Preamble to Universal horizontal slab and spherical cap Bouguer corrections

摘要

Equations are presented for calculating infinite horizontalslab and spherical cap Bouguer vertical gravity corrections forsurface and airborne observations, for both onshore or offshoresituations, and for both a geoid or ellipsoid vertical datum. Theequation for the gravity response of an infinite horizontal slab isrelatively simple. In the general case, Bouguer corrections for aslab geometry involve two infinite horizontal slabs: one for seawater and one for solid rock. The equation giving the gravityresponse for a spherical cap is more complex. It is based on theequation for the vertical gravity response of a spherical cone.In the general case, the equation for the spherical cap Bouguercorrection is expressed as the sum of the response for foursuch cones with different densities and radii. Armed with thesetools, the choice of whether to use a horizontal slab of sphericalcap geometry for Bouguer corrections can be made on bettercriteria than the availability of suitable equations. To assist withthe choice of geometry, comparisons of infinite horizontal slaband spherical cap Bouguer corrections are given for a range ofterrain clearances, water depths, and surface elevations. Thesecomparisons show that the differences between the correctionsare relatively small, that the corrections for a spherical capgeometry decrease in magnitude with increasing terrainclearance, and that the differences change polarity for a giventerrain clearance as the elevation of the terrain surface or thedepth of the ocean increases.