Resolution limits for wave equation imaging

Abstract

Formulas are derived for the resolution limits of migration-data kernels associated with diving waves, primary reflections, diffractions, and multiple reflections. They are applicable to images formed by reverse time migration (RTM), least squares migration (LSM), and full waveform inversion (FWI), and suggest a multiscale approach to iterative FWI based on multiscale physics. That is, at the early stages of the inversion, events that only generate low-wavenumber resolution should be emphasized relative to the high-wavenumber resolution events. As the iterations proceed, the higher-resolution events should be emphasized. The formulas also suggest that inverting multiples can provide some low- and intermediate-wavenumber components of the velocity model not available in the primaries. Finally, diffractions can provide twice or better the resolution than specular reflections for comparable depths of the reflector and diffractor. The width of the diffraction-transmission wavepath is approximately λ at the diffractor location for the diffraction-transmission wavepath. © 2014 Elsevier B.V.