in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques to guarantee a stable solution. Minimization of a weighted norm of model length is one commonly used secondary constraint. Tikhonov methods exploit low-order differential operators to select for solutions that are small, flat, or smooth in one or more dimensions. This class of regularizin...

An interferometric form of Fermat’s principle is presented for redatuming PS transmission traveltimes to be those for sources lowered to the target body. The velocity model does not need to be known for redatuming, so the distorting effects of uninteresting parts of the velocity model and statics are eliminated by this target-oriented approach. Thus, traveltime tomography applied to the redatum...