TY - GEN

T1 - Computation of seismic wave field kinematics in a three-dimensional heterogeneous isotropic medium

AU - Galaktionova, A.

AU - Belonosov, A.

PY - 2017/10/12

Y1 - 2017/10/12

N2 - The goal of this study is to develop algorithms and programs to compute wave travel times and directions at the nodes of a given 3D grid. We consider a velocity model that can be described analytically or presented by defining velocity values at the nodes of a 3D regular point grid. In the latter case, the velocity model is smoothed by a spatial low-pass filtering. An algorithm of 3D shooting is developed. The algorithm can be used in case of a point source and more generally for an initial wave front position defined as a parametric surface Φ(θ, φ). In the latter case, the initial points of rays on this surface are not known beforehand. In the case of a source point, the ray direction is determined by the variables θ, φ. We consider equations for partial derivatives with respect to the variables θ, φ together with the differential ray system. The entire system is solved by a fifth-order Runge-Kutta method with step-size and precision control. With known derivatives at ray points we can use Newton's iterative method, which guarantees quadratic convergence. Moreover, with these derivatives we can calculate geometrical spreading and thus the amplitudes. Different types of velocity structures such as homogeneous, gradient, etc. and different types of surface Φ(θ, φ) are considered. The results of numerical experiments are presented.

AB - The goal of this study is to develop algorithms and programs to compute wave travel times and directions at the nodes of a given 3D grid. We consider a velocity model that can be described analytically or presented by defining velocity values at the nodes of a 3D regular point grid. In the latter case, the velocity model is smoothed by a spatial low-pass filtering. An algorithm of 3D shooting is developed. The algorithm can be used in case of a point source and more generally for an initial wave front position defined as a parametric surface Φ(θ, φ). In the latter case, the initial points of rays on this surface are not known beforehand. In the case of a source point, the ray direction is determined by the variables θ, φ. We consider equations for partial derivatives with respect to the variables θ, φ together with the differential ray system. The entire system is solved by a fifth-order Runge-Kutta method with step-size and precision control. With known derivatives at ray points we can use Newton's iterative method, which guarantees quadratic convergence. Moreover, with these derivatives we can calculate geometrical spreading and thus the amplitudes. Different types of velocity structures such as homogeneous, gradient, etc. and different types of surface Φ(θ, φ) are considered. The results of numerical experiments are presented.

UR - http://www.scopus.com/inward/record.url?scp=85031674328&partnerID=8YFLogxK

U2 - 10.1063/1.5007421

DO - 10.1063/1.5007421

M3 - Conference contribution

AN - SCOPUS:85031674328

VL - 1895

T3 - AIP Conference Proceedings

BT - Application of Mathematics in Technical and Natural Sciences

A2 - Todorov, MD

PB - American Institute of Physics Inc.

T2 - 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017

Y2 - 21 June 2017 through 26 June 2017

ER -