Rigorous velocity bounds from soft τ (p) and X(p) data

Abstract

Summary. The convergence of two methods of inferring bounds on seismic velocity in the Earth from finite sets of inexact observations of τ (p) and X(p) are examined: the linear programming (LP) method of Garmany, Orcutt & Parker and the quadratic programming (QP) method of Stark & Parker. The LP method uses strict limits on the observations of τ and X as its data, while QP uses estimated means and variances of τ and X. The approaches are quite similar and involve only one inherent approximation: they use a finite‐dimensional representation of seismic velocity within the Earth. Clearly, not every Earth model can be written this way. It is proved that this does not hinder the methods ‐ they may be made as accurate as desired by increasing the number of dimensions in a specified way. It is shown how to get the highest accuracy with a given number of dimensions. Copyright © 1987, Wiley Blackwell. All rights reserved