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Unformatted text preview: 244 Chapter 8 Gravity and lsostasy GRAVITY MODELING Forward modelling of mass distributions is a powerful tool to visualize free air and
Bouguer gravity anomalies that result from different geologic situations. For large
tectonic features, gravity modeling can be even more insightful if considerations of
the isostatic state of the region are incorporated. A common method used to model gravity data is the twodimensional
approach developed by Talwani et a1. (1959). The gravity anomaly resulting from a
model is computed as the sum of the contributions of individual bodies, each with a
given density (p) and volume (V) (that is, a mass, In, proportional to p X V). The
twodimensional bodies are approximated, in cross section, as polygons (Fig. 8.25). Gravity Anomalies from Bodies with Simple Geometries Calculated Gravity Effects Model To appreciate contributions from complexshaped polygons, it is helpful to under
stand, first, the gravity expression of two simple geometric shapes: 1) a sphere and
2) a semiin ﬁnite slab .1 Sphere The attraction of a sphere buried below Earth’s surface can be
viewed in much the same way as the attraction of the entire Earth from some dis tance in space (Figs. 8.3; 8.26). The equation for both cases follows an inverse square
law of the form: FIGURE 8.25 Twodimensional gravity
modeling of subsurface mass distributions.
Bodies of anomalous mass are polygonal
in cross section, maintaining their shapes
to infinity in directions in and out of the
page. a) Relative to surrounding material,
a body with excess mass results in a
positive contribution to the gravity
anomaly profile (Ag). b) A negative
contribution results from a body with a
deficiency of mass. c) The gravity anomaly
for the simple model is the sum of the
contributions shown in (a) and (b). + a) Contribution from Mass Excess
IR + b) Contribution from Mass Deﬁcit + c) Total from Sam Contributions Mass Deﬂclt (A m) Gravity Modeling 245 b FIGURE 8.26 Analogy between the ' gravitational attraction of the Earth from
Earth's surface space and a sphere of anomalous mass
buried beneath Earth’s surface. a) Earth’s
gravitational acceleration (g) at a distant
observation point depends on the mass of
the Earth (M) and the distance (R) from
the center of mass to the observation
point. b) The change in gravity (Ag) due
to a buried sphere depends on the
difference in mass (Am, relative to the
surrounding material), and the distance
(r) from the sphere to an observation
point on Earth’s surface. FIGURE 8.27 Gravitational effect (Kg)
of a buried sphere of radius (R) and
anomalous mass (Am). a) The distance (r)
to the center of the sphere can be broken
into horizontal (x) and vertical (2)
components. b) The magnitude (Ag) of
the gravitational attraction vector can be
broken into horizontal (Agx) and vertical
(Agz) components. For a perfect sphere
with uniform Am, the angle 9 is the same
as in (a). A buried sphere may have excess or deficient mass (Am) relative to the sur
rounding material; its center lies a distance (r) from the observation point (Fig. 8.27a).
