虚谱法交错网格地震波场数值模拟

Pseudo spectral seismic wavefield simulation with staggered grid

(1.西南石油大学,四川成都610500;2.中国石油天然气股份有限公司塔里木油田分公司,新疆库尔勒841000)

Southwest Petroleum University,Chengdu 610500,China

提高空间差分精度、有效压制人为边界反射是波动方程波场模拟的关键。虚谱法利用模型空间的全部信息对波场函数进行傅里叶变换,可以得到精确的波场空间导数,使数值频散效应减弱,进而实现宽频带地震波场模拟。阐述了求解弹性波波动方程的方法原理,讨论了数值模拟中Gibbs效应和边界反射问题的解决方法,即在半网格点处计算空间导数并采用最佳匹配层边界条件。设计了5层水平层状介质模型,讨论了虚谱法的模拟精度和计算效率,试算表明,适当增大差分网格和时间延拓步长不会影响计算精度,但计算效率可以得到大幅度提高。分别采用不同的差分方法对Marmousi2模型和SEG/EAGE模型进行数值模拟,结果表明,虚谱法交错网格模拟结果信噪比高,在同等模拟精度条件下较其它方法具有更高的计算效率。

Enhancing the precision of spatial difference and effectively suppressing artificial boundary reflection is the key of wave equation wavefield simulation.Pseudo spectral method carried out Fourier transform on wavefield function by utilizing all information of model space,which can achieve accurate wavefield spatial deviative and attenuate numerical dispersion effect,and eventually realize wide frequency bandwidth seismic wavefield simulation.The principles for solving the wave equation of elastic wave were elaborated.The method for suppressing boundary reflection and Gibbs phenomena was discussed,that is calculating spatial deviative at point of half-grid and adopting perfectly matched layer boundary condition.A layered medium model with five horizontal layers was designed;the simulation precision and calculation efficiency of pseudo spectral method were discussed.The trial computation shows that properly increasing difference grid and time continuation step size can largely enhance computation efficiency without influencing computation precision.Numerical tests on Marmousi2 and SEG/EAGE show that simulation results by pseudo spectral method with staggered grid has higher S/N and higher computation efficiency with same simulation precision.