By JOZEF KRISTEK, AND LADISLAV HALADA PETER MOCZO
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Extra resources for The Finite-difference Method for Seismologists: An Introduction
25 – Oct. 2 2004 Moczo, Kristek, Halada: The Finite-Difference Method for Seismologists. An Introduction Ilan et al. (1975), and Ilan and Loewenthal (1976) solved the P-SV problem on the horizontal and vertical planar discontinuities with the homogeneous approach. Instead of the fictitious grid points they used Taylor expansions of displacement to couple the equation of motion with the boundary conditions. Kelly et al. (1976) presented their heterogeneous P-SV schemes with simple intuitive averaging of material parameters.
Higdon (1991) developed an approximation of the absorbing boundary condition that is based on the composition of simple 1st-order differential operators. Each operator gives perfect absorption for a plane wave impinging on the boundary at certain velocity and angle of incidence. Recently, Liu and Archuleta (2000) combined the Clayton-Engquist’s A1 formulas with those by Higdon (1991) and obtained a well-working nonreflecting boundary. Their formulas are given in Moczo et al. (2002). Here we show several nonreflecting boundaries in a unified representation.
Material Grid Parameters Material (or medium) grid parameters ρ I = ρ ( I h) and CI = C ( I h) used in the above equations can be understood as some appropriate discrete approximations to density and elastic modulus, respectively. If the medium is homogeneous, then, obviously, ρ I = ρ and CI = C for all grid points. If the medium is sufficiently smooth, local values of ρ and C will give good results. If the medium is not sufficiently smooth, then it is not trivial and intuitively obvious how to determine values of ρ I and CI .
The Finite-difference Method for Seismologists: An Introduction by JOZEF KRISTEK, AND LADISLAV HALADA PETER MOCZO