We consider the algorithm of true linearized inversion of the complete set of seismograms recorded for all shots during seismic reflection survey, based on the correspondence between the structural Gabor functions and the corresponding scattered Gaussian packets. The first step of this linearized inversion consists in specifying the finite set of structural Gabor functions to which the wanted deviations of the material parameters from the given velocity model will be decomposed. If possible, the shape of the Gabor functions should be optimized, and the Gabor functions should form a frame. We present a simple attempt to specify the finite set of structural Gabor functions for this inversion.
The shape of the Gabor functions and the space-wavenumber lattice of their central points are optimized analytically, but for a homogeneous velocity model only. The derived set of structural Gabor functions may be applied also to slightly heterogeneous models in which the shape of Gabor functions is not optimum but is still probably better than the shape of Gabor functions specified by chance. The envelopes of the structural Gabor functions are chosen isotropic, but are allowed to be complex-valued. The shape of Gabor functions is optimized for a zero-offset surface seismic reflection survey only, but is close to optimum for a narrow-offset surface seismic reflection survey.
Gabor function, Gabor transform, frame bounds, discretization error, phase-space metric tensor, elastic waves, Gaussian packets, wavefield inversion.
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