Ali Onceloncel@kfupm.edu.saDepartment of Earth SciencesKFUPMGravity Methods 1Introduction to GeophysicsIntroduction to Geophysics-KFUPMField Trip: Refraction SeismologyIntroduction to Geophysics-KFUPMField Trip: Refraction SeismologyIntroduction to Geophysics-KFUPMField Trip: Refraction SeismologyIntroduction to Geophysics-KFUPMField Trip: Refraction SeismologyIntroduction to Geophysics-KFUPMField Application by GravimeterIntroduction to Geophysics-KFUPMThis Wednesday, Mid TermNext Wednesday, May 10a The !ra"ity #ie$d is symmetricForce "ectors %arro&s' ha"e approximate$y e(ua$ ma!nitude and point to&ard the center o# the )arth)arth*s Gra"ity Potentia$ Fie$dIntroduction to Geophysics-KFUPM+ The ma!nitude and direction o# the ma!netic #ie$d is !o"erned +y positi"e %south' and ne!ati"e %north' po$es Ma!nitude "aries +y a #actor o# t&o #rom e(uator to po$e)arth*s Ma!netic Potentia$ Fie$dIntroduction to Geophysics-KFUPM,i##erences in )arth*s Potentia$ Fie$ds)arth*s !ra"ity #ie$d is simp$y compared to the ma!netic #ie$d-ines o# the #orce #or the !ra"ity #ie$d are directed to&ard the center o# the )arth &hi$e ma!netic #ie$d stren!th and direction depend on the )arth*s positi"e and ne!ati"e po$esIntroduction to Geophysics-KFUPMc The acce$eration due to !ra"ity %a.!' o# a +ody depends on$y the mass o# attractin! +ody %m/.M' and the distance to the center o# that mass % r.0 ' !.GM10/a The !ra"itationa$ #orce +et&een t&o o+2ects is direct$y proportiona$ to their masses %m1, m/', and in"erse$y proportiona$ to the s(uare o# their distance % r '+ The mass %m1', times the acce$eration %a' due to mass %m/', determines the !ra"itationa$ #orce %F'F.m1 a2122 112rm mG F =)30T4*5 G036IT7 FI)-,Introduction to Geophysics-KFUPM212EEsERmGmFg = =The "ariation o# g across the earth*s sur#ace pro"idesin#ormation a+out the distri+ution o# density contrasts in the su+sur#ace since m = V %ie density x "o$ume'ms sprin! mass,m) mass o# the earth. 89:; x 10/< =!0) radius o# the earth-i=e apparent conducti"ity and resisti"ity, the acce$eration o# !ra"ity %!' is a +asic physica$ property &e measure, and #rom &hich, &e in#er the distri+ution o# su+sur#ace density contrast)arth*s Gra"itationa$ 3cce$erationFor per#ect$y spherica$ and non-rotatin! )arth &ith uni#orm mass distri+ution, g

represents the acce$eration o# !ra"ity at a particu$ar point on the earth*s sur#ace> 0)m5m)Introduction to Geophysics-KFUPMa The mass %M' o# the )arth and radius % r 'to the )arth*s center determine the !ra"itationa$ acce$eration %!' o# o+2ects and a+o"e )arth*s sur#ace+ The acce$eration is the same %!', re!ard$ess o# the mass o# the o+2ect c?+2ects at )arth*s sur#ace %radius 01' ha"e !reater acce$eration than o+2ects some distance a+o"e the sur#ace %radius 0/' Introduction to Geophysics-KFUPMThe main #actors responsi+$e #or the di##erence in !ra"itationa$ acce$eration at the e(uator compared to the po$esGra"ity increases #rom 9;@,000 mGa$ at the e(uator, to a+out 9@A,000 mGa$ at the po$es6ariation in !ra"ity #rom e(uator to po$e, accordin! to 19:; 0e#erence Gra"ity #ormu$aIntroduction to Geophysics-KFUPMTheoretica$ Gra"ity( )2 42978.03185 1 0.005278895sin 0.000023463sinncmgs = + The a"era!e "a$ue o# !ra"ity #or a !i"en $atitude is approximated +y the Internationa$ 3ssociation o# Geodesy in 19:; !n .Norma$ Gra"ity> Gra"itationa$ acce$eration expected #or a rotatin! e$$ipsoida$ earth &ithout any !eo$o!ic comp$ications and no sur#ace #eaturesB.$atitudeGra"itation increase#rom the e(uator %B .0' .9;@,0A1@8 mGa$ to the po$e %B .0'.9@A,/1;;/ mGa$Introduction to Geophysics-KFUPMd!1d0C-0A0@ mGa$1md!1d0C a"era!e "a$ue #or the chan!e in !ra"ity &ith increasin! e$e"ationIntroduction to Geophysics-KFUPMFree 3ir Gra"ity Dorrection0isin! up&ard #rom )arth*s sur#ace, !ra"itationa$ acce$eration decreases +y a+out 0A0@ mGa$ #or e"ery meter o# hei!ht3 !ra"ity station at hi!h e$e"ation tends to ha"e a $o&er !ra"itationa$ acce$eration %!' than a station at $o&er e$e"ationIntroduction to Geophysics-KFUPMFree 3ir Gra"ity DorrectionEThe #ree air correction %F3D' accounts #or the extended radius to an o+ser"ation point, e$e"ated h meters a+o"e a sea $e"e$ datumE The a+o"e e(uation i$$ustrates that, #or e"ery A m %a+out 10 #eet' up&ard #rom the sur#ace o# the )arth, the acce$eration due to !ra"ity decreases +y a+out 1 mGa$Introduction to Geophysics-KFUPMGra"ity 3noma$y What is an anoma$yFE ,i##erence +et&een o+ser"ed !ra"ity and Internationa$ Gra"ity Formu$a %IGF' #or same $ocation or re$ati"e to $oca$ +ase station, termed the !ra"ity anoma$y, ,! ,! . !o+s - !nE di##erence is the resu$t o# density contrasts in the su+sur#ace +e$o& the measurement pointIntroduction to Geophysics-KFUPMFree 3ir Gra"ity 3noma$ygfa= g gt + FACG!#a . #ree !ra"ity anoma$y! . !ra"itationa$acce$eration o+ser"ed at station!t. theoretica$ !ra"ityIntroduction to Geophysics-KFUPMHou!uer DorrectionEThe extra mass o# mountains resu$ts in hi!her !ra"ity re$ati"e to areas near sea $e"e$E The Hou!uer Dorrection %HD' accounts #or the !ra"itationa$ attraction o# the mass a+o"e the sea-$e"e$ datumIntroduction to Geophysics-KFUPMHou!uer DorrectionEThus, to account #or the excess mass a+o"e a sea $e"e$ datum, the Hou!uer correction assumes an in#inite s$a+ o# density %I', &ith thic=ness %h' e(ua$ to the station*s e$e"ationHD. / J I G hG.Uni"ersa$ Gra"itationa$ Donstant %:,A:;,000 m'4. thic=ness o# the s$a+ %station e$e"ation'5u+stitutin! the "a$ues o# G and / J yie$ds> HD. 0