Seismic Wave Propagation And Imaging Using Time-space Wavelets

Using a tensor product of a local exponential frame vector as the time-frequency atom (a drumbeat) and a local cosine basis function as the space-wavenumber atom (a beamlet), we construct a localized ( t ω − , x ξ − ) atom (a drumbeatbeamlet). The imaging condition in the local t ω − domain is introduced and the propagator matrix in the local ( t ω − , x ξ − ) domain is derived. The compression of seismic data using the new decomposition is tested and simple numerical tests on the propagator matrix are performed. The sparseness in both data and propagator decompositions is demonstrated through these examples. The method has potential application in efficient representation of seismic data and wave-theory based seismic imaging using compressed data.