Open AccessReal and complex spectra – a generalization of WKBJ seismograms
Author(s) -
Heyman E.,
Felsen L. B.
Publication year - 1987
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.1987.tb01681.x
Subject(s) - slowness , seismogram , reflection (computer programming) , spectral line , generalization , gravitational singularity , plane wave , complex plane , geology , plane (geometry) , wave propagation , mathematical analysis , geometry , optics , physics , mathematics , computer science , seismology , quantum mechanics , programming language
Real plane‐waves constitute the building blocks for recently developed spectral techniques in synthetic seismology. While providing numerical convenience, real slowness‐spectra model certain wave phenomena in a distributed ‘unnatural’ way, whereas complex spectra model these phenomena in a compact, more ‘natural’ way. The theory of complex spectra, called by us the ‘Spectral Theory of Transients’ (STT) and developed elsewhere, is summarized here and contrasted with the real‐spectrum approach. Relying strongly on the theory of analytic functions, STT permits the transient responses to be classified and evaluated according to the singularities they introduce in the complex slowness plane. The method is illustrated for a number of 2‐D SH ‐wave model propagation environments, including interface reflection, head waves, multiple encounters with caustics due to concave boundaries or ducting medium inhomogeneities, and diffraction by structures with edges.