Study On Globally Convergent Method For Seismic Waveform Inversion On Viscoelastic Wave Equation

In recent years, energy demand for human is increasing greatly, however,conventional energy sources, such as oil and natural gas, are becoming less and less.Furthermore, the exploration difficulty become harder and harder, the shortage ofenergy has been a big obstacle of the economic development. Seismic waveforminversion is an important technique of the geological exploration. Hence there willbe a wide application background and hugely potential economic value by carryingout the research of seismic waveform inversion theory. Developing an efficient andreliable waveform inversion algorithm is of great practical and theoreticalsignificance.In this paper, we first introduce the research background and the currentsituation of waveform inversion method. Because the existing models have theirapplication limitation, starting from the constitutive equation of the Kelvinviscoelastic medium and using the relationship between the viscoelastic medium andideal elastic medium, the wave equations in the Kelvin medium are derived. Likedealing with the elastic wave equation propagating in the perfect elastic medium andaccording to the fact that the longitudinal wave is an irrotational field and thetransverse wave is a nondivergent field, this paper gives different forms of thelongitudinal wave and transverse wave in the viscoelastic medium. Then we choosethe volume strain coefficient equation and do approximation on the model, by usingthe priori information of longitudinal wave velocity and coefficient of viscosity. Thefundamental theory and specific form of the globally convergent method areprovided.Basing on these facts, the absorbing boundary conditions are introduced and wealso give the specific differential forms of these conditions in the paper. Then weuse the finite difference method to discrete the forward model. In the forwardmodeling, some wave field snapshots are provided, and we also compare thediffenent numerical results between the Dirchelet boundary conditions andabsorbing boundary conditions. From the numerical results of the forward modeling,we can conclude that the absorbing boundary conditions can well absorb thereflection wave. In the numerical experiments of the globally convergent method,we give the numerical inversion results, when there are some inclusions in thehomogeneous background medium. The results are also provided, when the velocitymodel is layered. The numerical results do not only certificate that the algroithm isstable, but that it is globally convergent.