Multidimensional seismic data reconstruction has emerged as a primary topic of research in the field of seismic data processing. Although there exists a large number of algorithms for multidimensional seismic data reconstruction, they often adopt the [Formula: see text] norm to measure the discrepancy between observed and reconstructed data. Strictly speaking, these algorithms assume well-behaved noise that ideally follows a Gaussian distribution. When erratic noise contaminates the seismic traces, a 5D reconstruction must adopt a robust criterion to measure the difference between observed and reconstructed data. We develop a new formulation to the parallel matrix factorization tensor completion method and adapt it for coping with erratic noise. We use synthetic and field-data examples to examine our robust reconstruction technique.

The Multichannel Singular Spectrum Analysis (MSSA) reconstruction algorithm denoises and reconstructs seismic traces on a regular grid. We present a modified version of MSSA that can cope with denoising and reconstruction of traces with irregular coordinates. The proposed method, Interpolated Multichannel Singular Spectrum Analysis (I-MSSA), connects off-the-grid observations to the desired gridded data via a non-invertible bilinear interpolation operator. The algorithm consists of two steps. In the first step, we use the steepest descent method to estimate the gridded data that honors off-the-grid observations. The second step guarantees convergence to a solution by applying the MSSA filter to the gridded data. The final solution is the reconstructed volume that honors off-the-grid observations. We apply the algorithm to synthetic and field data. We also provide an application where 3D prestack data corresponding to an orthogonal survey is fully reconstructed using cross-spread gathers. We use I-MSSA to reconstruct each subset individually. The output is a complete seismic volume described in a regular CMP grid.

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Iterative rank-reduction implemented via Multichannel Singular Spectrum Analysis (MSSA) filtering has been proposed for data deblending. The original algorithm is based on the projected gradient descent method with a projection given by the MSSA filter. Unfortunately, MSSA filters operate on data deployed on a regular grid. We propose to adopt a recently proposed modification to MSSA, Interpolated-MSSA (I-MSSA), to deblend and reconstruct sources in situations where the acquired blended data correspond to sources with arbitrary irregular-grid coordinates. In essence, we propose an iterative rank-reduction deblending method that can honor true source coordinates. In addition, we show how the technique can also be used for source regularization and interpolation. We compare the proposed algorithm with traditional iterative rank reduction that adopts a regular source grid and ignores errors associated with allocating off-the-grid source coordinates to the desired output grid. Synthetic and field data examples show how the proposed method can deblend and reconstruct sources simultaneously.

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