# Dictionary:Autocorrelation

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(o, tō, kor, ∂ lā’ sh∂n) Correlation of a waveform with itself. The normalized autocorrelation function for a continuous stationary waveform is

where *f*(*t*) represents a waveform (or seismic trace) and is the time shift or lag. For equally sampled (digital) data the autocorrelation is

An autocorrelation is usually evaluated only over a **gate** or **window**. The denominators in the preceding equations are the **normalizing factors** and sometimes are not included. The autocorrelation function is a measure of the statistical dependence of the waveform at a later time () on the present value, or the extent to which future values can be predicted from past values. The autocorrelation function contains all of the amplitude-frequency information in the original waveform but none of the phase information. An autocorrelation function is symmetrical about zero shift, that is, it is **zero phase**. Deconvolution operators are often based on autocorrelations; see Sheriff and Geldart (1995: 285-287, 292-403).