b'Bouguer corrections Feature(Equation 17), the response at a height of t + h above the surface of a cone of radius R is subtracted from the response at a height of t above the surface of a cone with the same density but a radius of R + h\x08g z,cap =g z,cone (R+h,t,)g z,cone (R,t+h,) (17)The equation for a general spherical cap Bouguer correction, g B,SC , has 4 terms that are grouped into two pairs, as indicated by the braces, where each of these pairs is the response of a spherical cap (Equation 18)\x08 As per equation 4 for the general horizontal slab Bouguer correction, the first of these pairsFigure 5.An image of the spherical cap correction values for onshore locations as a function of ground elevation and terrain clearance.provides the vertical gravity response that accounts for the sea water column beneath the observation\x08 The second pair of terms provides a correction for the crustal material between theexpression given by LaFehr (1991)\x08 This is an outcome that is ocean floor and the level of the vertical datum\x08 also noted by Argast et al (2009)\x08The inputs to the general spherical cap Bouguer correction (Figure 4) are the height of the surface above the vertical datumComparison of infinite horizontal slab and spherical ( h v) in metres, the surface clearance of the observation pointcap Bouguer corrections( d ) in metres ( 0), the ocean depth ( D ) in metres ( 0), the density of the terrain ( t ) in kg/m3 ( 0), and the density of seaAn image displaying the spherical cap correction for onshore water (sw) in kg/m3 ( 0)\x08 locations as a function of ground elevation and terrain clearance is given in Figure 5\x08 It is clear that the principal control on the The general spherical cap Bouguer correction is magnitude of the correction is the elevation of the ground, but it can be seen from the small angle that the contour lines make g B,SC (h,d,D, t , sw )=(g z,cone,A g z,cone,B ) with respect to the y-axis that there is also a subtle reduction (18) in the magnitude of the correction with increasing terrain +(g z,cone,C g z,cone,D ) clearance\x08 Bouguer corrections using an infinite horizontal slab are different in this respect since there is no change in these where corrections with terrain clearance\x08g z,cone,A =g z,cone (R 0 +h,d, sw )(19) To highlight some of the characteristics of the two Bouguer correction geometries, images showing the differences between the two corrections are provided\x08 The differences between these g z,cone,B =g z,cone (R 0 +hD,D+d, sw )(20) two corrections for onshore locations are presented in Figure 6 as an image for a range of surface elevations and heights above g z,cone,C =g z,cone (R 0 +hD,D+d, t ) (21) the ground\x08The first point to note is that the magnitude of the differences g z,cone,D =g z,cone (R 0 ,h+d, t ) (22) is 1% or less of the corrections themselves\x08 The conclusion that can be drawn from this is that the two corrections are very For specific situations, equation 18 can be simplified\x08 In the casesimilar to one another\x08of onshore observations, the 1st and 2nd terms in the definition of the spherical cap Bouguer correction cancel each other out\x08Next, we can look at the variation parallel to the x-axis for any With the further restriction of onshore observations madespecific terrain clearance\x08 As an example, the differences for directly on the surface, the first two terms reduce down to thezero elevation along the base of the image can be examined\x08 The difference is zero at the origin when the ground surface coincides with the vertical datum\x08 The difference between these two corrections reaches a maximum of around +15 m/s2 when the ground surface has an elevation of approximately 2000 m above the vertical datum\x08 The difference is again equal to zero Figure 6.Differences between spherical cap and infinite horizontal slab Bouguer corrections for onshore locations for terrain clearances of 0 m to Figure 4.Cross section for the general case of a spherical cap Bouguer. 2000 m and surface elevations of 0 m to 5000 m.45 PREVIEW APRIL 2021'