基于广义正交多项式迭积微分算子的地震波场数值模拟研究

Seismic Numerical Modeling is one of bases of the Exploratory Seismology and Academic Seismology, also is a research field in great demand. Essence of seismic numerical modeling is to assume that structure and parameters of the underground media model are known, simulate the wave-field and calculate the numerical seismic record that should be observed. Seismic numerical modeling is not only a means to know the seismic wave-field in complex inhomogeneous media, but also a test to the application effect by all kinds of methods. There are many seismic numerical modeling methods, each method has its own merits and drawbacks. During the forward modeling, the computation precision and the efficiency are two pivotal questions to evaluate the validity and superiority of the method. The target of my dissertation is to find a new method to possibly improve the computation precision and efficiency, and apply the new forward method to modeling the wave-field in the complex inhomogeneous media. Convolutional Forsyte polynomial differentiator (CFPD) approach developed in this dissertation is robust and efficient, it shares some of the advantages of the high precision of generalized orthogonal polynomial and the high speed of the short operator finite-difference. By adjusting the operator length and optimizing the operator coefficient, the method can involve whole and local information of the wave-field. One of main tasks of the dissertation is to develop a creative, generalized and high precision method. The author introduce convolutional Forsyte polynomial differentiator to calculate the spatial derivative of seismic wave equation, and apply the time staggered grid finite-difference which can better meet the high precision of the convolutional differentiator to substitute the conventional finite-difference to calculate the time derivative of seismic wave equation, then creating a new forward method to modeling the wave-field in complex inhomogeneous media. Comparing with Fourier pseudo-spectral method, Chebyshev pseudo-spectral method, staggered- grid finite difference method and finite element method, convolutional Forsyte polynomial differentiator (CFPD) method has many advantages: 1. Comparing with Fourier pseudo-spectral method. Fourier pseudo-spectral method (FPS) is a local operator, its results have Gibbs effects when the media parameters change, then arose great errors. Therefore, Fourier pseudo-spectral method can not deal with special complex and random heterogeneous media. But convolutional Forsyte polynomial differentiator method can cover global and local information. So for complex inhomogeneous media, CFPD is more efficient. 2. Comparing with staggered-grid high-order finite-difference method, CFPD takes less dots than FD at single wave length, and the number does not increase with the widening of the studying area. 3. Comparing with Chebyshev pseudo-spectral method (CPS). The calculation region of Chebyshev pseudo-spectral method is fixed in , under the condition of unchangeable precision, the augmentation of calculation is unacceptable. Thus Chebyshev pseudo-spectral method is inapplicable to large area. CFPD method is more applicable to large area. 4. Comparing with finite element method (FE), CFPD can use lager grids. The other task of this dissertation is to study 2.5 dimension (2.5D) seismic wave-field. The author reviews the development and present situation of 2.5D problem, expatiates the essentiality of studying the 2.5D problem, apply CFPD method to simulate the seismic wave-field in 2.5D inhomogeneous media. The results indicate that 2.5D numerical modeling is efficient to simulate one of the sections of 3D media, 2.5D calculation is much less time-consuming than 3D calculation, and the wave dispersion of 2.5D modeling is obviously less than that of 3D modeling. Question on applying time staggered-grid convolutional differentiator based on CFPD to modeling 2.5D complex inhomogeneous media was not studied by any geophysicists before, it is a fire-new creation absolutely. The theory and practices prove that the new method can efficiently model the seismic wave-field in complex media. Proposing and developing this new method can provide more choices to study the seismic wave-field modeling, seismic wave migration, seismic inversion, and seismic wave imaging.