Bouguer Correction Calculator
Our geology & geophysics calculator computes bouguer correction accurately. Enter measurements for results with formulas and error analysis.
Formula
Bouguer Correction = 0.04193 × ρ × h (mGal)
The Bouguer plate correction equals 2πGρh, which simplifies to approximately 0.04193 × ρ × h in milligals, where ρ is rock density in kg/m³ and h is elevation in meters. The free-air correction is 0.3086 × h mGal. The Bouguer anomaly combines these corrections with observed and theoretical gravity.
Worked Examples
Example 1: Mountain Station Survey
Problem: A gravity station at 1,500 m elevation with observed gravity 979,450 mGal and rock density 2,670 kg/m³.
Solution: Free-air correction = 0.3086 × 1,500 = 462.90 mGal\nBouguer correction = 0.04193 × 2,670 × 1,500 = 167.93 mGal\nCorrected gravity = 979,450 + 462.90 - 167.93 = 979,744.97 mGal
Result: Free-air: +462.90 mGal | Bouguer: -167.93 mGal
Example 2: Sedimentary Basin Survey
Problem: A station at 200 m elevation in a sedimentary area (density 2,400 kg/m³). Calculate the corrections.
Solution: Free-air correction = 0.3086 × 200 = 61.72 mGal\nBouguer correction = 0.04193 × 2,400 × 200 = 20.13 mGal\nNet correction = 61.72 - 20.13 = 41.59 mGal
Result: Free-air: +61.72 mGal | Bouguer: -20.13 mGal | Net: +41.59 mGal
Frequently Asked Questions
What is the Bouguer correction in gravity surveying?
The Bouguer correction (also called the Bouguer plate correction) accounts for the gravitational attraction of the rock mass between the observation point and the reference datum (usually sea level). Named after French mathematician Pierre Bouguer (1698-1758), this correction approximates the rock layer as an infinite horizontal slab (Bouguer plate) of uniform thickness and density. The formula is deltaG_B = 2 pi G rho h, where G is the gravitational constant, rho is the rock density, and h is the elevation above the datum. In milligals, this simplifies to approximately 0.04193 times rho times h. The Bouguer correction is subtracted from the observed gravity because the rock between the station and datum adds extra gravitational pull that must be removed to isolate subsurface density anomalies.
What is the free-air correction and how does it differ from Bouguer?
The free-air correction accounts for the decrease in gravitational acceleration with increasing distance from Earth's center, without considering any intervening mass. It assumes there is only air (free space) between the observation point and the datum. The free-air correction rate is approximately 0.3086 mGal per meter of elevation. For a station 100 meters above sea level, the free-air correction is +30.86 mGal (added to observed gravity because gravity decreases with altitude). The key difference is that the free-air correction only addresses the change in distance from Earth's center, while the Bouguer correction additionally accounts for the gravitational pull of the rock mass between the station and the datum. Together, they form the Bouguer anomaly: observed gravity plus free-air correction minus Bouguer correction minus theoretical gravity.
What rock density should I use for the Bouguer correction?
The standard density used for the Bouguer correction is 2,670 kg/m³ (2.67 g/cm³), which represents the average density of continental crustal rocks, approximately equivalent to granite. However, the appropriate density depends on the local geology. Sedimentary basins may require lower densities (2,200-2,500 kg/m³), while areas dominated by basalt or gabbro may need higher values (2,800-3,000 kg/m³). For precise surveys, the optimal density can be determined using the Nettleton method, which involves computing Bouguer anomalies across a topographic feature using different densities and selecting the one that minimizes correlation between the anomaly and topography. Alternatively, density can be estimated from borehole gravity measurements, laboratory measurements of rock samples, or published density data for the local geological formations.
What is a Bouguer anomaly and what does it tell us?
A Bouguer anomaly is the difference between the observed gravity at a station (after applying free-air and Bouguer corrections) and the theoretical gravity at that location. It reveals lateral variations in subsurface density. A positive Bouguer anomaly indicates denser material than expected below the surface, which could signify dense igneous intrusions, mineral ore bodies, or oceanic crust. A negative Bouguer anomaly indicates less dense material, suggesting features like sedimentary basins, salt domes, granitic batholiths, or mountain roots (isostatic compensation). Bouguer anomaly maps are essential tools in petroleum exploration for identifying sedimentary basins, in mining for locating dense ore bodies, in geotechnical engineering for mapping bedrock depth, and in academic research for studying crustal structure and isostasy.
How accurate are the results from Bouguer Correction Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.