基于平均导数的标量波频率域正演数值模拟方法

Frequency domain scalar wave forward modeling method based on an average-derivative method

频率-空间域正演模拟是频率域全波形反演的基础.传统旋转坐标系的有限差分格式仅适用于纵横空间采样间隔相等的情况,为了打破这一局限性,本文结合平均导数法与15点差分格式提出了一种基于平均导数法(average-derivative method简称ADM)的15点有限差方法,并运用最小二乘法求取加权优化系数,使得频散最小化,经优化后每个波长仅需2.85个网格点就能达到误差控制在1%内.本文通过引入最佳匹配层(perfectly matched layer简称PML)吸收边界条件,有效的压制人工边界反射.正演模拟测试验证了基于平均导数法的15点差分方法可以在不明显增加计算量的前提下,有效的压制数值频散,提高了频率域正演的效率.全波形反演模型测试验证了其矩形网格适合于大偏移距波形反演,具有广泛的实用性.

Frequency-domain modeling is the basis of full-wave inversion in frequency-domain. Traditional finite difference scheme based on rotating coordinate system can only be applied to the same vertical spatial sample interval and horizontal spatial sample interval. In order to break the limitation,this paper develops a 15-point finite difference scheme based on an average-derivative method（ ADM）,which combines average-derivative method and 15-point finite difference scheme. Then the paper applies the least-square method for determining weighted optimal coefficients to minimize dispersion,and per wavelength only needs 2. 85 point after the optimization. We put perfectly matched layer（ PML） into model to absorb the artificial boundary reflections. The numerical modeling test proves that ADM 15-point scheme can suppress numerical dispersion obviously and improve computational efficiency effectively. Full waveform inversion（ FWI） test also demonstrates that rectangular grid is suitable for large offset FWI,and can be generally applied to geologic model.