H.H.

New

SCHMID

title under the r e - o r g a n i z a t i o n of July, 1905 Director~ G e o d e t i c R e s e a r c h L a b o r a t o r y Institute for Earth S c i e n c e s Environmental Science Services Administration

:

REFORHATORY AND REVOLUTIONARY ASPECTS IN GEODESY

T h e growing recognition of the significance of processes related to the earth in its entirety requires the various disciplines in the geo-sciences to conduct their efforts -at least partially- on global concepts. F u r t h e r m o r e , the need is being recognized for correlating results into interdisciplinary programs. Geodesy, as one of the geo-sciences, is expected to develop its potential accordingly. B y the virtue of several theoretical developments, geodesy, in addition, finds itself confronted with trends which m e a n no less than a revolution of its theoretical foundations, and which d e m a n d the acceptance of n e w measuring concepts. During the last decades n u m e r o u s theoretical discussions have been published by geodesists which call attention to specific areas which are in a process of reforming classic approaches. Hirvonen [ 1 ], in an article published in 1961 in the M a y issue of the Journal of Geophysical Research, listed, as the areas directly affected, the disciplines of geometric geodesy, gravitational geodesy and the theory of adjustment. Until recently, the n e w ideas were not basically connected with each other, aside f r o m the fact that they express a trend toward the reformation of classic concepts in their particular domains. Therefore, the need has arisen for m o r e theoretical research to further develop these n e w ideas and to find ways and m e a n s for putting together again what has been taken apart. O n e a n s w e r to this problem has b e c o m e possible with the advent of close-to-the-earth satellites. With these vehicles, geodesy has been provided with a n e w tool. Because of the geometrical and dynamical characteristics of orbits, artificial satellites provide geodesy with the m e a n s for interconnecting the results of its geometrical and physieal studies on a globe-wide concept, by using three-dimensional models which are based on a m i n i m u m of a priori hypothesis. T h e concepts of m o d e r n mathematical statistics provide the basis for adjusting both classical and satellite observations, not only in t e r m s of the s o m e w h a t vague concept of errors , but by taking into account the continuously increasing interdisciplinary knowledge about the various p a r a m e t e r s of our physical world. If the m o d e r n concepts in geodesy are considered in connection with the possibilities offered by satellite geodesy, it b e c o m e s evident that a logical, unified approach to the basic problem of geodesy can n o w be envisaged which has, as its ultimate purpose, the establishment of all points on the physical surface of the earth in t e r m s of a world-

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wide three-dimensional coordinate system, the origin of which is at a point representative for the center of m a s s and one of w h o s e axes is the rotational axis of the earth. A more detailed examination of the specific geodetic disciplines undergoing changes suggests that in geometric geodesy, because of the potential of electronic computers, it is practical to abandon the two-dimensional s c h e m e of classic triangulations which is based on the theory of surfaces, by replacing the theoretically rather complicated concept of surface geodesics, which are not directly related to actual lines of observation, by an analysis in three-dimensional flat space, as, e.g., expressed by Cartesian coordinate systems. Such an approach is m o r e economical, simpler and theoretically m o r e transparent. The mathematics required consist of relatively simple closed formulae. Such an approach, as suggested a m o n g others by Brigadier Hotine [ 2 ], appears to be a valuable concept for the treatment of classic geodetic triangulation methods. H o w e v e r , the significance of three -dimensional geodesy b e c o m e s most evident in connection with geodetic satellite triangulation which, by the very nature of its geometrical and physical contents, d e m a n d s three-dimensional solutions. T h e revolutionary importance of geometrical satellite geodesy has to be assessed by the fact that a strictly geometrical solution of satellite triangulation provides geodesy, for the first time in its history, wlth the m e a n s to create a three-dimensional w o r l d - w i d e reference system with a m i n i m u m of a priori hypothesis; specifically, without reference to either the direction or magnitude of the force of gravity. The purposes of such a three-dimensional, strictly geometrical triangulation are : a. To provide a world-wide reference net to which all geodetictopographic end products can be related. Such a reference system would achieve economy and permanence in the collection and recording of data essential to the development of the geo-sciences. b. To replace the classic, time-consuming, long-are triangulation methods of determining the shape and size of the earth by a more economical and theoretically superior approach, in order to meet the requirements for modern astronomy and space research. e. To produce unified, three-dimensional reference nets on all accessible land masses, thus eliminating the troublesome discontinuities in map and survey systems which occur over most national frontiers and which seriously hamper the development in such areas. Furthermore, such continental triangulation nets will provide the necessary control for numerical photogrammetric aerial triangulation, executed from extremely high-flying aircraft or satellites, to further intensify the geodetic control pattern in local areas in order to provide control density in accordance with specific topographic mapping requirements. The creation of such a control pattern will provide the most economical approach to world-wide mapping programs, and at the same time furnish the geodetic community with a data library for fast-response mapping capability. d. To

