3D pyramid interpolation

Abstract:

Seismic data geometries are not always as nice and regular as we want due to various acquisition constraints. In such cases, data interpolation becomes necessary. Usually high-frequency data are aliased, while low-frequency data are not, so information in low frequencies can help us interpolate aliased high-frequency data. In this paper, I present a 3D data interpolation scheme in pyramid domain, in which I use information in low-frequency data to interpolate aliased high-frequency data. This is possible since in pyramid domain, only one prediction error filter (PEF) is needed to represent any stationary event (plane-wave) across all offsets and frequencies. However, if we need to estimate both the missing data and PEF, the problem becomes nonlinear. By alternately estimating the missing data and PEF, we can linearize the problem and solve it using a conventional least-squares solver.