Generalized diffraction tomography

Abstract

In this paper, the methodology of generalized diffraction tomography is presented in detail. The generalized diffraction tomography is a process of backpropagation plus deconvolution filtering using the resolving kernel in the scattering tomography in the local wavenumber domain. We use forward scattering renormalized Green's function in the model and the forward modeling is based on the De Wolf approximation. Through numerical tests of data sets generated using both the Born approximation and the finite-difference simulations of scalar wave for low frequencies using background velocity model of v(z) media, the blind areas in the spectra domain are partially filled in with multi-frequency spectra and the qualities of the local spectra are considerably improved in both coverage and uniformity in the local wavenumber domain. Numerical tests demonstrate the capability of generalized diffraction tomography, it can recover the long wavelength components of velocity perturbations of up to 23% with respect to the background velocity in a simple square box model, and it can also reconstruct the Marmousi velocity model with low wavenumber component very well comparing the multi-scale representation of the exact Marmousi velocity model with those of the reconstruction results generated using different background velocity models.