Accelerated seismic interpolation of measured data collected by a set of geophones arranged in an irregularly spaced grid

A system comprising:

• a processor configured to:
• receive seismic data measured by tomographic scanning using a transmitter emitting a series of incident waves that reflect at geological discontinuities throughout the subsurface geology of the Earth and collected by a set of geophones arranged in an irregularly spaced grid recording reflections of those waves in the subsurface geology of the Earth;
• transform the collected seismic data by a Radon transform from a spatial domain to a transform domain in which the seismic data is represented by an initial combination of multidimensional Radon basis functions,
• pre-compute a set of basis function correlation factors, which represent the temporal frequency dependent spectral leakage patterns between the multidimensional Radon transform basis functions, prior to computing an anti-leakage Radon transform of the seismic data by:
• dividing the transformed seismic data into a plurality of temporal frequency slices, and
• geometrically scaling a spatial geometry of each temporal frequency slice independently by a temporal frequency of the temporal frequency slice,
• compute the anti-leakage Radon transform of the seismic data by:
• iteratively progressing slice-by-slice, vertically through the geometrically scaled seismic data, to compute each jth Radon coefficient independently for each temporal frequency slice using the pre-computed basis function correlation factors, and
• repeating said iteratively progressing for each subsequent j+1th coefficient until a relative error between the collected seismic data and an approximation of the collected seismic data based on the Radon coefficients is less than a predetermined convergence threshold,
• wherein the Radon coefficients are computed solely in the transform domain based on the pre-computed basis function correlation factors, without reverse transforming to the spatial domain, and
• simulate seismic data collected in a regularly spaced grid by interpolating the anti-leakage Radon transform of the seismic data collected by the set of geophones arranged in the irregularly spaced grid;
• and
• a monitor, wherein the processor is configured to display an image of the simulated seismic data on the monitor.