establish

the necessary

geometric

142

fidelity for a

world-wide

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system of satellite tracking stations as a prerequisite for the accuraL~ determination of satellite orbits which, in turn, will provide data ideally suited for analyzing gravimetric and related geophysical parameters. These parameters, in turn, are the necessary prerequisites for determining the position of the center of m a s s and the overall shape of the gravitational field of the earth as it is associated with its m a s s distribution. In gravimetrie geodesy, difficulties in the classical theory are caused by the need for certain information which in praetiee eannot be ascertained. T h e theory postulates that certain groups of observations are executed at the geoid while they actually can obviously only be m a d e at points on the physical surface of the earth. Corresponding reductions depend on the knowledge of the distribution of m a s s inside the crust of the earth. This knowledge is also needed in the reduction of astrogeodetic observations for determining the curvature of the plumb lines. Furthermore, theoretical difficulties arise from the fact that the theory a s s u m e s that all m a s s e s of the earth are inside the geoid. The necessary e f f o r t s of r e g u l a r i z i n g t h e e a r t h a f f e c t t h e r e s u l t s in a c c o r d a n c e w i t h t h e p o s t u l a t e d t y p e of m a s s t r a n s p o r t . T h e n e w i d e a s i n d i c a t e t h a t t h e d e t e r m i n a t i o n of t h e g e o i d is not o n l y a n u n s o l v a b l e p r o b l e m , b u t , l i k e t h e i n t r o d u c t i o n of t h e q u a s i g e o i d s , m o r e o r l e s s U n n e c e s s a r y . F u r t h e r m o r e , t h e s e new t h e o r e t i c a l d e v e l o p m e n t s p o i n t out t h a t t h e d e v e l o p m e n t of t h e g r a v i t a t i o n a l f i e l d b y s p h e r i c a l h a r m o n i e s is o n l y an a p p r o x i m a t i o n , a n d t h e r e s u l t s a r e e s p e c i a l l y i m p a i r e d by l o c a l i r r e g u l a r i t i e s , r e p r e s e n t e d by h a r m o n i c s of v e r y h i g h d e g r e e . T h e new a p p r o a c h , a s e . g . , s u g g e s t e d by B j e r h a m m e r [ 3] a n d A r n o l d [4], is b a s e d on an i n t e g r a l f o r m u l a w h i c h would a l l o w o b t a i n i n g t h e c o m p l e t e s o l u t i o n by t h e p r o c e s s of i t e r a t i o n , t h u s o p e n i n g in p r a c t i c e t h e p o s s i b i l i t y of c a r r y i n g out at l e a s t s p e c i a l i n v e s t i g a t i o n s in l o c a l a r e a s . T h e i d e a s b a s e d on t h e s e t h e o r i e s a r e s t i l l f l u i d a n d m u c h w o r k r e m a i n s to be done b e f o r e d e t a i l s of t h e b e s t p r a c t i c a l a p p r o a c h c a n be s e t t l e d . Acknowledging the significance of t h e s e new i d e a s in g r a v i m e t r i c geodesy, the d i l e m m a still r e m a i n s that the s c a n t i n e s s and n o n - u n i f o r m i t y of t h e d i s t r i b u t i o n of g r a v i t y m e a s u r e m e n t s c a u s e s e r r o r s l a r g e r t h a n t h o s e c a u s e d by t h e d e f e c t s of t h e t h e o r e t i c a l d e v e l o p m e n t s . In a d d i t i o n , t h e c o r r e l a t i o n b e t w e e n t h e c l a s s i c g e o m e t r i c t r i a n g u l a t i o n r e s u l t s a n d t h e g r a v i m e t r i c d a t a s t i l l d e p e n d on c e r t a i n a p r i o r i a c c e p t e d hypotheses. T h e p o s s i b i l i t y of c a l c u l a t i n g t h e o r b i t s of a r t i f i c i a l s a t e l l i t e s in t e r m s of t h e p o t e n t i a l , is t h e b a s i c i m p o r t a n c e of s u c h v e h i c l e s f o r w o r l d - wide g r a v i m e t r i e g e o d e s y . B e c a u s e t h e p a r t i a l d e r i v a t i v e s of s a t e l l i t e o r b i t o b s e r v a t i o n s with r e s p e c t to t r a c k i n g s t a t i o n s a l l o w t h e d e t e r m i n a t i o n of t h e p o s i t i o n s of t h e s e s t a t i o n s r e l a t i v e to t h e c e n t e r of m a s s , a l i n k is p r o v i d e d b e t w e e n t h e g r a v i m e t r i c a l a n d g e o m e t r i c a l p r o b l e m s in g e o d e s y . In p r a c t i c e , h o w e v e r , t h e r e a r e e r r o r s of t h e r e l a t i v e p o s i t i o n s of t r a c k i n g s t a t i o n s w i t h i n i n d i v i d u a l d a t u m s . A l s o , r a t h e r s t r o n g c o r r e l a t i o n e x i s t s b e t w e e n c e r t a i n p e r t u r b a t i o n s c a u s e d by t h e v a r i a t i o n s of t h e g r a v i t a t i o n a l f i e l d , a n d o t h e r g e o p h y s i c a l p h e n o m e n a , a n d t h e s t a t i o n p o s i t i o n e r r o r s . To o v e r c o m e t h e s e d i f f i c u l t i e s in d e r i v i n g a s o l u t i o n to t h e g r a v i m e t r i c p r o b l e m , it i s , t h e r e f o r e , a d v a n t a g e o u s ,

