Complex envelope and procedures of combined group and phase correlation

B. Gelchinsky, E. Landa, V. Shtivelman

Research output: Contribution to conferencePaperpeer-review


In previous works by the authors, a procedure of phase and group correlation for analysis of wave fields in complex media was proposed, The procedure was based on analysis of trace envelopes and normalized seismograms (cosine of the phase). However, since this procedure implies that phase and group correlations are performed independently, in some cases difficulties in combined interpretation of results may arise. In order to overcome these difficulties, we propose a new method for combined group and phase correlation. The method assumes that the seismic signal has a narrow band spectrum; such a signal can be represented as a sum of two products of slowly and rapidly varying time functions. The slowly varying functions have a finite (or quasi-finite) spectrum and define the group properties of the signal. The rapidly varying functions are harmonic functions of time with high carrier frequency, and their variations in space define the phase properties of the signal. For such types of signal, a complex envelope can be naturally introduced; its absolute value coincides with the conventional envelope and its phase depends on the above mentioned slowly varying functions. Since the normalized seismogram is, by definition, the cosine of the total phase, it is now related to both group and phase properties of the signal and can be used for combined phase and group correlation. In this work we consider two different schemes of correlation using the normalized seismograms. In one, the group correlation is performed on the basis of a priori known phase traveltimes; the other scheme does not require knowledge of phase properties in order to perform group correlation. A number of examples illustrating the application of the correlation scheme are presented.

Original languageEnglish
Number of pages3
StatePublished - 1986
Externally publishedYes
Event1986 Society of Exploration Geophysicists Annual Meeting, SEG 1986 - Houston, United States
Duration: 2 Nov 19866 Nov 1986


Conference1986 Society of Exploration Geophysicists Annual Meeting, SEG 1986
Country/TerritoryUnited States


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