Fróðskaparrit - 01.01.1975, Side 72

80
Sea Level Fluctuations in Tórshavn, Preliminary Results
The MEM has been used previously in other branches of
Geophysics by a number of authors (ref. 2,3) and has been
used by Arne Nielsen to identify eigenmodes of the Baltic
(ref. 4). No detailed description of the method will be given
here; interested readers are referred to the papers by Burg,
Lacoss, Ulrych and Andersen (refs. 5 to 10). Suffice it to
mention that the PDS mav be calculated from a set of filter
coefficients a2> • • •, am by the formula
P„-At
P(f) =
|1 - E ak' exp(-2-n-i-k-At-f)I
-1 < f < 1
2 2At 2it
(2)
The filter is a »Prediction« filter designed to fulfill the equation
(3)
minimizing the power Po of the noise series rt . Methods for
calculating at,..., am and PD from a given time series were
constructed by Burg. The specific algorithm employed in this
study is the one given by Andersen (ref. 10); it has been pro-
grammed in FORTRAN and run on the UNIVAC 1110 com-
puter of the University of Copenhagen. The number of filter
coefficients is optional, resolution increasing with m, however
experience requires m to be less than one half (preferably one
third) of the number of data values ánalyzed.
Filter coefficients and power of noise having been computed,
P(f) may be evaluated and plotted for any wanted frequency f
in the Nyquist interval, and harmonic constituents- that is
periodic components — will show up as peaks in the spectrum.
In this way one may determine the significant frequencies f;
of eq. (1). To determine the amplitudes c^ consider that the
power Pj of an harmonic with amplitude c^ is
P fi+Af
Pi = \' CL = \ (4)
J fpAf
(Actually there is an additional factor of 2 as both positive and
negative frequencies are used. It will be omitted in the formulae