Sensitivity of seismic waves to structure: Wide-angle broad-band sensitivity packets

Ludek Klimes


We continue in studying how the perturbations of a generally heterogeneous isotropic or anisotropic structure manifest themselves in the wavefield, and which perturbations can be detected within a limited aperture and a limited frequency band. Infinitesimally small perturbations of elastic moduli and density are decomposed into Gabor functions. The wavefield, scattered by the perturbations, is then composed of waves scattered by the individual Gabor functions. The scattered waves are estimated using the first-order Born approximation with the paraxial ray approximation.

For each incident wave, each Gabor function generates at the most 5 scattered waves, propagating in specific directions and having specific polarizations. We refer to these scattered waves in the frequency domain as the sensitivity beams, and in the time domain as the sensitivity packets. The sensitivity packets are mostly represented by narrow-band Gaussian sensitivity packets studied in the previous paper, but may also be represented by a broad-band S to P (and even S to S in a strongly anisotropic background) converted wave scattered in a wide angle, or by a broad-band unconverted wave scattered in a forward or narrow-angle direction. In this paper, we concentrate on broad-band sensitivity packets scattered in wide angles. We still do not know to what extent our results may be applicable to a broad-band unconverted wave scattered in a forward or narrow-angle direction.

For a particular source, each sensitivity packet, scattered by a Gabor function at a given spatial location, is sensitive to a single linear combination of 22 values of the elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered wave does not fall into the aperture covered by the receivers and into the legible frequency band.


Elastic waves, elastic moduli, perturbation, Born approximation, paraxial ray approximation, wavefield inversion, seismic anisotropy, heterogeneous media.

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In: Seismic Waves in Complex 3-D Structures, Report 23, pp. 17-44, Dep. Geophys., Charles Univ., Prague, 2013.