精细积分法三维地震波正演模拟
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摘要
将任意差分精细积分法用于三维地震正演模拟,首先推导了求解三维波动方程的任意差分精细积分计算公式,并结合吸收边界条件实现了三维地下断层构造加穹隆的地质模型正演。该方法为半解析的数值方法。计算实例表明,子波数值频散现象得到较好的控制,反射信号走时准确,可方便地应用到三维实际地质模型的地震正演中。
In this paper, the arbitrary difference precise integral method was adopted in 3-D seismic forward modeling. Firstly we deduced the formula of arbitrary difference and precise integral that are used to solving 3-D wave equation. Secondly we presented an example of 3-D seismic forward modeling over a fault and a quaquaversal dome with absorption boundary. The ADPI is a half-analytic numerical method. Results showed that the numerical dispersion of seismic wave is well controlled, and the travel time of reflected seismic wave is accurate. This method can easily be used to 3-D wave equation forward modeling.
In this paper, the arbitrary difference precise integral method was adopted in 3-D seismic forward modeling. Firstly we deduced the formula of arbitrary difference and precise integral that are used to solving 3-D wave equation. Secondly we presented an example of 3-D seismic forward modeling over a fault and a quaquaversal dome with absorption boundary. The ADPI is a half-analytic numerical method. Results showed that the numerical dispersion of seismic wave is well controlled, and the travel time of reflected seismic wave is accurate. This method can easily be used to 3-D wave equation forward modeling.
引文
1钟万勰．单点子域积分与差分[J]．力学学报,1996,28 (2):159-163
2强士中,王孝国,唐茂林等．任意差分精细积分法及数值稳定性分析[J]．应用数学与力学,1999,20(3):256-262
3王润秋,耿伟峰,王尚旭．地震波正演模拟的任意差分精细积分方法[J]．石油地球物理勘探,2003,38(3):252- 257
4 Wang Runqiu. Hu Tianyue, Jia Xiaofeng. The precise finite difference method for seismic modeling[J]. Applied Geophysics. 2004,1(2): 1-7
5张明,张晓丹．解波动方程的精细积分法及其数值稳定性分析[J]．石油大学学报,2004,28(6):129-132
6 Berenger J P. A perfectly matched layer for the absorption of electromagnetics waves[J]. J . Comput. Phys. , 1994,114:185-200
7 Cesjan C. A nonreflecting boundary condition for discrete acoustic-wave and clastic-wave equation[J]. Geophysics, 1984, 50(4): 705 - 708
2强士中,王孝国,唐茂林等．任意差分精细积分法及数值稳定性分析[J]．应用数学与力学,1999,20(3):256-262
3王润秋,耿伟峰,王尚旭．地震波正演模拟的任意差分精细积分方法[J]．石油地球物理勘探,2003,38(3):252- 257
4 Wang Runqiu. Hu Tianyue, Jia Xiaofeng. The precise finite difference method for seismic modeling[J]. Applied Geophysics. 2004,1(2): 1-7
5张明,张晓丹．解波动方程的精细积分法及其数值稳定性分析[J]．石油大学学报,2004,28(6):129-132
6 Berenger J P. A perfectly matched layer for the absorption of electromagnetics waves[J]. J . Comput. Phys. , 1994,114:185-200
7 Cesjan C. A nonreflecting boundary condition for discrete acoustic-wave and clastic-wave equation[J]. Geophysics, 1984, 50(4): 705 - 708
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