Development of visualization tool for the wave propagation data onsphere
Mikito Furuichi 1 and Seiji Tuboi 1,211Institute for Research on Earth Evolution, Japan Agency for Marine-Earth Science and Technology (JAMSTEC)
3173-25 showa-mach, Kanazawa-ku Yokohama 236-0001, Japan
1
Data Research Center for Marine-Earth Sciences, Japan Agency for Marine-Earth Science and Technology(JAMSTEC) 3173-25 showa-mach, Kanazawa-ku Yokohama 236-0001, Japan

Introduction

An analysis of seismic waveform data on Earth surface plays animportant role in geophysical research because seismic waves
excited by earthquake source propagates various regions inside
the Earth and provide us information on physical state of theEarth. In order to visualize such wave data on global area incomputer graphics, we have developed a tool for creating apolygon from the scalar/vector data mapped on an unstructured
grid in two dimensions. In general, the data on the spheresurface is visualized, for example, by the color contour mappedon the sphere geometry. Our method utilizes the deformation of
the polygon coordinate from sphere geometry for representing
the wave form. Such a visualization method of wave form is notimplemented on commonly used application such as GMT(Generic Mapping Tools). In this paper, we present some detailsof our employed method to convert the unstructured data topolygon data, and demonstrate visualization result of global
seismic wave simulation.

andS n 1i , j Method

We consider the scattered data set a p ( p  1,2,3 ) defined atspherical coordinate (r , p ,  p ) on spherical surface (i.e.
r  constant). In our tool, this unstructured dataset isinterpolated to the data on structured mesh with a grid size ofn  n . The 2-D uniform mesh defined by ( i  (i  1)   , j  j   ) with    /(n  1)and   2 /(n  1)1
 1
constructs the cell which has center at  i  , j   .
2
 2
We first calculate a weight factor wp (i, j ) of p  th scatteredpoint to the node point at (i, j ) byw p (i, j )  max(( 1   p  i ) /  ), (1   p  i /  ) /( ),0)(1)

nI ,J)(4)I ,J

where ( I , J )  (i  1, j ) , (i  1, j ) , (i, j  1) and (i, j  1) , and () is a function defined by1 x  0.
(5)
0 x  0
The averaging procedures of (3) are iteratively applied to theempty node points until filling all of node data with S n i , j  0 .
After the mapping process described above, we reduce the meshsize in  direction on a polar region, in order to avoid theconcentration of the structured grid around the pole. The
reduced coarse mesh points are defined by(6) i , j  j  (i) and (i)  2 /(n (i) 1) , ( x)  where2

 (Sn (i)  n / 2 N (i )andN (i)  int log2 sin(i )

for( 1  i  n ) and N (1)  N (2) and N (n )  N (n  1) (Fig 2).
The fine grid data are remapped to the coarse one with a linear
interpolation. This coarsening scheme leads to 22.0-25.0% of
grid size reduction.
Then it is straight forward to create the polygons of sphereshape by dividing the structured grid cells to triangles. In ourmethod, only two types of polygon geometry are taken into
account: a division of simple square profile (Fig 1 (b)) and aninterface block between fine and coarse grid (Fig 1 (c)).
Finally, the polygon’s coordinate on sphere are deformed torepresent the scalar/vector data on each node. The scalarai , j  ((ai , j )1 ,0,0) or vector ai , j  ((ai , j )1 , (ai , j )2 , (ai , j )3 ) value oneach node is expressed by the displacement of the position fromsphere by (r  (ai , j )1 , i  (ai , j )2 , i , j  (ai , j )3 ) .

In Eq. (1), the weights of p  th scattered point wp (i, j ) aredistributed to four corners of the cell that includes the point, by
the simple first order accuracy scheme (Fig.1 (a)). The node
value is obtained asai , j  a w (i, j) / S
pp0i, jwith S 0 i , j  w (i, j) , (2)ppcells

pcells

where cells are four surrounding cells of the node point (i, j ) .
For the node points which have no entry of scattered data (i.e.
S 0 i , j  0 ), the procedure of (2) is skipped. Instead, empty nodedata are iteratively ( n  0,1,2... ) filled with the averaging ofsurround nodes byai , j  a  (SI ,JI ,JnI ,J)/ (SI ,Jn

I ,J),

(3)

3(a)

(b)

Acknowledgements
We thank Takashi Nakaga wa for discussions andsupport of this study. The present research was madepossible by Grant -in-Aid for Young Scientist(24740310) by Japan Society for the Promotion ofScience (JSPS).
(c)
Fig. 1 (a) Structured grid mesh and scattered data; (b) Divisionof normal cell; (c) Division at interface cell

References
[1]
[2]
[3]

[4]

[5]

Fig. 2 Example of the reduced grid cell for (n , n ) = (16,32)

3

ResultHere, we demonstrate visualization result by our developed tool
for the simulated global seismic wave propagation. This
simulation is performed by using the Spectral-Element Method[Komatitsch and Villote, 1998; Komatitsch et al., 2003] for theearthquake, which occurred in Tonga region on Septemebr 10,1992. The seismic waveform excited by this earthquake isanalysed in Butler and Tsuboi (2010). The output data of thissimulation is given by unstructured grid mesh. The polygon data
given by our tool are visualized by the lay tracing software Povray [1]. The picture of Fig3 shows a snap shot of visualization
result. The wave form given by the scalar value on the earth
surface is captured from two different points of view. Theanimation movie of this simulation result is also presented at [2].
From these result, our simple but powerful polygon making tool
is found to successfully visualize the wave form on the sphere in
the three dimensional representation.

Fig. 3 snapshot of the simulated seismic wave

POV-Ray: Available at http://www.povray.org/
http://www.youtube.com/watch?v=j4tLFeJiAhY&feature=player_embedded
Komatitsch, D., and J. P. Vilotte (1998), The spectral-element
method: an efficient tool to simulate the seismic response of 2D
and 3D geological structures, Bull. Seismol. Soc. Am., 88, 368–392.
Komatitsch, D., S. Tsuboi, C. Ji, and J. Tromp. A 14.6 billion
degrees of freedom, 5 teraflops, 2.5 terabyte earthquake simulationon the Earth Simulator. Proceedings of the ACM/IEEE
Supercomputing SC’2003 conference, 2003. published on CDROM and at www.sc-conference.org/sc2003.
Butler, R., and S. Tsuboi (2010), Antipodal seismic observationsof temporaland global variation at Earth ’ s inner ‐ outer coreboundary,Geophys.
Res.
Lett.,
37,
L11301,
doi:10.1029/2010GL042908.