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![]() | Shortest path ray tracing on parallel GPU devices | ![]() |
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The velocity model is represented as a weighted graph
where
is the set of vertices,
the set of
edges and
the set of edge weights. Each vertex depicts
a location
in the velocity model in such a way that
all locations form a regular rectangular grid that covers
the velocity model extension. Figure 1
shows a three layer velocity model. The black dots are
the vertex locations. We can also set a double index
to each vertex based in its column and row in the rectangular
grid. As there is a one to one correspondence between vertices
and indices, hereafter we will not distinguish
between them. The horizontal and vertical separations between
locations are
and
, respectivelly. For simplicity, we will
set
.
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velmodel
Figure 1. Rectangular grid of vertices in a velocity model. |
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Graph edges are defined between neighboring vertices. There are
various ways to accomplish this. One way is to choose a rectangular
neighborhood around the current vertex and define an edge
between every other vertex inside the neighborhood and the
current one. In Figure 2
displays two of such neighborhoods, one of radius and
the other of radius
. A neighborhood with radius
contains
vertices.
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order1neigh,order2neigh
Figure 2. Two vertex neighborhoods. (a) radius 1 (b) radius 2. |
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![]() | Shortest path ray tracing on parallel GPU devices | ![]() |
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