INTRODUCTION

A gravity anomaly is the difference between measured "g" and "g" of some standard earth model (often mislabeled "theoretical gravity"). There are several standard earth models. Which one to use depends on the goals of a particular study. We’ll look at several common anomaly definitions in terms of what they are made up of and their advantages and disadvantages.

FREE-AIR ANOMALY

The free-air anomaly is defined by a standard earth model consisting of the International Formula to account for the latitude and the free-air effect to account for elevation above sea-level. Thus it’s based on a smooth, rotating, ellipsoidal earth and a station hovering in free-air above the surface. It omits all mass that really exists above sea-level.

On a local scale up to a couple of hundred kilometers, the Free-Air anomaly strongly correlates with local elevation and reveals little about local underground density variations. Thus it is unsuitable for exploration. On a regional scale of hundreds of kilometers the Free-Air anomaly averages close to zero. At first glance that seems to pose a problem. We know the model omits mass above sea-level, yet, at the same time, the average value of zero suggests that the model resembles the earth. How do resolve this apparent contradiction?

The explanation is that the Free-Air model does not explicitly include the low-density roots that underlie high-elevation regions. In other words the model includes too much mass below sea-level but omits a roughly equal mass above sea-level. The effects of omitting these widespread two masses basically cancel out. Thus we use Free-Air anomalies in studying isostasy.

SIMPLE BOUGUER ANOMALY

The model that defines the simple Bouguer anomaly includes all the parts of the Free-Air anomaly as well as the "Bouguer slab". This is an infinite sheet of constant density that numerically approximates the gravitational attraction of rock between sea-level and the gravity station. When we use this anomaly we must be sure to state what our standard density is. For many years it’s been common to use 2670 kg/m^3, an early estimate for the mean density of continental crust. Some geophysicists prefer to use this quasi-standard density and introduce more realistic densities at the stage of modeling survey results. Others prefer to build in as much local density data as possible in defining the anomaly in the first place.

On a local scale the Bouguer anomaly values correspond to local density anomalies. That is, the values are high over dense rocks and low over light ones. Bouguer anomalies are the common ones used in applied geophysics.

Regionally Bouguer anomalies are strongly negative at high elevations and strongly positive over the deep ocean. This fact strongly supports the concept of isostasy. The standard Bouguer model omits the low-density "roots" of high areas and thus includes more mass than really is present in the earth. Therefore the anomaly is very negative. Over the oceans, the model ignores the thin crust and ocean water and contains too little mass.

COMPLETE BOUGUER ANOMALY

In defining the simple Bouguer anomaly we used a planar "slab" to represent material between sea-level and the gravity station. This procedure is acceptable in regions of low relief but in mountainous areas we need to represent the topography more accurately. The complete Bouguer anomaly incorporates hills rising above the Bouguer slab and depressions cutting into it. The masses above the station act to reduce gravity in the model according to Newton’s Law (they "pull up" on the gravity meter). The omitted holes in the slab also act to reduce gravity (they don’t "pull down").

These "terrain corrections" to the Bouguer slab are done numerically. There are many ways of doing this numerical integration so we must always be clear about how we’ve done it. Of course we must also state the density that we have used.

ISOSTATIC ANOMALY

The isostatic anomaly is based on a standard model that is even more elaborate than the complete Bouguer anomaly. Basically we specify densities of areas below sea-level in addition to including all the parts of the complete Bouguer anomaly. As the name implies, the isostatic anomaly is used to study crustal geology and upper mantle geology and how they relate to isostasy. We will not use isostatic anomalies in this course.

DELTA G/ DELTA T ANOMALIES

I’ve saved the simplest kind of anomaly for last. In some studies we use the rate of change of gravity with time rather than the differences in gravity from place to place. For example we might wish to monitor a growing cone of depression around a water well or to locate areas of different permeability. In the first case we would expect gravity to decrease as the cone grows larger. In the second gravity would decrease most rapidly over high permeability areas that drain rapidly compared to low permeability areas.