Interpolated Multichannel Singular Spectrum Analysis (I-MSSA): a reconstruction method that honors true trace coordinates
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.