地震波散射非线性反演问题不动点理论及方法的研究

How to create a new method to solve the problem or reduce the influence of that the result of the seismic waves scattering nonlinear inversion is not uniqueness is a main purpose of this research work in the paper. On the background of research into the seismic inversion, new progress of the nonlinear inversion is introduced at the first chapter in this paper. Especially, the development, basic theories and assumptions on some major theories of seismic inversion are analyzed, discussed and summarized in mathematics and physics. Also, the problems faced by the mathematical basis of investigations of the seismic inversion are discussed, and inverse questions of strongly seismic scattering due to strong heterogeneous media in the Earth interior are analyzed and viewed. What the kernel of paper is that gathers all our attention making a new nonlinear inversion method of seismic scattering. The paper provides a theory and method of how to introduce the fixed-point theory into the nonlinear seismic scattering inversion and how to obtain the solution, and gives the actually method to create a serials of contractive mappings of velocity parameter's in the mapping space of wave. Therefore, the results testify the existence of fixed point of velocity parameter and give the method the find it. Further, the paper proves the conclusion that the value obtained by taking the fixed point of velocity parameter into wave equation is the fixed point of the wave of the contractive mapping. Thence, the fixed point is the global minima since the stabilities quality of the fixed point. Based on the new theory, in the chapter three, many inverse results are obtained in the numerical value test. By analysis the results one could find a basic facts that all the results, which are inversed by the different initial model, are tended to the true value in theoretical true model. In other words, the new method mostly eliminates the non-uniqueness that which is existed in seismic waves scattering nonlinear inversion in degree. But, since the test results are quite finite now, more test is need here to positive our theory. As a new theoretical method, it must be existed many weaken in it. The chapter four points out all the questions which is bother us. We hope more people to join us to solve the problem together.