Elastic reverse-time migration in irregular tunnel environment based on polar coordinates
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Elastic reverse-time migration in irregular tunnel environment based on polar coordinates* Qu Ying-Ming♦1, Zhou Chang1, Worral Qurmet1, Li Zhen-Chun1, Wang Chang-Bo2, and Sun Jun-Zhi1 Abstract: When seismic exploration is conducted in a special geological environment such as a tunnel space, the traditional imaging method in the Cartesian coordinate system cannot accurately discretize the air column in that environment. Thus, obtaining Thus, obtaining highquality imaging results is difficult. Therefore, an elastic-wave reverse-time migration method based on the polar coordinate system is proposed. In this method, three boundary conditions exist: outer, inner, and corner boundaries. In the outer boundary, the polar-coordinated absorbing boundary in the radial direction is used to suppress the artificial-boundary reflection. The free-surface boundary condition is adopted in the tunnel space at the inner boundary. In the angular boundaries, we use two different boundary conditions for two cases. The air column in the tunnel space is usually not an irregular circle. Therefore, the irregular tunnelspace geological body in the polar coordinate system is meshed into curvilinear grids and transformed into a regular one in an auxiliary polar coordinate system using the mapping method. Finally, elastic reverse-time migration technology is applied into the auxiliary polar coordinate system. In the numerical examples, two typical models are used to test the proposed method, which verify that the proposed method can obtain accurate images from the datasets in the tunnel space. Keywords: Polar coordinate system; Irregular tunnel; Elastic; Reverse-time migration; Free surface
Introduction Reverse-time migration (RTM) produces images of the subsurface reflection interface by synthesizing the forward-propagated source wavefield and backpropagated receiver wavefield (McMechan, 1983; Whitmore, 1983; Baysal et al., 1983; Liu et al., 2017a;
Sun et al., 2017). Compared to the ray-imaging methods (Beylkin, 1985; Hill, 1990, 2001; Gray and Bleistein, 2009) and one-way wave-equation-based imaging method (Claerbout, 1985; Mulder and Plessix, 2004), RTM offers obvious advantages for imaging of complex media (Baysal et al., 1983; Chang and McMechan, 1986). However, in practice, the RTM based on acousticwave approximation is not accurate, and the S-wave
Manuscript received by the Editor January 15, 2019; revised manuscript received December 23, 2019. *This study work was financially supported by the National Natural Science Foundation of China (grant Nos. 41904101 and 41774133), Natural Science Foundation of Shandong Province (grant No. ZR2019QD004), Fundamental Research Funds for the Central Universities (grant No. 19CX02010A), the Open Funds of SINOPEC Key Laboratory of Geophysics (grant No. wtyjy-wx2019-01-03). 1. Department of Geophysics, School of Geosciences, China University of Petroleum (East China), Qingdao 266580, China; 2. Geophysical Research Institute, Shengli Oilfield Branch Co., SINOPEC, Dongying 257022, China. ♦Corresponding Author: Qu
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