The change in gravitational attraction (Ag) due to the sphere is: : G(Am) A
g r2 The density (p) of the material is defined as mass (m) per unit volume (V):
I p = m/ V
so that:
m = pV The excess (or deficient) mass of the sphere, in terms of the density difference (Ap)
between the sphere and the surrounding material, is therefore: Am = (Ap)V
the change in gravity is thus:
G(Ap)(V)
Ag = T The volume (V) of a sphere of radius R is:
V = 4/3 «R3 246 Chapter 8 Gravity and Isostasy so that: G( Ag = 3") (4/3 17113) 1‘ : 411R3G(Ap) 1 Since I2 = x2 + 22: Ag is the magnitude of the total attraction, at the observation point, due to Am (Fig. 8.27a). The total attraction is a vector sum of horizontal and vertical compo
nents (Fig. 8.27b): —> A72 = 58x + Agz
where: —g> = vector expressing magnitude (Ag) and direction of total attraction
due to the anomalous mass of the sphere A_g>x = horizontal component of A:} —> , ——> AgZ = vertical component of Ag Agx = Ag(sin6) = horizontal component of Ag
Agz = Ag( case) = vertical component of Ag 0 = angle between a vertical line and the Ag direction. The magnitude can be expressed as the vector sum of horizontal and vertical COIIIpOI’lCIltSI
A8 = \/(Agx)2 + (A8)2 A gravimeter measures only the vertical component of the gravitational attraction (Fig. 8.27b):
Agz = Ag (case) case = z/r From Fig. 8.27a: so that: 41TR3G(Ap) 1 z
A = A Z ——‘ —
g2 g(Z/T) 3 (X2 + 22) r
Again, using: r2 = x2 + 22, meaning r = (x2 + 22)”2 _ 41TR3G(Ap) 1 z
Z 3 (x2 + 22) (x2 + 22)“2 Substituting the value for 47/ 3: Ag 2
AP) (X2 + Z2)3/2 Agz = 4.1888 R3G( Gravity Modeling 247 Using G = 6.67 X 10‘11 Nmz/kgz: Z Agz = 0.02794 (Ap) R3 W where the variables and units are: AgZ = vertical component of gravitational attraction measured by a gravime
ter (mGal)
Ap = difference in density between the sphere and the surrounding material
(g/Cm3)
R = radius of the sphere (m)
x = horizontal distance from the observation point to a point directly
above the center of the sphere (m) z = vertical distance from the surface to the center of the sphere (In). Fig. 8.28a shows the variables in the above equation. The buried sphere model
illustrates some fundamental properties of gravity anomalies (Fig. 8.28b): 1) mass SmaIIAp orH Large Ap orF! + $0 2 4p FIGURE 8.28 a) Gravity anomaly profile (Agz) attributable to a buried sphere of radius (R1 in m), depth (2), and
anomalous density (Apl in g/cm3).The horizontal distance (x) is measured in negative (—x) and positive (+x) directions
from a point on the surface directly above the sphere. b) Form of gravity anomaly profiles due to (1) positive vs. negative
density contrasts; (2) changing mass anomaly; and (3,4) changing depth. 248 Chapter 8 Gravity and Isostasy excess (+Am, implying +Ap) causes an increase in gravity (+Agz), while mass
deficit (—Arn, implying —Ap) results in a gravity decrease (Ag); 2) the more mas—
sive the sphere (larger Ap and/or larger R), the greater the amplitude (mg) of the
gravity anomaly; 3) the anomaly is attenuated (smaller lAgzl) as the sphere is buried
more deeply within the Earth; 4) the width of the gravity anomaly increases as the
sphere is buried more deeply. SemiInﬁnite Slab Where there are density changes that can be approxi—
mated by horizontal layering, it is convenient to model lateral changes in gravity as
the effects of abrupt truncations of infinite slabs. An infinite slab (Fig. 8.2%) that
has excess mass (+Am) will increase the gravity (+AgZ), while mass deﬁcit (—Am)
will cause the gravity to decline (~Agz). Truncating the slab (Fig. 82%) results in:
1) essentially no gravity effect in regions far from the slab; 2) an increase (or
decrease) in gravity crossing the edge of the slab; and 3) the full (positive or nega
tive) gravity effect in regions over the slab but far from the edge. An infinite slab represents a mass anomaly (Am) that is a function of the thick
ness of the slab (Ah) and its density (Ap) relative to surrounding materials
(Fig. 8.29c). The amount the slab adds or subtracts to gravitational attraction (Agz) is
