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


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
Issue number3
StatePublished - Dec 1987


  • plane waves
  • spectral theory of transients
  • synthetic seismograms


Dive into the research topics of 'Real and complex spectra – a generalization of WKBJ seismograms'. Together they form a unique fingerprint.

Cite this