Geology Reference
In-Depth Information
Assemble
stratigraphic
series
Assess
sample
rate
Assess
gaps and
outliers
Select
uniform
resampling
Determine
frequency
resolution
Examine
secular
trends
Remove
mean and
trend
Chapter 4
Compute
power
spectrum
Estimate
noise
spectrum
Compute
evolutionary
spectrum
Tune
stratigraphic
series
Compute
tuned power
spectrum
Estimate
noise
spectrum
Compute tuned
evolutionary
spectrum
Chapter 5
Figure 4.1
Flow chart of the measurement, analysis, and modeling of time series in cyclostratigraphy discussed in
Chapters 4 and 5.
series (i.e., finite length) sampled from the stratigraphic record as opposed
to the engineering perspective that emphasizes controlled signals. The typ-
ical processing and analysis flow (Figure 4.1) show that for investigations of
geological phenomena, key decision-making begins at the data collection
stage, with selection of the dependent and independent variables.
The time series analysis procedures presented in this chapter are demon-
strated on synthetic signals and rock magnetic data collected from the Late
Eocene Arguis Formation, Pyrenees, Spain (Kodama et al. 2010), using
MATLAB functions and custom scripts (Appendix). The philosophy behind
each procedure is discussed together with directions for how to apply the
procedures in MATLAB.
4.2
Geological Time Series
Digital time series of geological processes occur in two broad classes:
“instrumental-time” or “near-time” and “deep-time.” Near-time data are
measures of processes that are ongoing or that occurred in the recent
past, with the independent variable referred to a controlled timekeeper,
e.g., mean-hourly air temperature from a thermometer. Deep-time data
are samples of processes that have been recorded in geological materials,
e.g., magnetic mineral deposition in deep-sea sediment, in which the
independent variable is referred to a proxy timescale that is spatial (core
depth or stratigraphic thickness).
Geological time series are further categorized according to the type of
process that they represent. Continuous processes evolve through time steadily,
supported by a background (continuum) level of random (stochastic) varia-
tion, and often accompanied by a comparatively prominent foreground of
nonrandom (deterministic) cycling. Discontinuous processes are character-
ized by intermittent variation, i.e., sudden, short-lived “events” separated by
long intervals of time of no action. Here we focus on the measurement and
analysis of continuous processes, although significantly, techniques for the
analysis of discontinuous processes are now in resurgence (e.g., Hinnov et al.
2012; Olson et al. 2013) (Figure 4.2).
