Seismic wavefield inversion with curvelet-domain sparsity promotion

Inverting seismic wavefields lies at the heart of seismic data processing and imaging–- whether one is applying ‘‘a poor man’s inverse’’ by correlating wavefields during imaging or whether one inverts wavefields as part of a focal transform interferrometric deconvolution or as part of computing the ’data verse’. The success of these wavefield inversions depends on the stability of the inverse with respect to data imperfections such as finite aperture, bandwidth limitation, and missing data. In this paper, we show how curvelet domain sparsity promotion can be used as a suitable prior to invert seismic wavefields. Examples include, seismic data regularization with the focused curvelet-based recovery by sparsity-promoting inversion (fCRSI), which involves the inversion of the primary-wavefield operator, the prediction of multiples by inverting the adjoint of the primary operator, and finally the inversion of the data itself –- the so-called ’data inverse’. In all cases, curvelet-domain sparsity leads to a stable inversion.