Frequency-domain elastic-wave modeling for polygonal topography using rotated average-derivative difference operators

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.