Wave-equation tomography: I , by Marta Jo Woodward

Wave-theoretic, diffraction tomography is usually formulated in the spatial-frequency domain. This paper reformulates the method in the space domain, for the purpose of clarifying its relation to ray-theoretic tomography. Where ray-theoretic tomography projects traveltimes back over raypaths, space-domain, wave-equation tomography projects differential wavefields back over wavepaths. Comparison of raypaths and wavepaths reveals the different assumptions the two methods make about the seismic experiment: specifically, about amplitudes, frequency dispersion and event discrimination. Through examination of these assumptions, wavepaths are identified as monochromatic raypaths, and bandlimited raypaths are defined as wavepaths averaged over frequency. Examples of ray-theoretic and wave-equation tomographic inversions are shown for a finite-difference data set.


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