Geology Reference
In-Depth Information
steps to follow. MATLAB
®
scripts are included in the Appendix that can help
with these analyses; however, two useful software packages will also be
referred to here. Analyseries (Paillard et al. 1996) includes routines that
evenly subsample a data series, apply a Gaussian filter, calculate Blackman-
Tukey, multitaper method (MTM), and maximum entropy spectral esti-
mates, as well as generate theoretical insolation series from Laskar et al.
(2004). Analyseries (the current version is 2.0.4.2) is an important tool for
time series analysis of rock magnetic data series and is available from the
Laboratoire des Sciences du Climat et de l'Environnement (
http://www.lsce.
ipsl.fr/logiciels/)
. Almost all of the steps mentioned here can be conducted
with Analyseries. The SSA-MTM toolkit (Ghil et al. 2002) is another pow-
erful software package for conducting time series analysis. It offers the cal-
culation of robust red noise (Mann & Lees 1996) for MTM spectral estimates
while Analyseries only calculates Thomson (1982) F-tests (with no adaptive
weighting) to estimate the significance of spectral peaks.
7.5.1
Preparation of the Data Series
As indicated in Chapter 4, the data series needs to be prepared for time series
analysis. The simplest preparation is to resample the series at even intervals
because the spectral estimation techniques used all require evenly spaced data.
Resampling can be done easily using Analyseries 2.0 provided the caveats
mentioned in Chapter 4 are kept in mind. Typically, the average sampling
interval used during field sampling sets the resampling interval. Linear inter-
polation between actual data points has given the best results in our studies.
It is sometimes necessary to remove linear trends or long wavelength var-
iations from the data. Long wavelength trends can yield very low frequency
spectral peaks with wavelengths longer than the data series. They may or
may not be the reflection of natural phenomena, but they cannot be ade-
quately resolved from the data, so they should be removed before spectral
analysis. Analyseries can remove linear trends from the input data series.
Taking a moving average of the data series is another way of removing long
wavelength trends. MATLAB's
smooth.m
can be used to remove low fre-
quency content; however, care should be taken that a true geologic signal is
not removed. Checking the smoothed data series for easily observed periodic
signals is important (see Figure 4.4).
Finally, as shown in some of the case studies in Chapter 6, it is sometimes
useful to take the log
10
of the data series to stabilize the variance of the data
and limit the effects of “spikey” data points on the spectral estimate.
7.5.2
Spectral Estimation
Spectral estimation is the centerpiece of this chapter. It is the “time series
analysis” that actually produces a power spectrum for the rock magnetic
data series. There are three different techniques available in Analyseries:
