Re: Spherical Bouguer correction
Lester Anderson <[email protected]> Fri, 22 Aug 2014 09:56:50 +0100
| Newsgroups | gmane.comp.gis.gmt.user |
|---|---|
| Message-ID | <[email protected]> |
--_d2abf0e3-f38e-44c6-8732-e72ef4cffe24_ Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Thanks for the clarification Walter > Date: Thu=2C 21 Aug 2014 16:59:19 -0400 > From: [email protected] > Subject: Re: [GMT-HELP] Spherical Bouguer correction > To: [email protected] >=20 > Lester=2C >=20 > The difference is a factor of 2=2C so obviously one of these has to be wr= ong. >=20 > If you derive both you find that you can be outside an entire sphere=2C a= nd so get the factor of 4=2C but you cannot be =93outside=94 an infinite sl= ab=2C you can only be on one side of it=2C hence the factor of 2. >=20 > However=2C in the course of the flat slab derivation you end up with some= thing involving an argument (to a logarithm?) like H/R=2C and taking the li= mit as R goes to infinity. Here=2C H is your slab thickness and R is the di= stance between a point in the slab and the point you are trying to correct. >=20 > Thus if your slab thickness=2C H=2C is short compared to the size of the = earth=2C then use the slab formula. The curvature of the Earth is negligibl= e if H is of order of the thickness of the crust=2C because H/R rapidly van= ishes before R gets big enough for you to sense the curvature. >=20 > Only if H is as thick as of the order of the radius of the earth do you n= eed the formula with the 4=2C but by that point the Bouguer correction is a= bsurd anyway and you should instead be calculating attractions directly. >=20 > In other words=2C the Bouguer correction only makes sense in the case tha= t H << R. >=20 > Walter >=20 >=20 >=20 > Walter H F Smith > Geophysicist=2C Laboratory for Satellite Altimetry > NOAA NCWCP code E/RA-31 > 5830 University Research Court=2C room 3752 > College Park MD 20740-3818 > 301-683-3377 (voice=2C my desk) > 301-683-3300 (voice=2C reception) > 301-683-3301 (fax=2C reception) > [email protected] > http://www.star.nesdis.noaa.gov/star/Smith_WHF.php >=20 >=20 > On Aug 18=2C 2014=2C at 5:50 AM=2C Lester Anderson <lester_anderson1963@H= OTMAIL.COM> wrote: >=20 > > Hi all=2C > >=20 > > Quick question (off topic)=2C but should one strictly be using the simp= le spherical correction (4piG(rho)H) as opposed to the "infinite" slab (2pi= G(rho)H) for the Bouguer calculation? > >=20 > > Trying to think at what point this would become a significant considera= tion in terms of a geographic area? > >=20 > > Cheers > > Lester > > Mailing list for GMT discussions of all kinds. If you are not sure you = have found a bug=2C discuss it here first. To formally report bugs or reque= st features=2C please register and add New Issue on gmt.soest.hawaii.edu To= unsubscribe=2C send the message "signoff gmt-help" [email protected]= .edu Note: gmt-help will become obsolete on Sept 1=2C 2014 - please use for= um on gmt.soest.hawaii.edu instead. >=20 > Mailing list for GMT discussions of all kinds. If you are not sure you h= ave found a bug=2C discuss it here first. > To formally report bugs or request features=2C please register and add Ne= w Issue on gmt.soest.hawaii.edu > To unsubscribe=2C send the message "signoff gmt-help" to [email protected]= awaii.edu > Note: gmt-help will become obsolete on Sept 1=2C 2014 - please use forum = on gmt.soest.hawaii.edu instead. = Mailing list for GMT discussions of all kinds. If you are not sure you have found a bug, discuss it here first. To formally report bugs or request features, please register and add New Issue on gmt.soest.hawaii.edu To unsubscribe, send the message "signoff gmt-help" to [email protected] Note: gmt-help will become obsolete on Sept 1, 2014 - please use forum on gmt.soest.hawaii.edu instead. --_d2abf0e3-f38e-44c6-8732-e72ef4cffe24_ Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable <html> <head> <style><!