A guide to the limits of resolution imposed by scattering in ray tomography

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Abstract
Tomographic imaging is now in widespread use in geophysical inversion. Most early work in this field used the ray approximation to wave propagation, but more recently scattering effects have been addressed via the formalism of diffraction tomography. However, if the correct image cannot be adequately represented as a perturbation of a simple background, this may demand considerably more computational resources than ray tomography. Therefore it is of some interest to determine the scalelength of variation below which scattering cannot be neglected, so that ray tomography is no longer reliable. In the hypothetical case of monochromatic illumination of a region consisting of small perturbations to a homogeneous background, the way in which the two reconstruction algorithms map the data into the Fourier components of the object may be directly compared to reveal the effect of neglecting scattering. These mappings begin to differ significantly at a wave‐number corresponding to the first Fresnel zone radius; it seems reasonable to expect that a similar result should apply to cases with more general background velocities, and so to iterative (nonlinear) inversions. Therefore some kind of inverse scattering approach must be employed to ensure accurate imaging beyond this wavenumber to the limit of twice that of the illuminating radiation.

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