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as a first step, to establish a geometric solution with satellite triangulation as previously mentioned. Both approaches together will eventually provide geodesy with the information necessary to establish a uniform world-wide reference system which is representative for both the geometry of the physical surface of the earth and the gravitational vector field associated with its m a s s distribution. H o w e v e r , there can be no doubt about the necessity of supporting gravimetric satellite geodesy with a continuous effort to improve our knowledge of the potential field in the immediate neighborhood of the physical surface of the earth by the collection of information at sea and on land. It is especially the lack of adequate sea data which leads to the undesirable non-uniformity of the distribution of gravity measurements. Aside from the disturbing factors of tides and currents, the surface of the ocean represents the geoid. A n e w tool of considerable theoretical and economical value b e c o m e s available with the tracking of satellites f r o m stations positioned by the afore-mentioned geometric satellite triangulation method. Portions of orbits of such satellites can n o w be determined m o r e or less continuously by using electronical ranging techniques (e.g. by S E C O R , Doppler or Laser). When equipped with R a d a r - altimeter or L a s e r ranging equipment, such satellites can m e a s u r e with an extremely high sampling rate, the separation between orbits and the surface of the ocean. The abundance of data obtained with such geoid-profiles, executed at different times in order to determine oceanographic effects, would provide, in a most desirable form, the badly needed gravimetric information at sea. These data not only would contribute essential information to the determination of the configuration of the potential surface close to the physical surface of the earth, as needed especially for developing a significant m o d e l of the m a s s distribution in the crust of the earth, but would, even if executed only locally, be of assistance in the study of off-shore regions for locating geological deposits. Therefore, satellites, when used in conjunction with precision spatial triangulation methods, provide gravitational geodesy with a tool which can contribute in a significant w a y to the problem of determining the configuration of the gravitational field, both near the physical surface of the earth and out to such depths of space where, for practical purposes, its effect vanishes. Considerable interest in the launching of a series of gravimetrie satellites has been documented, especially by D O D and N A S A , and valuable gravimetric data has, in the past, been obtained by the analysis of satellite orbits, especially by the Smithsonian Astrophysical Observatory [ 5 ], by N A S A [6] and by the Applied Physics Laboratory.in collaboration with the U.S. Naval W e a p o n s Laboratory [ 7]. In order to obtain quantitative results, theoretical geodetic considerations must always be related to physical m e a s u r e m e n t s . T h e corresponding processes of data adjustment and analysis will require the acceptance of a reformation in a third area of activity, which is concerned with m o d e r n mathematical statistics and amounts to a generalization of the classic least squares method. It is no longer sufficient to consider the purpose of an adjustment as a m e a n s of reducing observational

