27:
527:'s latitude later explained by vertical deflection. When these errors where acknowledged in 1866, it became urgent to proceed to a new measurement of the French arc between Dunkirk and Perpignan. The operations concerning the revision of the French arc linked to Spanish triangulation were completed only in 1896. Meanwhile, the French geodesists had accomplished in 1879 the junction of Algeria to Spain, with the help of the geodesists of the Madrid Institute headed by the late
807:
Jean-Étienne Duby, Rapport sur les travaux de la Société de
Physique et d’Histoire naturelle de Genève de juillet 1860 à juin 1861 par M. le Pasteur Duby. Lu à la séance du 13 juin 1861, in Mémoires de la Société de physique et d’histoire naturelle de Genève, 16 (1861-1862),
370:
exceeds the geodetic measuring accuracy by a factor of 5 to 50. Therefore, the data would have to be corrected exactly with respect to the global ellipsoid. Without these reductions, the surveys may be
289:
In practice, the deflections are observed at special points with spacings of 20 or 50 kilometers. The densification is done by a combination of DTM models and areal
206:
278:: as a vertical deflection describes the difference between the geoidal vertical direction and ellipsoidal normal direction, it represents the horizontal
504:) was affected by vertical deflection. The resulting discrepancy with Northern Hemisphere measurements was not explained until a visit to the area by
420:
ellipsoid), whereas the terrestrial heights refer to the geoid. We need accurate geoid data to combine the different types of measurements.
950:
607:
218:
replaces the old, with new geodetic latitudes and longitudes on a new ellipsoid, the calculated vertical deflections will also change.
528:
263:. Additionally, the very local variations of the vertical deflection can be computed from gravimetric survey data and by means of
196:(taking north latitudes to be positive and south latitudes to be negative); the latter is usually calculated by geodetic network
516:
293:. Precise vertical deflection observations have accuracies of ±0.2″ (on high mountains ±0.5″), calculated values of about 1–2″.
976:
786:
603:
611:
501:
91:
at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in
679:
Malys, Stephen; Seago, John H.; Palvis, Nikolaos K.; Seidelmann, P. Kenneth; Kaplan, George H. (1 August 2015).
636:
315:
region, very asymmetric peaks may have vertical deflections up to 100″ (0.03°). In the rather flat area between
509:
268:
398:
of VD components ξ,η and therefore can be calculated with cm accuracy over distances of many kilometers.
543:
482:
493:
1001:
944:
939:
720:
489:
1058:
1054:
546:
as an important source of error in geodetic surveys as early as 1756. A few years later, in 1828,
323:
the values are less than 15", but scatter by ±10″ for irregular rock densities in the subsurface.
471:
387:
275:
233:
1002:"Article Figure de la Terre, (Astron. Géog. Physiq. & Méch.), vol. VI (1756), p. 749b–761b"
935:
778:
The
Measure of All Things: The Seven-year Odyssey and Hidden Error that Transformed the World
264:
827:
692:
655:
547:
367:
359:
157:
8:
1079:
539:
260:
227:
186:
130:
831:
696:
851:
578:
467:
363:
214:(taking east longitudes to be positive and west longitudes to be negative). When a new
36:
259:(theoretical vertical) by geodetic network computation, which always takes place on a
982:
972:
855:
843:
782:
760:
743:
535:
192:
88:
1084:
1074:
911:
878:
835:
755:
700:
659:
651:
563:
438:
283:
279:
20:
871:"La méridienne de Dunkerque à Barcelone et la déterminiation du mètre (1972-1799)"
818:
Vaníček, Petr; Foroughi, Ismael (2019). "How gravity field shortened our metre".
776:
568:
430:
237:
1026:
301:
26:
839:
505:
478:
327:
297:
169:
705:
680:
664:
441:
to improve our knowledge of the Earth's interior. Additionally and similar to
1068:
847:
335:
241:
215:
126:
1025:
US Department of
Commerce, National Oceanic and Atmospheric Administration.
986:
602:
He had been president of the
International Geodetic Association (now called
286:
of the geoid (i.e., the inclination between geoid and reference ellipsoid).
943:
637:"Modern Determination of Vertical Deflections Using Digital Zenith Cameras"
177:
122:
870:
903:
882:
446:
165:
1053:
The NGS website gives vertical deflection anywhere in the United States
915:
429:. Because VD data are affected by the physical structure of the Earth's
523:, were long known to be mainly caused by an uncertain determination of
425:
372:
355:
290:
197:
118:
100:
55:
16:
Measure of the downward gravitational force's shift due to nearby mass
524:
497:
450:
434:
409:
383:
331:
211:
146:
134:
96:
106:
The vertical deflection are the angular components between the true
573:
413:
395:
312:
138:
320:
305:
204:
the product of cosine of latitude and the difference between the
150:
142:
92:
538:
was calculated in 1910, vertical deflections were considered as
247:
Vertical deflections are usually determined astronomically. The
30:
Earth's ellipsoid, geoid, and two types of vertical deflection.
