which includes a set of numbers for the size and shape of the Earth.（因此，为了在地图和海图【char

7、t海图、图表】上表示【represen】出水平 和高程位置，我们需要一个地球的数学模型，它包括一系列地球大小和形状的参数【number这里译为参数 parameter参数】）We will define a mathematical surface that approximates to the shape of the area under con siderati on and thenfit and orie ntate it to the Earth?s surface.（我们将定义一个数学表 面接近【approximates接近 v.】于被考虑的【under considerati

8、orj 区域的形状，然后 使之与地球表面相符合 【fit and orientate： fit 是适合的意思；orientate是定向的意思】） Such a surface is referred in survey ing as a ,refere nee ellipsoid?这样一个表面在测量里 被称为【refer提至U、涉及】 “参考椭球”）The Geoid （大地水准面）Since the physical surface of the Earth can?t beused as a computati onal surface, a mean sea level surface

9、is in sti nctively take n into con sideration.（由于【既然】 地球的自然表面 不能被当作一个计算面来用，平均海平面自然的【instinctively 本能地、自然地】 被考虑【被考虑作计算面】）Mean sea level （MSL） is defined as the average level of the ocean surface for all stages of the tide after long periods of observations平均海平面被定义为在经过长时间的海潮的 观测后得到的整个时期【stage阶段、时期】的海洋

10、表面的平均水平面）We use MSL as a pla ne upon which we can refere nee or describe the heights of features on, above or below the ground.（我们用平均海平面当作一个平面，在上面我们可以定位【refere nee原意为名词，这里词性改变动词：定位、参考】或描述高于、低于或在地面上特征的高度）By extending the earth?s MSL through the land areas, an equipotential surface approximately at MS

11、L would be formed.（将地球的平均海平面延伸穿过陆地，一个近 似【approximately 近似地】 于平均海平面的等位面【equipote ntial surface等位面】 形 成了）Such a surface is called the ,geoid?. Thus by definition, the geoid is an equipotential surface of the Earth gravity field that most closely approximates the mea n sea surface 这 样一个面被称为“打的水准面”。这样，依

12、照定义，大地水准面是一个地球重力场的 等位面【equipotential surfacei, 非常近似于平均海平面）The geoid is only a theoretical surface, which is perpendicular at every point to the direction of gravity.（大地水准面仅仅是一个理论的曲面，在每个点上都垂直【perpe ndicular垂直的】指向重力方向）You can?t see it, touch it or even dig down to find it. The shape of geoid can be ac

13、tually measured which is based on gravity data collected worldwide.（你看不至U它，摸不至U它， 更不能下挖来找到它。大地水准面的形状事实上可以被测出一一基于世界范围的重 力数据采集）Although the gravity pote ntial is everywhere the same and the surface is smoother tha n physical surface of the Earth, it still contains many irregularities which render it u

14、nsuitable mathematical location of planimetric position.（尽管重力位【gravity potential: potential 位、电压、潜能】是处处相等的【指的是大地水准面的】，并且该曲面必地球自然表 面药平滑的多，它依然包含了许多不规贝S之处【 irregularity】，使得【render】 它不适 于平面位置【planimetric position】 的精确定位【mathematical除有数学的意思， 也有精确的意思】These irregularities are thought to be due to mass ano

15、malies throughout the Earths 种不 规贝S被认为是由于【due to由于 due应当的】 遍及地球【throughout介词：遍及】 的 质量【mass这里是质量的意思】 分布不规贝卩【anomaly异常、不规则】）The geoid remains important to the surveyor, as it is the surface to which all terrestrial measurements are related.由于它是对于所有有关的陆地测量的参考面【 surface这里 译为参考面】，对测量者来说大地水准面依然【rema in】重要

16、）As the directi on of the gravity vector （termed the vertical） is everywhere no rmal to the geoid, it defi nes the directi on of the surveyor?s plumbbob line.（由于重力矢量（称之为【term 称为】 垂线【vertical垂线 n.、垂直的 adj.】）的方向在各处都垂直【normal垂 直的、正交的、垂线、法线】 于大地水准面，由测量者的铅垂线【 plumb-bob line】 方向 就可以 表示【define明确表示】）Thus an

17、y instrument which is horizontalized by means of a spirit bubble will be refereneed to the local equipotential surface.（因而任何依赖【by means of依赖】 水准气泡【spirit bubble】 整平【horizontalize】 的仪器都参考的是局域等位面）Elevatio ns are related to the equipote ntial surface pass ing through MSL高程就是关于通过平均海平面的等位面的数据）【或者翻译为：高程与过

18、平均海平面的等位面有关or高程参考的是过平均海平面的等位面】Such elevations or heights are called orthometric heights （H） and are the linear distances measured along the gravity vector from a point to the equipote ntial surface as a refere nee datum.（这样的高程或高度被称为正高（ H）,沿着重力矢量从一个点到作为参考基准的等位面的直线【linear直线的】距离）As such, the geoid is t

19、he equipotential surface that best fits MSL and heights in question, referred to as heights above or below MSL.（同样地，大地水准面是最符合 MSL的等位 面； 正被讨论的【in question正在讨论的、正在讨论】 高度，指的是【 refer to 提至U;as当作 合起来可以译为指的是】高于或低于MSL的高度）It can be see n from this that orthormetric heights are datum depe nden（由此可以看出， 正高由其基准

