Geology Reference
In-Depth Information
nonuniform sampling on spectral estimates (Section 4.3.5). If hypothesis
testing is to be undertaken with null models based on autoregressive
noise, then the average spacing must be used, or procedures for nonuni-
formly sampled time series.
Common pitfalls of interpolation are illustrated in Figure 4.3. The Arguis
ARM series has an average spacing of 0.6757 m across the entire 800 m of
section. However, if this interval is adopted as the uniform sample rate in an
interpolation, some segments of the series will be severely undersampled
(Figure 4.3c). Using spline fits are not recommended, as these can produce
large perturbations in the interpolation, especially where there are sudden
changes in direction over wide gaps (Figure 4.3d). For the demonstrations
below, the Arguis ARM stratigraphic series has been linearly interpolated to
a uniform spacing of Δd = 0.05 m, which captures practically all variability
with minimal introduction of artifacts.
4.3.2
Detrending, Smoothing, and “Prewhitening”
Frequently, variations and cycles of interest are riding atop a long-term
secular trend, which can be extremely high amplitude and quasiperiodic.
Estimation and removal of such trends can be crucial for spectral analysis,
i.e., to avoid spectral leakage from these high-power components into
frequencies of interest. Simple moving averages and weighted mean (“low-
ess,” “loess,” or “robust loess”) averages may be estimated and removed, in
a process called “prewhitening,” which will reduce interference of these
trends with the rest of the estimated spectrum. This requires experimen-
tation by the practitioner to identify the most appropriate averaging
(smoothing) window. Comparison of three 80-m smoothing approaches
in Figure 4.4 shows that the robust loess smoothing has picked up on the
~75 m cycling, which may be related to orbital eccentricity cycling
(Chapter 5). Thus, if the robust loess smoothing is used for the removal
of the long-term trend, signal power could be affected. The large “step-up”
in the data series at 182-185 m introduces an irregularity that could inter-
fere with spectral estimates of the low frequencies. Removing or reducing
it would diminish its obstructive effects. We selected the lowess smooth-
ing depicted in Figure 4.4 to remove the irregular long-term trend from
the Arguis series.
4.3.3
Filtering Basics
Filters are essential tools for isolating specific frequency components in
geologic data series for detailed examination. The ideal filter is the “brick
wall” filter, with four basic designs: lowpass, highpass, bandpass, and
notch. Figure 4.5 shows the basic parameters that are considered in
digital filter design, which are constrained to filter resolvable frequencies
