优化交错网格差分算子的井间地震数值模拟及其频散分析

摘要

In the finite-difference numerical simulation of well seismic,when using discretized higher-order differential equation approximate continuous derivative wave equation,it will inevitably lead to numerical dispersion.As numerical disper-sion directly affects the precision of numerical simulation of seismic wave,so in order to get more clear and accurate records of seismic wave field,we must try best to suppress numerical dispersion.In this paper,we are based on an order velocity-stress elastic wave equation,introducing two constraint conditions and construct a Lagrange function,then obtain new differential co-efficients by extremely conditions.Analyze and compare the numerical simulation of an order velocity-stress elastic wave equa-tion with high-order staggered grid differential operators by Taylor expansion and optimized differential operators,we con-clude that the numerical simulation using by optimized staggered grid differential operators can more effectively suppress the numerical dispersion and improve the accuracy of simulation.and provide a reliable basis for wave field imaging of high preci-sion seismic data in well and interpretation between P wave and S wave.%在井间地震有限差分数值模拟中，用离散化的高阶差分方程近似连续导数的波动方程时，不可避免地会产生数值频散，而数值频散程度则直接影响到地震波数值模拟精度，因此为了得到清晰准确的地震波场记录，必须尽可能地压制数值频散。这里在一阶速度应力弹性波方程的基础上，利用两个约束条件构造拉格朗日函数获取优化差分系数，与泰勒展开差分系数下的交错网格高阶差分模拟结果比较，发现改进的优化交错网格差分算子的高阶差分数值模拟能更有效地压制数值频散，进一步提高交错网格高阶差分数值模拟的精度，为高精度井间地震数据的波场成像、纵横波联合解释等提供可靠依据。