Sensitivity Gaussian packets

Abstract

Perturbations of elastic moduli and density can be decomposed into Gabor functions. The wave field scattered by the perturbations is then composed of waves scattered by the individual Gabor functions. The scattered waves can be estimated using the first-order Born approximation with the paraxial ray approximation. For a particular source generating a short-duration broad-band incident wave field with a smooth frequency spectrum, each Gabor function generates at most a few scattered sensitivity Gaussian packets propagating in determined directions. Each of these scattered Gaussian packets is sensitive to just a single linear combination of the perturbations of elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered sensitivity Gaussian packet does not fall into the aperture covered by the receivers and into the recording frequency band. We illustrate this loss of information using the difference between the 2-D Marmousi model and the corresponding smooth velocity model. We decompose the difference into Gabor functions. For each of the 240 point shots, we consider 96 receivers. For each shot and each Gabor function, we trace the central ray of each sensitivity Gaussian packet. If a sensitivity Gaussian packet arrives to the receiver array within the recording time interval and frequency band, the recorded wave field contains information on the corresponding Gabor function. We then decompose the difference into the part influencing some recorded seismograms, and the part on which we recorded no information and which thus cannot be recovered from the reflection experiment.