Bi-dimensional Fourier transform with irregular spatial sampling

Seismic data acquisition is frequently carried out at irregular sampling intervals along spatial coordinates. This causes problems in the subsequent multi-trace data processing which often requires equi-spaced traces and thus the data must be first regularised. To this end, we illustrate a frequency domain method to transform 2D data irregularly sampled in the spatial direction to equivalent equi-spaced data. We follow a probabilistic inversion where the a-posteriori model is the desired (correct and noise free) frequency spectrum, the a-priori model is computed through the Non Uniform Discrete Fourier Transform (also known as Riemann sum) and the noise introduced by the irregular sampling is described empirically, on the basis of the distances between samples. All the variables are assumed to have Gaussian distributions and are described by their means and covariances. Once the optimum frequency spectrum is estimated, a Fourier anti-transform brings the data back into the time-space at constant spatial intervals. The proposed method is applied to synthetic and real seismic data, with various degrees of sampling irregularities and offset gaps, and with different noise contaminations and dips of events. The results are satisfactory and are improved with respect to those obtained by applying a previously developed method.