Numerical methods have been widely applied to simulate seismic wave propagation. However, few studies have focused on internal multiples modeling. The formation mechanism and response of internal multiples are still unclear. Therefore, we develop a weighted-optimised-based internal multiples simulation method under 3D conditions. Using a one-way wave equation and full-wavefield method, the different-order internal multiples are computed numerically in a recursive manner. The traditional Fourier finite-difference (FFD) method has low numerical accuracy in a horizontal direction. A globally optimised FFD (OFFD) method is used to improve the lateral propagation accuracy of the seismic waves. Meanwhile, we adopt an adaptive variable-step technique to improve computational efficiency. The 3D internal multiples modeling technique is capable of calculating the different-order multiple reflections in complex structures. We use the present method to simulate internal multiples in several models. Theoretical analyses are consistent with the numerical results. Numerical examples demonstrate that the 3D internal multiples modeling technique has superior performance when adapting to lateral velocity changes and steep dip. This also implies that our method is fit for the simulation of internal multiples propagation in a 3D complex medium and can assist in identifying the internal multiples from full-wavefield data.

中文翻译：

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基于全局优化傅里叶有限差分法的3D自适应内部多次波建模

数值方法已广泛应用于模拟地震波传播。然而，很少有研究关注内部倍数模型。内部多次波的形成机制和响应尚不清楚。因此，我们开发了一种在 3D 条件下基于加权优化的内部倍数模拟方法。使用单向波动方程和全波场方法，以递归方式数值计算不同阶的内部多次波。传统的傅里叶有限差分（FFD）方法在水平方向的数值精度较低。采用全局优化的FFD（OFFD）方法来提高地震波的横向传播精度。同时，我们采用自适应可变步长技术来提高计算效率。3D 内部多次波建模技术能够计算复杂结构中的不同阶多次反射。我们使用本方法在几个模型中模拟内部倍数。理论分析与数值结果一致。数值例子表明，3D 内部多次波建模技术在适应横向速度变化和陡倾角时具有优越的性能。这也意味着我们的方法适用于模拟 3D 复杂介质中的内部多次波传播，并且可以帮助从全波场数据中识别内部多次波。数值例子表明，3D 内部多次波建模技术在适应横向速度变化和陡倾角时具有优越的性能。这也意味着我们的方法适用于模拟 3D 复杂介质中的内部多次波传播，并且可以帮助从全波场数据中识别内部多次波。数值例子表明，3D 内部多次波建模技术在适应横向速度变化和陡倾角时具有优越的性能。这也意味着我们的方法适用于模拟 3D 复杂介质中的内部多次波传播，并且可以帮助从全波场数据中识别内部多次波。