Geoscience Reference
In-Depth Information
5.7 Lomb-Scargle Power Spectrum
h e power spectrum methods introduced in the previous sections require
evenly-spaced data. In earth sciences, however, time series are ot en unevenly
spaced. Although interpolating the unevenly-spaced data to a grid of evenly-
spaced times is one way to overcome this problem (Section 5.5), interpolation
introduces numerous artifacts into the data, in both the time and frequency
domains. For this reason an alternative method of time-series analysis has
become increasingly popular in earth sciences, the Lomb-Scargle algorithm
(e.g., Scargle 1981, 1982, 1989, 1990, Press et al. 1992, Schulz et al. 1998).
h e Lomb-Scargle algorithm only evaluates the data of the time series
at the times
t
i
that are actually measured. Assuming a series
y
(
t
) of
N
data
points, the Lomb-Scargle normalized periodogram
P
x
, as a function of
angular frequency ˉ=2ˀ
f
> 0, is given by
where
and
are the arithmetic mean and the variance of the data (Section 3.2). h e
constant ˄, which is dei ned by the relationship
is an of set that makes P
x
(ˉ) independent of shit ing the
t
i
values by any
