SUMMARY
Computes the correlation function.
SYNTAX
COR {[N]UMBER n|ON|OFF}, {[L}ENGTH v}, {[T]YPE type}
{[P]REWHITEN ON|OFF|n}, {[S]TOCASTIC|[TR]ANSIENT}
where type is one of the following:
[HAM]MING [HAN]NING [C]OSINE [R]ECTANGLE [T]RIANGLE
INPUTS
NUMBER n: Fix number of windows to n. NUMBER {ON}: Fix number of windows to previous value. NUMBER OFF: Compute number of windows based upon data length and window length. There will be no data overlap when using this option. LENGTH v: Set window length to v seconds. TYPE type: Set window type. The advantages of each is discussed below. PREWHITEN {ON}: Turn prewhitening of data on. PREWHITEN OFF: Turn prewhitening of data off. PREWHITEN n: Turn prewhitening of data on and change number of coefficients to n. STOCHASTIC: Set correlation scaling assuming that the data is stochastic (random.) TRANSIENT: Set correlation scaling assuming that the data is transient (signal.)
DEFAULT VALUES
COR NUMBER OFF TYPE HAMMING PREWHITEN OFF
Note that if PREWHITEN is turned on without specifying the order, it will default to 6 unless it has been previously set by the WHITEN command in SPE.
DESCRIPTION
This correlation command assumes that the data is stationary. Under that assumption the data is segmented into many windows, and a sample correlation function is calculated for each window. These sample correlation functions are averaged to produce a more stable estimate of the underlying correlation function of the random process. The number of windows, the window length, and the window type (called a data window, to distinguish it from a window used in the PDS command) are under user control. If the window length times the number of windows exceeds the total data length, the program overlaps the windows. The amount of overlap is not under user control.
For a fixed data size, there is obviously a tradeoff between the number of windows to be used and the window size. This tradeoff ultimately results in a tradeoff between the bias and variance of the spectral estimates made using the correlation function.
The frequency-domain resolution of a spectral estimator depends on the length of the available correlation and, therefore, indirectly on the size of the data window. The larger the correlation window, the smaller the bias in the spectral estimate resulting from frequency-domain smoothing.
However, as the data window size is increased, fewer windows can be used in the averaging process. Consequently, the variance of the correlation function estimate increases, and with it, the variance of the spectral estimate.
The choice of data window type can be used to fine-tune the tradeoff between bias and variance. The smoother windows tend to taper the data off near the window edges, effectively reducing window length. Thus, the windows can be overlapped more, and more can be used. This choice decreases variance at the expense of increasing bias.
There is another important source of bias when the dynamic range of the spectrum is quite large. This is the effect of window leakage, that shows up most clearly when the PDS estimator is used. Power leakage through the sidelobes of the Fourier Transform of the correlation window puts a floor on the estimated spectrum. In typical seismic data, this floor is quite regular and appears at high frequencies, where the spectrum is typically quite small. The correlation function estimator has an optional prewhitening capability that mitigates the sidelobe-leakage problem. A low-order prediction error filter is used to flatten the spectrum of the data prior to the calculation of the correlation function. The effect of the filter is compensated for in the calculation of the spectrum.
Prewhitening of the data is done in place and thus corrupts the original signal. If you use prewhitening, quit the subprocess, and wish to use the original signal in some other operation, you MUST reread it into SAC.
This correlation function is used in the calculation of the spectral estimate.
COR must therefore be executed before PDS, MLM, or MEM.
You may plot the correlation function using the PLOTCOR command and save it as a SAC data file using the WRITECOR command. Such a file can then be read in using READCOR.
HEADER CHANGES
DEPMIN, DEPMAX, DEPMIN