Open AccessRigorous velocity bounds from soft τ ( p ) and X( p ) data
Author(s) -
Stark Philip B.
Publication year - 1987
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1987.tb05204.x
Subject(s) - convergence (economics) , quadratic equation , mathematics , representation (politics) , linear programming , quadratic programming , algorithm , mathematical analysis , mathematical optimization , geometry , politics , political science , law , economics , economic growth
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.