october, 1986...exploration gravimeter secured in an air-tight aluminum pressure case. this...
TRANSCRIPT
October, 1986
Blacksburg, Virginia
I
TIDAL GRAVITY ANOMALIES IN SOUTHEASTERN NORTH AMERICA
by
Dwight Allen Holland
Dr. Edwin S. Robinson, Chairman
(ABSTRACT)
Tidal variations of gravity were measured at fourteen sites in
southeastern North America for periods of between 40 and 199 days.
These measurements were used to obtain tidal gravity anomalies that
indicate the geologic effect of the earth on tidal gravity. The tidal
gravity anomaly is a vector quantity representing the difference between
measured tidal gravity and the theoretical tidal gravity on al
spherically symmetrical earth model subject to ocean tidal loading. The
real part of the anomaly vectors include 8 values in the range of :0.5
microgals, 4 values in the range of 0.5 to 1.5 microgals, 1 value of 1.5
to 2.5 microgals, and 1 other value in the range of -0.5 to -1.5
microgals, This grouping is consistent with a worldwide distribution of
values from regions where the asthenosphere is at intermediate depth,
the stress conditions are not excessive, and geothermal heat flow isE
approximately 60 mw/mz.l
’
iii”
ACKNOWLEDGMENTS
Dr. Edwin S. Robinson has given much professional direction and
guidance to this project and his expertise was willingly shared. His
role as advisor and friend has positively shaped my graduate experience.
Ors. Gilbert A. Bollinger and John K. Costain provided critical
review of the manuscript. at the Virginia Division of
Mineral Resources helped a great deal with the data acquisition at the
Charlottesville, Virginia station.
data from Morgantown, West Virginia and Columbia, South Carolina for
analysis.
was a valuable source of help in the drafting of
several figures.
The computer time for this research was paid for by the Department
of Geological Sciences, Virginia Polytechnic Institute and State
University.
iii
iv
This thesis effort is dedicated
to my grandparents,
along with of Emory and Henry College
with all my thanks.
iv
TABLE OF CONTENTS
E12ABSTRACT
ACKNOWLEDGMENTS .............................................. iii
LIST OF TABLES ............................................... V1
usr or Fxsumzs .............................................. *11INTRODUCTION ................................................. 1
THE TIDAL GRAVIMETRIC FACTOR ................................. 4
TIDAL GRAVITY MEASUREMENTS ................................... 8
HARMONIC ANALYSIS .....;...................................... 15
THE WORLD OCEAN TIDE ......................................... _ 21
LOADING RESPONSE FUNCTIONS ................................... 27
OCEAN TIDAL LOADING VECTORS .................................. 31
TIDAL GRAVITY ANOMALIES ...................................... 34
DISCUSSION OF RESULTS ........................................ 40
CONCLUSION ................................................... 45
BIBLIOGRAPHY ................................................. 46
APPENDIX ..................................................... 48
VITA ......................................................... 78
v
LIST OF TABLES
läs Ess1 General Description of Stations .................... 9
2 Gravimeter Calibration for Three Instruments ....... 14
3 Principal Harmonic Constituents .................... 17
4 Observed M2 Parameters ............................. gg
5 Gravimetric and Vertical Displacement Response‘ Functions .......................................... 3Q
6 Theoretical M2 Tidal Loading Vectors ............... 33
7 Tidal Gravity Anomalies ............................ gg
vi
LIST OF FIGURESl
Lime has1 Geographic Station Positions .................. 3
2 Typical 1 month Tidal Gravimeter Record ....... 11
3 Schwiderski M2 Cotidal-Corange Chart .......... 264 Gravimetric Response Function ................. 29
5 Vector Relationships Used for Analysis ........ 38
6 Real Y vs. Heat Flow for Europe and the world.. 42
7 Heat Flow Map Based upon Silica Geothermo-metry ......................................... 43
8 Three Histograms of Real H*in Different Ranges. 44
vii
‘INTRODUCTION
Recent tidal gravity studies have suggested that geotectonic
structures differ in their response to the gravitational attraction of
the sun and moon (Yanshin and others, in press). These differences are
indicated by tidal gravity anomalies which may reveal information about
broad areas of lateral inhomogeneity in the earth's asthenosphere and
lithosphere. A tidal gravity anomaly is the vector difference between
tidal gravity measured at a point on the earth and the theoretical tidal
gravity calculated for a spherically symmetrical earth model subject to
ocean tidal loading. .
