Inversion = migration + tomography

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 typically show that the high vertical wavenumber velocity perturbations are resolved in seismic reflection experiments where the sources and receivers are restricted to the Earth's surface but low vertical wavenumbers must be obtained using a separate step such as a velocity analysis or reflection tomography. I propose that an iterative inversion using a varying background velocity obtains all wavenumbers that are resolvable separately by migration and tomography. (The background velocity must contain abrupt discontinuities.) Reflectors in the background model simulate sources and receivers within the Earth so the source and receiver coverage in seismic reflection inverse problems is effectively the same as in medical imaging. Some synthetic examples verify the theoretical predictions and show that reflector locations and interval velocities can be obtained simultaneously.