Wavelet-Radon Domain De-aliasing And Interpolation of Seismic Data

Spatial aliasing is common in much seismic data and may have serious effects on the performance of multichannel data processing and migration. We develop a Multiscale Wavelet-Radon Algorithm (MWRA) for separating spatially aliased energy and unaliased signal where they are superimposed up to the Nyquist frequency or wavenumber. We assume that the signal is consistently located in time across wavelet scales. A seismic gather is first decomposed into different wavelet scales by translation-invariant wavelet transform (TIWT) decomposition over the time coordinate of each trace. A Radon decomposition is then performed for the traces at each wavelet scale. At the (slowness dependent) aliased scales, the locations of the wavelet coefficients related to the signals are approximated from those in an adjacent unaliased scale. The corresponding amplitudes are estimated from the current aliased scale via a weighting function and the amplitudes (overlapped in time) from the unaliased scales. This procedure can be recursively applied to estimate signals at the higher frequencies. For each slowness, a reconstruction of unaliased and aliased scales is performed to give a broadband signal reconstruction. Interpolation of the aliased seismic data is performed by redefining the spatial sampling rate in the Radon reconstruction. MWRA slightly outperforms F-X interpolations in suppressing aliasing and noise in aliased curved events, as shown in synthetic model. MWRA easily accommodates data with an irregular geophone spacing, unlike F-X interpolation.