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Why do local gravity effects appear less strongly on a geoid map than on a gravity-anomaly map?

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Diagram showing the deflection of the vertical from the geoid to the ellipsoid or spheroid, with labeled lines for geoid, spheroid, rock surface, ocean, and geoid height in a geology context. — geoid Deflection of the vertical from the geoid to the spheroid.

Local gravity effects appear less strongly on a geoid map than on a gravity-anomaly map due to the mathematical relationship between the two representations in spherical harmonic expansion.1

When constructing these maps, the undulation coefficients of the geoid ( $N_{l, m}$ ) are derived from gravity anomaly coefficients ( $Δ g_{l, m}$ ) by applying a reduction factor of $1 / (l - 1)$ , where $l$ represents the degree of the spherical harmonic term. As the degree $l$ increases—which corresponds to smaller-scale or more localized features—this reduction factor becomes increasingly significant. Consequently, while gravity-anomaly maps highlight these local variations, the geoid map effectively filters them out, resulting in a surface that emphasizes broader, long-wavelength features of Earth's gravitational field.1