Block modeling and segmentally iterative ray tracing in complex 3D media

Abstract

We propose using a set of blocks to approximate geologically complex media that cannot be well described by layered models. Interfaces between blocks are triangulated to prevent overlaps or gaps often produced by other techniques, such as B-splines, and to speed up the calculation of intersection points between a ray and block interfaces. We also use a smoothing algorithm to make the normal vector of each triangle continuous at the boundary, so that ray tracing can be performed with stability and accuracy. Based on Fermat's principle, we perturb an initial raypath between two points, generally obtained by shooting, with a segmentally iterative ray-tracing ͑SIRT͒ method. Intersection points on a ray are updated in sequence, instead of simultaneously, because the number of new intersection points may be increased or decreased during the iteration process. To improve convergence speed, we update the intersection points by a first-order explicit formula instead of traditional iterative methods. Only transmitted and reflected waves are considered. Numerical tests demonstrate that the combination of block modeling and segmentally iterative ray tracing is effective in implementing kinematic two-point ray tracing in complex 3D media.

Crustal velocity structure in the Emeishan large igneous province and evidence of the Permian mantle plume activity

“…By correcting the structural model many times and using forward calculation by ray tracing to calculate the travel times of multi-phases (Cerveny et al, 1988;Vidale, 1988;Zelt and Smith, 1992;Cerveny, 2001;Xu T et al, 2004;Xu et al, 2006Xu et al, , 2010Xu et al, , 2014bLi et al, 2013;Lan et al, 2013aLan et al, , 2013b, we obtained the final crust-mantle model. The identification of seismic phases has a great impact on the velocity structure and therefore the geophysical model for the study region needs to be the most accurate possible to adequately constrain the medium.…”

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

“…where v Vi and v Hi are the vertical and horizontal phase velocities of the three vertices in a triangular grid, respectively; u i is the corresponding area coordinate in a triangle (Xu et al 2004(Xu et al , 2005(Xu et al , 2006; and v V and v H are vertical and horizontal phase velocities of an given point, respectively. After these two steps, we can obtain the velocity distribution within the whole model space (Fig.…”

“…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 2006Xu et al , 2008Xu et al , 2010Xu et al , 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 2004Xu et al , 2007Xu et al , 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 (1992Zhao et al ( , 1994 and Zhao and Lei (2004) developed a method using the Snell's law to correct the path points on discontinuous interfaces.…”

“…How to accurately describe the geological model with undulating interfaces is very important for solving the seismic wave propagation. The methods always used include the approximation method with ladderlike grids , the model expansion method with regular grids (Hole 1992;Ma and Zhang 2014), the nonuniform grid spacing method (Sun et al 2012a, b), the hybrid grid spacing method (Sun et al 2009(Sun et al , 2012aBai et al 2010Bai et al , 2013Li et al 2013), the curved grid spacing method (Thompson et al 1985;Ruud 1994, 1998;Dong 2005;Wang and Liu 2006;Hestholm et al 2006;Lan et al 2012;Zhang 2011, 2013a, b;Ma and Zhang 2014) and the triangulated meshing method (Fomel 1997;Sethian 1999;Xu et al 2006Xu et al , 2010Kao et al 2008;Yu et al 2010;Bai et al 2012). The triangular grids are simple and flexible in modeling and can describe any undulating terrain with high degree of approximation.…”