Curvature corrections to upper mantle seismic refraction surveys

Abstract

Most upper mantle and crustal velocity determinations are made using conventional seismic refraction techniques under the assumption that the earth may be considered flat for distances up to about 1500 km. The flat earth assumptions do however lead to systematic errors which take the following forms: (i) the apparent velocity determinations are too large, and are a function of the refractor depth, (ii) apparent ’lateral variations’ in the upper mantle are produced, (iii) refractor depth calculations depart from correct values as the depth is increased beyond 60 km, (iv) misleading discrepancies occur when spherical ray theory is used with parameters determined from flat earth formulae.The measured apparent velocities v′ may be corrected for curvature to true velocities using v = [(R-H)/R]ý, where R is the radius of the earth and H the depth of the refractor. The magnitude of the corrections shows that the curvature of the earth cannot be ignored in crustal and upper mantle refraction surveys when the depth of the refractor is more than 10 km. An apparent 8.50 km/sec layer at a depth of 124 km, for example, becomes an 8.33 km/sec layer at a depth of 130 km when curvature correction are applied.Since curvature effects have been neglected in many refraction surveys, other geophysical investigations (such as gravity, near earthquake etc.) which have made either direct or indirect use of flat earth data, may be significantly affected.