Properties of singular points in a special case of orthorhombic media

The position of singular lines for orthorhombic (ORT) media with fixed diagonal elements the elasticity matrix cij, i=1…6 is studied under condition that c11, c22, c33>c66>c44>c55. In this case, off-diagonal coefficients c12, c13, c23 are chosen so some values d12=c12+c66, d13=c13+c55, d23=c23+c44 zero. For medium, where only one d12, d13, d23 zero, contains points in planes symmetry. If two or all three dij then ORT medium and discrete points. We call such pathological. A degenerate positive has at most lines, which intersection a quadratic cone sphere. pathological may have up to 6 on surface slowness. Singular described by more complex equations than conventional models. article proposes using squares x, y, z components slowness vector equations. new coordinate system, defining become linear quadratic. Intersecting plane x+y+z =1, they define straight ellipses, hyperbolas. non-zero increase, pass through four makes it possible describe evolution their change. Conditions derived curves models limiting d23. Formulas transforming surfaces into region group velocities. results demonstrated examples obtained from standard model changing zero