Research Of Least Square Acoustic Impedance Inversion Arithmetic

Inversion of acoustic impedance of underground medium using seismic data, it is a typical nonlinear inverse problem. For noisy seismic data, recursive inversions are instable, and the calculated errors are accumulated with the increasing depth. So the iterative inversion base on the model is the focus of recent research. It is well known that this method has two problems: selecting the initial model and evaluating the solution estimates. For example, the iterative inversion of nolinear is difficult to evaluate the solution estimate, for the seismic data have noises and system errors, and i t is impossible to analyze the changes of resolution and variance theoretically. In this paper, I have discussed a method of iterative inversion, which does not depend on the initial model and has high resolution. It will provide high resolution profile of acoustic impedance.Least square acoustic impedance inversion arithmetic, for the nonlinear inverse problem; using the successive linearization, in order to meet the demands of precision of solution, linearizes it. In seismic inversion, the inverse matrix is mostly huge singular, the ordinary methods cannot be directly used to solve the equation, and the SVD technique must be used. On the purpose to get solution estimate with high resolution, and the efficient parts do not go to worse, the combination of Wiggins and stochastic inverse techniques are used to modify the singular values. During the iteration, the damping factor is decreasing to improve the resolution of solution estimate; and therelax factor is added to control the iterative step, which make the search correct.In this paper, the key point is to introduce the chaotic theory and the fractal geometry, discuss the characteristic of the iterative output series, evaluate the solution estimates from the changes of resolution and variance, search new criterions to control iteration. The Lyapunov exponents in iteration are increasing form negative value, and finally go to a big positive value. At the second phase surface, the solution estimate has highest resolution and its variance is small, the Lyapunov approach zero. This can be taken as the new criterion to evaluate the solution estimates.the chaotic theory and fractal geometry reveal the characteristics of acoustic impedance inversion, describing the change of resolution and variance. The results of real seismic data have shown that this inverse method does not depend on the initial model and has high resolution.