TY - JOUR
T1 - Real and complex spectra – a generalization of WKBJ seismograms
AU - Heyman, E.
AU - Felsen, L. B.
PY - 1987/12
Y1 - 1987/12
N2 - 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.
AB - 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.
KW - plane waves
KW - spectral theory of transients
KW - synthetic seismograms
UR - http://www.scopus.com/inward/record.url?scp=84986397910&partnerID=8YFLogxK
U2 - 10.1111/j.1365-246X.1987.tb01681.x
DO - 10.1111/j.1365-246X.1987.tb01681.x
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AN - SCOPUS:84986397910
SN - 0016-8009
VL - 91
SP - 1087
EP - 1126
JO - Geophysical Journal of the Royal Astronomical Society
JF - Geophysical Journal of the Royal Astronomical Society
IS - 3
ER -