← Course Home Module Page Environmental Geophysics

Gravity Geometry & Depth Detective

Visualizing subsurface structures, their equations, and their gravity responses.

1. Reference: Geometries & Equations

Sphere

Salt Domes, Ore Pods, Cavities

z
Max Anomaly ($\Delta g_{max}$): $$ \frac{4}{3} \pi G \delta \rho \frac{r^3}{z^2} $$

Depth Rule:
$z \approx 1.305 \cdot x_{1/2}$

Horizontal Cylinder

Tunnels, Pipelines, Antiforms

Pipe z
Max Anomaly ($\Delta g_{max}$): $$ 2 \pi G \delta \rho \frac{r^2}{z} $$

Depth Rule:
$z \approx 1.0 \cdot x_{1/2}$

Vertical Cylinder

Volcanic Plugs, Kimberlite Pipes

Plug
Model requirement:
A finite vertical cylinder response depends on radius and the depths to both its top and base. Use a complete forward model when amplitude matters.

Teaching approximation:
$z_{top} \approx 1.732\,x_{1/2}$ for an idealized semi-infinite vertical cylinder.

Activity: Subsurface Depth Detective

Analyze the Gravity Graph (Top) to find the target. Visualize the Geology (Bottom) hidden below.