Premium
TRANSIENT FINITE INTEGRAL POINT SOURCE RESPONSE FROM A PLANAR ACOUSTIC INTERFACE: THE CAUSALITY APPROACH *
Author(s) -
HUBRAL P.,
TYGEL M.
Publication year - 1986
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1986.tb00449.x
Subject(s) - planar , limit (mathematics) , causality (physics) , point source , transformation (genetics) , physics , plane (geometry) , mathematical analysis , point (geometry) , reflection (computer programming) , symmetry (geometry) , interface (matter) , plane wave , classical mechanics , geometry , mathematics , optics , quantum mechanics , computer science , biochemistry , chemistry , computer graphics (images) , gene , programming language , surface tension , gibbs isotherm
Point source reflection/transmission responses from planar interfaces based on the Sommerfeld‐Weyl integral are causal and are given in the form of a solution integral with an infinite integration limit. They can be simply transformed to integrals with a finite limit by an approach that takes into account causality as well as time‐symmetry aspects. To introduce the fundamental principles involved, the transformation is applied to the simple case of a point‐source response from a planar acoustic interface. For a point source above a planar interface separating an upper and lower acoustic half‐space of velocity c 1 and c 2 the inhomogeneous plane waves in the Sommerfeld‐Weyl source representation do not contribute to the final result if c 1 ≤ c 2 and only a limited spectrum of inhomogeneous plane waves comes into play if c 1 c 2 .