起伏地表声波方程的数值模拟

在实际地震勘探中,经常会遇到形状复杂的起伏地表,而实际采集的有关地表形状和介质的数据在进行数值模拟时都可视为对某一区域进行矩形剖分后所得网格点上的值,也就是说所获得的地表是一个阶梯状的地表,与实际的地表存在很大差异。利用阶梯状地表数据对地震记录进行波动方程模拟时,在阶梯的角点处会产生严重的干扰,进而影响数值模拟结果。本文利用声波方程,对阶梯状地表数据进行样条插值处理,得到了与起伏地表比较吻合的四边形网格剖分。经理论模型和实际数据的计算结果对比表明,用样条插值的方法逼近地表后进行计算的结果可以消除由于角点的奇性而产生的误差,减少了干扰,提高了计算精度。

Numeric simulation of acoustic equation on relief surface.

In practical seismic exploration, the shape-complex relief surface is often met, but practically acquired data about surface shape and media can be seen as the value at each point of grid after rectangular partition of certain region when carrying out numeric simulation. The acquired surface is step surface that makes a great difference to real surface. Using step surface data for wave equation simulation of seismic data can produce serious interference at corner points of steps and further affect the results of numeric simulation. Using a-coustic equation, the paper conducts spline interpolation for step surface data and results in quadrilateral grid partition coincident with relief surface. The computational results of theoretical models and real data show the computation by using spline interpolation method to approach surface can eliminate the errors produced by the singularity of corner points, reduce the interference and improve the computational precision.