Some Geophysical Applications of Autoregressive Spectral Estimates

This paper discusses the practical application of autoregressive spectral analysis to three different geophysical data sets. In all cases the amount of available data was limited so that autoregressive methods might give more detailed spectra than those obtainable by the classical windowed spectral estimate methods. For each series, the Burg technique, which guarantees positive-definite autocorrelation functions, is used to determine the prediction error coefficients. The degree of spectral instability known to result from the use of Burg´s algorithm is not crucial to our results. Algorithms due to Akaike and Parzen are applied to the time series to aid in order-number determination. For the first example, autoregressive spectral analysis of a complex time series is applied to the log spectrum of short-period seismograms. The resultant spectrum, the so-called complex cepstrum, allows one to determine the depth below the earth´s surface at which the seismic event originated. The other examples concern the analysis of real time series due to two somewhat unusual data sets. One of these is the analysis of the time rate at which earthquakes occur. The purpose is to determine if periodicities exist that correspond to known astronomical and terrestrial rotational periods. The other is a study of biological and chemical parameters measured in core samples of oceanbottom sediments where displacement down the core is calibrated in geological time. The measurements directly infer the amount of ice on the earth´s surface.