exactly the same as that of the infinite slab used in the Bouguer correction (Fig. 8.9): Agz = 0.0419(Ap)(Ah) The gravity effect of a semiinfinite slab, however, changes according to position rel
ative to the slab’s edge (Fig. 8.29d): 1) far away from the slab, the contribution (Agz) a Inﬁnite Slab 'Am . 0.0419(4 pAh) mGal over slab
29m away from slab W
w ‘— FIGURE 8.29 a) An inﬁnite slab adds or subtracts a constant amount to the gravity field, depending on
whether the slab represents a positive (+Arn) or negative (—Am) mass anomaly. b) The gravity effect of a
semi—inﬁnite slab changes gradually as the edge of the slab is crossed. c) An infinite slab produces exactly the
same gravity effect as the slab used for the Bouguer correction. d) The gravity effect of a semiinfinite slab is equal to the Bouguer slab approximation far out over the slab (right), V2 of that value directly over the slab’s
edge, and zero far away from the edge (left). Gravity Modeling 249 is zero; 2) above the edge of the slab, the contribution is exactly 1/2 the maximum
value (AgZ = %[0.0419ApAh]); 3) over the slab, but far from the slab’s edge, AgZ is the
same as for an infinite slab (AgZ = 0.0419ApAh); 4) the rate of change in gravity (the
gradient of Agz) depends on the depth of the slab. Griffiths and King (1981) develop an equation for the anomaly caused by a
semiinfinite slab (Fig. 8.30a,b): Agz = G(Ap)(Ah)(2¢)
where: (I) = angle (in radians) from the observation point, between the horizontal
surface and a line drawn to the central plane at the slab’s edge
G = Universal Gravitational Constant (6.67 X 10—11 Nmz/kgz). The angle 4) can be expressed as: d) = 77/2 + tan—1(x/z) FIGURE 8.30 a) For a semiinfinite slab, the gravity anomaly measured at the surface is AgZ = G(Ap)(Ah)(2¢), where d) is
measured in radians. b) Away from the slab, d) < 11/2 (that is, ¢ < 90"). Over the slab, 4; > 'rr/2. c) Method to estimate the
change in gravity anomaly (Agz) at five horizontal distances (x, in km) from the edge of a semi—infinite slab. ’ l 250 Chapter8 Gravityandlsostasy Where: i , x = horizontal distance from a point on the surface above the slab’s edge
‘ l g z = depth of a horizontal surface bisecting the slab (central plane).
{ 2 T I» i 1 The equation is thus: , Agz=2G<Ap)(Ah)<w/2+ tan‘llx/zl) l ,
Q or: ' j Agz = 13.34 (Ap) (Ah) (Tr/2 + tan—1[x/z]) l ‘ when the units are: AgZ in mGal; Ap in g/cm3; Ah, x, z in km. Note five important
' ‘ points from the above equation, illustrated in Fig. 8.30c: 1. x = —00 => AgZ = zero => AgZ = 0(41.9ApAh).
x = —2 => AgZ = M its full value => AgZ = %(41.9ApAh).
x = 0 :> AgZ = V: its full value => Agz = V2(41.9ApAh).
 +2 => AgZ = % its full value => AgZ = 3A(41.9ApAh).
x = +00 => AgZ = its full value => AgZ = 1(41.9ApAh). 9‘99)!”
1 For layered cases, a quick estimate of the gravity change across the edge of an
anomalous mass can be made by calculating and plotting those five points. The semiinfinite slab approximation illustrates two fundamental properties
of gravity anomalies (Fig. 8.31). “I ‘ 1. The amplitude (full value) of the anomaly reﬂects the mass excess or deﬁcit
, v ‘ (Am). The mass excess or deficit depends on the product of density contrast (Ap) and thickness (Ah) of the anomalous body. 2. The gradient (rate of change) of the anomaly reﬂects the depth of the excess or
deﬁcient mass below the surface (2). The depth thus determines how abruptly ‘ . 1' the gravity anomaly changes from near zero to near its full value, according to
' " ‘ ‘ the term (1T/2 + tan _1[x/z]). A body near the surface results in a gravity FIGURE 8.31 Lateral change in gravity
, due to a semiinfinite slab of density " contrast (Ap) and thickness (Ah).The
amount of change (amplitude) depends
on the mass anomaly (Ap X Ah), while
the rate of change (gradient) depends on
the depth (2) to the central plane of the
slab. The greater the mass anomaly, the
greater the amplitude; the more deeply
buried the slab, the more gentle the
gradient. I; (Gentle Gradlan9\ ' Central Plane   Gravity Modeling 251 change with a steep gradient, while the same body deep within the Earth
