| In this paper, seismic wave propagation in viscoelastic isotropic media is mainly addressed by the technology of wave field numerical simulation. Many correlative techniques are involved, including seismic viscoelasticity, seismic wave theory, finite-difference and wave field modeling. The following sections character this paper: Firstly, the viscoelasticity is involved. Theoretical fundamental, studying wave propagation in viscoelastic media which sufficiently, takes into account the viscoelastic properties of media such as creep, relaxation, viscidity, damp, anelasticity and elastic drift. Secondly, the behavior of seismic wave in viscoelastic media is discussed, which clarified the relationship among the energy variation, attenuation coefficient and frequency of seismic wave, and rationally explained the difference between theoretical data sets and observed ones rather the classical elastic theory. Thirdly, the theoretical fundamental of finite-difference is introduced, including traditional FD and multi-grid FD. Although there are many approaches to numerical simulation, finite differences are simple to program and are efficient when compared to alternatives in cases where the accuracy requirements are fairly mild. In this sense, a good choice can be an FD algorithm that is second order in time and fourth order in space. Especially, with the development and application of high-order staggered FD, we can fulfill arbitrary order FD in both time and space, enhancing the accuracy of calculation and saving time greatly. Finally, the wave field is numerically simulated for the given geological models. Then, to analyze the characters of amplitude versus frequency, frequency variation with both offset and depth, spectral analysis of the synthetic seismogram is accomplished. Seismic numerical modeling is a technique for simulating wave propagation in the earth. The objective is to predict the assumed structure of the subsurface. This technique is a valuable inversion algorithm. Another important application of seismic modeling is the evaluation and design of seismic surveys. The full-wave equation methods are adopted, namely the wave field is the solution of wave equation. Based on theory aforementioned and available publications, the wave equations are derived which suit to viscoelastic media. To perform staggered grid FD, velocity-stress formula is simplified. Furthermore, a general high-order FD expression is presented and a staggered grid FD of second order in time and fourth order in space is applied in this paper. After considering both free-surface boundary condition and fluid-solid boundary conditions, the numerical simulations of both continental and marine geological models are carried out. From the numerical simulation results, we can draw the following conclusions:(1) The absorption and attenuation are adequately taken into account in the theory of viscoelasticity, which explain the difference between theoretical data sets and observed ones, rather the classical elastic theory. (2) Staggered grid FD is an effective numerical simulation method and enjoys absolute advantage in improving the speed and accuracy of calculation. Accordingly the method of high-order staggered grid FD might have wilder perspective. (3) The technique of forward modeling reveals the behaviors of seismic wave in the complex media. The characters of seismic wave could be obtained by synthetic snapshot and seismogram, which should be helpful for seismic inversion. (4) The absorption of seismic wave in viscoelastic media could be clearly presented in the synthetic seismogram, however its concretive affection should be further studying by reflection coefficient.(5) On the issue of synthetic seismogram for marine media model, the affection of multiple is not too much when the seawater is not very deep, whereas severe. As a result, suppression of multiples still remains a very important problem in seismic exploration, especially for the marine seismic survey.(6) Attenuation of amplitude in viscoelastic media is...
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