TY - JOUR

T1 - The algorithm for solving the direct kinematic problem of seismics in three-dimensional heterogeneous isotropic media

AU - Galaktionova, A. A.

AU - Belonosov, A. S.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - The solution of the direct kinematic problem of seismics is an important stage of the seismic data processing in seismology and seismic explorations, e.g., while solving the inverse kinematic problem of seismics by the method of nonlinear seismic tomography, in the method of the space-time Kirchhoff’s migration, etc. There are several approaches now to the solution of this problem: 1) methods based on the solution of two-point boundary value problems; 2) the wavefront construction method; 3) finite-difference methods for solving eikonal differential equations, etc. [2-3]. The method proposed in this paper relates to ray tracing methods and overcomes some of the limitations inherent in the above methods. The basis of the approach is the iterative Newton’s method. The algorithm of three- dimensional shooting is simple to implement and allows “almost” linear speedup from parallelization. Questions of convergence of the Newton method applied to this problem are not considered in this paper. In addition, we do not consider the applicability of the method in the presence of caustics, shadow zones, and diffraction.

AB - The solution of the direct kinematic problem of seismics is an important stage of the seismic data processing in seismology and seismic explorations, e.g., while solving the inverse kinematic problem of seismics by the method of nonlinear seismic tomography, in the method of the space-time Kirchhoff’s migration, etc. There are several approaches now to the solution of this problem: 1) methods based on the solution of two-point boundary value problems; 2) the wavefront construction method; 3) finite-difference methods for solving eikonal differential equations, etc. [2-3]. The method proposed in this paper relates to ray tracing methods and overcomes some of the limitations inherent in the above methods. The basis of the approach is the iterative Newton’s method. The algorithm of three- dimensional shooting is simple to implement and allows “almost” linear speedup from parallelization. Questions of convergence of the Newton method applied to this problem are not considered in this paper. In addition, we do not consider the applicability of the method in the presence of caustics, shadow zones, and diffraction.

KW - 3d shooting

KW - Ray tracing

KW - Ray-based method

UR - http://www.scopus.com/inward/record.url?scp=85084489298&partnerID=8YFLogxK

U2 - 10.25587/SVFU.2020.12.61.004

DO - 10.25587/SVFU.2020.12.61.004

M3 - Article

AN - SCOPUS:85084489298

VL - 27

SP - 53

EP - 68

JO - Математические заметки СВФУ

JF - Математические заметки СВФУ

SN - 2411-9326

IS - 1

ER -