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Tche.L.*2017216Version:1.2[1][2][3][4][5][6][7][8]*tcheliu@mail.ustc.edu.cn1Tche.L.xzuxuzxzxz[9]8:Lx(uxi;j)=1∆xN∑n=1C(N)n(uxi+2n 12;j uxi 2n 12;j)Lz(uzi;j)=1∆zN∑n=1C(N)n(uzi;j+2n 12 uzi;j 2n 12)(1)uuxuz∆x∆zxzC(N)n2N1:d(x)=dx;d(z)=dzPMLPMLPMLPMLPML2Tche.L.PML1PMLxz@@x !i!i!+dx@@x;@@z !i!i!+dz@@z!dxdzxz@u@t=A@v@xPMLi!u=A@v@xPMLxi!u=Ai!i!+dx@v@x(i!+dx)u=A@v@x(@@t+dx)u=A@v@x(2)PMLPMLA@vk@xjk@vkk∆tv∆tu(@@t+dx)uk=@uk@t+dxuk=uk+1/2 uk 1/2∆t+dxuk+1/2+uk 1/22(2)uk+1/2=2 ∆tdx2+∆tdxuk 1/2+2∆t2+∆tdxjk(3)(@@t+dx)uk=@uk@t+dxuk=uk+1/2 uk 1/2∆t+dxuk 1/2(2)uk+1/2=(1 ∆tdx)uk 1/2+∆tjk(4)PMLdx=dz=0PMLPMLdx=dz=03Tche.L.dxdz[10]d(i)=d0(inpml)pxziPMLnpmlPMLp14d0=log(1R) Vsnpml∆d0= Vs∆(c1+c2npml+c3n2pml)R 34Vs∆ciRci8:R=0:01;npml=5R=0:001;npml=10R=0:0001;npml=208:c1=815c2= 3100c3=11500@u@x=1∆xN∑n=1{C(N)n[u(x+2n 12∆x) u(x 2n 12∆x)]}+O(∆x2N)(5)C(N)n2Nu(x+2n 12∆x)u(x 2n 1x∆x)xTaylorC(N)n266666664113151(2N 1)1133353(2N 1)3153555(2N 1)5...............12N 132N 152N 1(2N 1)2N 1377777775266666664C(N)1C(N)2C(N)3...C(N)N377777775=266666664100...0377777775C(N)m=( 1)m+1N∏i=1;i̸=m(2i 1)2(2m 1)N∏i=1;i̸=m (2m 1)2 (2i 1)2 (6)4Tche.L.@2P@t2=v2P(@2P@x2+@2P@z2)(7)PvP8:@P@t= v2P(@vx@x+@vz@z)@vx@t= 1@P@x@vz@t= 1@P@z(8)vxvzxz(8)t(8)(7)PMLxz(8)xz8:P=Px+Pz@Px@t= v2P@vx@x@Pz@t= v2P@vz@z(9)PxPzPxz(8)(9)PML8:(@@t+dx)vx= 1@P@x(@@t+dz)vz= 1@P@z(@@t+dx)Px= v2P@vx@x(@@t+dz)Pz= v2P@vz@z(10)2(4)(5)PML2N5Tche.L.2:P;v2P▲vx;1/■vz;1/8:vx ki+1/2;j=(1 ∆tdx)vx k 1i+1/2;j ∆t∆xN∑n=1{C(N)n[P k 1/2i+1/2+(2n 1)/2;j P k 1/2i+1/2 (2n 1)/2;j]}vz ki;j+1/2=(1 ∆tdz)vz k 1i;j+1/2 ∆t∆zN∑n=1{C(N)n[P k 1/2i;j+1/2+(2n 1)/2 P k 1/2i;j+1/2 (2n 1)/2]}Px k+1/2i;j=(1 ∆tdx)Px k 1/2i;j v2P∆t∆xN∑n=1{C(N)n[vx ki+(2n 1)/2;j vx ki (2n 1)/2;j]}Pz k+1/2i;j=(1 ∆tdz)Pz k 1/2i;j v2P∆t∆zN∑n=1{C(N)n[vz ki;j+(2n 1)/2 vz ki;j (2n 1)/2]}(11)P=Px+Pzvx ki+1/2;j((i+1/2)∆x;j∆z)k∆tvx∆x∆zxz8:@2ux@t2=@@x[(@ux@x+@uz@z)+2@ux@x]+@@z[(@uz@x+@ux@z)]@2uz@t2=@@z[(@ux@x+@uz@z)+2@uz@z]+@@x[(@uz@x+@ux@z)](12)uxuzxz=(v2p 2v2s)=v2svpvs6Tche.L.