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.
STANFORD