Interpolation with Prediction-error Filters and Training Data a Dissertation Submitted to the Department of Geophysics and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

With finite capital and logistical means, interpolation is a necessary part of seismic processing, especially for such data-dependent methods as surface-related multiple elimination. One such method is to first estimate a prediction-error filter (PEF) on a training data set, and then use that PEF to estimate missing data, where each step is a least-squares problem. This approach is useful because it can interpolate multiple simultaneous, aliased slopes, but requires regularly-sampled data. I adapt this approach to interpolate irregularly-sampled data, marine data with a large nearoffset gap, and 3D prestack marine data with many dimensions. I estimate a PEF from irregularly-sampled data in order to interpolate these data onto a regular grid. I do this by regridding the data onto multiple different grids and estimate a PEF simultaneously on all of the regridded data. I use this approach to interpolate both irregularly-sampled 3D synthetic data and 2D prestack land data using nonstationary PEFs, both with reasonable results. Marine data typically contains a near-offset gap of several traces, which can be larger when surface obstacles are present, such as offshore platforms. Most methods that depend on lower-frequency information from the data fail for these large gaps. I estimate nonstationary PEFs from pseudoprimary data, which is generated by crosscorrelating data within each shot, so that the correlation of multiples with primaries creates data at the near offsets that were not originally recorded. I use this approach in t-x-y and f -x-y, on both the Sigsbee2B 2D prestack synthetic dataset, and a 2D prestack field data set. While this method is currently unfeasible in the crossline direction in 3D marine data, the larger crossline aperture of a wide-azimuth dataset