GLOBAL SOLUTION OF A LINEARIZED INVERSE PROBLEM FOR THE WAVE-EQUATION

High frequency linearized inversion estimates a critical component of the earth's velocity field from measurements of scattered acoustic wav es captured by various source and receiver pairs (acquisition geometry ). The method partitions the velocity field into two components: an as sumed long-scale velocity component and an unknown short-scale velocit y component. A standard imaging operation (migration) locates those po sitions where the short-scale velocity is non-zero. In strongly refrac ting velocity fields, several scattering paths (pairs of incident and reflected bicharacteristics) with equal travel times may produce artif acts ill tile short-scale image. This paper explains why these artifac ts arise and how they may be removed. For general acquisition geometry . we give an imaging condition: To product an artifact-free image, sca ttering paths gust. be reconstructible from two pieces of information; (a) The travel time for the pair of bicharacteristics and (b) The pro jection of the bicharacteristics at the source and receiver onto the c otangent bundle of the acquisition manifold.