Qingqing Li

Q-compensated migration by Gaussian beam summation method

Migration by the Gaussian beam summation method (MGBSM) combines the high efficiency and flexibility of Gaussian beam migration with the high accuracy of wave equation reverse-time migration, which can overcome the problems of caustics, handle all arrivals, yield good images of steep flanks, and is readily extendible to target-oriented implementation. The viscoacoustic prestack migration is of practical significance because it considers the viscosity of subsurface media. In this paper, we propose a MGBSM to perform seismic data compensation for frequency dependent absorption and dispersion. First, we derive the expressions for the attenuation equation and analyse the precision of the viscoacoustic Green function based on Gaussian beams. Then, the principle and procedure of compensation is presented. Finally we propose Q-compensated MGBSM. Numerical examples indicate that Q-compensated MGBSM has a higher imaging resolution than acoustic MGBSM when the viscosity of the subsurface is considered.

Modelling viscoacoustic wave propagation with the lattice Boltzmann method

In this paper, the lattice Boltzmann method (LBM) is employed to simulate wave propagation in viscous media. LBM is a kind of microscopic method for modelling waves through tracking the evolution states of a large number of discrete particles. By choosing different relaxation times in LBM experiments and using spectrum ratio method, we can reveal the relationship between the quality factor Q and the parameter τ in LBM. A two-dimensional (2D) homogeneous model and a two-layered model are tested in the numerical experiments, and the LBM results are compared against the reference solution of the viscoacoustic equations based on the Kelvin-Voigt model calculated by finite difference method (FDM). The wavefields and amplitude spectra obtained by LBM coincide with those by FDM, which demonstrates the capability of the LBM with one relaxation time. The new scheme is relatively simple and efficient to implement compared with the traditional lattice methods. In addition, through a mass of experiments, we find that the relaxation time of LBM has a quantitative relationship with Q. Such a novel scheme offers an alternative forward modelling kernel for seismic inversion and a new model to describe the underground media.