VTI介质中准P波方程的数值解法

为克服常规弹性波动方程正演结果的局限，研究了具有垂直对称轴的横向各向同性（VTI）介质中准P波方程的数值解法.首先从VTI介质中准P波方程出发，采用任意偶数阶精度有限差分算子构造了准P波方程数值求解的高阶有限差分格式，给出了其稳定性条件和边界条件的计算方法.为提高数值求解精度，引入通量校正算法压制数值频散，将震源置于各向同性介质内以消除准P波方程的误差解，在此基础上建立了VTI介质中准P波方程正演的数学模型.

Numerical solutions of quasi-P wave equations in VTI media

To overcome the shortage of normal elastic wave forward modeling result,the numerical solution of quasi-P wave equations in transversely isotropic media with a vertical symmetry axis(VTI) was studied.Based on the quasi-P wave equations in VTI media,a high-order finite-difference scheme was derived by using an even-order accurate difference operator,the stability conditions and the absorbing boundary conditions were also provided.In order to improve the precision of numerical solution,a flux-corrected transport technique was introduced to suppress the numerical dispersion,and by placing the source in isotropic media the error solution of quasi-P wave equations was eliminated completely.Using all above techniques the mathematical model for quasi-P wave equations simulation was established.