Seismic trace interpolation in the Fourier transform domain

Abstract

A data adaptive interpolation method is designed and applied in the Fourier transform domain (f‐k or f‐kx‐ky for spatially aliased data. The method makes use of fast Fourier transforms and their cyclic properties, thereby offering a significant cost advantage over other techniques that interpolate aliased data. The algorithm designs and applies interpolation operators in the f‐k (or f‐kx‐ky domain to fill zero traces inserted in the data in the t‐x (or t‐x‐y) domain at locations where interpolated traces are needed. The interpolation operator is designed by manipulating the lower frequency components of the stretched transforms of the original data. This operator is derived assuming that it is the same operator that fills periodically zeroed traces of the original data but at the lower frequencies, and corresponds to the f‐k (or f‐kx‐ky domain version of the well‐known f‐x (or f‐x‐y) domain trace interpolators. The method is applicable to 2D and 3D data recorded sparsely in a horizontal plane. The most common prestack applications of the algorithm are common‐mid‐point domain shot interpolation, source‐receiver domain shot interpolation, and cable interpolation.

Two effective approaches to reduce data storage in reverse time migration

“…Temporal interpolation has been studied extensively for seismic records with regular or irregular time sampling interval (e.g., Larner et al, 1981;Gülünay, 2003). Here, we employ the sinc interpolation (Claerbout, 1985) to interpolate seismic traces of the time interval Δt rec to that of Δt num for numerical stability.…”

Improved POCS interpolation using a percentage thresholding strategy and excessively zero-padded FFT

“…• Using the linear, spatial prediction filters to interpolate regularly sampled seismic data (Spitz, 1991;Porsani, 1999;Wang, 2002;Gulunay, 2003;Naghizadeh and Sacchi, 2007, just to name a few).…”

Curvelet-based POCS interpolation of nonuniformly sampled seismic records

“…Wang (2002) extended f-x to a f-x-y domain, and developed two interpolation algorithms using the full-step and the fractional-step predictions. Gulunay (2003) presented his data adaptive f-k method for spatially aliased data. Recently, Naghizadeh and Sacchi (2007) gave a multistep autoregressive (MSAR) method, trying to predict all the frequencies from the low frequency part.…”