Potential Field Theory and Gravity Anomalies

Gravity and magnetic fields are potential fields governed by Laplace's equation, and reducing raw gravity measurements into anomalies exposes the subsurface density variations that cause them.

Definition

Potential field theory is the body of mathematics describing fields, such as gravity, that derive from a potential satisfying Laplace's equation in source-free regions; gravity anomalies are the differences between measured gravity and a reference value after standard corrections, used to infer subsurface density.

Scope

This topic covers the mathematical framework of potential fields and its application to gravity data: the gravitational potential, Laplace's and Poisson's equations, and the harmonic properties that constrain field behavior. It treats the corrections that turn observed gravity into free-air and Bouguer anomalies (latitude, free-air, Bouguer slab, and terrain corrections), the inherent non-uniqueness of potential-field inversion, and the forward modeling and filtering used to interpret anomalies in terms of buried density structure. The emphasis is on the theory linking density to the measured field and on anomaly reduction.

Core questions

• Why are gravity and magnetic fields described by potential theory and Laplace's equation?
• What corrections convert observed gravity into free-air and Bouguer anomalies?
• Why is the inversion of potential-field data inherently non-unique?
• How are anomalies modeled and filtered to infer subsurface density?

Key concepts

• Gravitational potential and Laplace's equation
• Free-air, Bouguer, and terrain corrections
• Harmonic functions and upward continuation
• Non-uniqueness of potential-field inversion
• Forward modeling of density bodies

Key theories

Potential theory and Laplace's equation

In regions free of mass the gravitational potential is harmonic, satisfying Laplace's equation, which constrains how the field varies with position and underlies operations such as upward continuation and the separation of regional and residual anomalies.

Gravity reduction and anomalies

Observed gravity must be corrected for latitude, elevation, the mass of intervening rock, and terrain to yield free-air and Bouguer anomalies, which isolate the gravitational signal of subsurface density contrasts from predictable effects.

Mechanisms

A density contrast at depth perturbs the gravitational potential, and because the potential is harmonic away from sources, the resulting surface anomaly is a smoothed, depth-dependent expression of that buried mass; reduction removes the predictable variation due to latitude, height, and the bulk rock so that the residual anomaly reflects the lateral density variations of geological interest, though many density distributions can fit the same anomaly.

Clinical relevance

Gravity anomaly analysis maps sedimentary basins, ore bodies, salt domes, and crustal structure, supporting mineral and petroleum exploration, regional tectonic studies, and the definition of the gravity field used in geodesy.

History

Laplace and Poisson established the potential theory underlying gravity in the late eighteenth and early nineteenth centuries, Bouguer's eighteenth-century mountain measurements introduced the corrections that bear his name, and the development of sensitive gravimeters in the twentieth century made anomaly mapping a routine geophysical tool.

Key figures

• Pierre-Simon Laplace
• Pierre Bouguer
• George Gabriel Stokes

Seminal works

• blakely1995
• hofmannwellenhof2006
• telford1990

Frequently asked questions

What is the difference between a free-air and a Bouguer anomaly?

A free-air anomaly corrects only for the elevation of the measurement point, while a Bouguer anomaly additionally removes the gravitational attraction of the rock between the point and the reference level; the Bouguer anomaly therefore more directly reflects density variations below the surface.

Why can't gravity data give a unique picture of the subsurface?

Many different distributions of mass at depth can produce exactly the same gravity anomaly at the surface, so potential-field inversion is non-unique; geologists reduce the ambiguity by adding constraints from drilling, seismic data, and known geology.