Interpolation is a simple example of a geophysical inverse problem (Claerbout, 2014). The two prerequisites for local plane-wave interpolation are simply the sparse data which are to be interpolated and the structure to which the interpolation data is shaped. In the following examples, we start with a seismic image and find the image's local slope. A mask is applied to the image, leaving behind only a few nonzero traces. Following Clapp et al. (1998,2004), we call these traces ``wells" as a reference to the applicability of this method to well log data which may be desired everywhere but only provided in certain locations. Thus, the two inputs are the wells (to be interpolated) and the dip field (giving the direction of interpolation). In this way, structural information can be well-preserved. By comparing the reconstruction to the original (non-sparse) data, we can quantify the quality of the interpolation by measuring the model error.
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