[3]8:@2ux@t2=@ xx@x+@ xz@z@2uz@t2=@ xz@x+@ zz@z xx=(+2)@ux@x+@uz@z zz=(+2)@uz@z+@ux@x xz=(@ux@z+@uz@x)(13)( xx; zz; xz)(13)(12)PMLvx=@ux/@tvz=@uz/@t8:@vx@t=1(@ xx@x+@ xz@z)@vz@t=1(@ xz@x+@ zz@z)@ xx@t=(+2)@vx@x+@vz@z@ zz@t=(+2)@vz@z+@vx@x@ xz@t=(@vx@z+@vz@x)(14)xzPML(9)8:vx=vxx+vzx;@vxx@t=1@ xx@x;@vzx@t=1@ xz@zvz=vxz+vzz;@vxz@t=1@ xz@x;@vzz@t=1@ zz@z xx= xxx+ zxx;@ xxx@t=(+2)@vx@x;@ zxx@t=@vz@z zz= xzz+ zzz;@ xzz@t=@vx@x;@ zzz@t=(+2)@vz@z xz= xxz+ zxz;@ xxz@t=@vz@x;@ zxz@t=@vx@z(15)7Tche.L.3:□vx;1/■vz;1/◦ xx; zz;(+2); xz;PML8:(@@t+dx)vxx=1@ xx@x;(@@t+dz)vzx=1@ xz@z(@@t+dx)vxz=1@ xz@x;(@@t+dz)vzz=1@ zz@z(@@t+dx) xxx=(+2)@vx@x;(@@t+dz) zxx=@vz@z(@@t+dx) xzz=@vx@x;(@@t+dz) zzz=(+2)@vz@z(@@t+dx) xxz=@vz@x;(@@t+dz) zxz=@vx@z(16)8:vx=vxx+vzxvz=vxz+vxz xx= xxx+ zxx zz= xzz+ zzz xz= xxz+ zxz(17)3(4)(5)PML2N8Tche.L.8:vxx k+1/2i;j=(1 ∆tdx)vxx k 1/2i;j+∆t∆xN∑n=1{C(N)n[ xx ki+(2n 1)/2;j xx ki (2n 1)/2;j]}vzx k+1/2i;j=(1 ∆tdz)vzx k 1/2i;j+∆t∆zN∑n=1{C(N)n[ xz ki;j+(2n 1)/2 xz ki;j (2n 1)/2]}vxz k+1/2i+1/2;j+1/2=(1 ∆tdx)vxz k 1/2i+1/2;j+1/2+∆t∆xN∑n=1{C(N)n[ xz ki+1/2+(2n 1)/2;j+1/2 xz ki+1/2 (2n 1)/2;j+1/2]}vzz k+1/2i+1/2;j+1/2=(1 ∆tdz)vzz k 1/2i+1/2;j+1/2+∆t∆zN∑n=1{Cn(N)[ zz ki+1/2;j+1/2+(2n 1)/2 zz ki+1/2;j+1/2 (2n 1)/2]} xxx k+1i+1/2;j=(1 ∆tdx) xxx ki+1/2;j+(+2)∆t∆xN∑n=1{C(N)n[vx k+1/2i+1/2+(2n 1)/2;j vx k+1/2i+1/2 (2n 1)/2;j]} zxx k+1i+1/2;j=(1 ∆tdz) zxx ki+1/2;j+∆t∆zN∑n=1{C(N)n[vz k+1/2i+1/2;j+(2n 1)/2 vz k+1/2i+1/2;j (2n 1)/2]} xzz k+1i+1/2;j=(1 ∆tdx) xzz ki+1/2;j+∆t∆xN∑n=1{C(N)n[vx k+1/2i+1/2+(2n 1)/2;j vx k+1/2i+1/2 (2n 1)/2;j]} zzz k+1i+1/2;j=(1 ∆tdz) zzz ki+1/2;j+(+2)∆t∆zN∑n=1{C(N)n[vz k+1/2i+1/2;j+(2n 1)/2 vz k+1/2i+1/2;j (2n 1)/2]} xxz k+1i;j+1/2=(1 ∆tdx) xxz ki;j+1/2+∆t∆xN∑n=1{C(N)n[vz k+1/2i+(2n 1)/2;j+1/2 vz k+1/2i (2n 1)/2;j+1/2]} zxz k+1i;j+1/2=(1 ∆tdz) zxz ki;j+1/2+∆t∆zN∑n=1{C(N)n[vx k+1/2i;j+1/2+(2n 1)/2 vz k+1/2i;j+1/2 (2n 1)/2]}(18)(17)vxx k+1/2i;j(i∆x;j∆z)(k+1/2)∆tvxx9Tche.L.[1]AltermanZ.,KaralF.C.,1968.Propagationofelasticwavesinlayeredmediabyfinitedifferencemethods[J].BulletinoftheSeismologicalSocietyofAmerica,58(1),367-398.[2]VirieuxJ.,1984.SH-wavepropagationinheterogeneousmedia:velocity-stressfinite-differencemethod[J].Geophysics,49(11),1933-1942.[3]VirieuxJ.,1986.P-SVwavepropagationinheterogeneousmedia:Velocity-stressfinite-differencemethod[J].Geophysics,51(4),889-901.[4]SaengerE.H.,GoldN.,ShapiroS.A.,2000.Modelingthepropagationofelasticwavesusingamodifiedfinite-differ