Open AccessUse of the spherical layer matrix in inhomogeneous media
Author(s) -
FIazer L. Neil
Publication year - 1977
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1977.tb01345.x
Subject(s) - helmholtz equation , computation , matrix (chemical analysis) , spherical wave , mathematical analysis , layer (electronics) , physics , type (biology) , classical mechanics , geometry , mathematics , geology , materials science , optics , boundary value problem , algorithm , composite material , paleontology
Summary Exact solutions of the reduced Helmholtz equation are derived for the case of a spherically symmetric medium in which the velocity has the form v = ar ‐b . If the Earth is modelled in shells of this type then these solutions can be used to approximate the radial wave functions needed for body‐wave computations. The spherical layer matrix technique is adapted to the case where velocities vary smoothly within layers.