基于余弦调制Chebyshev窗的弹性波高精度正演

High precision elastic wave equation forward modeling based on cosine modulated Chebyshev window function

有限差分时间域正演是弹性波逆时偏移和全波形反演的基础,正演的计算精度也控制着偏移结果的准确性,若精度不高,则在偏移、反演后会带来假象.为了有效提高正演精度,本文结合窗函数优化方法,在窗函数截断伪谱法空间褶积序列以逼近有限差分算子的基础上,提出了一种基于Chebyshev窗的余弦调制模型,在原始Chebyshev窗的基础上引入了调制次数和调制范围,通过调节这两个参数可以人工可视化的调节截断误差,新的窗函数继承了Chebyshev窗的特点,在不明显降低截断谱范围的基础上明显降低了截断误差.本文针对不同正演阶数N,给出了一组经验调制系数,并通过数值模拟方法,对比了新方法、改进二项式窗和基于最小二乘优化方法的正演效果.结果表明,基于余弦调制的Chebyshev窗控制数值频散的能力更强,在大网格下可以得到更精确的正演结果.从经济角度分析,该方法减小了计算花费,提高了计算效率.

The finite difference forward modeling is the basis of elastic wave reverse-time migration and full waveform inversion in the time domain.The accuracy of forward modeling also controls the accuracy of seismic imaging and inversion.The migration or inversion will bring illusion if the accuracy is not high.We can get optimized explicit finite difference operators by using the window function to truncate spatial convolution counterpart of the pseudo-spectral method.Based on this,a cosine modulated Chebyshev window is designed.On the basis of the original Chebyshev window,the modulation times and modulation domain are introduced,and we can adjust truncation error visually by controlling these two parameters.As the new window function inherits the character of Chebyshev window,we observe that the spectral range using the modulated window function for truncation is significantly broader than using the conventional window function with stable error.For different forward modeling orders N,we give a set of empirical modulation factors and compare the forward modeling effect of the new method andimproved binomial window by the numerical simulation method.The results demonstrate that the operators based on the cosine modulated Chebyshev window can efficiently suppress the numerical dispersion and get more accurate forward modeling results on the large grid.From economic perspective,this method reduces the computational cost and improves efficiency.