Seismic data interpolation using frequency‐domain complex nonstationary autoregression

Abstract

We have developed a novel method for missing seismic data interpolation using f‐x‐domain regularised nonstationary autoregression. f‐x regularised nonstationary autoregression interpolation can deal with the events that have space‐varying dips. We assume that the coefficients of f‐x regularised nonstationary autoregression are smoothly varying along the space axis. This method includes two steps: the estimation of the coefficients and the interpolation of missing traces using estimated coefficients. We estimate the f‐x regularised nonstationary autoregression coefficients for the completed data using weighted nonstationary autoregression equations with smoothing constraints. For regularly missing data, similar to Spitz f‐x interpolation, we use autoregression coefficients estimated from low‐frequency components without aliasing to obtain autoregression coefficients of high‐frequency components with aliasing. For irregularly missing or gapped data, we use known traces to establish nonstationary autoregression equations with regularisation to estimate the f‐x autoregression coefficients of the complete data. We implement the algorithm by iterated scheme using a frequency‐domain conjugate gradient method with shaping regularisation. The proposed method improves the calculation efficiency by applying shaping regularisation and implementation in the frequency domain. The applicability and effectiveness of the proposed method are examined by synthetic and field data examples.

EWR‐Net: Earthquake Waveform Regularization Network for Irregular Station Data Based on Deep Generative Model and ResNet

“…Although this type of method has a good anti‐aliasing performance, its limitations include its inability to effectively deal with irregular seismic data. Liu and Chen (2018) proposed a regular/irregular seismic data regularization method using f ‐ x domain‐regularized nonstationary autoregression (RNA). By improving the smoothness of the adjacent local prediction filter coefficient, RNA can achieve excellent results even with irregular data.…”

Oriented extrapolation of common‐midpoint gathers in the absence of near‐offset data using predictive painting

“…Chen et al ., 2014) developed based on shaping operators in different transformations such as Fourier transform. Another type of signal‐processing reconstruction method is based on data prediction in frequency–wavenumber ( f–k ) domain (Gülünay, 2003; Liu & Sacchi, 2004; Xu et al ., 2005) and in frequency–space ( f–x ) domain (Spitz, 1991; Porsani, 1999; Trickett, 2003; Naghizadeh & Sacchi, 2007; Liu & Chen, 2018).…”