20、面决定【dependent由”决定的、依靠的】 ）The Reference Ellipsoid （参考椭球）The ellipsoid is a mathematical surface which provides a convenient model of the size and shape of the Earth.（参考椭球是一个数学曲面，可以提供一个 关于地球的大小及形状的 方便的【convenient】模型）It is represented by an ellipse rotated about its minor axis and is defined by its sem

21、i-major axis a or the flattening f.（由一个椭圆绕它的短轴【minor axis】 旋转【rotate】 表示， 用它的长半轴a和扁率f来定义）The ellipsoid is chosen to best meet the needs of a particular geodetic datum system design.（这个椭球被选择来最满足特定大地基准系统设计的需要【meet ones n eed满足,，的需要】）【即在设计一套特定的大地基准系统前首先选择一个满足系统设计的椭球】Although the ellipsoid is a concept

22、and not a physical reality, it represents a smooth surface for which formulas can be developed to compute ellipsoidal dista nee, azimuth and ellipsoidal coordinates.（尽管参考椭球是一个概念，不是一个物理实体，它去卩表现出 一个光滑的表面，由此公式可以被发展来计算椭球距离，方位和椭球坐标。）Due to the variable shape of the geoid, it is not possible to have a glo

23、bal ellipsoid of reference for use by all countries,由于【due to】 大地水准面的起伏不定的形状，不可 能有一个适用于所有国家的全球【global】 参考椭球）The best-fitting global geocentric ellipsoid is the Geodetic Referenee System 1980（GRS80）, which has the following dimensions: semi-major axis is 6378137.0 m and semi-minor axis is 6356752.314

24、 m（最适合的全球地心【geocentric地心的】椭球是1980 大地坐标参考系统【80椭球，注意：我国使用的 80坐标系使用的是 75椭球】，尺寸【dimension尺寸、元】如下：长半轴为 6378137.0 m,短半轴为6356752.314 m）The relati on ship of all three surfaces which are terra in, geoid and ellipsoid is illustrated in this Figure.（所有三个面：地表、大地水准面和椭球面的关系，由这个图图解说明【illustrate图例说明】）We n ote that

25、 the orthometric height H is the height with refere nce to the MSL, whereas the geodetic height h is the height of anything above the reference ellipsoid 我们注意至U，正 高H是参考MSL的高度，而【whereasi大地高h是参考椭球面的高度）The relation between the two kinds of heights is shown in the Figure, where the quantity N, the heigh

26、t of the geoid above the reference ellipsoid or the perpe ndicular dista nce betwee n the geoid and the refere nce ellipsoid at a poin t, is usually called the geoidal height （geoid undulation）.（这两种高度之间的关系如图所示，N 这个量【quantity】，某个点 上大地水准面高于参考椭球面或者说大地水准面和参考椭球面之间的垂直距离【perpendicular distance垂直距离】，通常被称为大地

27、水准面高【geoidal height】（大 地水准面差距【geoid undulation; undulation 波动】）Thus, the kno wledge of the geoid is n ecessary for tran sformi ng the geodetic to orthometric heights and vice versa.（这样，把大地高转换为正高，大地水准面的知识就是必需的， 反之亦然【vice versa反之亦然】）Once we determ ine the geoid, we can compute the differe nce betwee n

28、 the two surfaces, the ellipsoid and the geoid any where in the coun try.（ 旦我们确定了大地水准面，我们 就可以计算这两个面的差距一一国家的无论何处的椭球面和大地水准面）The expressi onellipsoidal heightfor (geodetic) height of an ythi ngfetencethe reellipsoid is also used compari ng the accepta nee of the sta ndard geodetic term ofheight ”（相对于标准

29、的大地测量学术语“大地水准面高”的采用【 acceptanee接受、 认同】，“椭球高”这个 表示高于参考椭球面的高度（大地高）的表达【 expression! 也 被米用。）Surveyors used to worki ng with spirit levels have referen ced orthometric heights (H) to the “ average( surface of the earth, as depicted by测量者习惯于参考【referenee to 地球“平均(表面一一用 MSL来描述【depicte】，利用水准测量，获得正高(H) The su

30、rface of MSL can be approximated by the geoid.( MSL 这个面可以近似的当作大 地水准面)The differenee between the two surfaces arises from the fact that seawater is not homoge neous and because of a variety of dyn amical effects on the seawate这两个面的 差别出现在一个事实上一一海水不均匀并且有各种不断变化的影响在其上)The height of the MSL above the geoi

31、d is called the sea surface topography (SST). MSL 高于大地水准面的高度称为海面地形【sea surface topography】【还有一个 SSTsatellite-to-satellite tracking 卫星跟踪卫星技术； 不要混了】 )It is a very difficult quantity to obtain from any measurements; consequently, it is not yet known very accurately.【consequently】，它尚未【not yet尚未】 非常准确的得知)GPS heights are refereneed to the ellipsoid, a mathematical model that does not physically exist. (GPS高参考的是椭球面，是一个数学模型，并不物理地存在)