Abstract: FX and FK Interpolation Methods and Further Developments for Irregularly Spaced Traces; #90211 (2015)

FX and FK interpolation methods are compared and their advantages and shortcomings arediscussed. Auto-regressive (AR) modeling is the basic idea behind FX interpolation methods(Spitz, 1991; Porsani, 1999). In this case, the underlying model for data reconstruction is a modelwhere a few plane waves are considered within the data aperture. In a similar manner, FKinterpolation methods (Gulunay, 2003) also assume that the data are composed of a few planewaves. In both cases, processing small apertures is required to validate the assumptions on whichthese methods were built on. Regardless of the aforementioned shortcomings, these methodsprovide a robust way of interpolating aliased data. It is desirable, however, to extend these ideasto the irregular sampling case. This problem can be tackled with an AR formulation for continuousprocesses (Larsson and Torsten, 2002). The performance of the irregular AR trace interpolationdepends on the following parameters a) the number of missing traces b) the size of the biggestand smallest gaps c) the location of the gaps inside the data aperture d) the dip of events.Statistically, it is quite important to have a well-sampled distribution of distances between tracesand to have enough data to obtain an unbiased estimator of the prediction filter components forthe irregularly sampled data. ReferencesGulunay, N. (2003). Seismic trace interpolation in the fourier transform domain. Geophysics 68(1), 355–369.Larsson, E. and S. Torsten (2002). Identification of continuous-time AR processes from unevenlysampled data. Automatica 38, 709–718.Porsani, M. (1999). Seismic trace interpolation using half-step prediction filters. Geophysics 64(5), 1461–1467.Spitz, S. (1991). Seismic trace interpolation in the f-x domain. Geophysics 56 (6), 785–796.Datapages/Search and Discovery Article #90211 CSPG© 2015 CSPG/CSEG/CWLS Convention 2006, What’s New? Where is Our Industry Heading? Calgary, AB, Canada, May 15-18, 2006