]44

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REVOLUTIONARY

ASPECTS

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errors. T h e ultimate goal m u s t be to m a k e a set of m e a s u r e d quantities compatible with an economized mathematical model. T h e basic idea underlying this approach is that all quantities used in the construction of a specific mathematical m o d e l are a s s u m e d to be m e a s u r e d quantities which, in turn, are considered to be samples of stochastic variables. B y assigning to these variables in advance relative variances and covariances between the limits of zero and infinity, the least squares method will provide unbiased estimates for all variables, even if they are not normally distributed[8]. Human judgment, based on experience in assigning corresponding variance and co-variance values, plays a major role for obtaining significant results. The interpretation of the discrepancies between the observed quantities and the chosen mathematical model will provide the information necessary for analyzing the soundness of the theory on which, in the first place, the economized model was based. The data evaluation in interdisciplinary projects and the adjustment of hybrid measuring systems, as they mast be envisaged, especially in modern geodetic and photogrammetric data collection systems, demand the acceptance of the broader concept of mathematical statistics in the adjustment of the various types of raw data. It is the potential of the high- speed electronic computer which allows the application of these sophisticated methods of numerical analysis. In the area of data acquisition methods, precision photogrammetry, especially, is developing new measuring techniques which will merge the geodetic and photogrammetric disciplines. Electronic computing techniques have made possible a reorientation of photogrammetry from analogue to digital data evaluation methods. This development will demand the recognition of some of the photogrammetric sensors as precision angle and direction measuring devices. Together with the development of precision optical-electronic ranging methods, photogrammetry will play a decisive role in establishing a new geodetic world datum by observing active and passible geodetic satellites. Equally significant is the objective of automatizing the modelcompilation process by using electronic image correlation techniques together with on-line electronic computers. Such techniques not only open the way for the evaluation of unconventional raw material, but provide the means for treating the numerous perturbations encountered in precision photogrammetry as deviations from the concept of the central perspective. The increasing data-handling capacity points to the possibility of replacing the classic point match technique by the concept of area match which, if it can be extended to cover the whole model area, will provide for an optimum solution in terms of metric precision and economy [ 9 ]. Drastic reorientation in terms of theory and measuring techniques, as presently under way, may very well require us to re-examine our classic attitudes toward geodetic-topographic end products. Both the information contents and the graphic presentation of geodetic information in the form of maps depend to a large extent on the data acquisition and data reduction methods in use. Unconventional data acquisition methods, used under unorthodox, geometrical conditions, and evaluated with equipment based on new concepts of data handling and automation, are likely to produce an end product different from the

