Elastic wave pre-stack reverse-time migration based on the second-order P- and S-wave decoupling equation

Abstract

Abstract The problems of large computation, large storage and low-frequency noises have been the key factors limiting the development of elastic wave pre-stack reverse-time migration (RTM). Most research has centered on the wave equation of first-order velocity stress and using Helmholtz separation to get pure primary and secondary waves. However, the cost is enormous and the amplitude and phase of wavefields will be changed. So, we use the second-order P- and S-wave decoupling equations to construct seismic wavefields that reduce the number of variables, and the storage space required for boundary wavefields is reduced by ∼78%. Then we bring the boundary-saving approach into our study during the wavefield extrapolation process so that we can reconstruct the source wavefields completely. Finally, for the wave equations of second-order displacement used in this study, the Poynting vector expressed by the traditional method was not applicable. Therefore, we derived the formula of the energy flux density vector represented by displacements and used it in directional traveling wave decomposition to suppress low-frequency noise in the imaging profile. Subsequently, based on the inner product imaging conditions, the RTM of the 2-D salt dome model was calculated. The results illustrate the effectiveness and practicability of the proposed solution.