b'Bouguer corrections FeatureThe equations for spherical cap Bouguer corrections presented here are based on the equations that define the vertical gravity response of a spherical cone (Figure 2)\x08 The equations are given by Argast et al (2009) and are reproduced here for convenience as equations 5 through to 16\x08The cone has its apex at the centre of a sphere, C, with radius S 0metres\x08 It subtends an angle of 2 at the apex and has a density ofkg/m3\x08 The measurement point, P, is at a height of t metres above the surface of the sphere\x08The vertical gravity response for this spherical cone, g z(S 0 , t, ), inm/s2 is given byg z,cone (S 0 ,t,)=2G((S 0 +t)(1+)t(1+) (5)Figure 1.Cross section for the general case of a Bouguer correction using infinite horizontal slabs. whereIn the general case (Figure 1), we can write the horizontal slab=R b /R 0 (6)Bouguer correction, g B,HS , at a point P at height d above the ocean surface as =t /(S 0 +t)(7)g B,HS =(2G SW D)+(2G t [hD])(4) =(1/3) 2 (8)where D is the ocean depth in metres ( 0),swis the density of=S 0 /(S 0 +t) (9)sea water in kg/m3 ( 0),tis the density of the terrain in kg/m3k=sin 2 ()(10)( 0), and h vis the height of the ocean or ground surface above the level of the vertical datum\x08 f =cos()(11)Since the correction is independent of the height of thed=3cos ()2(12)2observation point above the surface, the correction in equation 4 can be applied not just to observations made on the groundm=3cos()sin 2 ()(13)or ocean surface but to airborne observations, for either onshore or offshore situations, and for either a geoid or ellipsoid=(1/3) ( (d+f+ 2 ) ((f ) 2 +kvertical datum\x08mln ( (f )+ ((f ) 2 +k) ) )Bouguer corrections for a spherical cap (14)Spherical cap Bouguer corrections use a portion of a sphericalb=2cos 2 (/2)(15)shell as the model geometry\x08 By convention, the cap has a=(1/3)(d+2mln(b)) (16)surface radius of 166\x08735 km\x08and R bis the Bullard B surface radius 166735 m (Bullard, 1936; LaFehr, 1991), R 0is the mean radius of the Earth, which for the GRS80 ellipsoid is 6371008\x087714 m (Moritz, 2000), and G is the gravitational constant 6\x0867430e-11 m3 kg1 s2 (Tiesinga et al, 2019)\x08The response of a spherical cap can be obtained from the response for a pair of spherical cones (Figure 3)\x08 To obtain theresponse for the shaded spherical cap at point PFigure 3.Cross section through a spherical cap (shaded area) that is defined as the difference between two spherical cones, one of radius R + h and another Figure 2.Cross section through a spherical cone. with radius R.APRIL 2021 PREVIEW 44'