CAJ | 학술논문

频率空间域正演模拟是频率域及 Laplace-Fourier 域全波形反演的基础，起伏地表条件下波形反演算法的关键是正演算法中考虑起伏地表的影响。基于带 PML 吸收边界的声波波动方程，在已有最优9点有限差分正演算法的基础上构建了起伏地表条件下频率空间域正演算法。通过应用变网格技术，进一步提高算法的计算效率、降低内存开销，使得大规模起伏地表模型的频率域正反演问题成为可能。理论分析及数值测试表明：通过对近地表区域进行局部网格加密，可有效地压制由于矩形网格离散引起的角点散射；结合变网格技术可较易获得5倍以上计算效率的提高及内存占用的降低，且随着模型尺度的增加及地表起伏高程差的减小，倍数将显著增加；在细网格与粗网格交界处产生的虚假反射振幅幅值控制在原始波场的2％以内，满足地震波场正反演的需求。
빈솔공간역정연모의시빈솔역급 Laplace-Fourier 역전파형반연적기출，기복지표조건하파형반연산법적관건시정연산법중고필기복지표적영향。기우대 PML 흡수변계적성파파동방정，재이유최우9점유한차분정연산법적기출상구건료기복지표조건하빈솔공간역정연산법。통과응용변망격기술，진일보제고산법적계산효솔、강저내존개소，사득대규모기복지표모형적빈솔역정반연문제성위가능。이론분석급수치측시표명：통과대근지표구역진행국부망격가밀，가유효지압제유우구형망격리산인기적각점산사；결합변망격기술가교역획득5배이상계산효솔적제고급내존점용적강저，차수착모형척도적증가급지표기복고정차적감소，배수장현저증가；재세망격여조망격교계처산생적허가반사진폭폭치공제재원시파장적2％이내，만족지진파장정반연적수구。
Seismic wave modeling in frequency-space domain is the foundation of full waveform inversion in frequency and Laplace-Fourier domain.An accurate seismic wave modeling with surface topography is the kernel of full waveform inversion which can direct process data recorded on relief surface.Based on acoustic wave equation with PML absorption boundary condition,the free surface condition on relief surface is included into the optimized 9-points finite difference algorithm in frequency space domain.Then the variable grid method which refines the grid near the surface and remains the rest unchangeable is introduced to increase the computational efficiency and decrease the memory cost.The theoretical analysis and numerical test show that:1)the diffraction caused by grid discretization of the relief surface can be suppressed by refining the grid;2)through the variable grid method,computational efficiency can be improved for several times and the memory cost can also be decreased for several times easily;3)the energy of artificial reflection caused by the boundary of fine and coarse grid is less than 2%of the energy of the original wavefield which is acceptable for the seismic wavefield modeling and inversion.