黏声波高阶傅里叶有限差分法参数优化成像

Parameter optimization and imaging of visco-acoustic media using high-order Fourier finite-difference method

黏声波高阶傅里叶有限差分法数值模拟可以更精准地反映具有大地吸收效应的高倾角地层地震响应,它能适应任意横向速度变化并压制大倾角处有限差分法出现的频散现象及背景噪声。高倾角地层偏移精度取决于差分算子常系数确定及阶数的求取。本文使用梯度下降法对傅里叶有限差分算子中的高阶有限差分校正项进行了优化,根据相对误差和约束系数优化结果,在不提高方程阶次的情况下达到更高阶方程的逼近效果,并将其扩展到黏声介质。通过设计的模型算例可以得出,文中方法适应具有吸收衰减效应的强空间变速介质的正演模拟,且具有较高的计算精度和计算效率,能对复杂地质构造进行准确的地震数值模拟。

The numerical simulation of visco-acoustic media using the high-order Fourier finite-difference method can reflect the seismic response of high-dip strata with geo-absorption effects more accurately.It can adapt to any lateral speed changes and suppress the dispersion and background noise at large dip angles caused by the finite-difference method.The migration precision of the high-dip strata depends on the determination of the constant coefficient of the difference operator and the calculation of the order.In this study, the gradient descent method was used to optimize the high-order finite-difference correction item in the Fourier finite-difference operator.According to the optimization results of the relative errors and constraint coefficients, the approximation effects of higher-order equations were achieved without increasing the order of the equation and then were expanded to viscoelastic media.Using the designed model, it can be concluded that the proposed method is applicable to the forward simulation of the strong spatial variable speed media with absorption and attenuation effects and has high calculation accuracy and efficiency.Accurate seismic numerical simulation of complex geological structures further confirmed the effectiveness of this method.