would produce a more gentle gradient. Models Using SemiInfinite Slab Approximations ll Semiinfinite slab models can be used to approximate contributions to the freeair
gravity anomaly at regions in isostatic equilibrium. Two insightful examples are the
transition from continental to oceanic crust along a passive continental margin and
the thickening of crust at a mountain range. Passive Continental Margin Thin oceanic crust at passive margins is under—
lain by mantle at the same depth as the mid—tolower crust of the adjacent conti—
nent. The mass excess (+Am) of the mantle exerts a force that pulls the oceanic
crust downward. By the Airy model, the resulting ocean basin subsides until it has
exactly enough water (—Am) so that the region is in isostatic equilibrium. The model in Fig. 8.32 is in Airy isostatic equilibrium, according to parameters
modified from Fig. 8.20: Densities: pw = density of the water = 1.03 g/cm3
pc = density of the crust = 2.67 g/cm3
pIn = density of the mantle = 3.1 g/cm3. Thicknesses for the ocean side: hW = thickness of the water column = 5 km
(he)O = thickness of the oceanic crust = 8 km hm = thickness of the extra mantle column = ? Thickness for the continent side:
(hr)c = thickness of the continental crust = ? The two unknowns [(hm) and (hc)c] can be determined from equations expressing
the two conditions for local isostatic equilibrium: I Continent Ocean
Equal Pressure: pc(hc)c = pw(hw) + pc(hc)0 + pm(hm)
Equal Thickness: (he)C = hW + (he)0 + h,In
' FIGURE 8.32 Airy isostatic model ofthe Ign] transition from thick continental to thin
[ma )0 ' I G o oceanic crust at a passive continental Water (A,  1.03: hw 5 km) margin. Densities of crust and mantle are
simplified so that reasonable contrasts
result for the water vs. upper continental
crust (—1.64 g/cm3) and the mantle vs.
lower continental crust (+ 0.43 g/cm3).
See text for definition of Variables. l (l‘
l l“. 'V milliler i, 1" , ,
1 ;*l‘1.‘ .' ll . ill limit ‘ , Distance from Continent / Ocean Boundary (km) 1
l
r. 1 ill 1 l ill 1 ll .44.“! < . ‘k 252 Chapter 8 Gravity and lsostasy a Water Contribution é 6 Emmy Conﬂibuﬂon (mGaD é Gravity/inomay (mGai)
a Continent Ocean
Water 01, 1.03; A p  1.64 g/cm“ ‘ 450 0 150
, Distance from Cont/nent/ Oman Boundary (km)
‘ l ‘ FIGURE 8.33 The main gravity contributions at a passive continental margin have equal amplitude but different gradient. a)
The water effect is shallow, causing an abrupt change (steep gradient). b) The extra mantle beneath the oceanic crust is a
deeper effect, giving a less abrupt change in gravity (gentle gradient). c) The free air gravity anomaly at a passive continental r ‘ margin is a positive/negative “edge effect,” due to the summing of contributions that have equal amplitudes but different
" gradients. «3i , Solving the two equations for the two unknowns yields:
% . ” ‘ i i i (hc)c = 31.84 km and hm = 18.84 km The water deepening seaward represents a mass deficit (—Am), a function of
the product of the water depth (hw) times the density difference at upper crustal levels
(Ap = pw — p0 = —1.64 g/cm3). Fig. 8.33:1 shows that this negative contribution to Gravity Modeling 253 the gravity anomaly is an abrupt change, along a steep gradient where the water
deepens. The mass excess (+Am) that compensates the shallow water relates to the
amount of shallowing of the mantle (hm) times the difference between mantle and
crustal densities (Ap = pm — pC = +0.43 g/cm3; Fig. 8.33b). At great distance from
the continental margin, the positive contribution to gravity (due to the mantle shal
lowing) has the same amplitude as the negative contribution (due to the water deep
ening), because the two effects represent compensatory mass excess and deficit,
respectively. The gradient for the mantle contribution is more gentle, however,
.because the anomalous mass causing it is deeper. The free air gravity anomaly (Agfa) for the simple, passive margin model is the
sum of the contributions from the shallow (water) and deep (mantle) effects
(Fig. 8.33c). Note that the anomaly is near zero over the interiors of the continent and
