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Gravity Anomaly Due to Buried Sphere
- The gravity anomaly due to a buried sphere is straightforward
- We’ll start by assuming the sphere is a point source
x = 0
x
θ
2 z
m g (^) vert G
δ = δ^2 cos^ θ
r
m g (^) vert G
Directly over the sphere (r = z) all of
the additional acceleration is vertical
and given by the relationship derived
earlier.
At some location, x, away from the sphere,
only part of the acceleration is vertical and
the vertical component is found by
trigonometry.
δ gnet = δ g vert
δ gnet
z = r z r δ g vert
δ g horiz
Gravity Anomaly Due to Buried Sphere
- Now lets put the equation into a more useful form…
It is not convenient to calculate θ, so
we can reformulate the equation in
terms that are more convenient.
r
z
cosθ = ( )
2 2 1 /^2 r = x + z
x
z r^ θ
Now plug these back into the previous
equation…
δ cos θ
2 r
m g (^) vert G
3 r
mz g (^) vert G
δ =
Subs in cos θ…
Subs in r = …
2 2 3 /^2 x z
mz g (^) vert G
δ =
But this is based on a mass change of a
point source. Sub in the mass change of
a sphere with radius = R and density
contrast Δρ
2 2 3 /^2
3
3
x z
G R z
g (^) sphere
∆ m =^ ( Vol^ )(^ ∆ρ)
Other Gravity Anomalies
- Spherical targets :: diapirs and/or plutons
- Cylindrical targets :: tunnels/caves
- Note that all anomalies lack a sharp edge
- Subsurface geometry is non-unique
Other Gravity Anomalies
- Sheets :: dikes, veins
- Anomaly shape
depends on
- Density contrast
- Depth
- Length of sheet
- Dip of the sheet
