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![]() | An algorithm for interpolation using Ronen's pyramid | ![]() |
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A Prediction Error Filter (PEF) is good at characterizing a 1-D spectrum. A short simple PEF will easily model a narrow bandwidth, a broad one, or a combination -- whatever fits. Unfortunately, the spectrum characterized by a PEF is a temporal spectrum or a spatial spectrum, when in practice it is more generally the dip spectrum that we seek a good representation for.
Although the helix transform brings us the power of PEFs to 2-D and 3-D data it does not directly offer us exactly what often seek, a dip spectrum. Shuki Ronen's pyramid transform does. It brings PEF power from time and space axes to the dip axis.
First we review Ronen's principles noticing that raw data traces are moved to radial traces on a new grid. The 1-D PEF must be found on this new grid. But the new grid has empty spaces (missing data) between the known radial traces. Thus we approach the problem as one of nonlinear least squares which we propose to solve by iterative linear least squares.
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![]() | An algorithm for interpolation using Ronen's pyramid | ![]() |
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