Geology Reference
In-Depth Information
4
Time Series Analysis
for Cyclostratigraphy
Abstract:
This chapter reviews the time series analysis of cyclostratigraphy and
stresses the detection of variations potentially associated with astronomical forc-
ing. Methods of interpolation,
smoothing
, filtering, and spectrum estimation are
presented, with special emphasis on the Thomson multitaper estimator. Synthetic
and real-data examples that use basic MATLAB
®
functions and custom scripts
accompany the presentations. This is followed by an introduction to noise mod-
eling and hypothesis testing. Time-frequency analysis of nonstationary data is
addressed with
evolutionary spectrograms
and complex signal analysis. Spectral
coherency estimation with worked examples relevant to astronomical forcing
concludes the chapter.
4.1
Introduction
Digital signal processing techniques that were developed for electrical
and communications engineering and geophysics (seismology) make up
the toolkit that is used today to analyze geological time series. Typical
procedures involve preprocessing, spectrum estimation, time-frequency
analysis, and correlation. Preprocessing prepares a time series for more
advanced procedures such as spectrum estimation, and can involve inter-
polation, resampling, detrending, and filtering. Deep-time data requires
tuning to convert the proxy timescale of the independent variable, usually
stratigraphic thickness, into a true timescale. Time-frequency methods
such as spectrograms, wavelet analysis, and complex demodulation are
used to study the spectral properties of a time series. Coherency and
cross-phase spectral analysis measures the correlation of two time series
as a function of frequency.
This chapter provides a step-by-step guide to the main procedures that
are currently used for the analysis and modeling of cyclostratigraphic time
series. The presentation is tailored to the special problems of truncated data
