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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.
The forward modeling of frequency-space domain is the basis of full-waveform inversion in frequency domain.The finite difference scheme of the traditional rotating coordinate system is only suitable for the cases where the vertical and horizontal spatial sampling intervals are equal. In order to break this limitation, Point Difference Scheme A 15-point finite difference method based on the average-derivative method (ADM) is proposed. The weighted least square method is used to obtain the weighted optimization coefficients so that the dispersion is minimized. After optimization, each wavelength is only 2.85 mesh points can be achieved within 1% error control.In this paper, by introducing the best matching layer (perfectly matched layer referred to as PML) absorbing boundary conditions, effectively suppress the artificial boundary reflection.The forward modeling test verifies the average derivative The method of 15-point difference method can effectively suppress the numerical dispersion and improve the efficiency of forward modeling in the frequency domain without significantly increasing the computational load.The test of the full waveform inversion model verifies that the rectangular grid is suitable for large offset From the waveform inversion, has a wide range of practicality.