Shortest path ray tracing with sparse graphs

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 987-996 ◽  
Author(s):  
Robert Fischer ◽  
Jonathan M. Lees
Keyword(s):  
Ray Tracing ◽  
Shortest Path ◽  
Computational Efficiency ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Low Velocity ◽  
Sparse Graphs ◽  
Time Savings ◽  
Snell’S Law ◽  
Snell's Law

A technique for improving the efficiency of shortest path ray tracing (SPR) is presented. We analyze situations where SPR fails and provide quantitative measures to assess the performance of SPR ray tracing with varying numbers of nodes. Our improvements include perturbing the ray at interfaces according to Snell’s Law, and a method to find correct rays efficiently in regions of low velocity contrast. This approach allows the investigator to use fewer nodes in the calculation, thereby increasing the computational efficiency. In two‐dimensional (2-D) cross‐borehole experiments we find that with our improvements, we need only use 2/3 as many nodes, saving up to 60 percent in time. Savings should be even greater in three dimensions. These improvements make SPR more attractive for tomographic applications in three dimensions.

VECTORIZATION AND PRECISE REFRACTIONS IN BEAM TRACING

2004 ◽  
Vol 04 (02) ◽  
pp. 325-339
Author(s):  
KAZUHIRO KOYAMA ◽  
YOSHIAKI TOMIZAWA ◽  
MINORU OKADA
Keyword(s):  
Ray Tracing ◽  
Computational Cost ◽  
Image Synthesis ◽  
Improved Method ◽  
Projection Screen ◽  
Snell’S Law ◽  
Snell's Law ◽  
Region Segment ◽  
Tracing Method

In this paper we propose two improvements to the beam tracing method, one is to reduce the final redundant-drawing of pixel fragments into the frame buffer, and the other is to use Snell's law instead of the tangent law. It is well known that the ray tracing scheme is one of the most effective methods for high quality CG image synthesis. The beam tracing method was introduced because traditional ray tracing algorithms have a significant calculation cost. In the improved method, the projection screen is recursively divided into non-overlapping coherent region segments based on the coherence of the ray-trace-tree structure of a given scene, and an image can be synthesized after the segmentation process by tracing one or several rays in each region segment. We introduced Snell's law for the refractions of the rays. Therefore, we can reduce the computational cost of ray tracing, eliminate the extra calculations caused by overlapping polygons on a screen, and increase the quality of CG images generated by our proposed method.

Snell's Law and Ray Tracing

2017 ◽  
Author(s):  
Julie Bentley ◽  
Craig Olson
Keyword(s):  
Ray Tracing ◽  
Snell’S Law ◽  
Snell's Law

Collimation of Two-Dimensional Ballistic Electrons Using Equivalent Snell's Law

1993 ◽  
Vol 32 (Part 1, No. 11A) ◽  
pp. 5014-5018 ◽  
Author(s):  
Mitsuhiro Noguchi ◽  
Hideki Sakakibara ◽  
Toshiaki Ikoma
Keyword(s):  
Two Dimensional ◽  
Snell’S Law ◽  
Snell's Law

Wave tracing: Ray tracing for the propagation of band-limited signals: Part 2 — Applications

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE385-VE393 ◽  
Author(s):  
John K. Washbourne ◽  
Kenneth P. Bube ◽  
Pedro Carillo ◽  
Carl Addington
Keyword(s):  
Ray Tracing ◽  
Real Data ◽  
Modeling Method ◽  
Simulation Accuracy ◽  
Arrival Times ◽  
Velocity Models ◽  
Depth Images ◽  
Snell’S Law ◽  
Band Limited ◽  
Snell's Law

Modeling seismic propagation is critically important to our work; unfortunately, we often must trade simulation accuracy for reduced computational expense. We present a new seismic-modeling method that is as simple and computationally efficient as Snell’s law ray tracing but provides propagation paths and arrival times more consistent with finite-bandwidth data. We refer to this modeling method as wave tracing and apply it to nonlinear traveltime tomography and depth imaging. By replacing Snell’s law ray tracing with wave tracing, we get better ray coverage, more robust and faster ray bending (fewer iterations), and a much more robust and faster algorithm for nonlinear tomography (fewer iterations, too). A very significant benefit is increased stability and robustness of tomographic inversion with respect to small changes in model parameterization and regularization. A related benefit is the increased stability of depth images with respect to small changes in velocity, which can increase confidence in interpretation. The velocity models that result from wave tracing match picked arrival times in band-limited data better and generate improved depth images. These advantages of wave tracing relative to conventional Snell’s law ray tracing have been tested on both synthetic and real data examples for crosswell seismic geometry.

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