583:
391:
316:
107:
551:
520:
519:
determination, which affected the original definition of the
417:
114:
111:
46:
971:. Encyclopedia Universalis. 1996. pp. Vol 10, p. 302.
346:
Vertical deflections are principally used in four matters:
308:
252:
678:
635:
Hirt, C.; Bürki, B.; Somieski, A.; Seeber, G. N. (2010).
454:
403:
634:
311:. The approx. values are ξ = +50″ and η = −30″. In the
1024:
512:
resurvey ultimately confirmed
Everest's conjecture.
904:"Sur les progrès des travaux géodésiques en Europe"
811:
954:. Vol. 8 (11th ed.). pp. 801–813.
394:values to 10–50 m. They are adequate to the
382:(mean sea level) and for exact transformation of
1066:
608:International Committee for Weights and Measures
817:
481:passes more than 100 m to the east of the
251:is observed astronomically with respect to the
999:
375:by some centimeters or even decimeters per km.
267:(DTM), using a theory originally developed by
934:
477:Vertical deflection is the reason why modern
145:irregularities and can amount to angles of 10
768:
610:, and one of the 81 initial members of the
542:. Plumb line deviations were identified by
466:Vertical deflections were used to measure
461:
868:
759:
704:
663:
304:(3,798 m), the highest peak of the
25:
149:in flat areas or 20–50″ in mountainous
1067:
901:
741:
723:. Astronomical Society of South Africa
362:are oriented with respect to the true
774:
445:, the VD data can support the future
156:The deflection of the vertical has a
969:Géodésie in Encyclopedia Universalis
604:International Association of Geodesy
517:meridian arc of Delambre and Méchain
483:historical astronomic prime meridian
961:
612:International Statistical Institute
390:amount to 50–100 m, and their
296:The maximal vertical deflection of
133:(chosen to approximate the Earth's
13:
681:"Why the Greenwich meridian moved"
656:10.1061/(ASCE)SU.1943-5428.0000009
19:For the CRT rastering method, see
14:
1096:
1047:
1000:d'Alembert, Jean Le Rond (1756).
869:Levallois, Jean-Jacques (1991).
761:10.1046/j.1468-4004.2002.43225.x
644:Journal of Surveying Engineering
326:More recently, a combination of
221:
1018:
993:
928:
596:
895:
862:
801:
742:Warner, Brian (1 April 2002).
735:
713:
672:
628:
341:
184:is the difference between the
87:, is a measure of how far the
1:
621:
529:Carlos Ibañez Ibáñez de Ibero
502:de Lacaille's arc measurement
412:measurements refer to a pure
300:seems to be a point near the
945:"Earth, Figure of the"
232:The deflections reflect the
137:surface). VDs are caused by
81:deflection of the plumb line
7:
1006:enccre.academie-sciences.fr
557:
350:For precise calculation of
10:
1101:
840:10.1007/s00190-019-01257-7
606:), first president of the
225:
73:deflection of the vertical
18:
940:Helmert, Friedrich Robert
706:10.1007/s00190-015-0844-y
510:Maclear's arc measurement
494:Nicolas-Louis de Lacaille
334:have also been used, see
244:and its inhomogeneities.
240:, for they depend on the
85:astro-geodetic deflection
902:Hirsch, Adolphe (1865).
748:Astronomy and Geophysics
589:
550:proposed the concept of
490:meridian arc measurement
951:Encyclopædia Britannica
744:"Lacaille 250 years on"
544:Jean Le Rond d'Alembert
472:Schiehallion experiment
462:Historical implications
276:astrogeodetic levelling
234:undulation of the geoid
936:Clarke, Alexander Ross
265:digital terrain models
129:to the surface of the
60:
721:"Arc of the Meridian"
386:. The global geoidal
29:
1027:"What is the geoid?"
883:10.5169/seals-234595
548:Carl Friedrich Gauss
416:system (usually the
207:astronomic longitude
916:10.5169/seals-88030
832:2019JGeod..93.1821V
697:2015JGeod..89.1263M
380:geoid determination
261:reference ellipsoid
228:Geoid determination
187:astronomic latitude
141:and by underground
131:reference ellipsoid
65:vertical deflection
58:-oriented ellipsoid
35: Ellipsoid of
820:Journal of Geodesy
775:Alder, K. (2002).
685:Journal of Geodesy
665:20.500.11937/34194
579:Vertical direction
449:of raw materials,
443:applied geophysics
257:ellipsoidal zenith
61:
37:astro-geodetically
978:978-2-85229-290-1
788:978-0-7432-1675-3
536:Hayford ellipsoid
284:geoid undulations
238:gravity anomalies
193:geodetic latitude
99:networks and for
89:gravity direction
79:), also known as
1092:
1041:
1040:
1038:
1037:
1031:geodesy.noaa.gov
1022:
1016:
1015:
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1012:
997:
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990:
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958:
947:
932:
926:
925:
923:
922:
899:
893:
892:
890:
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860:
859:
826:(9): 1821–1827.
