19:
334:
It can be helpful to think of the free-air anomaly as comparing observed gravity to theoretical gravity adjusted up to the measurement point instead of observed gravity adjusted down to the geoid. This avoids any confusion of assuming that the measurement is made in free air. Either way, however, the
81:
to measure the departure of observed gravity from a theoretical gravity value to identify anomalies due to geologic features below the measurement locations. The computation of anomalies from observed measurements involves the application of corrections that define the resulting anomaly. The free-air
700:
Here we have assumed that measurements are made relatively close to the surface so that R does not vary significantly. The value of the free-air correction is positive when measured above the geoid, and negative when measured below. There is the assumption that no mass exists between the observation
94:
The free-air correction adjusts measurements of gravity to what would have been measured at mean sea level, that is, on the geoid. The gravitational attraction of Earth below the measurement point and above mean sea level is ignored and it is imagined that the observed gravity is measured in air,
572:
335:
Earth mass between the observation point and the geoid is neglected. The equation for this approach is simply rearranging terms in the first equation of this section so that reference gravity is adjusted and not the observed gravity:
106:
For studies of subsurface structure, the free-air anomaly is further adjusted by a correction for the mass below the measurement point and above the reference of mean sea level or a local datum elevation. This defines the
709:
Over the ocean where gravity is measured from ships near sea level, there is no or little free-air correction. In marine gravity surveys, it was observed that the free-air anomaly is positive but very small over the
440:
417:
228:
714:
in spite of the fact that these features rise several kilometers above the surrounding seafloor. The small anomaly is explained by the lower density crust and mantle below the ridges resulting from
695:
445:
325:
294:
612:
434:
with the distance at which the measurement is made from the mass. The free air correction is calculated from Newton's Law, as a rate of change of gravity with distance:
53:
at which a measurement is made. It does so by adjusting these measurements of gravity to what would have been measured at a reference level, which is commonly taken as
264:
144:
638:
718:. This lower density is an apparent offset to the extra height of the ridge indicating that Mid-Ocean Ridges are in isostatic equilibrium.
567:{\displaystyle {\begin{aligned}g&={\frac {GM}{R^{2}}}\\{\frac {dg}{dR}}&=-{\frac {2GM}{R^{3}}}=-{\frac {2g}{R}}\end{aligned}}}
341:
152:
920:
844:
779:
646:
99:
that approximates the more complex shape of the geoid. Gravity is computed on the ellipsoid surface using the
95:
hence the name. The theoretical gravity value at a location is computed by representing the Earth as an
771:
427:
701:
point and the reference level. The
Bouguer and terrain corrections are used to account for this.
303:
269:
759:
580:
938:"Free-air gravity anomalies in the world's oceans and their relationship to residual elevation"
836:
737:
236:
828:
949:
873:
122:
8:
990:
732:
328:
100:
953:
877:
962:
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727:
715:
623:
431:
967:
916:
889:
840:
829:
795:
775:
18:
620:
The free-air correction is the amount that must be added to a measurement at height
957:
881:
74:
23:
909:
Whole Earth
Geophysics: An Introductory Textbook for Geologists and Geophysicists
711:
108:
70:
42:
54:
984:
971:
912:
893:
767:
78:
30:
885:
96:
50:
861:
83:
69:
Studies of the subsurface structure and composition of the Earth's
835:(2nd ed.). Cambridge: Cambridge University Press. pp.
58:
614:
412:{\displaystyle g_{F}=g_{obs}-(g_{\lambda }-\delta g_{F})}
223:{\displaystyle g_{F}=(g_{obs}+\delta g_{F})-g_{\lambda }}
826:
764:
649:
626:
583:
443:
344:
306:
272:
239:
155:
125:
827:
Telford, W.M.; Geldart, L.P.; Sheriff, R.E. (1990).
690:{\displaystyle \delta g_{F}={\frac {2g}{R}}\times h}
689:
632:
606:
566:
411:
319:
288:
258:
222:
138:
982:
936:Cochran, James R.; Talwani, Manik (1977-09-01).
935:
822:
820:
796:"Introduction to Potential Fields: Gravity"
22:Circular free-air gravity anomaly over the
817:
961:
754:
752:
17:
983:
906:
758:
640:to correct it to the reference level:
900:
859:
749:
860:Ervin, C. Patrick (December 1977).
