【作者】 李健；

【导师】 孙建国；

【作者基本信息】 吉林大学 ， 地球探测信息与技术， 2008， 硕士

【副题名】有限余弦变换法

【摘要】 本文的研究目的是提出一种解决起伏地表条件下地震波场数值模拟的方案。研究方法是将网格映射和有限积分变换-有限差分法(FIFT—FD)相结合。全文共分六章,第一章对现有的起伏地表地震波场数值模拟方法进行了概述;第二章介绍了有限积分变换方法的原理,此方法在数学物理问题中和在地球物理学中的发展概况;波动方程FIFT-FD法应用在第三章进行了讨论,在这一章给出了水平和起伏地表条件下的波动方程FIFT—FD法的离散方程形式;第四章首先讨论震源函数类型,然后对震源的限积分变换处理进行说明;第五章主要对FIFT-FD法解弹性波方程时出现的高振荡函数积分进行计算并编制程序,给出算法的实例并分析其近似效果;第六章根据导出来的变换域波动方程的FIFT-FD法对水平地表的情况进行地震波场数值模拟;最后,在第七章对全文的研究结果做了总结,提出了对今后进一步深入研究的方向。更多还原

【Abstract】 Seismic exploration is an important geophysical methods. The useful geological information was carried from seismic waves, so the characteristics of the seismic wave field awareness is very important.Generally, the study seismic waves There are two ways: physical methods and mathematical methods, often referred to as the physical simulation and numerical simulation. Physical simulation is by a certain scale, with certain materials to and the actual geological body in shape, structure and properties, and so on the main features of proportion to the physical models in the laboratory simulation of this physical model of seismic exploration of the field work, Various methods of data collection, given the necessary seismic records and collection of data and make the appropriate process. Physical simulation was accomplished in the laboratory. Beacuase the physical parameters, structural and tectonic patterns of physical model was known, and the sources can be controlled, the seismic wave field reflects the characteristics clearly, and help us to interpret the actual formation lithology and structure.In contrast with the physical simulation, numerical simulation is in a given mathematical model (such as elastic wave equation, acoustic equation, etc.), the source, and underground geometry interface, physical parameters (rock density, velocity, etc.). studied acoustic or elastic waves’dynamic features. Numerical simulation can be intuitive understanding of seismic wave field, and provide the necessary basis for exploration seismic data inversion (the so-called inversion is the methods of using the observation wells in the ground or the data or physical phenomena within the media to speculate the Earth’s physical state).Seismic wave field of numerical simulation in seismic data processing method plays a very important role, it is one of the means to study and understand the importance of seismic wave field, in the oil and gas exploration and development occupies a very important and irreplaceable status. On the one hand, use of numerical simulation of seismic records, test results of the seismic data processing quality and effectiveness of the treatment. On the other hand, forward modeling can be used as the basis of the study inversion. In this paper, the limited integral transformation - finite difference method (FIFT-FD) is one of the many numerical simulation technologies.Called combination of finite integral Fourier transform and finite difference technique (FIFT-FD) will be researched in this paper. The method was firstly proposed byМихайленко.Б.Г.firstly, based on the principles of the method, two versions are deduced for acoustic wave equations. Then finite difference equations are created for the methods. At last, utilizing appropriate source functions, seismic responses are calculated for homogeneous and layered earth. Based on the same principle, the method is adapted to elastic wave equations for many other earth models, And discrete forms of the equations are deduced.This article combinated mesh mapping and limited integral transformation - finite difference, a surface mapping will be ups and downs to the rules of a rectangular grid coordinate system, according to transform guided by the use of the limited domain wave equation integral transformation finite difference method Seismic wave field of numerical simulation methods to solve the rugged surface under conditions of simulated. Through this work, the limited DCT-based Fourier Fourier limited or sine-wave seismic methods numerical simulation was more widely applied.By the work of this thesis, the new characters of FIFT-FD method can be gained:(1)Finite sine/cosine transform belongs to classical method of solution partial differential equation(PDE). It can decrease the PDE’s spacial dimension, that is able to transform the PDE to ordinary differential equation(ODE), which would be more easy to solve.(2) The FIFT-FD used to model SH wave. We found it could be applied widely. For example we used this method to model acoustic wave equation. It also adapted to the elastical wave equation in isotropic medium. The only difference was the given medium parameter.(3)The method enabled extend the model to infinite in transform direction, so that was suitable for large scale problems. When dealed with arbitrary velocity or density distribution, this method nearly no computation increment.(4)The FIFT-FD transformed function to sine/cosine functions, then accumulated the function series. Not like pseudospectral method, it had no folding effect resulted from the periodicity of Fourier transform, and it had infinite order accuracy.(5)The selection of surface function was very important when the surface was irregular, and it effected the equation’s difference scheme and the accuracy of solution.Anyway we can draw a conclusion that the FIFT-FD was a simple, efficient and parsimonious method. However, its disadvantage was not neglectable. Because it included the finite integral of derivative of wave equation parameter, so the given parameter model must sufficient smooth.In this paper, the method of study on a formula derived and the computation of integral of high-oscillation function. Because of the time relatively tight, the specific examples of calculation the rugged surface models have not given, but given the plane surface examples. The rugged surface of the calculation example would be research and analysis in the further.更多还原