How to Calculate and Solve for Gravity Anomaly for an Infinitely Long Cylinder | Gravity

The image above represents gravity anomaly for an infinitely long cylinder.

To compute for gravity anomaly for an infinitely long cylinder, five essential parameters are needed and these parameters are Gravitational Constant (G), Anomalous Density (Δρ), Radius of Cylinder (b), Depth Buried (d) and Horizontal Distance (x).

The formula for calculating gravity anomaly for an infinitely long cylinder:

δgx = GΔρ2πb²d / x² + d²

Where:

δgx = Gravity Anomaly for an Infinitely Long Cylinder
G = Gravitational Constant
Δρ = Anomalous Density
b = Radius of Cylinder
d = Depth Buried
x = Horizontal Distance

Let’s solve an example;
Find the gravity anomaly for an infinitely long cylinder when the gravitational constant is 6.67E-11, the anomalous density is 9, the radius of cylinder is 11, the depth buried is 8 and the horizontal distance is 10.

This implies that;

G = Gravitational Constant = 6.67E-11
Δρ = Anomalous Density = 9
b = Radius of Cylinder = 11
d = Depth Buried = 8
x = Horizontal Distance = 10

δgx = GΔρ2πb²d / x² + d²
δgx = 6.67e-11(9)2π(11)²(8) / (10)² + (8)²
δgx = 6.67e-11(9)2π(121)(8) / (100) + (64)
δgx = 6.67e-11(9)(6082.123) / 164
δgx = 0.000003651098 / 164
δgx = 2.226e-8

Therefore, the gravity anomaly for an infinitely long cylinder is 2.226e-8 mGal.

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