黏声波方程常被用于描述地下介质的黏弹性及波的传播现象,频域有限差分(finite difference frequency domain,FDFD)方法是黏声波和黏弹性波波场模拟的常用工具.目前FDFD黏声波模拟常用的二阶五点方法和优化九点方法在一个波长内的网格点数小于4时误差较大.通过令FDFD系数随一个波长内的网格点数自适应从而提高FDFD方法的精度,本文针对黏声波波场模拟发展了一种适用于不同空间采样间隔之比的通用格式自适应系数FDFD方法.同时,为了验证自适应系数FDFD方法对一般黏声波模型的有效性,本文针对三个典型的黏声波模型,分别采用解析解和基于高阶FDFD的参考解验证了所提出方法的有效性.本方法的FDFD格式通过在传统的二阶FDFD格式的基础上引入相关校正项得到,其中校正项按网格点与中心点的距离进行分类选取,同时校正项对应的自适应FDFD系数不仅和空间采样间隔之比相关,还和一个波长内的采样点数相关.所需的自适应FDFD系数可通过声波方程的数值频散关系和查找表高效给出.数值频散分析表明,在空间采样间隔相等或不等的情况下,以相速度误差不超过1％为标准,通用格式自适应系数FDFD方法所需的一个波长内的采样点数均小于2.5.数值模拟实验表明,对于不同的空间采样间隔之比,相对于常用的二阶五点FDFD方法和优化九点FDFD方法,通用格式自适应系数FDFD方法均可在相似的计算量和内存需求下,有效提高黏声波模拟的精度.
General adaptive-coefficient finite-difference frequency-domain method for wavefield simulation of viscoacoustic equation
Viscoacoustic wave equation has been widely applied to describe the viscoelasticity of subsurface media and the wave propagation characteristics.The finite difference frequency domain(FDFD)method is a practical approach for the simulation of viscoacoustic and viscoelastic wavefields.At present,the second-order five-point FDFD method and optimal nine-point FDFD method commonly used in viscoacoustic wave simulation exhibit large errors when the number of points per wavelength is smaller than 4.By adjusting the FDFD coefficients adaptive to the number of points per wavelength for improving the accuracy of FDFD method,we propose a general adaptive-coefficient FDFD method for viscoacoustic wave simulation with different ratios of spatial grid sizes.Furthermore,to verify the validity of the adaptive-coefficient FDFD method for general viscoacoustic wave models,we adopt the analytic solution as well as high-order FDFD as reference solutions for the three typical viscoacoustic models.The FDFD scheme in the proposed method is obtained by introducing some correction terms to the conventional second-order FDFD scheme,where the correction terms are selected based on the distance between grid point and central point.The adaptive coefficients of correction terms are related to both the ratio of spatial grid sizes and the number of points per wavelength.The required adaptive coefficients can be efficiently determined by applying the acoustic numerical dispersion relation and lookup table.Numerical dispersion analysis shows that within a phase velocity error of 1％,the number of points per wavelength required by the proposed general adaptive-coefficient method can be less than 2.5 for both equal and unequal spatial grid sizes.Numerical simulation results show that for the different ratios of spatial grid sizes,compared to the commonly used second-order five-point FDFD and optimal nine-point FDFD,the general adaptive-coefficient FDFD method can effectively improve the accuracy of viscoacoustic wave simulation,while requiring the similar computational cost and computer memory.
Viscoacoustic waveFinite difference frequency domainAdaptive coefficientWavefield simulationGeneral scheme
徐文豪、巴晶、J.M.Carcione、朱鹤松
展开 >
河海大学地球科学与工程学院,南京 211100
National Institute of Oceanography and Applied Geophysics-OGS,Borgo Grotta Gigante 42/c,Trieste,Sgonico 34010,Italy
万方数据
维普
