b'Bouguer corrections FeatureUniversal horizontal slab and spherical cap Bouguer correctionsof the terrain at and surrounding each observation point is calculated in one step by calculating the full response for a terrain model extending out to some radius, generally taken to be 166\x08735 km\x08 In equation 2, this response is calculated in two parts: (i) the Bouguer correction, and (ii) a terrain adjustment which is the difference in response between that obtained for the simple depiction of the Earth used in (i) and the response of a full terrain model\x08 The terrain adjustment, g ta , is often referred to as a terrain correction, but I use the word adjustment to avoid confusion with g tc \x08The focus of this paper is the Bouguer correction, g B \x08 The Earth model used for the Bouguer correction can be either an infinite horizontal slab or a spherical cap\x08 It is straightforward to use Richard Lanethe equation for the vertical gravity response of an infinite Geoscience Australia horizontal slab to deduce the correction for any possible scenario of surface or airborne location, for either onshore or offshore situations, and for either a geoid or ellipsoid vertical Abstract datum\x08 It is more challenging to do this for a spherical cap geometry\x08 LaFehr (1991) gave the equations for the gravity Equations are presented for calculating infinite horizontalresponse of a spherical cap when the observation is made slab and spherical cap Bouguer vertical gravity corrections fordirectly on the surface of the spherical cap\x08 Argast et al (2009) surface and airborne observations, for both onshore or offshorerepeated the derivation for observations made on the surface situations, and for both a geoid or ellipsoid vertical datum\x08 Thein onshore locations but then went on to extend the range of equation for the gravity response of an infinite horizontal slab issolutions to airborne observations above onshore locations relatively simple\x08 In the general case, Bouguer corrections for aand to observations made on the surface of the ocean\x08 The slab geometry involve two infinite horizontal slabs: one for seaavailable solutions unfortunately omit the scenario of airborne water and one for solid rock\x08 The equation giving the gravityobservations in offshore locations\x08 This gap is closed in the response for a spherical cap is more complex\x08 It is based on thefollowing with the presentation of a general equation for equation for the vertical gravity response of a spherical cone\x08spherical cap Bouguer corrections\x08In the general case, the equation for the spherical cap Bouguer correction is expressed as the sum of the response for four such cones with different densities and radii\x08 Armed with these tools,Bouguer corrections for an infinite horizontal slabthe choice of whether to use a horizontal slab of spherical cap geometry for Bouguer corrections can be made on betterThe vertical gravity response, g z,HS , in m/s2 for an infinite criteria than the availability of suitable equations\x08 To assist withhorizontal slab geometry is given by the equationthe choice of geometry, comparisons of infinite horizontal slab and spherical cap Bouguer corrections are given for a range ofg z,HS ,= 2Gh (3)terrain clearances, water depths, and surface elevations\x08 Thesewhere G is the gravitational constant which has an accepted comparisons show that the differences between the correctionsvalue of 6\x0867430e-11 mkgsat this time (Tiesinga et al, 3 1 2are relatively small, that the corrections for a spherical cap2019),is the density of the material making up the slab ingeometry decrease in magnitude with increasing terrainkg/m , and h is the thickness of the slab in metres\x083clearance, and that the differences change polarity for a given terrain clearance as the elevation of the terrain surface or theThe horizontal slab Bouguer correction for an onshore location depth of the ocean increases\x08 involves the gravity response of a single slab that has its upper surface at the level of the ground surface vertically below Introduction the observation point and its lower surface at the level of the vertical datum, regardless of whether this is a geoid or an Complete Bouguer Anomaly gravity values (g CBA ) are derivedellipsoid vertical datum\x08from observations of the vertical component of gravity (g obs ) via a sequence of corrections\x08 There are two options for performingIn the case of an offshore location and a geoid vertical datum these corrections (Equations 1 and 2): that coincides with the ocean surface, the horizontal slab Bouguer correction once again involves a single slab between g CBA =g obs g t g atm g fac g tc , or (1) the ocean bottom and the ocean surface\x08When an ellipsoid vertical datum is used, as recommended g CBA =g obs g t g atm g fac g B g ta , (2) by Hinze et al (2005) and implemented in Australia (Tracey etal, 2007), a pair of slabs must be used to derive the Bouguer where g tis the theoretical gravity correction, g atmis thecorrection\x08 The first slab accounts for the sea water column atmospheric correction, g facis the free air correction, g tcis thebeneath the observation\x08 The second slab provides a correction full terrain correction, g Bis the Bouguer correction, and g tais thefor the crustal material between the ocean bottom and the level terrain adjustment\x08 In equation 1, the vertical gravity responseof the vertical datum\x0843 PREVIEW APRIL 2021'