Re: Spherical Bouguer correction

Lester,

The difference is a factor of 2, so obviously one of these has to be =
wrong.

If you derive both you find that you can be outside an entire sphere, =
and so get the factor of 4, but you cannot be =93outside=94 an infinite =
slab, you can only be on one side of it, hence the factor of 2.

However, in the course of the flat slab derivation you end up with =
something involving an argument (to a logarithm?) like H/R, and taking =
the limit as R goes to infinity. Here, H is your slab thickness and R is =
the distance between a point in the slab and the point you are trying to =
correct.

Thus if your slab thickness, H, is short compared to the size of the =
earth, then use the slab formula. The curvature of the Earth is =
negligible if H is of order of the thickness of the crust, because H/R =
rapidly vanishes before R gets big enough for you to sense the =
curvature.

Only if H is as thick as of the order of the radius of the earth do you =
need the formula with the 4, but by that point the Bouguer correction is =
absurd anyway and you should instead be calculating attractions =
directly.

In other words, the Bouguer correction only makes sense in the case that =
H << R.

Walter



Walter H F Smith
Geophysicist, Laboratory for Satellite Altimetry
NOAA NCWCP code E/RA-31
5830 University Research Court, room 3752
College Park MD 20740-3818
301-683-3377 (voice, my desk)
301-683-3300 (voice, reception)
301-683-3301 (fax, reception)
[email protected]
http://www.star.nesdis.noaa.gov/star/Smith_WHF.php


On Aug 18, 2014, at 5:50 AM, Lester Anderson =
<[email protected]> wrote:

> Hi all,
>=20
> Quick question (off topic), 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?
>=20
> Trying to think at what point this would become a significant =
consideration in terms of a geographic area?
>=20
> Cheers
> Lester
> Mailing list for GMT discussions of all kinds. If you are not sure you =
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gmt.soest.hawaii.edu To unsubscribe, send the message "signoff gmt-help" =
[email protected] Note: gmt-help will become obsolete on Sept =
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Mailing list for GMT discussions of all kinds.  If you are not sure you have found a bug, discuss it here first.
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Note: gmt-help will become obsolete on Sept 1, 2014 - please use forum on gmt.soest.hawaii.edu instead.