Introduction

As for conventional P-wave seismic data, the simplest imaging methods for PS data produces images in the time domain. For PS data, however, even these simple methods are more complicated than their counterparts in conventional PP seismic processing.

The conventional PP-NMO processing yields an estimate of the P-wave propagation velocity. For stratified media, this estimate is known as the RMS velocity Dix (1955). In contrast, PS-NMO processing estimates two parameters that relate both the P-wave velocity and the S-wave velocity. The first parameter is the product of both velocities, i.e effective velocity ($v_{\rm eff}$). The second parameter is the ratio between the two velocities, that is the the $\gamma$ value. For the purpose of this thesis, I will define the P-to-S velocity ratio as $\gamma = v_p/v_s$.

Another imaging operator, Dip Moveout, introduces a dip-dependent correction for a more appropriate transformation of prestack data into zero-offset data, in the presence of dipping layers. Harrison (1990), Huub Den Rooijen (1991), Xu et al. (2001) discuss the DMO correction for converted-wave data. Throughout this chapter, I present a fast PS-DMO operator that is more accurate than existing PS-DMO operators. This new PS-DMO operator is implemented in the frequency-wavenumber log-stretch domain, this operator is the starting point for the partial-prestack migration operator introduced in Chapter 4.

Throughout this chapter, I present the derivation of basic PS imaging operators. For complex geological structures, basic PS imaging operators, like PS-NMO, PS-DMO and poststack time or depth migration, are not able to provide a satisfactory image of the subsurface. This chapter concludes with the prestack wave-equation depth migration as the most suitable operator to image PS seismic data.