Concavities on the zonal slowness section of a transversely isotropic elastic material

✍ Scribed by V.I. Alshits; P. Chadwick

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 799 KB
• Volume: 25
• Category: Article
• ISSN: 0165-2125
• DOI: 10.1016/s0165-2125(97)00006-1

✦ Synopsis

The section of the slowness surface of a transversely isotropic elastic material in a zonal plane consists of an ellipse and a quartic curve with two nested branches, the inner of which is convex. Concavities can therefore occur only on the outer branch S and five possibilities arise: (I) S is convex; (II) S has two axial concavities (centred on the points of intersection of S with the axis of transverse isotropy); (III) S has two basal concavities (centred on the points of intersection of S with the basal plane); (IV) S has two axial and two basal concavities; (V) S has four oblique concavities, neither axial nor basal. The first and last of these are commonly realized in actual materials, the others only rarely. A unified treatment of stationgry points and concavities on S is given in the course of which some previous results are simplified and their relationship clarified.