ocean, but showsa maximum over the continental edge and a minimum over the edge
of the ocean. This positive/negative couple, known as an edge eﬁect, results because
the contributions due to the shallow and deep sources have different gradients. The passive margin model shows two important attributes of the free air grav—
ity anomaly for a region in isostatic equilibrium (Fig. 8.34a): 1) values are near zero
(except for edge effects), because the mass excess (+Am) equals the mass deficit
(—Am); 2) at edge effects, the area under the curve of the gravity anomaly equals
zero, because the integral of the anomaly, with respect to x, is equal to zero. The second point is worth further discussion, because it provides a quick test
for local isostatic equilibrium. The free air anomaly curve for the passive margin
model is the sum of two contributions (Fig. 8.33): Agz = Agz(bath) + Agz(moho)
= zGrAptmhibw/z + ran1 [x/zbi)
+ 2G<Ap)m(Ah)m(1T/2 + tan‘1[x/zm])
where: AgZ = free air anomaly
Agz(bath) = contribution to the free air anomaly due to the mass defi
ciency of the water deepening seaward (bathymetry)
Agz(moho) = contribution to the free air anomaly due to the mass excess
of the mantle shallowing seaward
(Ap)b = density contrast of the water compared to upper continental
crust
(Ap)m = density contrast of the shallow mantle compared to lower
continental crust
(Ah)b = thickness of semiinfinite slab of water
(Ah)m = thickness of semiinfinite slab of elevated mantle
x = horizontal distance from the continent/ocean boundary
2b = vertical distance from sea level to the central plane of the
semi—infinite slab of water
zm = vertical distance from sea level to the central plane of the
semi—infinite slab of elevated mantle. The equation can be simplified: Agz : 2G {(Ap)b(Ah)b(“T/2 + tan_1[X/Zb]) }
+ (Ap)m(Ah)m(1T/2 + tan“1 [x/sz Wm rm». was; 254 Chapter 8 Gravity and Isostasy Free A], Anomaly Free Air Anomaly Values Near Zero,
with Area Under Curve  0 (Positive Area  Ne ative Area
because im m  AA mp 150 0 150 a
it,
s
g
S
('5
Continent Ocean
2 an Bouguer Corrected Water (p  . A p = 0 0
Distance from Continent / Ocean Boundary (Km) FIGURE 8.34 Free air and Bouguer gravity anomalies for passive continental margin in local isostatic equilibrium.
3) Isostatic equilibrium means the absolute value of excess mass (+Aml) equals the absolute value of deficient mass
(FAml). With this equality, the integral of the change in gravity with respect to x (ng2 dx) = 0. The zero integral
means that the positive and negative areas under the free air anomaly curve sum to zero. b) The Bouguer correction
at sea (Fig. 8.9b), applied to the free air anomaly in (21), yields the general form of the Bouguer anomaly at a passive continental margin.
Let:
A = horizontal surface area of a slab (same for each slab).
The density of a slab is:
p = m/ V
where: m 2 mass of a slab
V = volume of a slab = A(Ah). x
l
l Gravity Modeling 255 therefore:
In = pV = pA(Ah)
For each slab:
Am = (Ap)A(Ah)
(Ap)(Ah) = Am/A
so that:
AgZ = 2G {([Amh/AXn/Z + tan_1[x/zb]) } + ([Am]m/A)(Tr/2 + tan.—1 [x/sz
'where: [Am]b = mass deficit of the water slab
[Am]m = mass excess of the mantle slab. Airy isostatic equilibrium implies that:
[Amlb = —[Amlm
so that:
Agz = 2G([Amlb/A) {(17/2 + tan ‘1 [X/sz  (W2 + tan—1 [X/Zml)}
Agz = 2G<tAm]b/A>(mn1[x/zu — ran'l [x/sz The area under the free air anomaly curve is the integral of Agz, with respect to X:
+00 L AgZ dx = 2G([Am]b/A)J (tan’1 [X/Zb] * tan‘1[x/zm]) dx —co Standard integral tables show that, regardless of the depths of the slabs (2b and zm),
the integral from —00 to +00 is zero: J, (tan‘1[x/zb]  tan‘1[x/zm]) dx = 0 therefore: The last expression demonstrates that the area under the curve for the free air
anomaly equals zero (Fig. 8.34a). This relationship is seen in each of the models
below that are in a state of local isostatic equilibrium. Fig. 8.35 shows an observed free air gravity anomaly profile, and a density
model, for the passive continental margin on the east coast of the United States.
