On dynamic ray tracing in three dimensional inhomogeneous media

1980 ◽  
Vol 24 (3) ◽  
pp. 317-318
Author(s):  
Peter Hubral ◽  
I. Pšenčík
Keyword(s):  
Ray Tracing ◽  
Three Dimensional ◽  
Inhomogeneous Media ◽  
Dynamic Ray Tracing

Three‐dimensional primary zero‐offset reflections

Geophysics ◽  
1993 ◽  
Vol 58 (5) ◽  
pp. 692-702 ◽  
Author(s):  
Peter Hubral ◽  
Jorg Schleicher ◽  
Martin Tygel
Keyword(s):  
Ray Tracing ◽  
Large Scale ◽  
Initial Conditions ◽  
Fresnel Zone ◽  
Three Dimensional ◽  
Normal Incidence ◽  
Careful Analysis ◽  
Point Sources ◽  
Dynamic Ray Tracing ◽  
Zero Offset

Zero‐offset reflections resulting from point sources are often computed on a large scale in three‐dimensional (3-D) laterally inhomogeneous isotropic media with the help of ray theory. The geometrical‐spreading factor and the number of caustics that determine the shape of the reflected pulse are then generally obtained by integrating the so‐called dynamic ray‐tracing system down and up to the two‐way normal incidence ray. Assuming that this ray is already known, we show that one integration of the dynamic ray‐tracing system in a downward direction with only the initial condition of a point source at the earth’s surface is in fact sufficient to obtain both results. To establish the Fresnel zone of the zero‐offset reflection upon the reflector requires the same single downward integration. By performing a second downward integration (using the initial conditions of a plane wave at the earth’s surface) the complete Fresnel volume around the two‐way normal ray can be found. This should be known to ascertain the validity of the computed zero‐offset event. A careful analysis of the problem as performed here shows that round‐trip integrations of the dynamic ray‐tracing system following the actually propagating wavefront along the two‐way normal ray need never be considered. In fact some useful quantities related to the two‐way normal ray (e.g., the normal‐moveout velocity) require only one single integration in one specific direction only. Finally, a two‐point ray tracing for normal rays can be derived from one‐way dynamic ray tracing.

Application of the Modified Differential Approximation (MDA) for Radiation Transport to Arbitrary Three-Dimensional Geometry

2009 ◽  
Author(s):  
Mahesh Ravishankar ◽  
Sandip Mazumder
Keyword(s):  
Ray Tracing ◽  
Radiation Transport ◽  
General Procedure ◽  
Three Dimensional ◽  
Inhomogeneous Media ◽  
Computational Time ◽  
View Factor ◽  
Differential Approximation ◽  
Participating Media ◽  
Major Shortcoming

The first-order spherical harmonics method (or P1 approximation) has found prolific usage for approximate solution of the radiative transfer equation (RTE) in participating media. However, the accuracy of the P1 approximation deteriorates as the optical thickness of the medium is decreased. The Modified Differential Approximation (MDA) was originally proposed to remove the shortcomings of the P1 approximation in optically thin situations. This article presents algorithms to apply the MDA to arbitrary geometry—in particular, three-dimensional (3D) geometry with obstructions, and inhomogeneous media. The wall-emitted component of the intensity was computed using a combined view-factor and ray-tracing approach. The Helmholtz equation, arising out of the medium-emitted component, was solved using an unstructured finite-volume procedure. The general procedure was validated against benchmark Monte Carlo results. The accuracy of MDA was found to be far superior to the standard P1 approximation in optically thin situations, and comparable to the P1 approximation in optically thick situations. Calculation and storage of the view-factor matrix was found to be a major shortcoming of the MDA, and several strategies to reduce both memory and computational time are discussed and demonstrated. In addition, for inhomogeneous media, calculation of optical distances requires a ray-tracing procedure, which was found to be a bottleneck from a computational efficiency standpoint.

Indirect-approach method for specified-end points seismic ray tracing in three dimensional inhomogeneous media

1998 ◽  
Vol 11 (3) ◽  
pp. 321-328
Author(s):  
Chao-Fan Xu ◽  
Xian-Kang Zhang ◽  
Jian Yang ◽  
Zhuo-Xin Yang ◽  
Hong-Zhao Deng ◽  
...  
Keyword(s):  
Ray Tracing ◽  
Three Dimensional ◽  
Inhomogeneous Media ◽  
End Points ◽  
Indirect Approach ◽  
Approach Method

Assessment of troposphere mapping functions using three-dimensional ray-tracing

GPS Solutions ◽  
2013 ◽  
Vol 18 (3) ◽  
pp. 345-354 ◽  
Author(s):  
Landon Urquhart ◽  
Felipe G. Nievinski ◽  
Marcelo C. Santos
Keyword(s):  
Ray Tracing ◽  
Three Dimensional ◽  
Mapping Functions

Differential ray tracing in inhomogeneous media

1997 ◽  
Vol 14 (10) ◽  
pp. 2824 ◽  
Author(s):  
Bryan D. Stone ◽  
G. W. Forbes
Keyword(s):  
Ray Tracing ◽  
Inhomogeneous Media
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