TTI介质的交错网格伪P波正演方法

研究了三维弱各向异性近似下,利用伪P波(伪纵波)模拟弹性波场P分量在倾斜对称轴的横向各向同性(TTI)介质中的传播过程,并对比了分别基于弹性Hooke定律、弹性波投影和运动学色散方程所建立的三种二阶差分伪P波方程的正演特点.目前这些伪P波方程数值计算主要采用规则网格差分,但是规则网格在TTI模拟中有低效率、低精度以及不稳定的缺点.为了提高计算的精度,本文构建出相应方程的交错网格有限差分格式.通过对比伪P波方程在三维TTI介质中不同的数值模拟的表达形式,本文认为基于色散方程所建立的伪P波方程在模拟弹性波中P波传播的过程中具有最小的噪声.本文分析不同的各向同性对称轴空间角度的频散特征,并引入适当的横波速度维持计算的稳定.二维模型算例表明,本文提出的交错网格正演算法可以得到稳定光滑的伪P波正演波场.使用本文交错网格算法对二维BP TTI模型的逆时偏移也具有较稳定的偏移结果.

Forward modeling of pseudo P waves in TTI medium using staggered grid

A tilted transversely isotropic(TTI) medium is a good approximation for anisotropic problems. We discuss the property of a 3D tilted transversely isotropic(TTI) medium and use pseudo P waves to simulate the P component of the elastic wave field in the weak elastic anisotropy approximation. We compare forward features of 3 second-order difference equations of pseudo P waves based on Hooke's law, elastic wave projection and dispersion equation, respectively. Now numerical calculation of these equations uses regular grid finite difference method, which is of low efficiency, low accuracy and is unstable in TTI simulation. In order to improve the calculating accuracy, this paper builds the staggered grid finite difference format for each forwarding simulation. Comparing three different numerical expressions of pseudo P wave equation in a 3D TTI medium, we find that the method based on dispersion equation is more convenient to simulate elastic P wave propagation and has lowest numerical noise. By analyzing the frequency dispersion characteristics based on different angles of isotropic symmetry axis, we introduce appropriate SV wave velocity in calculation to keep calculation stable. An example of a 2D simple synthetic model shows that the staggered grid forwarding method allow us to obtain a smooth and stable pseudo P wave field. With this strategy, 2D BP TTI reverse time migration can also achieve basically stable migration results.