The free air anomaly shows clearly the edge effect due to the water deepening as
the mantle shallows (Fig. 8.33). Some isostatic imbalance is also evident, because the
negative area (under the curve) is greater than the positive area. The Bouguer gravity anomaly (AgB) for the simple, passive margin model
results from correcting the mass deficit of the water to approximate that of the
upper part of the crust (Fig. 8.34b). The passive margin model thus illustrates the
general form of the Bouguer anomaly for a region in local isostatic equilibrium:
1) values are near zero over normal continental crust; 2) the Bouguer anomaly mimics 256 Chapter 8 Gravity and lsostasy . — Observed
‘  Calculated West I East 150 0 km 150 ‘ ' FIGURE 8.35 Observed free air gravity anomaly from the passive continental margin off the Atlantic
3, : coast of the United States. The dashed line is the anomaly calculated from the twodimensional density model. Note the edge effect, with the high toward the continent, the low over the ocean. The
zero crossing is near the edge of the continental shelf, where the water column deepens abruptly. Line IPOD off Cape Hatteras, North Carolina. From “Deep structure and evolution of the Carolina
Trough,” by D. Hutchinson, I. Grow, K. Klitgord, and B. Swift,AAPG Memoir, no. 34, pp. 129—152, © 1983. Redrawn with permission of the American Association of Petroleum Geologists, Tulsa,
Oklahoma, USA. the Moho, increasing to large positive values as the mantle shallows beneath the
ocean; 3) the form of the Bouguer anomaly is somewhat a mirror image of the topography (or bathymetry); the increase in the anomaly thus correlates with deep
ening of the water. Mountain Range As continental crust thickens during orogenesis (Figs. 2.18, 7' 6.35), the crustal root exerts upward force, due to its buoyancy relative to sur
5; I, W. " rounding mantle. By the Airy model, the topography (+Am) grows until its weight
5; i exactly balances the effect of the lowdensity root (—Am). The mountain range model (Fig. 8.36) is in Airy isostatic equilibrium, according to parameters modified
M . _. from Fig. 8.20: i; , Densities: pa 2 density of the air = 0
pc = density of the crust = 2.67 g/cm3 Gravity Modeling 257 Normal FIGURE 8.36 Airy isostatic model 0f2
, ' km high mountain range. Densities of
COI'It Mountains crust and mantle are simplified so that
(he )0  35 km (he )M' 4942 km /T0P0 " 2 km reasonable contrasts result for the topography vs. air (+2.67 g/cm3) and the
crustal root vs. mantle (—0.43 g/cm3). 0km 400 pIll = density of the mantle = 3.1 g/cm3. Thicknesses at the Normal Continental Crust: h3 = thickness of the air column = 2 km
(he)C = thickness of crust outside mountains = 35 km
hIll = thickness of the extra mantle column = ? Thickness at the Mountains: (he)M = thickness of total crust at mountains = ? As with the passive margin model, the two unknowns can be determined from
the two conditions for local isostatic equilibrium: Normal Continent Mountains
Equal Pressure: pa(ha) + pc(hc)C + pm(hm) = pc(hc)M
Equal Thickness: ha + (he)C + hm = (he)M Solving the two equations for the two unknowns yields: hm = 12.42 km and (hJM = 49.42 km (Moho depth = 47.42 km) The contribution to the freeair anomaly due to topography of the mountains
(Fig. 8.37'a) results from the mass excess of the material above sea level (+Am). This
excess is a function of the product of the mountain height (equal to ha) times the
density difference at upper crustal levels (Ap = pC — pa = +2.67 g/cm3). Note that,
as with the water effect for the passive margin, the contribution is abrupt, resulting
in a steep gradient. The crustal root provides a mass deﬁcit (—Am) that compensates the extra
weight of the topography (Fig. 8.37b). The deficit relates to the product of the
amount of deepening of the crust (equal to hm) times the difference between
crustal and mantle densities (Ap = pc — pm = —0.43 g/cm3). If the mountain range
is wide (several hundred km), the negative contribution due to the crustal root has
the same amplitude as the positive contribution due to topography.The gradient for
the crustal root contribution is more gentle, however, because that anomalous mass
is deeper. 258 Chapter 8 Gravity and lsostasy Hoot Conmbutlon