-- .hmmessage P { margin:0px=3B padding:0px } body.hmmessage { font-size: 12pt=3B font-family:Calibri } --></style></head> <body class=3D'hmmessage'><div dir=3D'ltr'>Thanks for the clarification Wal= ter<br><br><div>>=3B Date: Thu=2C 21 Aug 2014 16:59:19 -0400<br>>=3B Fr= om: [email protected]<br>>=3B Subject: Re: [GMT-HELP] Spherical Bo= uguer correction<br>>=3B To: [email protected]<br>>=3B <br>>= =3B Lester=2C<br>>=3B <br>>=3B The difference is a factor of 2=2C so ob= viously one of these has to be wrong.<br>>=3B <br>>=3B If you derive bo= th you find that you can be outside an entire sphere=2C and so get the fact= or of 4=2C but you cannot be =93outside=94 an infinite slab=2C you can only= be on one side of it=2C hence the factor of 2.<br>>=3B <br>>=3B Howeve= r=2C in the course of the flat slab derivation you end up with something in= volving an argument (to a logarithm?) like H/R=2C and taking the limit as R= goes to infinity. Here=2C H is your slab thickness and R is the distance b= etween a point in the slab and the point you are trying to correct.<br>>= =3B <br>>=3B Thus if your slab thickness=2C H=2C is short compared to the= size of the earth=2C then use the slab formula. The curvature of the Earth= is negligible if H is of order of the thickness of the crust=2C because H/= R rapidly vanishes before R gets big enough for you to sense the curvature.= <br>>=3B <br>>=3B Only if H is as thick as of the order of the radius o= f the earth do you need the formula with the 4=2C but by that point the Bou= guer correction is absurd anyway and you should instead be calculating attr= actions directly.<br>>=3B <br>>=3B In other words=2C the Bouguer correc= tion only makes sense in the case that H <=3B<=3B R.<br>>=3B <br>>= =3B Walter<br>>=3B <br>>=3B <br>>=3B <br>>=3B Walter H F Smith<br>&= gt=3B Geophysicist=2C Laboratory for Satellite Altimetry<br>>=3B NOAA NCW= CP code E/RA-31<br>>=3B 5830 University Research Court=2C room 3752<br>&g= t=3B College Park MD 20740-3818<br>>=3B 301-683-3377 (voice=2C my desk)<b= r>>=3B 301-683-3300 (voice=2C reception)<br>>=3B 301-683-3301 (fax=2C r= eception)<br>>=3B [email protected]<br>>=3B http://www.star.nesd= is.noaa.gov/star/Smith_WHF.php<br>>=3B <br>>=3B <br>>=3B On Aug 18=2C= 2014=2C at 5:50 AM=2C Lester Anderson &[email protected]= M>=3B wrote:<br>>=3B <br>>=3B >=3B Hi all=2C<br>>=3B >=3B <br>&= gt=3B >=3B Quick question (off topic)=2C but should one strictly be using= the simple spherical correction (4piG(rho)H) as opposed to the "infinite" = slab (2piG(rho)H) for the Bouguer calculation?<br>>=3B >=3B <br>>=3B = >=3B Trying to think at what point this would become a significant consid= eration in terms of a geographic area?<br>>=3B >=3B <br>>=3B >=3B C= heers<br>>=3B >=3B Lester<br>>=3B >=3B Mailing list for GMT discuss= ions of all kinds. If you are not sure you have found a bug=2C discuss it h= ere first. To formally report bugs or request features=2C please register a= nd add New Issue on gmt.soest.hawaii.edu To unsubscribe=2C send the message= "signoff gmt-help" [email protected] Note: gmt-help will become = obsolete on Sept 1=2C 2014 - please use forum on gmt.soest.hawaii.edu inste= ad.<br>>=3B <br>>=3B Mailing list for GMT discussions of all kinds. If= you are not sure you have found a bug=2C discuss it here first.<br>>=3B = To formally report bugs or request features=2C please register and add New = Issue on gmt.soest.hawaii.edu<br>>=3B To unsubscribe=2C send the message = "signoff gmt-help" to [email protected]<br>>=3B Note: gmt-help wi= ll become obsolete on Sept 1=2C 2014 - please use forum on gmt.soest.hawaii= .edu instead.<br></div> </div></body> </html>= Mailing list for GMT discussions of all kinds. If you are not sure you have found a bug, discuss it here first. To formally report bugs or request features, please register and add New Issue on gmt.soest.hawaii.edu To unsubscribe, send the message "signoff gmt-help" to <a href=3D"mailto:[email protected]">[email protected]</a> Note: gmt-help will become obsolete on Sept 1, 2014 - please use forum on gmt.soest.hawaii.edu instead. --_d2abf0e3-f38e-44c6-8732-e72ef4cffe24_--