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classic concept in terms of accuracy and contents. The question of whether such results are useful and desirable must be approached with an open mind and must not be prejudiced by slavishly clinging to our present end products as the only acceptable forms for presenting geodetic-topographic information. With the launching of manned, earthorbiting laboratories, which will become available to the scientific community in the next few years, the possibility will arise for executing relevant experiments. Equally significant will be the potential of precision numerical photogrammetry when applied to the tasks of geodetic control surveys, including cadastral applications. The principles of numerical aerial triangulation will provide, in particular, economical benefits for various kinds of mapping projects within the United States as well as for large area mapping programs in the developing countries. These techniques will, furthermore, provide a practical technique for supporting mapping projects in connection with space exploration. Specifically, the already envisaged tasks of determining the figure of the m o o n and mapping parts of its surface for and during the Apollo mission, m a y very well depend entirely on precision photogrammetric techniques. SUMMARIZING The general field of theoretical and practical geodesy is being affected by reformatory and revolutionary changes. These changes, to a considerable extent, are caused by the technical progress m a d e in rocketry; specifically, by the capability to launch satellites. For geometric geodesy, the primary significance of m a n - m a d e satellites is simply the fact that the m a x i m u m possible dimensions for three -dimensional triangulation schemes have increased in direct proportion to the increase in height of the auxiliary target points. That is to say, that with the help of satellites, a basic, geodetic, worldwide reference frame can be established with a net of triangles, each of which is about I0,000 times larger than an average triangle in classic first-order triangulation. For gravimetric geodesy satellites provide a n e w tool. Their orbits provide the means for sampling, in a systematic manner, the potential field outside of the physical earth. This is accomplished by determining the geometry of orbits, which in turn can be considered as instantaneous and continuous analogue presentations of certain characteristics of the potential field of the earth. In addition, a purely geometric determination of the shape of the geoid over the oceans can be envisaged. Revolutionary developments of new sensors and, correspondingly, of n e w data acquisition methods, have increased sampling rates by several magnitudes. These developments m a k e it possible to execute spatial triangulations with higher precision ( less noise) and higher accuracy (smaller biases). Last, but certainly not least, the ever increasing potential of electronic computing allows the hendling of very large amounts of data in a statistically significant manner in conjunction with complex mathematical formulations. The previously discussed trends toward changes in geodesy

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are not academic, in the sense of future eventualities, but are already upon us. N A S A is firmly committed to launching, for both the gravimetric and the geometric solutions, a family of satellites. These launchings are scheduled to begin during the second half of calendar year 1965. The spectacular results already obtained from satellite observations, especially in gravimetric geodesy, clearly indicate the potential of the method. The feasibility of the practlcal execution of geometric solutions has been proven. The Coast and Geodetic Survey, using the balloon satellites E C H O I and E C H O II, has executed spatial triangulation within the U S A over triangles with 800 mile side lengths. The accuracy, as distinguished from merely precision of the corresponding measurements, is about i p a r t in 400,000 [i0], [ii] , [12]. P r e s e n t l y , the C o a s t and G e o d e t i c S u r v e y , in c o o p e r a t i o n with the D e p a r t m e n t of D e f e n s e and NASA, is a c t u a l l y planning a w o r l d - w i d e net. T h e s e plans a r e being m a d e in a n t i c i p a t i o n of N A S A ' s c o n t e m p l a t e d launching of an ECHO I type s a t e l l i t e in a p o l a r , n o m i n a l l y - c i r c u l a r o rb i t of about 4 , 2 0 0 km height d u r i n g J u n e , 1966. T h e e n c l o s e d f i g u r e c o n v e y s an idea of the s u p e r - l a r g e g e o m e t r y which has b e c o m e a p r a c t i c a l p o s s i b i l i t y f o r g e o d e s y with the advent of s a t e l l i t e s . T h e s m a l l t r i a n g l e s show the t y p i c a l s i z e of c l a s s i c f i r s t - o r d e r t r i a n g u l a t i o n c h a i n s . T h e l a r g e t r i a n g l e s a r e the f i r s t 800 m i l e t r i a n g l e s o b s e r v e d by the C o a s t and G e o d e t i c S u r v e y d u r i n g the i n i t i a l phas e of its s a t e l l i t e t r i a n g u l a t i o n p r o g r a m , and the h e a v y line is one side of the c o n t e m p l a t e d w o r l d net. Th e net has a p p r o x i m a t e l y 40 s t a t i o n s , f o r m i n g about 70 t r i a n g l e s with s l i g h t l y m o r e than 100 s i d e s ; n e v e r t h e l e s s , it e n c o m p a s s e s the whole e a r t h . It should be noted that, b e c a u s e of the g e o g r a p h i c p a t t e r n of i s l a n d s , it is p o s s i b l e to e s t a b l i s h a t r i a n g u l a t i o n net with a l m o s t i d e a l c o n fi g u rat i o n . T h e r e a l i z a t i o n of such a t r i a n g u l a t i o n is no l o n g e r a q u e s t i o n of t e c h n i c a l f e a s i b i l i t y , but it will depend u l t i m a t e l y on our s u c c e s s in c o n v i n c i n g the c o n t i n u o u s l y expanding p o l i t i c a l w o r l d that the e a r t h has s h r u n k t e c h n o l o g i c a l l y to such an extent as to r e q u i r e w o r l d - w i d e c o o p e r a t i o n in o r d e r to enhance o u r g e o p h y s i c a l knowledge. G e o d e s y , with its n o v e l p o s s i b i l i t i e s , is r e a d y to c o n t r i b u t e its s h a r e .

