Hybrid ray tracer and amplitude calculation with finite difference, graph theory and ray bending

2006 ◽  
Author(s):  
Chaoshun Hu ◽  
Kirk McIntosh ◽  
Harm van Avendonk ◽  
Paul Stoffa
Keyword(s):  
Graph Theory ◽  
Finite Difference ◽  
Difference Graph ◽  
Ray Bending

Minimum traveltime calculation in 3-D graph theory

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1895-1898 ◽  
Author(s):  
Ningya Cheng ◽  
Leigh House
Keyword(s):  
Graph Theory ◽  
Finite Difference ◽  
Finite Difference Methods ◽  
Velocity Model ◽  
Two Dimensions ◽  
Prestack Migration ◽  
Runge Kutta Method ◽  
Path Search ◽  
Crucial Part ◽  
Shortest Path Search

Traveltime calculation is a crucial part of seismic migration schemes, especially prestack migration. There are many different ways to compute traveltimes. These methods can be divided into three categories: (1) Ray tracing (Julian and Gubbins, 1977; Červený et al., 1977). These treat the problem as a initial value problem by shooting rays from the source to the receivers. Or they can also treat the problem as a two‐point boundary value problem. An initial raypath is bent using perturbation theory until Fermat’s principle is satisfied. Nichols (1994) also computed traveltimes with the amplitude information attached to it in two dimensions. (2) Finite‐difference methods (Reshel and Kosloff, 1986; Vidale, 1988; van Trier and Symes, 1991). These solve the eikonal equation directly by using different numerical schemes such as the Runge‐Kutta method, wavefront expansion, or upwind finite difference. (3) Graph theory (Moser, 1991; Fisher and Lees, 1993; Meng et al. 1994). This method recasts the traveltime problem into a shortest path search over a network, which is constructed from the velocity model. This method is guaranteed to find a stable minimum traveltime with any velocity model.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

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