,,, ], 3000 m 3000 m 3000 m, 10 m Aki [4 ] (1977) [5

Transcription

1 1 7 3 Vol 17 No ( ) PROGRESS IN GEOPHYSICS Sept 2002 ( ) [ ] Coons Bezier B [ ] ;Coons ;Bezier ;B ; [ ] P315 [ ] A [ ] (2002) [1 ] [2 ] Cagniard Fourier Cagniard Fuchs [3 ] 3000 m 3000 m 3000 m 10 m Aki [4 ] (1977) [5 ] (1989) 8 ] [6 [ ] ; [ ] [ ] ( ) [ ]

2 Langan [9 ] Cer2 veny [10 ] [11 ] (1991) B [12 ] (1992) [13 ] [14 ] (1993) Michelini [15 ] (1995) B [16 ] (1997) 19 ] [17 Gjoystdal [20 ] (1985) C + + Coons Bezier B Mao WJ [21 ] [22 (1997) XYZ B ] (1998) XYZ Coons Coons [ ] [25 ] Delaunay 1 XYZ Coons Bezier XY X Y X Y Z s - t XYZ 1 1 Coons Coons Coons Hermite Coons Coons Coons n m x y z x x s t Coons s t t s s t s t s t

3 3 : 447 y z XYZ Coons Coons s t 1 2 Bezier Bezier Bezier ( m + 1) ( n + 1) b ij ( i = 0 1 n ; j = 0 1 m) m n Bezier n : P ( s t) = B i n ( s) B j m ( t) b ij 0 s t 1 (1) i = 0 m j =0 { B i n ( s) } n Bernstein b ij Bezier : (1) Bezier (2) Bezier (3) Bezier (4) n m Bezier ( n + 1) m Bezier n ( m + 1) Bezier Bezier Bezier G 1 ( ) Coons Bezier Coons Bezier Bezier Bezier Bezier Bezier Coons Bezier Coons Bezier Bezier 1 3 B B Bezier Bezier Bezier Bezier B B ( m + 1) ( n + 1) P ij ( i = 0 1 m j = 0 1 n) m P ( s t) = P ij N i k ( s) N j l ( t) s t [0 1 ] (2) i =0 n N i k ( s) N j l ( t) k l B 1 4 j = 0

4 ] Bezier B [27 [32 ] : 1 (Fig 1) 1 T 1 T 2 T 3 T 1 T 2 T 3 T 1 T 2 T 3 P ( u 1 u 2 u 3 ) u 1 = PT 2 T 3 T 1 T 2 T 3 u 2 = T 1 PT 3 T 1 T 2 T 3 u 3 = T 1 T 2 P T 1 T 2 T 3 (3) [ PT 2 T 3 ] PT 2 T 3 P T 2 T 3 [ PT 2 T 3 ] PT 2 T 3 P T 2 T 3 [ PT 2 T 3 ] PT 2 T 3 s P s 1 P s 1 P : 2 ABC A A B C A B C ABC ABC ABD ABC AB ABD 2 (Fig 2) AB FAD ACF ABC ABD A FAD A (a) (b) Coons Bezier Coons Bezier (c) 356 (d)

5 3 : Fig 3 Different curve2face model (a) Coons (b) Bezier (c) (d) 3 Coons Bezier B [1 ] [J ] : [2 ] P G [ M] : [3 ] E [ M] : 1992

