Seismic Data Regularization with the Anti-Alias Anti-Leakage Fourier Transform

The anti-leakage Fourier transform (ALFT) is a regularization method using an iterative procedure for computing the spectrum of irregularly sampled data. For each iteration a discrete Fourier transform is performed. Then, the maximum Fourier component is selected and transformed back to the irregular grid. The component is subtracted from the input data, and
the result is used in the next iteration. For irregularly sampled data, the ALFT can handle very steep dips, but for regularly sampled data, the aliased Fourier components of a certain event have the same amplitude as the true component. Consequently, the aliased components may be estimated, and the event is not properly reconstructed. In practice, results can also be degraded for situations where the sampling is close to regular. In this article, we show the results of using the un-aliased lower frequencies to provide spectral weights for the higher frequencies. This helps to avoid selection of the aliased component. It is shown on 2D synthetic and 3D field data that the method can give a significant improvement for data with steeply dipping events.