id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
esrj-21263	Piedrahita, Carlos; Piedrahita, Carlos; Salinas, Trino; Altamar, Hernando; Pachano, Karen	SLOWNESS SURFACE CALCULATION FOR DIFFERENT MEDIA USING THE SYMBOLIC MATHEMATICS LANGUAGE MAPLE®	2004	5	.pdf	application/pdf	1789	97	56	Stiffness matrix for sandstone (Thomsen, 2000) CONCLUSIONS The theoretical study of anisotropic media is important for studying the effect of different type of media on wave propagation. C[3,4]:=C34: C[3,5]:=C35: C[3,6]:=C36: C[4,4]:=C44: C[4,5]:=C45: C[4,6]:=C46: C[5,5]:=C55: C[5,6]:=C56: C[6,6]:=C66: evalm(C); Ray director cosines matrix > L:=Matrix(6,3): L[1,1]:=l[1]: L[2,2]:=l[2]: L[3,3]:=l[3]: L[4,2]:=l[3]: L[4,3]:=l[2]: L[5,1]:=l[3]: L[5,3]:=l[1]: L[6,1]:=l[2]: L[6,2]:=l[1]: evalm(L); Christoffel Matrix > GAMMA:=Transpose(L).C.L; Eigenvalues and Eigenvectors The elastic constants should be declared according to the chosen anisotropy case: consts:=C11=16.57*10^10,C12=6.39*10^10,C44 =7.956*10^10,rho=2332: (Cubic anisotropy) > consts:=C11=3.46E10,C13=1.07E10,C33 =2.84E10,C44=8.36E9,C66=1.26E10,rho=2500: (VTI elastic constants) >dir_l:=l[1]=sin(theta),l[2]=0,l[3]=cos(theta): >Ch:=CharacteristicMatrix(subs(dir_l,GAMMA), k); > d:=Determinant(Ch); > factor(d); > K:=[solve(d,k)]; > map(simplify,%,trig); > A:=subs(k=K[3],Ch); > A:=map(simplify,subs(k=K[3],Ch),trig); > solve({A[1,1]*u1+A[1,2]*u2=0},{u1}); > simplify(%,trig); > solve({A[2,1]*u1+A[2,2]*u2=0},{u1}); > simplify(%,trig); > Rank(A); > eg:=map(simplify,ColumnSpace(A)); > plot([subs(consts,dir_l,sqrt(rho/K[1])),subs(consts ,dir_l,sqrt(rho/K[2])),subs(consts,dir_l,sqrt(rho/K	cache/esrj-21263.pdf	txt/esrj-21263.txt