二阶弹性波动方程高精度交错网格波场分离数值模拟

给出了一种等价的二阶弹性波动方程,以解决弹性波场中完全弹性波动方程不能完全分离耦合的纵、横波波场问题.应用高阶交错网格有限差分法求解该波动方程,并使用通量校正技术(FCT)进一步压制频散,采用均匀介质模型和层状介质模型进行波场分离数值试验,精确得到了混合波场、完全分离的纯纵波及纯横波波场.数值结果分析表明,本文方法在均匀介质情况下准确可靠,在分离后的纯纵、横波波场中可观察到较为丰富的能量转换信息,这对认识复杂弹性波的传播规律及弹性波理论具有重要意义.

WAVE FIELD SEPARATION NUMERICAL MODELING OF SECOND ORDER ELASTIC WAVE EQUATION BY HIGH-PRECISION STAGGERED-GRID FINITE DIFFERENCE SCHEME

This paper proposes an equivalent second order elastic wave equation to solve the problem of being unable to completely separate the coupled P and S wave by full elastic wave equation. Through solving this equivalent wave equation by high-order staggered-grid finite difference scheme together with Flux Correction Technology (FCT) and separating wave fields of the isotropic model and layered model, the authors accurately obtained the hybrid wave field and completely separated fields of pure P wave and pure S wave fields. An analysis of the numerical results shows that the method is effective and reliable in isotropic media, and there exists abundant energy transform information in separated pure P and pure S wave field. The result of the study is of significance in understanding the propagating law and the elastic wave theory in the complex wave field.