of V,, includes the first half-cycle of the 30-sec periodic component noted in the V, curve. A
new error curve (the dashed line in Fig. B.2) in which a parabcla approximates the half-cycle
between 7 and 24 sec was fitted to the V, data and evaluated as
Ey, = —0,0017995t? + 0.05578t — 0.30228
The negative derivative of Ey, is the second acceleration correction function
Ca, =—-Ea, = +0.0001177t — 0.0017323
Integration of the newly corrected acceleration over the interval 9.5 to16.5 sec results in the
curve V; of Fig. B.3. This curve emphasizes the 1.5-cps signai. However, integration of the
9.05
I
~
V
cC
0.05 +
va
.
—
c
AAA \}Fe
LMT
2
°
°
aa
-
-
Y.
-0.05
|
10
{
12
|
TIME, SEC
14
\h
|g CY
|
-_+
o
6
~
y
am
-0.05
|
l
16
10
Fig. B.3—— Velocity from acceleration data corrected for sinusoidal drift as indicated by dashed line of Fig. B.2.
|
12
|
TIME, SEC
14
oom
|
{6
Fig. B.4—Velocity from acceleration data corrected for shift as indicated by
dashed lines of Figs. B.3 and B.5.
V, data gives the displacement curve D, in Fig. B.5, in which the 1.5-cps signal has become
submerged in a long-period component which can be approximated between 10 and 16 sec by the
parabola shown superimposed on the data. The equation for this error function is
Ep, = 0.025833t* — 0.795t + 5.14667
which upon differentiation gives the linear error function
Ey, = 0.004306t — 0.06625
represented by the dashed line in Fig. B.3. This results in a third correction term for the acceleration
Cy, =-E,, =—0.0001337
Finally, integration of the acceleration corrected for Ea, between 9.5 and 16.5 sec yields the
velocity curve V, of Fig. B.4, which in turn gives the displacement curve D, of Fig. B.6.
There is still a 5-sec periodic componentevident in the displacement curve which undoubtedly affects the maximum values of the curve. However, the 1.5-cps signal is strong, and
peak-to-peak amplitudes of this componentin the D, curve ure probably reasonable approximations of maximum excursion of the ground at the instrument. station.
54