815:
809:
805:
799:
798:
796:
795:
772:
766:
765:
763:
754:(2): 2.25–2.26.
739:
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732:
730:
728:
717:
711:
710:
708:
676:
670:
669:
667:
641:
632:
615:
600:
564:Deviation survey
280:spatial gradient
274:VDs are used in
180:). The value of
53:
44:
34:
21:Cathode-ray tube
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633:
629:
624:
619:
618:
601:
597:
592:
569:Gravity anomaly
560:
468:Earth's density
464:
437:are engaged in
354:. The geodetic
352:survey networks
344:
230:
224:
200:. The value of
172:component
59:
56:Gravimetrically
51:
49:
42:
40:
32:
24:
17:
12:
11:
5:
1098:
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1048:External links
1046:
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787:
781:. Free Press.
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566:
559:
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515:Errors in the
506:George Everest
485:in Greenwich.
479:prime meridian
463:
460:
459:
458:
421:
399:
376:
358:and levelling
343:
340:
328:digital camera
298:Central Europe
269:Vening-Meinesz
223:
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50:
41:
39:oriented datum
31:
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541:
540:random errors
537:
532:
531:(1825–1891).
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336:zenith camera
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245:
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242:gravity field
239:
235:
229:
222:Determination
219:
217:
216:mapping datum
213:
209:
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127:normal vector
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1034:. Retrieved
1030:
1020:
1009:. Retrieved
1005:
995:
968:
963:
956:see page 811
955:
949:
930:
919:. Retrieved
907:
897:
886:. Retrieved
874:
864:
823:
819:
813:
803:
792:. Retrieved
777:
770:
751:
747:
737:
725:. Retrieved
715:
691:(12): 1263.
688:
684:
674:
647:
643:
630:
598:
533:
514:
487:
476:
465:
442:
433:and mantle,
424:
402:
379:
351:
345:
325:
302:Großglockner
295:
288:
273:
256:
248:
246:
231:
205:
201:
191:
185:
181:
173:
161:
155:
123:tangent line
105:
84:
80:
76:
72:
68:
64:
62:
908:E-Periodica
875:E-Periodica
447:exploration
414:geometrical
388:undulations
360:instruments
356:theodolites
342:Application
249:true zenith
198:coordinates
158:north–south
101:geophysical
1080:Geophysics
1069:Categories
1036:2022-12-23
1011:2022-12-23
921:2022-12-23
888:2022-12-23
794:2020-08-02
622:References
435:geodesists
426:geophysics
410:satellites
384:elevations
368:deflection
366:, but its
291:gravimetry
255:, and the
226:See also:
160:component
143:geological
119:plumb line
103:purposes.
856:146099564
848:0949-7714
727:27 August
525:Barcelona
508:in 1820;
500:in 1752 (
498:Cape Town
496:north of
453:, gas or
396:integrals
373:distorted
332:tiltmeter
212:longitude
170:east–west
168:) and an
139:mountains
135:sea-level
97:surveying
987:36747385
942:(1911).
808:196-197.
650:: 1–12.
574:Isostasy
558:See also
492:made by
392:regional
378:For the
364:vertical
313:Himalaya
306:Austrian
210:and the
190:and the
125:and the
1085:Gravity
1075:Geodesy
828:Bibcode
693:Bibcode
470:in the
406:surveys
321:Hungary
282:of the
151:terrain
93:geodesy
985:
975:
854:
846:
785:
584:Zenith
534:Until
439:models
408:. The
317:Vienna
108:zenith
95:, for
54:
52:
45:
43:
33:
852:S2CID
640:(PDF)
590:Notes
552:geoid
521:metre
431:crust
418:WGS84
253:stars
115:curve
112:nadir
71:) or
47:Geoid
1059:here
1057:and
1055:here
983:OCLC
973:ISBN
844:ISSN
783:ISBN
729:2020
488:The
455:ores
423:For
401:For
330:and
319:and
309:Alps
236:and
202:η is
83:and
63:The
912:doi
879:doi
836:doi
756:doi
701:doi
660:hdl
652:doi
648:136
451:oil
404:GPS
178:eta
153:).
77:DoV
1071::
1029:.
1004:.
981:.
948:.
938:;
906:.
873:.
850:.
842:.
834:.
824:93
822:.
752:43
750:.
746:.
699:.
689:89
687:.
683:.
658:.
646:.
642:.
554:.
474:.
338:.
271:.
166:xi
121:)
69:VD
1061:.
1039:.
1014:.
989:.
924:.
914::
891:.
881::
858:.
838::
830::
797:.
764:.
758::
731:.
709:.
703::
695::
668:.
662::
654::
614:.
457:.
182:ξ
176:(
174:η
164:(
162:ξ
147:″
117:(
110:–
75:(
67:(
23:.
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