Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Earthquake Science, Nov 2017

Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameterization in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in transversely homogeneous elliptically anisotropic media. Seismic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in elliptically anisotropic media with an irregular surface.

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Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Earthq Sci Ray tracing of turning wave in elliptically anisotropic media with an irregular surface 0 T. Xu CAS Center for Excellence in Tibetan Plateau Earth Sciences , Beijing 100101 , China 1 T. Xu Z. Bai Y. Liu G. Yu State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Science , Beijing 100029 , China 2 M. Zhang (&) Key Laboratory of Earthquake Geodesy, Institute of Seismology , China Earthquake Administration, Wuhan 430071 , China 3 G. Yu University of Chinese Academy of Science , Beijing 100049 , China 4 J. Hou Institute of Geophysics , China Earthquake Administration, Beijing 100081 , China Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameterization in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in transversely homogeneous elliptically anisotropic media. Seismic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in elliptically anisotropic media with an irregular surface. Ray tracing; Elliptically anisotropic media; Vertical and horizontal phase velocity; Irregular surface; Triangular grids 1 Introduction A large number of researches and explorations confirm that seismic anisotropy is common in the crust and upper mantle (Hess 1964; Christensen and Crosson 1968; Francis 1969; Crampin 1978, 1984; Crampin et al. 1980; Helbig 1983; Lyakhovitskiy 1984; Thomsen 1986; Kaneshima 1990; Wild and Crampin 1991; Weiss et al. 1999; Zhang 2002a, b; Gao and Teng 2005; Wang and Zhao 2009; Li et al. 2011; Ouyang et al. 2015) . The propagation of seismic waves in anisotropic media is the foundation of the anisotropic research. The methods to solve the propagation of seismic waves mainly include wave-field simulation (Carcione et al. 1992; Lan and Zhang 2011; Liu et al. 2014a, b) , seismic ray tracing (Cerveny 2001; Cardarelli and Cerreto 2002; Xu et al. 2006, 2008, 2010, 2014) and traveltime calculation using eikonal equation (Faria and Stoffa 1994; Lan and Zhang 2013a, b) . Compared with the method of traveltime calculation using eikonal equation, ray tracing methods not only can obtain the traveltime of the seismic wave field, but also can get the ray trajectories in the ground (Shearer and Chapman 1989; Cerveny 2001) . Traditional ray tracing methods include shooting methods (Langan et al. 1985; Virieux and Farra 1991; Xu et al. 2004, 2007, 2008) and bending methods (Julian and Gubbins 1977; Thurber and Ellsworth 1980; Aki and Richards 1980) . Based on the bending method, Um and Thurber (1987) developed the pseudo-bending method, which was used to solve the twopoint ray tracing in continuous media (Um and Thurber 1987; Pereyra 1992; Xu et al. 2006) , while is not suitable for the presence of strong velocity discontinuities. To solve this problem, Zhao et al. (1992 , 1994) and Zhao and Lei (2004) developed a method using the Snell’s law to correct the path points on discontinuous interfaces. Xu et al. (2010, 2014) developed a ray tracing perturbation scheme of combination of pseudo-bending methods and segmentally iterative methods. In recent decades, the ray tracing methods developed include wavefront reconstruction methods (Vinje et al. 1993, 1996a, b, 1999) , slowness matching methods (Symes 1996; Symes and Qian 2003) , Huygens wavefront tracing methods (Sava and Fomel 2001), shortest path methods (Moser 1991; Fischer and Lees 1993; Zhou and Greenhalgh 2005) and simulated annealing methods (Bona et al. 2009) . Rough topography is very common, and we have to deal with it during the acquisition, processing and interpretation of seismic data (Neuberg and Pointer 2000; Bean et al. 2008; Lan and Zhang 2011; Lan et al. 2012; Bevc 2012) . How to accurately describe the geological model with undulating interfaces is very important for solving the seismic wave propagatio (...truncated)


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Minghui Zhang, Tao Xu, Zhiming Bai, Youshan Liu, Jue Hou, Guiping Yu. Ray tracing of turning wave in elliptically anisotropic media with an irregular surface, Earthquake Science, 2017, pp. 219-228, Volume 30, Issue 5-6, DOI: 10.1007/s11589-017-0192-5