高精度傅里叶有限差分法模型正演  

Forward modeling by Fourier finite-difference approach

作　　者：刘文革[1] 贺振华[2] 黄德济[2] 杜增利[3] 

机构地区：[1]四川省成都市成都理工大学信息工程学院,610059 [2]成都理工大学信息工程学院 [3]西南石油大学

出　　处：《石油地球物理勘探》2007年第6期629-633,733+604-605,共5页Oil Geophysical Prospecting

基　　金：高等学校博士学科点专项科研基金资助(20040616001)

摘　　要：波动方程数值模拟方法分为有限差分法和频率—波数域法两类,其中有限差分法的计算精度取决于波场外推算子的近似程度、离散网格间距及差分方程阶数,它能适应速度任意横向变化,但在大倾角处易出现频散现象及背景噪声。频率—波数域法算法简单、精度高、噪声小,能适应任意地层倾角情况,但不适于速度场的任意横向变化。文中结合有限差分法和频率—波数域法的优点,应用傅里叶有限差分法(FFD)实现在多域用高精度延拓算子对模型进行地震记录的数值模拟,其波场外推算子由相移项、折射项(时移项)和有限差分补偿项组成。对FFD法进行了理论与误差分析,并用单程声波方程分别进行了层状模型和SEG/EAGE盐丘模型的数值模拟试验。数值试验的对比分析表明,FFD法适用于速度场横向剧烈变化情形,且具有精度高、无频散、背景噪声弱等优点,模拟结果反射特征清楚,能对复杂地质构造进行准确的地震数值模拟。There are tow kinds of wave equation numeric modeling methods: finite-difference approach and approach in frequency-wavenumber domain,among which the computation precision of finite-difference method depends on the approximate degree of wavefield extrapolation operator,discrete grid interval and order of finite-difference equation,it is adapted for any lateral variations of velocity,but the dispersion and background noise are easily presented in large dip. The algorithm in frequency-wavenumber domain is characterized by simple,high-precision,small noise and adaptive to any dips of strata,but inadequate for any lateral variations of wavefields.Combining the advantages of frequency-wavenumber domain with Finite-Difference approach,the paper used Fourier Finite-Difference (FFD) approach to finish the numeric simulation of seismic records of model by using high-precision continuation operator and in multi-domain.The extrapolation operator of wavefield is composed of phase-shift item,refraction item (time-shift item) and finite-difference compensation item.The theoretical and error analyses are carried out for FFD method,and one-way acoustic wave equation is used to do numeric simulation test for layered model and SEG/EAGE salt model respectively.The correlation of numeric tests showed the FFD method is adaptive for severe lateral change of velocity field and characteristics of high precision,no-dispersion and weak background noise,and the reflection feature is distinguishable in simulated results,which can carry out accurate numeric seismic simulation of complex geologic structure.

关 键 词：波动方程 地震数值模拟 有限差分法 频率一波数域法 傅里叶有限差分法 

分 类 号：P631.44[天文地球—地质矿产勘探]