correlations have amplitudes of little more than this. Thus some of the features in figures such as 7 may well be spurious; the consequence of inadequate data or an inadequate treatment. The improvement in accuracy of the field, even without extending it to a higher order, should there fore be one of the first goals for future work in this area. Only then can we be sure about the existence of those features that we are trying to correlate with other geophysical data. The second improvement required is the resolution of the solution. At present only those features of areal extent greater than about 1200 km can be found so that many interesting areas on the globe pass by unnoticed. A now classical example is the geoid variation over the Puerto-Rican trench. This feature is, according to Von-Arx [28], associated with a variation in geoid height of about 15 meters over a distance of about 100 km. Yet it does not appear in the global solution which has an accuracy of about three meters. The resolution is also re quired for studying the detail of the anomalies now observed. Successive solutions in the past for the earth's gravity field have indicated a breaking up of the major features as the resolution improved and this tendency may well continue beyond the resolution discussed here. The first type of improvement is fairly readily ob tained with present methods but using more, better distributed, and more precise laser range data. There are now seven satellites with retroreflectors in orbit around the earth and there are now twelve laser stations routinely used for tracking these objects. The international observing campaign now being coordinated by the Centre National d'Études Spatiales, will make an important contribution in this respect. However, as we discussed in the first part of this paper, the improvement in laser tracking will not contribute significantly to impro vements in the resolution: With a good distribution of 20 cm accurate data we obtain a resolution of only about 900 km! New methods, which will mea sure the earth's potential, or its shape will conse quently be required to give this improvement. One of the most important of the new methods is satellite altimetry. The potential of satellite-borne 52 altimetry has been recognized since the early days of the space age as both a navigation guidance system for spacecraft and, more important, as a means of increasing our knowledge of the earth's shape. The necessary space technology is now suffi ciently far developed to make such a program fea sible if we are seeking accuracies of about one or two meters. If a radar on board of a satellite transmits a pulse towards the earth and the reflected signal is received back at the satellite, the time delay between the transmitted and received pulses gives a direct mea sure of the distance between the satellite and the point from which the signal is reflected. This is simply the inverse of the more conventional ground based radar tracking of satellites. If the satellite is gravity-gradient stabilized so that the radar pulse reaching the earth contains the point of nearest approach, the height of the satellite over the ocean is measured directly. For a satellite in a polar orbit such observations could be made over 75% of the total surface of the earth in a very short time indeed. If we knew, from ground based tracking data, the satellite orbit, the combination of this orbital data with the measured heights gives a direct measure of the height of the ocean surface with respect to some more or less arbitrary reference. This ocean surface will to within a meter correspond to the geoid. If both the reference orbits and the altimetry data are accurate to a meter or better, all the detail that is reflected in the geoid with an amplitude of about a meter and with a spatial resolution of only a few tens of kilometers can be measured. At the moment we have not yet reached this level ot refinement in our orbital computations, but the altimeter data can also be incorporated, together with the ground based tracking data, to improve the accuracy of the reference orbits as well as providing the detailed information on the geoid. A major problem with the altimetry data becomes the question of how to mathematically represent the earth's surface. If we continue using the spher ical harmonics we quickly run into difficulties. For a resolution of 500 km we require an expansion to degree 36, or about 1400 coefficients and this is still manageable with large modern computers. For ngt 72

Digitale Tijdschriftenarchief Stichting De Hollandse Cirkel en Geo Informatie Nederland

Nederlands Geodetisch Tijdschrift (NGT) | 1972 | | pagina 14