Geodesic
Certain Criterion for the Horizontal Homogeneity of a Medium in Inverse Kinematic Problem of Seismics
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 3-19
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In framework of inverse kinematic problem of seismics the approaches to the quantitative evaluation of the structure of velocity level systems are suggested. In particular we investigate a degree of its horizontal homogeneity. Formulations of inverse kinematic problem of seismics are described shortly. Certain constructive methods of investigations of multidimensional inverse kinematic problem of seismics are described. The methods consist in construction of functionals which depend on initial and end points of geodesic along which travel times are measured. General principle of constriction such functionals is given. Some partial cases are considered. Local and integral criterions of the horizontal homogeneity of a medium are proposed. Numerical investigation of these criterions on numerical simulation is shown.
Keywords: inverse seismic problem, kinematic data, level lines of the velocity, functional of travel times, approximation, $B$-splines, numerical simulation. 
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     title = {Certain {Criterion} for the {Horizontal} {Homogeneity} of a {Medium} in {Inverse} {Kinematic} {Problem} of {Seismics}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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Yu. E. Anikonov; Yu. S. Volkov; S. B. Gorshkalev; E. Yu. Derevtsov; S. V. Maltseva. Certain Criterion for the Horizontal Homogeneity of a Medium in Inverse Kinematic Problem of Seismics. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 3-19. http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a0/

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