13:
963:10.1111/j.1365-246X.1977.tb01334.x
803:U.S. Geological Survey Fact Sheets
14:
1002:
942:Geophysical Journal International
89:
82:anomaly can be used to test for
862:"Theory of the Bouguer Anomaly"
704:
64:
929:
853:
788:
406:
377:
204:
169:
114:
49:is applied to account for the
1:
743:
422:
119:The free-air gravity anomaly
101:International Gravity Formula
320:{\displaystyle g_{\lambda }}
289:{\displaystyle \delta g_{F}}
7:
721:
607:{\displaystyle 2g/R=0.3086}
10:
1007:
772:Cambridge University Press
428:Gravitational acceleration
146:is given by the equation:
37:, often simply called the
35:free-air gravity anomaly
259:{\displaystyle g_{obs}}
691:
634:
608:
568:
413:
321:
290:
260:
224:
140:
26:
907:Lillie, R.J. (1998).
692:
635:
609:
569:
414:
322:
291:
266:is observed gravity,
261:
225:
141:
139:{\displaystyle g_{F}}
84:isostatic equilibrium
77:employ surveys using
21:
774:. pp. 205–206.
647:
624:
581:
441:
342:
304:
270:
237:
153:
123:
86:over broad regions.
954:1977GeoJ...50..495C
878:1977Geop...42.1468E
733:Reference ellipsoid
329:theoretical gravity
298:free-air correction
47:free-air correction
831:Applied Geophysics
716:seafloor spreading
687:
630:
604:
564:
562:
432:inverse square law
409:
317:
286:
256:
220:
136:
41:, is the measured
27:
922:978-0-13-490517-4
886:10.1190/1.1440807
846:978-0-521-32693-3
805:. FS–239–95. 1997
781:978-0-521-89307-7
679:
633:{\displaystyle h}
577:At 45° latitude,
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478:
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712:Mid-Ocean Ridges
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430:decreases as an
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39:free-air anomaly
24:Chicxulub Crater
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728:Earth's gravity
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109:Bouguer anomaly
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43:gravity anomaly
12:
11:
5:
1004:
994:
993:
978:
977:
948:(3): 495–552.
928:
921:
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852:
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816:
787:
780:
766:(2 ed.).
760:Fowler, C.M.R.
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90:Survey methods
88:
66:
63:
55:mean sea level
9:
6:
4:
3:
2:
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992:
989:
988:
986:
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947:
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913:Prentice Hall
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769:
768:Cambridge, UK
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40:
36:
32:
25:
20:
16:
945:
941:
931:
908:
902:
869:
865:
855:
830:
807:. Retrieved
802:
790:
763:
708:
705:Significance
699:
619:
576:
426:
333:
297:
232:
118:
105:
93:
68:
65:Applications
46:
38:
34:
28:
15:
872:(7): 1468.
115:Calculation
79:gravimeters
991:Gravimetry
866:Geophysics
744:References
423:Correction
31:geophysics
972:0956-540X
894:0016-8033
682:×
651:δ
543:−
512:−
394:δ
391:−
386:λ
375:−
313:λ
274:δ
216:λ
208:−
192:δ
97:ellipsoid
51:elevation
985:Category
762:(2005).
722:See also
45:after a
950:Bibcode
874:Bibcode
296:is the
233:Here,
57:or the
970:
919:
892:
843:
809:30 May
778:
602:0.3086
300:, and
75:mantle
33:, the
839:–12.
799:(PDF)
738:WGS84
71:crust
59:geoid
968:ISSN
917:ISBN
890:ISSN
841:ISBN
811:2019
776:ISBN
617:/m.
615:mGal
73:and
958:doi
882:doi
327:is
103:.
29:In
987::
966:.
956:.
946:50
944:.
940:.
915:.
911:.
888:.
880:.
870:42
868:.
864:.
837:11
819:^
801:.
770::
751:^
331:.
111:.
61:.
974:.
960::
952::
925:.
896:.
884::
876::
849:.
813:.
784:.
685:h
677:R
673:g
670:2
664:=
659:F
655:g
628:h
599:=
596:R
592:/
588:g
585:2
556:R
552:g
549:2
540:=
533:3
529:R
524:M
521:G
518:2
509:=
499:R
496:d
491:g
488:d
474:2
470:R
465:M
462:G
456:=
449:g
407:)
402:F
398:g
382:g
378:(
370:s
367:b
364:o
360:g
356:=
351:F
347:g
309:g
282:F
278:g
252:s
249:b
246:o
242:g
212:g
205:)
200:F
196:g
189:+
184:s
181:b
178:o
174:g
170:(
167:=
162:F
158:g
132:F
128:g
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