非均匀介质中地震波应力场的WNAD方法及其数值模拟

A WNAD method for seismic stress-field modeling in heterogeneous media

通过对近似解析离散化(NAD)方法的分析,给出了一种求解声波和弹性波方程的带权重的近似解析离散化(WNAD)方法,并用WNAD方法、Lax-Wendroff修正格式(LWC)和二阶中心差分方法计算了二维波动方程初值问题的应力场数值误差.结果表明WNAD方法具有更高的数值精度.用WNAD方法、LWC和四阶交错网格法对二维非均匀介质中弹性波传播的应力场进行了数值模拟.应力场快照和地表地震记录表明,即使是在粗网格条件下WNAD方法的模拟结果仍无可见的数值频散和源噪声.另一方面,由于WNAD方法同时计算了地震位移和梯度场,使得应力的计算更为便捷和精确.而且WNAD方法中波位移梯度局部连接关系的使用使得应力在间断处能够自动近似地满足应力连续性.

In this article, we first present the weighted nearly analytic discrete （WNAD） method for acoustic and elastic wave equations. Then we compute numerical error of the stress-field for the 2 D acoustic initial value problem using the WNAD method, the conventional finite-difference method and the fourth-order Lax-Wendroff correction （LWC） scheme. Numerical calculations of the relative errors show that WNAD method has the highest accuracy among these methods. Finally, we present the stress-field snapshots generated and compare the numerical results computed hy the WNAD method with those of the fourth-order LWC scheme and the fourth-order staggered-grid FDM for the 2-D inhomogeneous medium case. Promising numerical results illustrate that the results of the WNAD method have no visible numerical dispersion or source- noises even though too coarse grids are used. What＇s more, the WNAD method computes not only the values of the displacement U, but also the gradients of U, which makes it more convenient and accurate for computing the stress fields. The continuity of the stress is satisfied automatically even when the models have large velocity contrast between adjacent layers because of using local connection relations of the displacement U and its gradients.