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论文第 51 卷第 17 期 006 年 9 月 ( 100080; CSIRO Petroleum ARRC Technology Park Bentley WA 610 Australia. E-mail: bigsun6909@yahoo.com). : ( ) ( ). ( ) ( )....... -... (finite difference FD). (standard staggered grid SSG) [1~3] [4] [56] [7~9] : (ⅰ) - [10] [11] [6] ; (ⅱ) [34]. (rotated staggered grid RSG) [113] SSG.. ( ) 4 ( ).. (perfectly matched layer PML) [5781415]. PML. Festa Nielsen [16] PML. PML. PML. PML. PML. PML www.scichina.com 1985

第 51 卷第 17 期 006 年 9 月论文 PML. 1 Saenger [1]. - [1] - [13]... 1.. ( ) ( ) ( ) ( ). ( )... [6]. [1] Δ Δ = + Δr Δr (1) Δ Δ = Δr Δr () Δ r = Δ (3) Δ r = + Δ (4) Δ Δ Δr Δ r = Δ +Δ.. Saenger [1]. PML PML Berenger [1718]. Chew Liu [14] PML 1 (a) ; (b). (b) 1986 www.scichina.com

论文第 51 卷第 17 期 006 年 9 月. PML. Collino Tsogka [5] PML Zeng [8] Sheen [7]. PML : [15] [14]. : PML PML. PML. PML. PML PML PML.. PML. ( ) ( ) ( ) ( ) ( ). PML PML PML. ( η) ( η) v = v σ = σ T η= η= v = [ v v] σ = [ σ σ σ] η =. - ρv j t = σα j α (5) σ α jt = cα jγβvγ β (6) ρ v j j σα j c α j γβ. : α α t 1 T 3. : η η = e ()d s s 0 η eη = aη + i ωη / ω ( η = ) i = 1 ωη 0 ω. a η = 1. / η η = 1/eη η. (7) (5) (6) : ( η) ( η) ρ( a + ω ) v = D τ (8) η t η v ( η) ( η) η t + ωη = Dσ ( a ) τ v. (9) D ( ζ ) v D ( ζ ) τ ( ) 1 0 0 ( ) 0 1 0 D v = D v = 0 0 1 0 0 1 c11 c15 c15 0 ( ) ( ) Dσ = 0 c35 Dσ = c35 c33 c 15 c. 55 c 55 c 35 PML ω. ω [5] : 3 log(1/ R) Vp η ωη = (10) 3 L Δη L PML η PML PML η Vp R Δη η.. PML. Biot [190] σ ij ( ) σ = μe + Ae+ Qε δ (11) ij ij ij σ = Qe + Rε (1) e ij σ s s ( j i + i j) f ii u / u / / ε = u e ij = e= e ii i= 13 μ η s u u f A Q R Biot www.scichina.com 1987