This study examined the variation of the tidal gravity anomalies
obtained from the lunar semi-diurnal tidal harmonic (M2) in southeastern
North America. Tidal gravimeter measurements were made at the fourteen
sites shown in Figure 1. The M2 tidal harmonic constituent has been
selected for analysis because it is the strongest and best separated
,wave in the tidal spectrum, and the corresponding M2 constituent of the
world ocean tide is thought to be reasonably well understood. The M2
wave is that harmonic constituent of the total tide which would be
produced by an object with a mass equal to the moon traveling in a
circular orbit within the plane of the earth's equator.
Determination of tidal gravity anomalies requires knowledge of the
world ocean tide, the capability to calculate the elastic deformation of
the earth caused by the ocean tide, and careful analysis of tidal
gravity records. A discussion of each of these topics will be presented
1
· 2
as well as some aspects of the tidal gravity record acquisition and
analysis.
In recent studies of tidal gravity anomalies in Eurasia and Africa,
Yanshin and others (in press) and Melchior and Deßecker (1983)
recognized patterns of variation that could be correlated with geologic
and heat flow provinces. The present study is the first attempt to
identify similar patterns in North America. The results appear to
confirm those found in Eurasia and Africa.
I I 2
5;; T so' es' 6o° 1s'1o°I
‘~°¤
IL-—--3{ { ·
•%?E
‘
~•
E }" T "‘ Ä ‘°
-..- . W°IWY¢·'i I{ I \N
/L1</~\‘L
H“
I I "’ PCI
'T * "' ‘ °7.¤"“’ KNX}//____ ., M,Ä.„---§-·‘·I Cf.I I I .II1--~
.1 1•T 5 .° I I EG
}l_____
\ •""\..•-•
-*31% Z5.AI; \\
o soo‘
' miles
I I
Figure 3. Tide] Gravity Station sites in the southeastern UnitedStates. Letter designations are identified in Tab1e°1.
THE TIDAL GRAVIMETRIC FACTOR
A gravimeter operated continuously at a site on the earth's surface
detects a cyclic fluctuation which is the tidal variation of gravity.
It is produced by the masses and motions of the moon and sun, and the
elastic response of the earth to the luni-solar tidal force. A measure
l of this elastic response is given by a term called the tidal gravimetric
jagtgg. This term is the ratio of the measured tidal variation of
gravity at a point on the earth and the corresponding theoretical
variation on a rigid globe predicted from the astronomy of the
earth-moon-sun system.
It is conventional to express the cyclic tidal variation of gravity
at some location as a series of harmonic constituents. Methods of
harmonic analysis for calculating the amplitudes and phase angles of
these constituents from a tidal gravity record are discussed later. The
common practice in tidal gravity studies is to determine values of the
tidal gravimetric factor separately from the amplitudes of different·
harmonic constituents.
The physical significance of the tidal gravity factor can be
described as follows. A point on the earth experiences four effects
that contribute to the measured·tidal variation of gravity. These
effects are:
1. The direct gravitational attraction of the sun and moon;
2. Deformation of the solid earth caused by the lunisolar
gravity;
4 .
