Seismic Inverse Scattering Theory And Depth Imaging

In seismic data processing, the main research directions are seismic migration, seismic tomography and wave equation coefficient inversion in late 20th century. In these methods, seismic migration is the most successful to study the subtle structure in the earth. Seismic tomography and wave equation coefficient inversion have greatly improved. But, these methods have a dead problem, i.e., the velocity model is necessary. The inverse results depend on the velocity model. If the model is correct, then the result is credible. Otherwise, the result is false. But the velocity of seismic wave is an important parameter in seismic prospecting. If we obtain the velocity model, it is not necessary to do inversion. So solving the problem is a great subject at present and in the future.The other problem in seismic inversion is that the frequency information and amplitude real value recorded by seismograph are incomplete and severely absent. The absence of high frequency information influences distinguishing location of layer. And the absence of low frequency information leads to fail to reconstruct the wave impedance. Technical parameters and characters of sampling system determine that seismic wave amplitude recorded by seismograph is approximate relative amplitude. Using these data necessarily leads to serious distortion of inverse parameters. So using Born approximation can only obtain the location of interface even if the earth medium is little disturbance. In fact, our aims are not to obtain all parameters, only know the discontinuity or singularity of interface in most case by applied opinion.Considering problem mentioned in above part and founding on Bleistein's and Cohen's researches on Born approximation, the author carries out depth imaging inversion by using inverse scattering series for obtaining the singularity locations of layers. Because of taking only advantage of the first item in scattering series, method of Born approximation inversion is only suitable to little disturbance imaging. And it will produce great error in condition of great perturbation. The inversion theory advanced in this paper can also obtain the real location and shape of interface in great perturbation as a result of using the high items in scattering series. It solves the imaging problem in great contrast.In chapter 2, the author deeply studies and analyzes the arithmetic of the method of Born approximation inversion and points out the limitations and disadvantage of the method. The good inverse results can be obtained in little disturbance by Born approximation. But the singularity location inversed by Born approximation inversionis false except the first interface. With reflect coefficients increasing, the error is rapidly enlarged.In chapter 3, the author studies the scattering theory and analyzes the physical meaning of each item in scattering series. At same time, the author deduces the formula of scattering fields in one dimension. Then, the singularity inversion arithmetic of inverse scattering series is deduced in one dimension. Using perturbation method to solve inverse scattering series, the author obtains a set of inverse formula and verifies its validity through model data. In chapter 4, the author studies the singularity inversion arithmetic of inverse scattering series in three dimensions and proves validity of arithmetic through 2.5D theoretic model data.The study in the paper is based on acoustic wave equation, but its research methods are also suitable to elastic and viscoelastic wave equation.