Schmucker, 1970 (Scripps) - MTNet

26
Bulletin, Scripps Institution of Oceanography
with high-speed computers (cf. program GMV, App. IV). It is often desirable
to begin the data reduction with a simple preliminary analysis while the field
operations are still in progress. This may help to add new field stations in
the most effective way within anomalous ZOnes.
Parkinson (1959) and Wiese (1962) described suitable graphical methods to
treat peak-value readings from numerous single events, yielding length and
direction of the (in-phase) induction arrows. Untiedt's method (1964), which
is now widely accepted, results in comparable arrows but employs continuous
readings from a few outstanding disturbances. The method presented here is
analytic on the basis of a least-square fit and follows directly from equation
3.22 in section 3.11. Let H, D, Z be the amplitudes of quasi-sinusoidal disturbances,
observed simultaneously at one particular site. Maximum deflections
in the three components may not coincide exactly in time, but such
phase shifts are disregarded. Hence, the products
< H • D> = HD
when averaged over numerous events of the same quasi-period, shall represent
the now real cross spectrum between H and D. We ignore the anomalous
parts in Hand D and rewrite equation 3.22 in the form
with
ZH DD - ZD HD
z = ------..,,.__
H DD HH _ HD2
- - -]1/2
E Z = [1 - (zH ZH + zD ZD)/ZZ
(3.27)
as residual of the correlation analysiS (from eq. 3.17). Thus determined
"peak-value" transfer functions can be put together to preliminary (in-phase)
induction arrows (eq. 3.19) with a corresponding circle of confidence (eq.
3.20) for various quasi-periods.
3.14 Contribution of Scaling Errors to Residuals
Consistent scaling errOrs, arising for instance from calibration errors or
from wrong clock corrections, are undetectable in the course of the data reduction
and should be kept to a minimum. Random scaling errors, on the
other hand, augment the residuals of the correlation analysis (cf. sec. 3.9).
Their contributions are denoted as "error residuals" to distinguish them
from those which reflect a genuine lack of correlation between the anomalous
and normal parts.
Let a and i3 be estimates of the mean relative scaling error and the timing
-error, respectively, both varying at random within the assemblage or sequence
of analyzed events (cf. sec. 3.3). In the frequency domain a becomes