We propose an improved block modeling technique to describe complex 3‐D media. A geological medium is represented as an aggregate of geological blocks rather than layers, which have their own attributes such as shape, size, density and seismic wave velocity. The structure of a blocky model is Body → Block → Interface → Point. We construct interfaces in the model with triangles, which fit most complex media. For normal vectors change abruptly across the linked boundaries, normal vectors to the interfaces are everywhere smoothed by an approximate estimation and thus approximately C2 continuous to generate relatively accurate ray tracing. We present some methods for shooting ray tracing in 3‐D: triangle‐subdivision, triangle‐division and subtriangle methods. Our calculation indicates that the subtriangle method is most efficient. We present real cases for some complex models and ray tracing results on these models.

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.

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