Gravity Anomalies of Polygonal Sheets With Linear Density Variation

Thin planar sheets are useful target models for geological structures such as dykes and veins, which are essentially two-dimensional on survey scales. We derive the gravity potential, field and field gradient for such targets. We concentrate on triangular sheets, because these can be assembled into a drape surface, with continuous densities across the boundaries, so as to approximate general curved surfaces. We verify the correctness of the anomaly formulae via numerical testing, and model a scenario with dyke curvature and density compaction.