Sensitivity of seismic waves to the structure

Summary

We study 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. A short-duration broad-band incident wavefield with a smooth frequency spectrum is considered. 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 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 most 5 scattered waves, propagating in specific directions. A Gabor function corresponding to a low wavenumber may generate a single broad-band unconverted wave scattered in forward or narrow-angle directions. A Gabor function corresponding to a high wavenumber usually generates 0 to 5 narrow-band Gaussian packets scattered in wide angles, but may also occasionally generate a narrow-band P to S or S to P converted Gaussian packet scattered in a forward direction, or a broad-band S to P (and even S to S in a strongly anisotropic background) converted wave scattered in wide angles.

For a particular source, each wave scattered by a Gabor function at a given spatial location is sensitive to just 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.

The derived approximate solution of the forward scattering problem may be utilized in designing the migration algorithm based on true linearized inversion of the complete set of seismograms recorded for all shots.

Keywords

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

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Revised version

Klimes, L.: Sensitivity of seismic waves to structure. Stud. geophys. geod., 56 (2012), 483-520.

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