Essentials of Geophysical Data Processing

The power spectrum describes how the variance of a time series is distributed over frequency. The variance (mean squared signal value per time sample) is a broadband statistic measuring power, while the power spectrum at a given frequency is a statistic measuring the power in a narrow frequency band. Similarly, the coherence spectrum describes how the broadband correlation coefficient between two time series varies with frequency. The DFT is the main tool for estimating both the power and coherence spectra and will be our main focus, but we also compare the DFT (periodogram) results with estimates made using the prediction error filter (PEF) developed in . Using examples we show that PEF estimates tend to be smooth, but the choice of PEF order introduces some variability in these estimates. Periodogram spectrum estimates tend to be erratic but can be tamed at the expense of diminished frequency resolution. We describe standard methods of assigning confidence intervals to periodogram spectrum estimates.