147

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R E F E R E N C E S

[1 ]

R.A.

H I R V O N E N : The R e f o r m a t i o n of G e o d e s y , J o u r n a l of Geophysical Research, The A m e r i c a n G e o p h y s i c a l Union, Vol. 66, N'5, May 1961.

[2]

M. H O T I N E

: Three Dimensional

tionary on G e o p h y s i c s [3

]

A.

: On

BJERHAMMAR

Boundary Reference,

an

Value The

Geodesy,

(1964),

Explicit Problem Royal

Solution

for an Institute

sion : Geodesy, Stockholm, N" DA-91-591-EUC-2033. [4 ]

K.

ARNOLD

: Numerische

Figur 1960.

[5 ]

[6 ]

I.G.

W.M.

der

IZSAK Nature, KAULA

[7

]

H.H.

SCHMID Satellite

[S ]

[9 ]

H.

U.V.

SCHMID

Society March,

and

E.

Geodetic

Survey, : An

N "3,

in

the

1962,

the

Contract

Theorie

Inst.

Earth's Wash. Vol.

der

Potsdam,

Geopotential,

Gravitational

D.C. The I, N'4.

American

of a World-Wide System, presented

Photogrammetry

SCHMID

for

Publication

of

Gravimetric

Meeting

Passive at the in

Wash.,

1964.

Solution

HELAVA

of

the

strengen Geod.

Geophysics, Nov. 1963,

: Accuracy Aspects Triangulation

American D.C.,

zur

: Tesseral Harmonics 199, 137-139, 1963. : Determination

of

November

VerDffentl.

Field, Reviews of Geophysical Union"

Dic-

Ellipsoidal Surface of of Technology, Divi-

30

Beispiele

Erde,

International

(in the press).

the

Generalized

Least

Measuring_SSystems~

U.S.

Ultimate of

: A

Hybrid

Dept. Solution

Finnish

1962.

149

of

Commerce,

of Society

Relative of

Squares Coast

June~

and 1965.

Orientation~ Photogrammetry~

H.H.

[i0]

H.H.

SCHMID

: Accuracy

SCHMID

Aspects

of a W o r l d - W i d e

Passive

Satellite Triangulation S y s t e m , p r e s e n t e d at the A m e r i c a n Society of P h o t o g r a m m e t r y M e e t i n g in Wash., D.C.~

March,

1964.

[ii]

H.H.

S C H M I D : P r e c i s i o n and A c c u r a c y _ c o n s i d e r a t i o n s for the E x e c u t i o n of G e o m e t r i c S a t e l l i t e T r i a n g u l a t i o n , p r e s e n t e d to the Second International S y m p o s i u m on : " T h e U s e of A r t i f i c i a l Satellites for G e o d e s y " , Athens, Greece, April, 1965.

[12]

H.H.

S C H M I D : The Status of G e o m e t r i c S a t e l l i t e Triangu__Clation at the Coast and Geodetic Survey, p r e s e n t e d to the A C S M / A S P C o n v e n t i o n at Washington, D.C., March~ 1966.

150