VSP wave field separation: An optimization method based on block relaxation and singular value thresholding

In this paper, we present a high-fidelity new method for wave field separation of vertical seismic profiling (VSP) data. The method can keep the characteristics of waveform and amplitude variation along with the wave propagation. As a basic assumption, we assume that the wave field data of each event flattened regular wave is a low-rank matrix. Then, we construct an optimization equation to formulate the VSP wave field separation problem. To solve the equation, we combine block relaxation (BR) with singular value thresholding (SVT) to construct a new algorithm. We apply the method proposed in this paper to both synthetic and real data, and compare the results with that of the median filter based method, which is widely used in engineering practice. We conclude that the method proposed in this paper can offer a wave field separation with higher fidelity and higher signal to noise ratio (SNR).