Algorithms of phase and group correlation

Abstract

In this paper we consider algorithms of phase and group correlation which are based on different assumptions regarding the character of wave field. In order to construct the correlation algorithm, the wave field is presented as a product of an envelope and a normalized seismogram. Phase correlation is performed on the normalized seismogram, while group correlation is performed on the perigram, a low cut version of the envelope function. The central point of the correlation algorithm is the construction of a functional which characterizes the main correlation properties of the wave field. This functional is computed for different values of parameters which appear in the expressions approximating phase and group traveltime curves. Several types of correlation functionals are considered. The next step of the correlation algorithm is analysis of the previously obtained functionals; this is performed using a system of inequalities based on a number of assumptions regarding the properties of wave fields. The results of this analysis permit us to make a decision regarding the presence of a signal and to estimate the parameters of detected waves. Examples illustrating application of the proposed algorithm to synthetic and field data are presented.