Decomposition of P and S waves in a vector seismic wavefield using dispersion relationship

We acquire total elastic wavefield using multi-component geophone. Since the acquisition of both P and S wave characteristics yields better insights into subsurface rock properties than of only P wave, multi- component data acquisition is of importance in seismic exploration. It is, however, often assumed in multi- component processing that the vertical and the horizontal radial components contain only P and P-SV wave arrivals, respectively. This assumption may actually be violated with increasing offset due to later phase arrivals. The recognition of P and S arrivals would be of importance to process multi-component seismic data, but not so many trials have been conducted except in vertical seismic profiling (VSP).wavefield Some methods for the wavefield separation have been proposed. Devaney and Oristaglio (1986) proposed a two-dimensional method for separating VSP data using dispersion relationship. Al-anboori, et al. (2005) proposed an approximate wavefield separation scheme based on a data rotation in the "Ñ-p domain and applied to two-dimensional reflection seismic wavefield. Tokunaga, et al.(2006) applied the method of Devaney and Oristaglio (1986) to surface reflection seismic data and introduced a method to accommodate three dimentional decomposition of tri-component geophone data acquired in a single line. None of the above method, obviously, could perform the decomposition of three dimentional seismic data. The methodology to decompose a vector seismicwavefield needs to be developed for future seismic exploration. We describe two methods to separate a three-dimensional elastic wavefield recorded at three-component receivers into P, SV, and SH waves. One is a method to separate wavefield into each wave in F-K domain, and the other in "Ñ-p domain. Both of the separating methods are based on a plane-wave decomposition of elastic wavefields using the dispersion relationship. The separation scheme is based on a simple rotation or polarization of data recorded in the Cartesian coordinates to ray coordinates using the incidence angle of arriving waves. Such a rotation is not easily implemented in the x-t domain because each trace contains multiple arrivals with time varying incidence angles. For the sake of applying the above-mentioned polarization, we applied the Fourier and "Ñ-p transforms to synthetic data, respectively. It becomes simpler after the transform into F-K or "Ñ-p domain to determine the incidence angle of the arriving waves. In the F-K domain, observed wavefield is a function of horizontal wave numbers, kx and ky, and the frequency f. Likewise, observed wavefield becomes a function of the horizontal slownesses, px and py, and time t in "Ñ-p domain. We determine the incidence angle of each arriving wave using the dispersion relationship, which define the relation between the wave numbers, frequency, and the phase velocity of the wave in the F-K domain, or apparent slownesses and the phase velocity of the waves in the "Ñ-p domain. These methods require only both P and S phase velocities in the vicinity of geophones. In our study, we apply these two methods to three-dimensional synthetic data created by finite difference method. After these processing, we confirmed that both of the methods could decompose elastic wavefield into each of P, SV, and SH waves. Our results demonstrates that these two methods yield significantly higher S/N ratio and help us to analyze the S wave characteristics. We think that both of these methods would be of fundamental and powerful processing tools for multi-component seismic exploration.