Complete Gravity Exploration & Data Reduction

Part 1: Theoretical Foundations

Understanding the shape of the Earth and Equipotential Surfaces

The Geoid

The Geoid is the surface of constant gravitational potential. It coincides with Mean Sea Level (MSL) if the ocean were still.

                Warping:
                Mass Excess (Mountains): Pulls Geoid UP.
Mass Deficiency (Valleys): Pulls Geoid DOWN.

            

Visualizing the Warp

Excess mass creates a stronger pull, lifting the potential surface.

Interactive Lab: Latitude Effects

Gravity is not constant! Use the slider to travel from the Equator to the North Pole. Observe how Earth's Shape and Centrifugal Force change gravity.

Gravity Vector

Centrifugal Force

Lat ($\phi$): 0°

Theoretical Gravity ($g_\phi$)

9.78032

m/s²

Diff. from Equator

mGal

Part 2: Data Reduction

Correcting raw readings to isolate geological anomalies

Why Reduce Data?

A raw gravimeter reading ($g_{obs}$) includes effects from tides, elevation, and latitude. Data Reduction removes these to find the Bouguer Anomaly.

Temporal Corrections

Drift: Correction for instrument spring stretch over time.
Tides: Correction for Sun/Moon pull (up to 0.3 mGal).

The "Big Three" Spatial Corrections

1. Latitude Correction ($g_\phi$)

Subtracts theoretical gravity using the GRS67 Formula:

$$ g_\phi = 9.780318 \left( 1 + 0.0052789 \sin^2 \phi + 0.0000235 \sin^4 \phi \right) \text{ m/s}^2 $$

2. Free-Air Correction (FAC)

Corrects for elevation above sea level.

$\delta g_F = 0.3086 \times h$

3. Bouguer Correction (BC)

Subtracts the attraction of the rock slab between the station and sea level.

Formula: $\delta g_B = 0.0419 \times \rho \times h$

Quick Slab Calculator

Rock Density ($\rho$):

Slab Thickness (m):

Correction: 11.19 mGal

Terrain Correction (TC)

Hills pull up; Valleys fail to pull down. Both reduce the reading. Therefore, TC is always positive (+).

Isostasy

Large mountain ranges float on the mantle. Airy Hypothesis: Mountains have deep roots. Pratt Hypothesis: Mountains are less dense.

Part 3: The Analyst's Toolkit

Interactive Calculators for Survey Analysis

Bouguer Anomaly Calculator

$$ BA = g_{obs} - g_{\phi} + FAC - BC $$

Observed ($g_{obs}$ mGal):

Latitude ($\phi$):

Elevation (m):

Density ($\rho$):

Result: --

Depth Estimator (Half-Width Rule)

Estimate depth ($z$) of a buried anomaly based on the width of the curve at half its maximum amplitude ($x_{1/2}$).

Half-Width Distance ($x_{1/2}$ in meters):

Sphere ($z \approx 1.3 x_{1/2}$): --
Cylinder ($z \approx 1.0 x_{1/2}$): --

Reference Tables

Common Densities (Mg/m³)

Material	Density
Sediments	1.7 - 2.3
Sandstone	2.35 - 2.55
Granite	2.67 (Std)
Basalt	2.99 - 3.20
Mantle	3.30+

Units Glossary

Gal: 1 cm/s².
milliGal (mGal): $10^{-3}$ Gal. (Standard).
Gravity Unit (g.u.): 0.1 mGal.
$\mu$Gal: Micro-gravity surveys.