Page 264 - Whole Earth Geophysics An Introductory Textbook For Geologists And Geophysicists

mode]
mass
247
material
gravime-
1)
directly
(m).
z)
sphere
Shallow (Small
Modeling
8.28b):
a
surrounding
a
sphere
by
buried
point
measured
(Fig.
Gravity
the

a
equation. The
anomalies
to
of
the
+
0

point
center
attraction
Paap
and
LargeAporR
~
+x (m),,
<X{m)_™
Zz
:
observation
sphere
the
gravity
to
above
wx
of gravitational
(m)
surface
the
(Ap)
of
_
S
sphere
1
between
the
SmallAporR
the
properties
0.02794
the
in
from
(m)
the
variables
from
are:
Nm?/kg”:
density
sphere
of
component
distance
=
fundamental
units
center
distance
Surtace
Ag,
0
2
the
in
the
and
107")
(121Gal)
horizontal
difference
the
shows
of
(g/em’)
vertical
variables
vertical
—tA P
radius
above
x
some
6.67
+
ter
8.28a
S
=
=
Il
Ul
=
(opm) 737
the
illustrates
Ap
z
x
Fig.
R
Ag,
G
a
where
Using
b
(z), and m), depth in to a buried sphere of radius (R, attributable (Ag,) Gravity anomaly profile a) 8.28 FIGURE (+x) directions positive and (x) is measured in negative (—x) distance horizontal in g/cm’). The (Ap anomalous density of gravity anomaly profiles due to (1) positive vs. negative the sphere. b)
Am
to compo- vertical attraction
due attraction and
point, vertical and of total gravitational
observation horizontal direction direction. horizontal of the to? 22)!” 22)! Zr

7R3) 1 r 1 2’) + (x? the at of and sphere of Ag of Ag Ag the sum (Ag,)? of + (x? = z + (x? 2”) Z ng (x?
(4/3 sum => Ag, + (Ag) the of component and vector + component (cos) z/r = SRG) r 1 +
G(Ap) 3 47R°G(Ap) 3 4nR°G(Ap) 3 attraction, vector > Ag, = magnitude mass —> Ag of =—> Ag component line the V(dg,)? Ag = = cos@ meaning (x? R°G(Ap)
= total a is — 2 of vertical as = vertica] Ag, 27, 4aR3G(Ap) 3 4.1888
isostesy Ag Ag = the attraction anomalous component component horizontal vertical a expressed Ag the Se(e/1) + x? 47/3: =
and of expressing the = = between be only = Se, = r = Ag, for Ag,
Gravity magnitude total vector to due is horizontal x vertical Ag(sin®) Ag(cos®) angle can measures value
the The (Fig. 8.27b): ut 8.27a: the
8 is 8.27a). —> Ag Ke, Re, Ag « = Ag, 8 magnitude gravimeter 8.27b): Fig. using:
Chapter that: so Ag (Fig. nents where: The com ponents: A (Fig. From that: so Again, Substituting
246