Seismic Data Processing and Reconstruction without Fourier Phase Information

The most advanced seismic data processing/imaging algorithms fail to achieve an acceptable result when there are strong phase errors in the observations. To remedy this deficiency, I replace the time domain misfit term in such algorithms by a Fourier magnitude fidelity term in order to recover the desired signal from just the amplitude spectrum of the observed wavefield. The generated problem is used to tackle two common phase problems arising in seismic processing: data recovery in the presence of residual static shifts and deconvolution with missing wavelet phase. The primary applications of interest are interpolation and deconvolution. It is shown that under appropriate constraints, both problems can be solved accurately using just the amplitude spectrum of the observed data. Numerical experiments show that in both cases the proposed phase retrieval algorithm is able to obtain significantly better results than similar method that work in the time domain