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The role of X(p) constraints in linear, extremal inversion of explosion profile data

GEOLOGICAL RESEARCH DIVISION SCRIPPS INSTITUTION OF OCEANOGRAPHY UNIVERSITY OF CALIFORNIA, SAN DIEGO, LA JOLLA, CALIFORNIA 92093

Abstract

We demonstrate the utility of imposing epicentral distance constraints upon the delay time extremal inverse problem. The inference of delay times from a seismic profile is straightforward and stable since the association of these times with specific ray parameters is unnecessary. The estimation of distance data at specific ray parameters is a much noisier and unstable process, but can provide coarse constraints upon the inverse problem. These distance data act as linear smoothing constraints upon the delay time inverse problem. Furthermore, if a triplication exists in the observed travel-time data, the requirement of such a triplication can be imposed upon the extremal inverse problem using linear programming. Travel-time data from Eastern Iceland and the Pacific Basin are used to demonstrate the value of these constraints.

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