Harichandran, R. S. (1987). "Correlation analysis in space-time modeling
of strong ground motion." Technical Note, Journal of Engineering
Mechanics, ASCE, 113(4), 629-634.
Abstract
An important part of the study of the space-time variation of earthquake
ground motions is to analyze and model the frequency-dependent
correlation function of accelerograms recorded at different spatial
location. The correlation function between the harmonic components of
two accelerograms at a specified frequency, known as the
frequency-dependent correlation function, is closely related to the
coherency spectrum. Using this relationship and the conventional method
of estimating coherency spectra, it is possible to estimate the
frequency-dependent correlation functions of the accelerograms.
In recent literature another technique for directly estimating
frequency-dependent correlation functions has become popular. This
"moving window" approach uses a narrow window in the frequency domain to
obtain approximately harmonic components of accelerograms, and then
estimates the correlation functions between these components as the
frequency-dependent correlation functions. The relationship between this
approach and the conventional method is derived. It is shown that unless
precautions are taken to correct for time delays between the two
accelerograms being analyzed, the moving window approach yields
estimates with larger biases than those obtained by the conventional
method. This feature is further illustrated through an example.