Inversion = migration + tomography

Abstract Seismic inversion, broadly enough defined, is equivalent to doing migration and reflection tomography simultaneously. Diffraction tomography and inversion work best when sources and receivers surround the region of interest, as in medical imaging applications. Theoretical studies have shown that high vertical wavenumber velocity perturbations are resolved by inverting surface seismic reflection data, but the low vertical wavenumbers must be obtained using a separate step, such as velocity analysis or reflection tomography. I propose that a nonlinear iterative inversion that updates a varying background velocity obtains all wavenumbers that are resolvable separately by migration and tomography. The background velocity must contain reflectors to provide data on both upward and downward transmission paths through the earth and hence the low wavenumbers. By considering the downward transmission paths to be between surface sources and buried image geophones and the upward transmission paths to be between surface geophones and buried image sources, the source and receiver coverage is effectively the same as in medical imaging; although the depth of the image sources and geophones must be determined in the inversion by finding the reflector depths. Synthetic examples verify the theoretical predictions and show that reflector locations and interval velocities can be obtained simultaneously even when there is no prior knowledge of reflector location. However, a good initial 'very low-wavenumber' model is normally required to ensure convergence to the global inverse solution.