第 51 卷第 17 期 006 年 9 月论文 δij Kronecker. : s f τ = σ + σδ = ρ u + ρ u (13) ij ij ij 1 i tt i tt τ ρ 1 = ρ s (1 φ) ij ρ = ρφ f ρ s ρ f φ. Darcy s f s f σ i + bu ( i t ui t) = ρ1 ui tt + ρ ui tt. (14) (11)~(14) - s s s f σ ij t = μ( vi j + vj i ) + ( A+ Q) vk k Qwk k ) δ ij (15) s f σ = ( Q+ R) v Rw (16) t k k k k s s f ij j = σij j + σ i = ρ1 vi t + ρ vi t wi t f s s f σ i bvi ρ1 vit ρ ( vit wit ) τ ( ) (17) + = +. (18) (15) (16) s s f f σ = ( μ + A + Qv ) + ( A+ Qv ) Qw Qw (19) σ s s f f ( A Qv ) ( μ A Qv ) Qw Qw s s σ μv μv s s f f ( Q R)( v v ) R( w w ) = + + + + (0) = + (1) σ = + + +. () (17) (18) s f v = Rσ R σ + br w (3) it 1 i ij j 3 i f f it 3 σij j 1 σ i i w = R + S + bs w (4) ρ 1 + ρ = φρ f ρ1 = ρa ρ11 + ρ1 = (1 φ) ρs R = ρ /( ρ ρ ρ ) 1 1 1 11 R = ρ /( ρ1 ρ11ρ) R3 = ( ρ1 + ρ)/( ρ1 ρ11ρ) S1 = ( ρ11+ ρ1)/( ρ1 ρ11ρ) 11 1 1 11 S = ( ρ + ρ + ρ )/( ρ ρ ρ ). : b = φ η/ κ η κ f wi s vi. ρa (19)~(4) -. (19) () (6). 5. (19) () PML (6) (19) () PML. PML : ( ) s f t ω σ μ ( a + ) = ( + A+ Q) v Qw ( ) s f t ω σ ( a + ) = ( A+ Q) v Qw ( ) s t ω σ μv ( a + ) = ( ) s t ω σ μv ( a + ) = ( ) s f t ω σ ( a + ) = ( Q+ R) v Rw ( ) s f t ω σ ( a + ) = ( Q+ R) v Rw. (19) PML (1) PML (). (0) PML (19). (3) (4) w PML (5). t i i f( ) t f( ) i ω wi dτ f i aw f( ) + ω w f( ) dτ aw +. f() f() w. (3) PML ( ) t + ω = 1 σ σ ( a ) v R R f( ) t f( ) + ( aw + ω w d τ ) ( ) f( ) t f( ) t 3 ( a + ω ) v = R σ + br ( w + ω w d τ). 3 PML (5) PML PML. =. (5) ρ = σ (5) vjt r αβ α j β r αβ. (5) ρv = r σ + r σ + r σ + r σ (6) t 11 1 1 ρv = r σ + r σ + r σ + r σ. (7) t 11 1 1 (6) (7) PML : f i 1988 www.scichina.com

论文第 51 卷第 17 期 006 年 9 月 ( ) t v r11 r1 ρ( + ω ) = σ + σ (8) ( ) t v r r1 ρ( + ω ) = σ + σ (9) ( ) t v r11 r1 ρ( + ω ) = σ + σ (30) ( ) t v r1 r ρ( + ω ) = σ + σ. (31). (a) PML (b) PML (c) PML (d) PML PML PML. PML. (a) (b) PML PML. (8) (31) (a) (b) (9) (30). 4 ( ) (8) (31) 4 PML PML PML (c). (c) PML 4. (8) (31) PML (8) (30) (9) (31) ( ) ( ) ( ) ( ) t( v v ) v v ρ + + ω + ω = r11 σ + r1 σ + r1 σ + r σ (3) ( ) ( ) ( ) ( ) ρ t( v + v ) + ω v + ω v = r11 σ + r1 σ + r1 σ + r σ. (33) ( ) ( ) ( ) ( ) ρ t( v + ω v ) + ρ t( v + ω v ) = σ + σ (34) ( ) ( ) ( ) ( ) ρ t( v + ω v ) + ρ t( v + ω v ) = σ + σ. (35) (3) (35) ( ) ( ) ρ ( v + ω v ) = σ (36) t ( ) ( ) t( v v ) ( ) ( ) t( v v ) ( ) ( ) t( v v ) ρ + ω = σ (37) ρ + ω = σ (38) ρ + ω = σ. (39) (8) η = (36) (39) (8). 4 PML : ( ) ( ) t( v v ) ( ) ( ) t( v v ) ( ) ( ) t( v v ) ( ) ( ) t( v v ) ρ + ω = σ (40) ρ + ω = σ (41) ρ + ω = σ (4) ρ + ω = σ. (43) (a) (b) PML PML 4. PML 4. PML (a) PML 45 ; (b) (a) 45 ; (c) PML; (d) PML PML. PML www.scichina.com 1989

第 51 卷第 17 期 006 年 9 月论文 (b) (c) PML. (d) PML PML ( PML ). PML PML. PML PML. PML PML PML. 4 PML. 3000 1800 m/s 500 kg/m 3. 56 56. (64 64) 10 kh. 6. 0. 10 m 0.5 μs. 3(a). 3(b) PML 0 5. PML.. 4 PML PML. PML 4. 4. PML - PML. PML 4(d) PML 0 40. PML. PML. 0.34 m 0.3 m(680 640 ). 0.5 10 3 m.5 10 8 s. c 11 = 16.5 10 10 Pa c 13 = 5 10 10 Pa c 33 = 6. 10 10 Pa c 55 = 3.96 10 10 Pa ρ = 7100 kg/m 3. c 11 = 16.5 10 10 Pa c 55 = 3.96 10 10 Pa ρ = 7100 3 (a) ; (b) ( ) ( ) 5 1990 www.scichina.com