6 [ 4 ] Aki K Chritoffersson A Husebye E S Determination of the three dimensional seismic structure of the lithosphere[j ] J Geophys Res : [5 ] complex 22D and 32D isotropic media [ J ] Geophysics [J ] :46 61 [6 ] [ M] : [22 ] 1993 [7 ] [J ] :36 45 [8 ] Cerveny V [ A ] : [A] 50 Durk J Doornbos [ M] : 1992 [9 ] Langan R T Lerche I Culter R T Tracing of rays through heterogenous media : An accurate and efficient procedure [J ] Geophysics : [10 ] Cerveny V [ M] [26 ] Kajiya J Ray tracing parametric patches Proceeding of : 1986 [11 ] [J ] : [12 ] SIGGRAPH 85 [J ] Computer Graphics (3) :171 [J ] : [13 ] [M] : [ 28 ] Joy K I Bhetanabhotla M N Ray tracing parametric surface 1988 [14 ] Proceeding of SIGGRAPH 86 [J ] Computer Graphics [J ] : [15 ] Michelini A An adaptive2grid formalism for traveltime to2 mograph[j ] GeophysJ Int : [16 ] (4) : [J ] : [17 ] [M] : ray tracing NURBS surfaces [J ] Computers & Graphics 1981 [18 ] [M] : [31 ] Manocha D Krishnan S Algebraic pruning : a fast tech [19 ] [M] : 1995 [20 ] Gjoystdal H Reinhardsen J E Astebol K Computer repre2 sentation of complex 32D geological structures using a new solid modeling technique [J ] Geophysical Prospecting (8) : [21 ] Mao WJ Stuart G W Rapid multi2wave2type ray tracing in (1) : [J ] (6) : [23 ] [M] : : 1998 [24 ] [M] : 2001 [25 ] Delaunay [J ] 1999 B( ) :87 91 SIGGRAPH 82 [J ] Computer Graphics (3) : [27 ] Toth D On ray tracing parametric surfaces Proceeding of 179 patches utilizing numerical techniques and ray coherence (4) : [ 29 ] Barth W Sturzlinger W Efficient ray tracing for Bezier and B - spline surfaces[j ] Computers & Graphics [ 30 ] Kaihuai Qin Minglun Gong A new method for speeding up (5) : nique for curve and surface intersection [J ] Computer - Aided Geometric Design (9) : [32 ] Nishita T Sederberg T W Ray tracing Trimmed Rational Surface Patches Proceeding of SIGGRAPH 90 [J ] Com2 puter Graphics (4) : ( 455 ) (to be continwed on p 455)

7 3 : GPS 455 Study of Algorithms Employed in Inverting Terrestrial Atmospheric Parameters by GPS Radio Occultation J IANG Hu 1 HUANG Cheng 1 ZHANG Yun2gan 2 (1 Shanghai Astronomical Observatory the Chinese Academy of Sciences Shanghai China ; 2 Center for National Satellite Meteorology Bureau of Meteorology of China Beijing China) [ Abstract] Taking into account shortcomings in algorithms employed in inverting terrestrial atmo2 spheric parameters by GPS radio occultation a variable transform is raised in this text By this trans2 form we have managed to solve the problem that original form of Abel integral was digitally integrated to comparatively poor accuracy To make comparisons we assess the refractivity under two different al2 gorithms assuming that the bending angle due to refractive atmosphere decreases exponentially with the increase of distance of the considered point from the geocenter It shows that the maximum of absolute difference between two algorithms reaches roughly as large as 7 refractivity units and absolute differ2 ence decreases with increasing altitude ; whereas on the other hand the relative difference of refrac2 tivities increases with the increasing altitude which is diametrically different from the trend of absolute difference [ Keywords] Radio occultation ; Atmospheric parameters ; Algorithm ( 450 ) (continued from p 450) The Methods of Describing the Underground Model LI Ying2chun XU Guo2ming XU Tao ( Department of Earth and Space Sciences University of Science and Technology of China Hefei China) [ Abstract] The methods describing models can be classified into two categories : discrete and contin2 uous The discrete methods divide the model into many little blocks using regular or irregular grids The continuous methods use analytic functions or interpolation methods One important element of the continuous method is how the interface is described Considering the techniques developed greatly in the subjects of computer graphics and computer aided geometry design the modele introduced with Coons surfaces Bezier surfaces B - spline surfaces and triangle meshes Especially for the need of the exploration s data acquisition system a scheme using triangle meshes is giving [ Keywords] Three dimension model ; Coons surfaces ; Bezier surfaces ; B2spline surfaces ; Triangle meshes