Real and complex spectra – a generalization of WKBJ seismograms

E. Heyman*, L. B. Felsen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1087-1126
Number of pages40
JournalGeophysical Journal of the Royal Astronomical Society
Volume91
Issue number3
DOIs
StatePublished - Dec 1987

Keywords

  • plane waves
  • spectral theory of transients
  • synthetic seismograms

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