An Iterative Zero-Offset VSP Wavefield Separating Method Based on the Error Analysis of SVD Filtering

Wavefield separation is one critical step in the vertical seismic profiling (VSP) data processing. In this letter, we present an iterative zero-offset VSP wavefield separating method based on analyzing the error of the singular value decomposition (SVD) low-pass filtering. The error of the SVD low-pass filtering can be divided into the incomplete error and the truncated error. The incomplete error is caused by the incompleteness of subspace, while the truncated error is related to discarding small singular values and corresponding eigenimages. Flattening the strongly correlated component in the 2-D signal can reduce these two errors, and the flattened component can be extracted precisely with the SVD low-pass filtering. The zero-offset VSP data set in seismic data processing records downgoing and upgoing wavefields, which have different propagating directions. By flattening the downgoing and upgoing wavefields alternatively, we propose one iterative zero-offset VSP wavefield separating method. In each iteration, we first flatten the downgoing wavefield to increase its correlation and estimate the downgoing wavefield by using the SVD low-pass filtering, and then, we flatten the upgoing wavefield in the residual to increase its correlation and estimate the upgoing wavefield by using the SVD low-pass filtering. The proposed method is applied to one synthetic data set and one real zero-offset VSP data set. Compared with the commonly used wavefield separation method, our method can have better separation results and reduce the separation error.