垂直地震剖面的有限元正演模拟

Forward Modeling VSP by Finite Element Method

应用有限元法和差分法对弹性波波动方程及其定解条件进行数值模拟，得到了无震源形式下的波动方程递推解．引入震源，对有限波场区域进行垂直地震剖面模拟调试，发现空间离散间隔、时间采样间隔与弹性介质速度、震源最大频率之间存在制约关系，满足该关系可使模拟结果收敛、稳定．对４个地层模型（简单模型、垂直断层模型、正断层模型和多层介质模型）进行模拟计算表明，在模拟剖面上清晰可见直达波、反射纵波、反射横波、转换波和多次波能量，与理论分析一致．

The recursive solution for elastic wave equation is derived within no source, a linear source is introduced and VSP modeling data are computed. There are some constraints among the spatial discreted interval, time sampling interval and elastic wave velocities, maxium frequency of the source wavelet. When these conditions are satisfied,modeling results are stable and convergent. On the modeling sections for four models, first arrival, reflected P- wave and S - wave as well as mutiples are visible. These results are consistent with theoretical analysis.