可变交错网格优化差分系数法地震波正演模拟

传统变网格有限差分系数是通过Taylor级数展开得到的,在大的波数范围内,数值频散较严重。为此,提出一种基于最小二乘算法的可变交错网格优化差分系数法,即建立基于频散关系的平方误差函数,并引入约束条件,通过求取条件极值得到可变交错网格优化差分算子。频散分析表明,可变交错网格优化差分系数法能在更大波数范围内满足频散关系。模型正演结果证明,相同的空间差分算子长度,可变交错网格优化差分系数法相比Taylor级数展开法,能有效提高正演模拟的精度。

Traditional variable grid finite-difference coefficients are obtained by Taylor series expansion,and numerical dispersion is severe for a wide range of wave numbers.An optimized difference coefficient method of a variable staggered-grid based on the least squares theory is proposed in this paper.First,a square error function based on the dispersion relation is established.Next,with the constraint condition,the optimized difference operators for the variable staggered-grid are obtained by solving the conditional extremum,which can effectively suppress the numerical dispersion.Dispersion analyses show that the optimal variable staggered-grid finite-difference scheme can satisfy the dispersion relation for a wider wave number range.Numerical examples demonstrate that,for the same spatial difference operator length,the proposed optimized finite-difference scheme offers more accurate seismic wave field forward modelling than the Taylor expansion method.

国家科技重大专项(2016ZX05006-002-03)资助。