【摘要】 波动方程有限差分法是一种使用广泛的地震波数值模拟方法.但是有限差分法本身固有存在着数值频散问题,会降低地震波场模拟的精度与分辨率.为了克服常规有限差分算子的数值频散,本文针对VTI介质地震波数值模拟问题,构造了频率-空间域qP波波动方程高精度有限差分优化算子,根据最优化理论中高斯-牛顿法确定了高精度有限差分算子的优化系数.利用常规差分算子和高精度优化差分算子对归一化相速度的频散关系精度进行了对比分析,并对均匀各向同性介质和均匀VTI介质中的qP波地震波场进行了有限差分数值模拟,通过频散关系精度分析和波场数值模拟结果表明:有限差分优化算子具有较高的波场数值模拟精度,有效压制了传统有限差分算子数值模拟中的数值频散现象,提高了有限差分算子精度,为VTI介质频率-空间域qP波正演模拟奠定了基础.更多还原

【Abstract】 Finite-difference method for wave equation is widely implemented in seismic wavefield numerical simulation.Finite-difference method has inherent numerical dispersion,which reduces the accuracy and resolution of seismic wavefield simulation.In order to decrease the numerical dispersion of conventional finite-difference operators,we present high precision finite-difference operators of qP wave equation in frequency–space domain for seismic wavefield numerical simulation in VTI media,and obtain the optimal coefficients of high precision finite-difference operators according to the Gauss-Newton method in optimization theory.We analyze dispersion relation accuracy of normalized phase velocity using conventional finite-difference operators and high precision optimal finite-difference operators separately,and do finite-difference numerical simulation for qP wave in homogenous isotropic media and VTI media.The results of dispersion relation accuracy analysis and numerical simulation indicate that optimal finite-difference operators have high precision in wavefield numerical simulation,and can efficiently decrease the numerical dispersion in conventional finite-difference numerical simulation,and improve accuracy of the finite-difference operators,which can provide the foundation of qP wave simulation in frequency–space domain in VTI media.更多还原