5
3. The vertical displacement of a point due to the change in
the shape of the earth; and
4. Ocean tidal loading perturbations.
Neglecting for the moment the perturbation induced by ocean
loading, the tidal gravimetric potential (W) at a point on the earth's
surface may be written (Garland, 1971):
H = Ht + wm - gdN
where Ht is the lunisolar potential, Wm is the potential related to the
tidal change in the shape of the earth, gdN is the potential related to
a vertical displacement dN at the point, and g is the gravitational
attraction at a point due to the earth's mass. Wm is the potential of
the mass of the tidal bulge produced in response to the tide-producing
forces of the sun and moon. The quantity gdN is the potential change
·due to the variation in the vertical position of the observation point
also known as the free air effect. The potentials Hm and gdN are
assumed to be proportional to Ht:
Wm = kwt and
gdN = hHt
where the constants of proportionality h and k are Love‘s numbers
(Melchior, 1966). Therefore, the tidal potential can be written in
,
6 T
terms of Love numbers as‘
w¤wt(1+k-h)
The tidal variation of gravity (dg) in terms of Love numbers is then
obtained by differentiating this potential:
dg. ä‘;-%.1@.¤BR 3R BR
where R is the radius of the earth.
The tidal potential caused by a body of mass m can be represented
(Melchior, 1966) as ·
w = GMR2(3 cosz 6 - 1)’¢ TT2r
.where 6 is the time varying angular position of the heavenly body
relative to the zenith of the observer, with r as the distance between
the center of the earth and the heavenly body, and m and R are the
earth's mass and radius. Differentiation shows that:
awt awtER- =° T °
The term ggü is the attraction of mass redistribution needed to changethe earth's shape. It can be represented by a surface density function
7 .
given by a surface harmonic series. By differentiating this series termw 3w• •
m = -m
•by term, it is found that ER. ER. . The vertical gradient ofgravity is, gg. = - ä., as can be shown by differentiating Newton's
Universal Law of Gravitation. Making these substitutions, tidal gravityZw 3W, _ __; m _ 2 dN =at a point on Sue earth is found to be dg R + T .9R.
(1-3/2 k + h) ääi . But on a perfectly rigid body h = k = 0 so that theBW
tidal gravity would be dgt =.äRE. Therefore, the gravimetric factor is
6= dg/d9t=1-3/2k+h.
For an idealized model consisting of concentric spherical shells
with elastic properties corresponding to those of the principal zones of
the earth the values of the Love numbers_are close to k = 0.61 and h =
0.30. Therefore, the tidal gravimetric factor is close to 1.16 (Alsop
and Kuo, 1964). Differences between this and measured values of the
tidal gravity factor can be attributed to effects of ocean tidal
loading, which are quite well understood, and to inhomogenieties
presumably in the lithosphere and asthenosphere whose effects are poorly
understood. The purpose of this study is to detect evidence of these
latter effects. To accomplish this, adjustments must first be made to
account for the former effects. -
TIDAL GRAVITY MEASUREMENTS
Tidal gravity measurements have been made at 14 stations in the
southeastern United States with 5 different Geodynamics gravity meters.
Ten of the sites included in this study were described by Robinson
(1974). This initial tidal gravity survey has been extended by more
recent measurements of approximately three and six months duration in
Morgantown, West Virginia, and Charlottesville, Virginia, respectively.
Additional six-month records were obtained in Blacksburg, Virginia and
Columbia, South Carolina. Also, a three-month record obtained by Wilson
(1978) at Bay St. Louis, Mississippi and a two·month record from
Knoxville, Tennessee are included in this study. Station locations,
instruments and record lengths are given in Table 1. Typical tidal
gravimeter records are reproduced in Figure 2.
The geodynamics tidal gravimeter is a modified North American
exploration gravimeter secured in an air-tight aluminum pressure case.
This instrument is designed for long-term recording with low drift
rates. The air-tight pressure case is enclosed inside an insulated
wooden case with the manufacturer stating that temperature control on
the functional part of the instrument is within 0.005 degrees C near an‘
optimum ambient temperature of 36°C. Internal temperature control,
important for meter stability, is maintained by an AC thermister bridge
directing the inner and outer heating coils. ~Gravitational field changes are sensed by monitoring the beamv
position in the gravimeter by a differential capacitor transducer. This
8
I4
T
I.>
~•&
••—
-
I•U
UA
HQ
ß••
••‘
09
-0
ce
qI.
0.
Ig
-«:0
An
0sn
0;
I:0
;••
an
g0
.0>
¤„
I0
5u
s.
,,3.-
0.
.1:...
