Geology Reference
In-Depth Information
10
9
8
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6
Arguis ARM series
80 m moving average
80 m lowess
80 m robust loess
5
4
3
2
1 0
100
200
300
400
Meters upsection
500
600
700
800
Figure 4.4 Smoothing with simple moving average (green curve), lowess (blue curve), and robust loess (grey curve)
methods applied to the Arguis ARM stratigraphic series (red curve) that has been linearly interpolated to Δd = 0.05
m (as in Figure 4.3), over an 80 m window and using MATLAB's smooth.m (smooth(data,80/0.05,'moving'),
smooth(data,80/0.05,'lowess'), and smooth(data,80/0.05,'rloess')). The depicted lowess curve will be subtracted
from the Arguis series prior to spectral analysis (shown in Figure 4.21).
1
π
Stopband
Stopband
Passband
0.5
0
Magnitude response
Phase response
- π
0
0
f stop
f pass
f pass
f stop
f nyquist
Figure 4.5 Ideal filter compared with practical filter design for a digital signal. The diagram is in the frequency domain
from f = 0 to f nyquist and shows an ideal passband between two “f pass ” frequencies and two “f stop ” frequencies designating
frequencies passing >50% power. Shaded areas in the stopbands do not pass significant power. The blue curve shows the
magnitude response of a typical digital filter with this passband; the green curve shows the filter's phase response, which
for cyclostratigraphy needs to be zero in the passband. As a rule, digital filters (such as those provided in MATLAB in the
time domain) do not have a zero-phase response (unless applied forward and backward, e.g., using filtfilt.m ).
within the Nyquist frequency range, i.e., [0, f nyquist = 1/(2Δt)]. Low-pass
filtering (“smoothing”) is a common application in cyclostratigraphy and
can be conducted with simple or weighted averages (Section 4.3.2) as well
as with the digital filters (Section 4.3.4). Band-pass filtering is also com-
monly applied to extract signals embedded in cyclostratigraphic
sequences that are related to eccentricity, obliquity, and precession forc-
ing. Filtering played a major role in the astronomical tuning of the Arguis
Formation (Chapter 5).
 
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