摘要
有限差分方法被广泛应用于地震波数值模拟和传播.传统有限差分法采用Taylor级数展开实现空间偏导数的差分,但该方法会因为网格离散化而产生数值频散,降低地震波模拟的精度.优化差分系数正演方法能在一定程度上压制部分频散,然而纵、横波速度取值差异较大,在弹性波有限差分正演模拟中,在满足纵波最大速度确定的稳定性条件下,浅层低速横波波场往往会产生明显的频散现象.为了削弱弹性波场正演数值频散,提高数值模拟精度,本文首先采用优化差分网格系数降低数值频散,然后再采用通量校正传输(Flux-Correction Transport, FCT)法来进一步压制弹性波场有限差分数值频散.常规的FCT法是对弹性波场直接进行频散压制,但由于弹性波场中纵、横波速度差异明显,横波波场频散明显强于纵波,为了压制横波波场的数值频散,往往需要选取较大的频散压制参数,但这会使频散较弱的纵波产生假象.因此本文提出基于纵横波分离FCT弹性波正演频散压制方法,对分离之后的纵横波场分别选择合适的频散压制参数进行通量校正,可以有效压制数值频散,削弱纵波FCT产生的假象.通过理论分析和数值算例发现,本文方法能有效削弱弹性波场有限差分数值频散,相对于常规FCT方法没有假象产生.
The finite difference method is widely used in the numerical simulation and propagation of seismic wavefield.The traditional finite difference method uses Taylor series expansion to calculate the spatial partial derivative,but this method will produce numerical dispersion due to grid discretization,which reduces the accuracy of seismic wavefield simulation.The numerical simulation method of optimizing the difference coefficient can suppress some dispersion to a certain extent.However,under the stability condition of the maximum P-wave velocity,due to the large difference of P-and S-wave velocities,the elastic wavefield numerical simulation will lead to obvious numerical dispersion in the shallow low velocity S-wave.To reduce the numerical dispersion and improve the simulation accuracy,this paper first uses the optimized difference grid coefficient to reduce part numerical dispersion,and then uses the FCT(Flux-Corrected Transport)method to further suppress the finite difference numerical dispersion of elastic wavefield.The conventional FCT method directly suppress the elastic wavefield dispersion.But due to the obvious difference in the P-and S-wave velocity,the dispersion of the S-wave is stronger than that of the P-wave.To suppress the S-wave numerical dispersion,it needs to select a larger dispersion suppression parameter,while this will produce artifacts for P-waves.Therefore,this paper proposes a suppression of dispersion method in elastic wavefield simulation by FCT of separated P-and S-waves.By selecting appropriate dispersion suppression parameters for the separated P-and S-wave to perform flux correction,the numerical dispersion can be effectively suppressed and the P-wave artifacts can be weakened.Through theoretical analysis and numerical examples,it is found that the method in this paper can effectively reduce the numerical dispersion of elastic wave equation finite-difference,and there are no P-wave artifacts compared with the conventional FCT method.
作者
刘聪
周熙焱
常旭
王一博
程冰洁
LIU Cong;ZHOU XiYan;CHANG Xu;WANG YiBo;CHENG BingJie(Key Laboratory of Earth Exploration and Information Technology Ministry of Education(Chengdu University of Technology),Chengdu610059,China;College of Geophysics,Chengdu University of Technology,Chengdu610059,China;Key Laboratory of Petroleum Resource Research,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing100029,China)
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2023年第6期2534-2549,共16页
Chinese Journal of Geophysics
基金
国家自然科学基金项目(42074160)资助。
关键词
弹性波正演
有限差分
纵横波分离
FCT
频散压制
Elastic wave simulation
Finite-difference
P-and S-wave separation
FCT
Suppression of dispersion
