NATURE VOL. 332 24 MARCH 1988 -NEWS AND VIEWS 301 Making the geoid respectable again With the recognition that surface measurements of gravity cannot be extrapolated backwards into the Earth's interior, the concept of the geoid became unfashionable. But its fortunes may be on the turn. EvERYBODY knows, of course, that the of mean sea level would indeed be an when there are ample measurements of geoid is that surface of equal gravitational ellipsoid of rotation. One of the practical gravity on which to base inferences. potential which coincides with mean sea­ I difficulties with which geodesists are con­ Hipkin gives the example of a ploughed level. Most of us also have it clearly in fronted is that the measurements of sea field, the furrows of which would yield mind that the geoid is an ellipsoid with level at tidal stations must be corrected for small but still measurable periodic varia­ rotational symmetry about its shorter such sources of variation as ocean cur­ tions of gravitational potential just above polar axis, which allows for the flattening rents, departures of seawater density from the surface which, if projected downwards of the Earth by rotation. But that must the means, not to mention other seasonal in a simple-minded fashion, would imply plainly be a fairy story, possibly applicable effects, but in principle there is a wealth of variations of the height of the equipoten­ to the oceanic surfaces of the Earth, but places scattered around the world at which tial surface of as much as 1 km just a few unlikely to make very much sense else­ the ellipsoidal parts of the geoid might be metres below the surface. where. The snag, as can be learned from a defined precisely, especially now that Hipkin's goal is to find a sensible and glance at a recent article by R. G. Hip kin satellite ranging data may provide loca­ consistent way of projecting surface mea­ from the University of Edinburgh ( Geo­ tions more precisely (or at least more con­ surements of gravity downwards. This he physical Journa/92, 53; 1988), is that it is veniently) than by timing stars. does by splitting the measured gravity much easier to stick to the fairy-story than One superficial complication is that the anomalies at the surface into two parts - to tell just where the geoid is on dry land. reference ellipsoid and the set of concen­ that due to variations from flatness of the Hipkin's opening sentence may be a tric ellipsoids corresponding to different terrain in the immediate neighbourhood sufficient explanation: values of the gravitational potential define and that represented by what is usually Physical geodesy has become a dauntingly a downward gravitational attraction called the Bougier anomaly, and which esoteric branch of applied mathematics (called "normal gravity" and calculated as corresponds to deep-seated gravity which, in the achievement of greater rigour, y = \l U, where \l is the laplacian opera­ anomalies such as the departures from has distanced itself from many practical tor and U is the potential field) that will hydrostatic balance, more precisely geodesists. This is particularly unfortunate differ both in magnitude and in direction isostacy. when greatly improved measurement techni­ from true gravity, g (notionally calculable The proof of the recipe is, as always, ques have become available, both for surface from the true gravitational potential Was whether it works. On the face of things, gravimetry and for geometrical positioning 0.179W). and for a careful set of data collected in from space vehicles. Hipkin does not differ from others in northern Scotland, the answer is encour­ Hipkin might have added that geodesy remarking that it is in principle possible to aging. First, it appears practicable to deal may not be the only offender in this relate measurements of gravity (including with the effects of topographic variations regard. the departure of its direction from that of (of which there are many, called moun­ Whatever the validity of that canard, the line to the centre of the Earth) at tains, in northern Scotland) by making the there is clearly plenty of room for intricate inland surface sites to measurements at simple assumption that they consist of argument about even the elementary coastal tidal stations by a combination of material of constant density and then by definitions on which geodesy is founded. levelling and gravity measurements (but estimating their contribution to local Hipkin's approach is refreshingly that of a care is needed to distinguish between the gravity by means of a contour-following logical positivist of the machian school. In normals to the ellipsoidal surfaces and the technique. Second, the downward pro­ pursuit of the principle that the only quan­ direction of a plumb line). jection of the Bougier anomaly itself can tities appearing in equations should be The essence of the difficulty is that of be arranged in a consistent fashion by measurable quantities, he even rejects telling what happens to the force of gravity careful control of the wavelength of the Newton's scheme (really, a gedanken­ beneath the surface, within the contin­ measured surface gravity field. experiment) for defining the geoid every­ ental crust for example. Formally, nothing The result, for northern Scotland, is a where by building a series of wells and can be done without a knowledge of the more detailed account of where the geoid canals within the body of the Earth; the density distribution of material within the lies than any other part of the world is construction would vitiate the observa­ body of the Earth. While, as every school­ provided with. On the face of things, the tions, he says. boy knows (or, perhaps, should know), height of the geoid there is defined with a With that said, Hipkin's interest is to the external gravitational field of the precision of less than 10 em. These vari­ rescue the concept of the geoid from the Earth is uniquely determined by a know­ ations become apparent after allowing for limbo into which it may be expelled by ledge of its value and gradient at each an east-west tilt in the surface of the geoid excessive rigour. (With tongue firmly in point on the surface, nothing can be said from one side of Scotland to the other. In cheek, he quotes two writers from twenty about the gravitational field within the principle, and in due course, this should years ago who say that this ambition is a Earth without a detailed knowledge of the provide grist for the mills of those wishing "concession to conventional concep­ density distribution within the solid Earth. to speculate about the reasons why, for tions"). But the difficulties are consider­ That seems to be the starting point, example, there should be a relative able, as Hipkin's article shows clearly apparently established by the Soviet depression of the geoid amounting to a enough. mathematician Molodensky, for the maximum of more than 1.5 m off the Were it not for the continents, and recently rigorous trend in geodesy. northern coast of Aberdeenshire. But the anomalies of gravitational potential such Plainly, there are also serious math­ general interest of what Hip kin has done is as that in the south-west Atlantic or the ematical problems in extrapolating down­ to make the concept of the geoid respec­ non-circularity of the Equator, the surface wards from the surface of the Earth even table again. John Maddox