Frequency-domain elastic-wave modeling for polygonal topography using rotated average-derivative difference operators
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RESEARCH ARTICLE - APPLIED GEOPHYSICS
Frequency‑domain elastic‑wave modeling for polygonal topography using rotated average‑derivative difference operators Zheng Li1,2,3 · Jing‑Bo Chen1,2,3 · Jian Cao1,2 Received: 4 February 2020 / Accepted: 5 September 2020 / Published online: 18 September 2020 © Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2020
Abstract 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. Keywords Irregular topography · Frequency-domain modeling · Rotated coordinate system · Average-derivative difference scheme
Introduction The surface of the earth is not a flat plane. The irregular surface could distort the recorded data significantly. It also brings new challenge to seismic exploration. Numerical simulations with the surface topography describe more * Zheng Li [email protected] Jing‑Bo Chen [email protected] Jian Cao [email protected] 1
Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
2
Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China
3
University of Chinese Academy of Sciences, Beijing 100049, China
realistic seismic wave propagation. Thus, it is critically useful to study a numerical simulation method that considers the irregular topography. To incorporate the irregular topography, the numerical methods based on the weak form of wave equation are commonly used. For example, Komatitsch and Tromp (1999) presented seismic wave field simulation with a relief surface by utilizin
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