Summary
The real Earth medium has viscoelastic property, so it is necessary to take absorption and attenuation effects into consideration in full-waveform inversion. In this paper, according to the viscoelastic wave equation based on generalized standard linear solid (GSLS) model, the firstorder velocity-stress visco-acoustic wave equation is obtained. Based on this wave equation, the P-wave velocity gradient expression is derived, and then based on conjugate gradient method, the 2D time-domain visco-acoustic full waveform inversion method is implemented. Model test results demonstrate the effectiveness of this method, and compared with the inverted P-wave model without considering absorption and attenuation effects, the inverted P-wave velocity model is much more accurate using the visco-acoustic full waveform inversion method in this paper.
Introduction
Though the Earth medium is elastic in most research and application, the real Earth medium has viscoelastic property, which will affect amplitudes, phases and other characteristics of seismic waves, especially when seismic waves propagate in the near surface strong attenuation layers or gas bearing areas (Liu et al, 1976; Robertsson et al, 1994). If the absorption and attenuation effects of Earth medium are not considered, there will be great difference between synthetic data and observed data, and this will further lead to inaccurate inversion results in full waveform inversion (Bai et al, 2012). So it is necessary to considerate the absorption and attenuation effects in full waveform inversion.
Through viscoelastic medium attenuation mechanism research, different viscoelastic models are proposed by many scholars (Emmerich et al, 1987; Schiessel et al, 1995; Jiang et al, 1995), and scholars have shown that in seismic frequency range, the Earth medium presents a nearly constant Q property (Liu et al, 1976), and this property can be described well using generalized standard linear solid (GSLS) model (Blanch et al, 1995). By use of the secondorder visco-acoustic wave equation based on GSLS model constituted by only one Maxwell body, Bai et al (2014) carried out visco-acoustic full waveform inversion on synthetic data and field data successfully.
In this paper, in order to better describe the nearly constant Q property in seismic frequency range, the first-order velocity-stress visco-acoustic wave equation based on generalized standard linear solid model constituted by several Maxwell bodies is used, and the corresponding P-wave velocity gradient expression is derived, and then, by use of conjugate gradient method and high-order staggered grid finite-difference method, the 2D time-domain viscoacoustic full waveform inversion method is realized. Note that, unlike the second-order equation used by Bai et al (2014), the first-order velocity-stress equation is more convenient to apply staggered grid finite-difference method.
