We have developed an optimal method to determine expansion parameters for flexible stencils in 2D scalar-wave finite-difference frequency-domain (FDFD) simulation. Our stencil only requires the involved grid points to be paired and rotationally symmetric around the central point. We apply this method to the transition zone in discontinuous-grid modeling, in which the key issue is designing particular FDFD stencils to correctly propagate the wavefield passing through the discontinuous interface. Our method can work in an FDFD discontinuous grid with arbitrary integer coarse- to fine-grid spacing ratios. Numerical examples are developed to determine how to apply this optimal method to discontinuous-grid FDFD schemes with spacing ratios of 3 and 5. The synthetic wavefields are highly consistent to those calculated using the conventional dense uniform grid, and the memory requirement and computational costs are greatly reduced. For velocity models with large contrasts, our discontinuous-grid FDFD method can significantly improve the computational efficiency in forward modeling, imaging, and full-waveform inversion.

中文翻译：

---

具有柔性模板的最优频域有限差分算子及其在不连续网格建模中的应用

我们已经开发出一种最佳方法，可以在2D标量波有限差分频域（FDFD）模拟中确定柔性模板的扩展参数。我们的模板仅要求配对的网格点成对并且围绕中心点旋转对称。我们将此方法应用于不连续网格建模中的过渡区域，其中的关键问题是设计特定的FDFD模板以正确传播通过不连续界面的波场。我们的方法可以在具有任意整数的粗到细网格间距比的FDFD不连续网格中工作。通过数值算例确定如何将这种最佳方法应用于间距比为3和5的不连续网格FDFD方案。合成波场与使用常规密集均匀网格计算得到的波场高度一致，并且大大降低了内存需求和计算成本。对于具有较大对比度的速度模型，我们的不连续网格FDFD方法可以显着提高正向建模，成像和全波形反演的计算效率。