There is a lot of confusion around the use of the gravity anomaly in a
geophysical context.
I have been discussing this topic with
Vanderlei for many years
now.
It's been in our minds ever since our first gravity and magnetics undergraduate
course back in 2007.
I'm sure we were the source of many headaches for Professor Eder
Molina, who was
teaching the course at the time.

This short paper is our attempt at bringing a geophysical modeling point of
view to the debate.

Abstract

The gravity anomaly is defined as the difference between the Earth's gravity on
the geoid and the normal gravity on the reference ellipsoid. Because these
quantities are not at the same point, the anomaly contains centrifugal
accelerations and cannot be considered a harmonic function. The gravity
disturbance is the difference between gravity and normal gravity at the same
point. Consequently, the centrifugal effects can be neglected and the
disturbance can be considered a harmonic function. This is the premise behind
most potential-field data processing techniques (e.g., upward/downward
continuation). Unlike the anomaly, the disturbance is due solely to the
gravitational effects of geologic sources, making it the most appropriate for
geophysical purposes. Use of the gravity anomaly in geophysics carries with it
the implicit assumption that it is a good approximation for the gravity
disturbance. However, bear in mind that the difference between the gravity
disturbance and the free-air anomaly can be larger than 10 mGal worldwide. In
fact, we argue that the assumptions made during gravity forward and inverse
modeling imply that the quantity being modelled is the disturbance, not the
anomaly.

Map of the difference between the gravity disturbance and the free-air anomaly worldwide.
This is the error committed when assuming that the free-anomaly is a good
approximation for the disturbance.

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@leouieda.

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