高精度傅里叶有限差分法模型正演
|
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.
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.
引文
[1]Alford R Met al.Accuracy of finite-difference mod-eling of the acoustic wave equation.Geophysics,1974,39:838～842
[2]马在田.高阶有限差分偏移.石油地球物理勘探,1982,17:6～15
[3]Edward J et al.I maging using optional rational ap-proxi mationto the paraxial wave equation.Expanded Abstracts of68th SEG Mtg,1998
[4]Claerbout J F.Imagingthe earth's interior.Black-Well Scientific Publications,Inc.1985
[5]Stolt R H.Migration by Fourier transform.Geophys-ics,1978,43,23～48
[6]Gazdag J.Wave equation migration with the phase-shift method.Geophysics,1978,43:1342～1351
[7]Stoffa P L et al.Split-step Fourier migration.Geo-physics,1990,55,410～421
[8]Kessinger W.Extended split-step Fourier migration.Expanded Abstracts of62nd SEG Mtg,1992,917～920
[9]Ristow D et al.Fourier finite-difference migration.Geophysics,1994,59,1882～1893
[10]Lamer Ket al.Cascaded migration:I mproving the ac-curacy of finite-difference migration.Geophysics,1987,52,618～643
[2]马在田.高阶有限差分偏移.石油地球物理勘探,1982,17:6～15
[3]Edward J et al.I maging using optional rational ap-proxi mationto the paraxial wave equation.Expanded Abstracts of68th SEG Mtg,1998
[4]Claerbout J F.Imagingthe earth's interior.Black-Well Scientific Publications,Inc.1985
[5]Stolt R H.Migration by Fourier transform.Geophys-ics,1978,43,23～48
[6]Gazdag J.Wave equation migration with the phase-shift method.Geophysics,1978,43:1342～1351
[7]Stoffa P L et al.Split-step Fourier migration.Geo-physics,1990,55,410～421
[8]Kessinger W.Extended split-step Fourier migration.Expanded Abstracts of62nd SEG Mtg,1992,917～920
[9]Ristow D et al.Fourier finite-difference migration.Geophysics,1994,59,1882～1893
[10]Lamer Ket al.Cascaded migration:I mproving the ac-curacy of finite-difference migration.Geophysics,1987,52,618～643
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心