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![]() | Seismic data interpolation using streaming prediction filter in the frequency domain | ![]() |
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With the limitation of field geometries, uniform data acquisition is rarely achieved in practice; instead, it always displays irregular or undersampled data distribution in spatial directions. However, many subsequent processing steps, such as multiple elimination and migration, are based on the prerequisite of regular data distribution. Seismic data interpolation has become a key technique in seismic data processing workflows. A failed interpolation method may create artifacts, which affect the accuracy of seismic imaging. Recently, high-density and wide-azimuth seismic acquisition can achieve large-scale field data; however, increasing computational costs and nonstationary signal recovery have posed challenges to data interpolation. Many interpolation methods have been proposed to reconstruct missing data, which are based on signal processing or seismic kinematic/dynamic principles. Low-rank methods (Gao et al., 2017,2013; Trickett et al., 2010; Chen et al., 2016) assume that seismic data are low rank in the mapping domain, and rank-reduction operators are used to recover the missing data. Plane wave decomposition (Hellman and Boyer, 2016; Fomel, 2002) reconstructs missing data by using local slope information. Compressive sensing framework with different sparse domains, e.g., Fourier transform (Wang et al., 2010a; Abma and Kabir, 2006) and seislet transform (Fomel and Liu, 2010; Gao et al., 2015; Liu and Fomel, 2010), iteratively recover the missing traces. Machine learning has become a popular research direction, and is also used for data interpolation (Jia and Ma, 2017; Kaur et al., 2019; Oliveira et al., 2018; Zhang et al., 2020; Mandelli et al., 2019). However, these methods always encounter high computational cost.
Prediction filter (PF) provide an important approach for seismic data
interpolation. Spitz (1991) proved that high-frequency components
can be estimated with the PF calculated from low-frequency components,
and an
-
interpolation method beyond aliasing was proposed.
Sacchi and Ulrych (1997) used an autoregression moving average (ARMA) model to
calculate the PF and interpolated near-offset missing gaps in the
-
domain. Porsani (1999) proposed a half-step PF to
efficiently interpolate missing data. Wang (2002) extended
different kinds of PFs in high dimensions to implement the
-
interpolation algorithm. Abma and Kabir (2005) made comparison of several PF
interpolation methods. Naghizadeh and Sacchi (2008) used an exponentially
weighted recursive least squares (EWRLS) for the adaptive PF to
interpolate data in the
-
domain. Wang et al. (2010b) created the
virtual traces from marine seismic data and utilized the matching
filter or nonstationary prediction error filter (PEF) to fill gaps.
Liu and Fomel (2011) proposed an approach to interpolate aliased data based
on adaptive PEF and regularized nonstationary autoregression (RNA) in
the
-
-
domain. Li et al. (2017) proposed multidimensional
adaptive PEF to reconstruct seismic data in the frequency domain.
Liu and Chen (2018) introduced an efficient method based on the
-
RNA
for regular and irregular missing data interpolation in the
-
domain. Liu et al. (2019) designed the multiscale and multidirectional
PEF to improve the accuracy of filter coefficients while
reconstructing seismic data.
It is difficult to balance the computational cost and the
interpolation accuracy while dealing with large-scale data in most
iterative methods. However, the framework of the streaming
computation (Fomel and Claerbout, 2016; Sacchi and Naghizadeh, 2009) can directly solve the
nonstationary autoregression problem. Liu and Li (2018) proposed an
orthogonal
-
streaming PF (SOPF) for random noise attenuation,
and Guo et al. (2020) provided an initial idea for the
-
SPF with a
1D spatial constraint and tried to efficiently eliminate seismic
random noise. Therefore, we further improved the noniterative
framework of the streaming computation in the frequency domain and
used the SPF with new frequency-domain constraints for seismic data
interpolation. The new adaptive PF can reduce the computational cost
in the interpolation problem while capturing details of nonstationary
seismic data. In this study, we first discussed the two-step
interpolation strategy for PF. With the two-step strategy, we derived
the theory of the new
-
SPF and
-
-
SPF based on the
streaming framework. The relevant interpolation algorithm and filter
design were developed to help the SPF solve the problem of the
nonstationary data reconstruction with a feasible computational
cost. Numerical examples demonstrate the effectiveness and efficiency
of the proposed methods.
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![]() | Seismic data interpolation using streaming prediction filter in the frequency domain | ![]() |
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