Migration operator compression by wavelet transform: Beamlet migrator

Summary We study one-way wave propagation in the frequency- wavelet domain (frequency-beamlet domain) for dif- ferent wavelet bases, and compare their performances for migration/imaging. We show that the Kirchhoff operator in space domain is a dense matrix, while the compressed beamlet-propagator matrix which is the wavelet decomposition of the Kirchhoff opera- tor (or other one-way wave propagators), is a highly sparse matrix. For sharp and short bases, such as the Daubechies 4 (D4), both the 'interscale and in- trascale coupling are strong. However, the interscale coupling is relatively weak for smooth bases, such as higher-order Daubechies wavelets, Coiflets, and spline wavelets. The images obtained by the compressed beamlet operator are almost identical to the images from a full-aperture Kirchhoff migration. Compared with the limited aperture Kirchhoff migration, beam- let migration can obtain much wider effective aper- tures, hense higer resolution and image quality, with similar computational efficiency. The compression ra- tio of the migrator ranges from a few times to a few hundred times, depending on the frequency, step length and the wavelet basis. Combining with the data (wavefield) compression, even greater efficiency can be expected.