Creating high-fidelity images – a convolution approach to gridding airborne data using a SINC kernel

Abstract

Airborne geophysical data sampled at a constant time-interval along lines and with a nominal spatial-separation across lines are quasi-periodic and are therefore amenable to interpolation onto a regular grid by convolving the original line data with a 2D SINC kernel. This method has advantages over commonly used minimum curvature or bidirectional gridding algorithms because it better maintains the spatial fidelity of the original data as per the sampling theorem. Unlike splines, the SINC function does not suffer from over- interpolation, although ringing can be problematic. Lastly, the smooth SINC kernel places no lower bound on cell sizes, except computation time. The method first uses a 1D SINC interpolation to resample the along-line data. An SVD matrix inversion is then used to move each line from its true to its nominal location before interpolating the inter-line areas of the grid with the 2D kernel. Ringing and aliasing are mitigated by employing a window function to dampen the effects of the ideal RECT function in the wavenumber domain. Through judicious selection of the along- and across-line maximum wavenumbers, the SINC kernel can improve the continuity of lineaments trending obliquelyto the flight lines.