Seismic Reflection Tomography

Abstract

Lilke in medicine or non-destn¡ctive testing, tomography has now becore a well established inaging tool. In reflection seismology it is used to image the velocity or the rcflectivity of the earttr particularly in surface, resewoir, borehole, and crosshole seismology. Originaly based on ray theory it ca¡r now bo developed frrom the wave equation as described by Huygen's principle given in form of KirchhofFs integral for acoustic and elastic media Tomography thus, has undergone a similar transition as seismic migration theory and both theories in fact veqi much relafe to each other. Accepting the Born approximation for the medium ûo be imaged one can formulate the tomographic imagFng approach as a cônsistent and comprehensive theory of linearized inversion. This incorporates such methods as transmission and reflection tomography for arbitrary ftrequencies as well as
high-frequency computerized tomography that involves the Radon transform. The general framework'of linea¡ized scalar diftaction tomography will be discussed from first principles. Emphasis is put on refloction tomography. lhe case of zero-offset reflection tomography is treated for a Born scatterer as well as for a layered medium with reflectors buried into an arbitrary inhomogeneous velocity field.