Bandwidth Support Map for Non-uniform Spatial Sampling of Geophysical Data

We introduce a novel technique for creating maps of bandwidth supported locally by non-uniform sampling schemes of geophysical data. The input data required are solely the coordinates of the actual sampling locations. The term “bandwidth supported locally by non-uniform sampling” refers here to the maximum bandwidth of data with a flat amplitude spectrum that could be reconstructed by an optimum “sinc-function” like linear operator at arbitrary sampling locations within the survey area without unacceptable high reconstruction error. Our technique creates individual maximum wavenumber estimators for selected locations, such that two-dimensional data can be reconstructed at non-sampling locations as long as the square root of the product of the two maximum spatial wavenumbers of the data is below the computed wavenumber estimator. For higher n-dimensional sampling, this extends to a wavenumber support estimator as the nth root of the product of the n maximum wavenumbers of the data. We outline how these maps can be computed from the local average of the size of cells designated to each sampling point, and give an example of a two-dimensional bandwidth support map for the midpoint locations of a part of a land seismic cross spread.