An analytical solution to separate P‐waves and S‐waves in VSP wavefields

Abstract

An analytical solution to separate P‐waves and S‐waves in vertical seismic profile (VSP) wavefields is derived using combinations of certain terms of the formal solution for forward VSP modeling. Some practical applications of this method to synthetic seismograms and field data are investigated and evaluated. Little wave distortion is recognized, and the weak wavefield masked by dominant wavetrains can be extracted with this method. The decomposed wavefield is expressed in the frequency‐depth (f-z) domain as a linear combination of up to the third‐order differential of traces, which is approximated by trace differences in the practical separation process. In general, five traces with single‐component data are required in this process, but the same process is implemented with only three traces in the acoustic case. Two‐trace extrapolation is applied to each edge of the data gather to enhance the accuracy of trace difference. Since the formulas are developed in the f-z domain, the influence of anelasticity can be taken into account, and the calculation is carried out fast enough with the benefit of the fast Fourier transform (FFT).