Modeling of seismic wave propagation in areas with irregular topography is an important topic in the field of seismic exploration. As a popular numerical method for seismic modeling, the finite difference method is nontrivial to consider the irregular free surface. There have been extensive studies on the time-domain finite difference simulations with irregular topography; however, the frequency-domain finite difference simulation considering irregular topography is relatively less studied. The average-derivative approach is an optimal numerical simulation scheme in the frequency domain, which can produce accurate modeling results at a relatively low computational cost. Nevertheless, this approach can only deal with the modeling problems with a flat free surface. To address this issue, we design a new frequency-domain finite difference scheme by introducing the polygonal representation of topography into the average-derivative method. The irregular topography is represented by line segments with various slopes. An extension of the conventional average-derivative difference operator in the local rotated coordinate system is used for formulating the spatial derivatives aligned with the topographic line segments. As a result, new average-derivative difference schemes are obtained for irregular topography. In this way, the average-derivative optimal method is generalized to the model with irregular topography. Numerical examples show the effectiveness of the presented method.

在具有不规则地形的区域中地震波传播的建模是地震勘探领域中的重要课题。作为一种流行的地震建模数值方法，有限差分法对于考虑不规则自由表面是很重要的。对于具有不规则形貌的时域有限差分模拟已经进行了广泛的研究。然而，考虑不规则形貌的频域有限差分模拟研究相对较少。平均导数方法是频域中的最佳数值模拟方案，可以以相对较低的计算成本产生准确的建模结果。然而，这种方法只能处理具有平坦自由表面的建模问题。为了解决这个问题，通过将地形的多边形表示引入平均导数方法，我们设计了一种新的频域有限差分方案。不规则地形由具有各种斜率的线段表示。传统的平均-微分差算子在局部旋转坐标系中的扩展用于公式化与地形线段对齐的空间导数。结果，获得了用于不规则形貌的新的平均-微分差分方案。这样，将平均导数最优方法推广到具有不规则形貌的模型。数值算例表明了该方法的有效性。不规则地形由具有各种斜率的线段表示。传统的平均-微分差算子在局部旋转坐标系中的扩展用于公式化与地形线段对齐的空间导数。结果，获得了用于不规则形貌的新的平均-微分差分方案。这样，将平均导数最优方法推广到具有不规则形貌的模型。数值算例表明了该方法的有效性。不规则地形由具有各种斜率的线段表示。传统的平均-微分差算子在局部旋转坐标系中的扩展用于公式化与地形线段对齐的空间导数。结果，获得了用于不规则形貌的新的平均-微分差分方案。这样，将平均导数最优方法推广到具有不规则形貌的模型。数值算例表明了该方法的有效性。这样，将平均导数最优方法推广到具有不规则形貌的模型。数值算例表明了该方法的有效性。这样，将平均导数最优方法推广到具有不规则形貌的模型。数值算例表明了该方法的有效性。