Dealiased Seismic Data Interpolation Using Seislet Transform With Low-Frequency Constraint

Abstract

Interpolating regularly missing traces in seismic data is thought to be much harder than interpolating irregularly missing seismic traces, because many sparsity-based approaches cannot be used due to the strong aliasing noise in the sparse domain. We propose to use the seislet transform to perform a sparsity-based approach to interpolate highly undersampled seismic data based on the classic projection onto convex sets (POCS) framework. Many numerical tests show that the local slope is the main factor that will affect the sparsity and antialiasing ability of seislet transform. By low-pass filtering the undersampled seismic data with a very low bound frequency, we can get a precise dip estimation, which will make the seislet transform capable for interpolating the aliased seismic data. In order to prepare the optimum local slope during iterations, we update the slope field every several iterations. We also use a percentile thresholding approach to better control the reconstruction performance. Both synthetic and field examples show better performance using the proposed approach than the traditional prediction based and the $F\mbox{--}K$ -based POCS approaches.