Rigorous velocity bounds from soft ? (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 ~(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 7 and X as its data, while QP uses estimated means and variances of 7 and X. The approaches are quite similar and involve only one inherent approximation: they use a finitedimensional 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.