b'Bouguer corrections Featurehorizontal components. If vertical was defined with respect to thecombine to produce a terrain correction equivalent to geoid, there would only ever be a vertical component since verticala spherical cap with arc length 166.7 km. The Bullard C would be defined by the direction of the gravity vector! correction introduces further refinements for variations in surface topography for locations within the extent The maths that I show are developed for a spheroid (not anof the spherical cap. The application of Bullard A, B and ellipsoid), and for a spherically symmetric Earth such that the geoidC corrections gives rise to Complete Bouguer Anomaly and spheroid coincide. The horizontal components of both thevalues. The common practice when calculating Bullard C infinite horizontal slab and the spherical cap are zero under thesecorrections is to use a Cartesian framework and to then circumstances. make a correction to account for the curvature of the Earth. As per (a), I can add this information to the paper. I shall leaveHinze etal. (2005) describe a set of revised procedures for the maths for elliptical cap corrections to greater minds thanmaking the common adjustments to observed gravity myself. values that produce various anomaly values (i.e., residual values). They combine the Bullard A and B corrections into == = ==a single spherical cap Bouguer correction for an arc length of 166.7 km. It is worth noting that the terrain correction c) 166.7 km procedures used by Hinze etal. (2005), that are equivalent to the Bullard C corrections, account for curvature effects You are not alone in wondering where this number comes from. Ifor source locations beyond 14 km rather than the previous wrote about this as part of an ASEG abstract in 2009. standard of using a Cartesian framework for all sources The short answer is that a radius of 166.7 km or an arc length ofwithin an arc length of 166.7 km. The spherical cap and 12958 for a spherical Earth of radius 6371 km was the outerterrain corrections are both truncated at an arc length radius of Zone O defined by Hayford and Bowie (1912). This wasof 166.7 km by convention rather than for any solid the outer limit of a set of near zones A through to O. This distancereasoning. They note that the terrain corrections of limited became more entrenched when Bullard (1936) chose this distanceextent associated with Bouguer Anomaly values should as the radius of the Bullard B corrections. The combination ofbe supplemented with corrections for the effects of distant infinite slab (Bullard A) and Earth curvature (Bullard B) correctionstopographic and bathymetric relief. This is precisely the approximate spherical cap corrections. approach that was used by both Hayford and Bowie (1912) and Bullard (1936) in their pioneering work. More recently, Following is a more lengthy extract from that 2009 abstract. Karki etal. (1961) and Mikuka etal. (2006) present modelling results for distant terrain and isostatic effects in the case The figure of 166.7 km as the threshold distance whenof Karki etal. (1961) that were calculated in a spherical curvature effects become extremely significant arose fromframework. These can be used with the anomalies obtained an analysis by Hayford and Bowie (1912). This distanceafter applying the Bullard A, B and C corrections.corresponds to the outer limit of what became known as Hayford-Bowie gravity terrain correction Zone O. This wasBullard, E.C., 1936, Gravity measurements in East Africa: defined as an angular distance of 12958 for a sphericalPhilosophical Transactions of the Royal Society of London, Series A, Earth of radius 6371 km. Hayford and Bowie wished to235, 445-534.calculate gravity terrain and isostatic effects to assistHayford, J.F., and Bowie, W., 1912, The effect of topography and with geodetic and geological applications. There were noisostatic compensation upon the intensity of gravity: Special precedents to provide guidance on whether gravity andPublication No. 10 of the U.S. Coast and Geodetic Survey, surface topography information for the entire Earth neededWashington D.C.to be considered, nor whether curvature effects needed to be taken into account. Since the computations were carriedKarki, P., Kivioja, L., and Heiskanen, W.A., 1961, Topographic-out by hand, significant time savings could be achieved if aisostatic reduction maps for the world for the Hayford Zones 18-1, Cartesian modelling approximation could be used for all, orAiry-Heiskanen System, T = 30 km: The Isostatic Institute of the the majority, of the work. A number of trial calculations forInternational Association of Geodesy, Helsinki, Finland.both Cartesian and spherical frameworks established thatMikuka, J., Pasteka, R., and Marusiak, I., 2006, Estimation of distant the error budget for the terrain correction of 1 part in 200relief effect in gravimetry: Geophysics, 71, J59-J69.would be exceeded if curvature effects for the contributions beyond Zone O were ignored, and also established thatAfter Richards death I suggested that the draft of his paper, contributions from the entire Earth were indeed required. Annow called Universal horizontal slab and spherical cap arc length of 166.7 km has since become the default distanceBouguer corrections be published in the pages of Preview\x08 for modellers to start to worry about curvature effects.Geoscience Australia gave their permission and the paper However, widespread acceptance of this distance figure doesappears below\x08 It contains Richards original diagrams, partly not take into account the specific accuracy requirementsbecause they are an indication that the paper is in draft form, for any particular job at hand, the majority of which wouldbut also because they are a mark of the man - detailed and show little resemblance to the issue of calculating terrain andmeticulously composed\x08isostatic corrections to an accuracy of 1 part in 200!A final word about someone I counted as a dear friend and The apparent importance of an arc length of 166.7 kmcolleague: Richard did not accept a lack of rigour in the thinking became further entrenched through common use of a 3-partof his professional colleagues\x08 However, rather than engaging procedure for calculating terrain corrections for gravityin confrontation he would return to the subject a day or so later introduced by Bullard (1936). The Bullard A correction is thewith a fully developed rejoinder, not only to the betterment of infinite Bouguer slab correction that gives rise to Simplethe individual, but also to the evolution of their practice\x08 Would Bouguer Anomaly values. The Bullard A and B correctionsthat we all lived with his grace and courage\x08APRIL 2021 PREVIEW 42'