Two groups of problems discussed in the book. The first is connected with the output of formulas treatment discontinuous locus refraction seismic waves (the general case) propagating in a vertically heterogeneous elastic isotropic media. Also obtained solving treatment locus waves propagating upward from the source, reflected and converted waves. To determine the beam parameters based convex cubic spline approximating the experimental hodograph. The numerical decision along the multidimensional inverse kinematics problem of seismic (tasks seismic tomography). The second range of problems connected with the definition of coordinates hypocenters close and distant earthquakes. A new, sustainable approach to solving these problems based on the minimization of the residual functional majorant estimates times. The book is intended for specialists in the fields of applied and theoretical seismology, and will be useful to students and graduates in related disciplines.