/Gonde Gradient Crustal Boat
(in  26” rIlIlllIln Topo  0
Dlstanoe from Center of Mountains (Km) FIGURE 8.37 Contributions to gravity for mountain range in Airy isostatic equilibrium (Fig. 8.36). a) A sharp increase,
with nearly full amplitude, results from mass excess of topography. b) Mass deficit of crustal root gives a more gradual
decrease. c) The free air gravity anomaly profile for a mountain range in local isostatic equilibrium has edge effects due to
the differing gradients of the shallow (a) and deep (b) contributions. Unless the range is very broad, so that the deep effect
of the root approaches full amplitude, the free air anomaly has significant positive values over the range. As in the passive margin model, the free air gravity anomaly (Agfa) for the
mountain range is the sum of the contributions from the shallow and deep sources
(Fig. 8.370).~ The anomaly is zero over the normal thickness continent and
approaches zero over the central part of the mountains. It shows edge effects, how
ever, along the ﬂanks of the range. The free air gravity anomaly for a mountain range often illustrates some of the
fundamental properties of a region in local isostatic equilibrium (Fig. 8.38a): 1) val—
ues are near zero because the mass excess (+Am) of the topography equals the
mass deficit (—Am) of the crustal root; 2) significant edge effects occur because
shallow and deep contributions have different gradients; 3) the area under the curve
of the anomaly sums to zero. Fig. 8.39 shows observed and modeled free gravity anomalies across western
South America. Note that the observed free air gravity anomaly profile shows classic
edge effects, suggesting that the region is close to local isostatic equilibrium (Fig. 8.383).
The model shows that the crust is very thick (z 60 km), beneath the high topography
of the Andes Mountains. Thinner crust ﬂanks the mountains, as normal thickness Positive Area Gravity Modeling 259 FIGURE 8.38 Free air and Bouguer Free Air Anomaly local isostatic equilibrium. at)
Compensatory positive (+Am) and WWII/II/I/I/l/I/ﬂ/IWM/A free air gravity anomaly is zero under the curve” sums to zero. b) The level (Fig. 8.37a). Bouguer anomaly
profiles of mountain ranges thus Crustal Root
(p  267) contribution of the crustal root (Fig. Bouguer gravity anomalies form the
“Batman anomaly” characteristic of a
mountain range in local isostatic
equilibrium. X (Km) ("Batman ” Anomaly)
Free Aernomaly\5.,l. 'II III
'IllllIIIlIIIIIIIIIIIIIHIIIIII'” Bouguer Corrected =
Topography (p 0) AP 0 Crustal Root
(9 " 257) a _ .
Distance from Center of Mountains (Km) continental craton to the east and oceanic crust to the west. The broad region is thus a
mountain range close to a state of Airy isostasy (Fig. 8.36). Deviations from local
isostasy (discussed below) occur at the subduction zone on the west side, where the
edge effect low is exaggerated at the trench and a ﬂexural bulge high occurs over the
adjacent oceanic crust. The Bouguer gravity anomaly (AgB) for the mountain range results from sub—
tracting the effect of the mass excess of the topography from the free air anomaly
(Fig. 8.9a). Attributes of the Bouguer gravity anomaly that result from isostatic
equilibrium are illustrated in Fig. 8.38b: 1) values are near zero over continental
crust of normal thickness; 2) the form of the Bouguer anomaly mimics the root con
tribution; the anomaly decreases as the Moho deepens beneath the mountains;
3) the form of the Bouguer anomaly is almost a mirror image of the topography; the
anomaly decreases where the topography of the mountains rises. gravin anomalies for mountain range in negative (—Am) mass anomalies mean
that the integral, with respect to x, of the
(ng2 dx = 0). In other words, the “area
Bouguer correction (BC) removes most
of the contribution of the mass above sea commonly show low values reﬂecting the 8.37b).Taken together, the free air and ...
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This note was uploaded on 07/23/2008 for the course GEOSC 203 taught by Professor Anandakrishnan during the Fall '07 term at Pennsylvania State University, University Park.
 Fall '07
 ANANDAKRISHNAN

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