论文第 51 卷第 17 期 006 年 9 月 4 PML (a) PML 10 ; (b) PML 0 ; (c) PML 40 ; (d). (a) (b) (c) 1 6. PML 5 (d) 5 36 μs (a) 50 μs (b) kg/m 3. (0.17 m 0.16 m) 170 kh (340 30). (0.19 m 0) (380 0). 5. PML. PML. 300 300. ρ s = 500 kg/m 3 ρ f = 1040 kg/m 3 www.scichina.com 1991

第 51 卷第 17 期 006 年 9 月论文 φ = 0. v f p = 3890 m/s v s = 1800 m/s v f = 1550 m/s. 50 H (150 150) (50 150). 6(a) t 0.5 10 4 s = = 1 m; 6(b) 6(a). 6(a) (b). 6(b) v s p /( Δ fhigh) =.1 v s p Dai [0] 100 m/s f high 4. 8 3 [3] 4 6 1. 6(b) 3 ; 3. 6(a) = = 0.5 m 3. v s p /( Δ fhigh ) > 3.. Dai [0]. - PML. 400 400 mm 0.8 m 0.8 m 0.5 μs. 1500 m/s 1000 kg/m 3 ; 3000 m/s 1800 m/s 500 kg/m 3. (00 00) (0.4 m 0.4 m) 10 kh. (40 00). 7. 8 -. 7. 8 -. PML. PML -. 5 PML PML 6 (a) ; (b) 199 www.scichina.com

论文第 51 卷第 17 期 006 年 9 月 7 - (a) ; (b) ( ). (a) (b) 8 - (a) (b) (c) (p) 0.04 0.10 0.16 0.94 ms PML -. www.scichina.com 1993

第 51 卷第 17 期 006 年 9 月论文 PML PML PML PML. PML. PML PML PML PML. PML.. ( : 10534040). 1 Virieu J. P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method. Geophysics 1986 51: 889 901 [DOI] Graves R W. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences. Bull Seism Soc Am 1996 86: 1091 1106 3.. G : 004 34(5): 481 493 4 Robertsson J O A. A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography. Geophysics 1996 61: 191 1934 [DOI] 5 Collino F Tsogka C. Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 001 66: 94 307 [DOI] 6 Igel H Mora P Riollet B. Anisotropic wave propagation through finite-difference grids. Geophysics 1995 60: 103 116 [DOI] 7 Sheen D H Tuncay K Baag C E et al. Wave propagation in porous media: A velocity-stress staggered-grid finite difference method with perfectly matched layers. 73th Annual Internat Mtg Dallas TX 003 8 Zeng Y Q He J Q Liu Q H. The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media. Geophysics 001 66: 158 166 [DOI] 9.. 003 46(6): 84 849 10 Robbert van Vossen Robertsson J O A Chapman C H. Finite-difference modeling of wave propagation in a fluid-solid configuration. Geophysics 00 67: 618 64 [DOI] 11 Moco P Kristek J Vavryčuk V et al. 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities. Bull Seism Soc Am 00 9: 304 3066 [DOI] 1 Saenger E H Gold N Shapiro S A. Modeling the propagation of elastic waves using a modified finite-difference grid. Wave Motion 000 31: 77 9 [DOI] 13 Saenger E H Bohlen T. Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid. Geophysics 004 69: 583 591 [DOI] 14 Chew W C Liu Q H. Perfectly matched layers for elastodynamics: A new absorbing boundary condition. J Comput Acoust 1996 4: 7 79 15 Wang T Tang X M. Finite-difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach. Geophysics 003 68: 1749 1755 [DOI] 16 Festa G Nielsen S. PML absorbing boundaries. Bull Seism Soc Am 003 93: 891 903 [DOI] 17 Berenger J P. A perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 1994 114: 185 00 [DOI] 18 Berenger J P. Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 1996 17: 363 379 [DOI] 19 Biot M A. Mechanics deformation and acoustic propagation in porous media. J Appl Phys 196 33: 148 1498 0 Dai N Vafidis A Kanasewich E R. Wave propagation in heterogeneous porous media: A velocity-stress finite-difference method. Geophysics 1995 60(): 37 340 [DOI] (006-06-01 006-07-17 ) 1994 www.scichina.com

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