.1E
.0
;0
00
..0
0:
0I
vu
•-•e
>-••
_:
3:
mu
•>„-
•„.I.
TI,.
9..;
ug
.·
-Z
..
.•-
·-•¤
:—
>„Q
un0
_•
•>
„
Qg
e5
;.5
.5
u·•·•»
.g
0U
I0
00
00
on
Q.:
-I/1•-*
«•«
Q·..
..•-0
•>.—
-••
en.-
0•0
Q-•
03
02
>~S
wA
A0
I3
>~
00
:0
:0
00
:a
nn
;•
0>—e
.:2
0-In
;-J
UV
!B
-U
E-E
Uv
tu
UU
••-«>
*'
I[I
°_
gg
gg
•\•
§•
\•O
.«in
hnu
e;
I0
uu
0-Q
I-0
00
0g:
00
0O
b
:u
n>
•sn
1,,;,
00
·-
:0
00
>•
HA
I:0
0••
0>
IQ
-;•0
UA
Q0
Qu
w,_
IQ
Qu
Q-
I0
60
••~
II
0-
|*•‘
EF
I0
00
0:
10
•E
0=
G-¤
Eu
Isn
um
Ev
EQ
E:
I°
...1yü
uIh
un
ub
hl:
uU
0:
0I:
GQ
nc-
-••0
I-0
I.0s•0
I-0
0:
00
0<
>~
•>
•>
<¤"70
--0
1-
luI
.:0¤
—··«
ms-
¤•—•
ß-
¤*-·
0.-
00
.•I
00
00
:§
00
:0
:w
w0
00
-•N
uI
mo
cvs-
••o
:Q
:C
Zo
uco
am
II-=
.I
'Q1
•Q
0I:
‘0
•·
0«I
>,Q
64
94
-«Q
üb
0Q
4Q
Ivr
I1
lI~
f0
¤Q
¤Q
40
~¤vw
~a~0
SI
8I
-1
:I
II
I•q
9In
-9
9vw
•-•r~sb
99
ang
I0
64n
eu
nn
In-
¤I._
hl64
MQ
I[
QI~
I~•~
Qr~
•~¢
QI
UU
r~I
QI
IIII
III
ÜO
II
II
0I
s-U
UU
UU
UU
-U
MU
UU
-.:
'0
¢szzx
Q¢
=¢
I_¢
¢4:
U0
I-I-I-I-I-
I-|->
I-I-
I-I-
I.:
hnI.-
I
20E
‘S
ZI
35
...
1‘..
EI
SS·
uI.-0
64
Inv\_
9Q
Ii
n9
•-¤
0I
0,4
INrs
0IN
___•-
an0
QI
•P4
0•-
•-·IN
‘
I>
•
···I
00
Il
I•-In
I-hl
I0
Is
I.
NU
IQ
nvw
nQ
-«,0
Q„
3n
•~4••s
64Q
4Q
rurs
Ile
M4
~0c
0I
-•0
0I
Ies
4Q
0•-
QIn
0I
Ig
0:¤
unes
-•~0
es•¤
I-¤
I
I0
4-IA
I1I-I
2E
212:
I,.S.
I3
4IN
•·•0
0{
es0
..I-2
*•0
•^W
6;vs
vsI
I.n
esn
nQ
¤"In
nn
I0
·.1:
II•
<l
vv9
I0
¤Q
Isn
11
61
•
1Q
1u
1ee
66
1[6
U!
QU
11
laß
eae
•u
g>•
5IN
66
••••61
u6
*••6
•-•U
—•
66
61
-•I6
·•-•
06
6:
1•q
Z)
•6
ln
1•6
l1
Nu
»>
,6
6u
6u
e•·•6
6_¤
>6
6:
11
Q>
Q~
a6
u••
61
Inß
1•¤
•en
•¤•Q
HI
nn
u·y••
-1
11
Sg
6:
>•1
12
38
>••¤
•E
8:1
.:-=
5en
II
ul-•
11
h•g
ha
:e
ng
hah
au
än
aß
1ß
l6
Q>
66
6•-•¤•
[Q6
61
y}6
¤a
~n
I1
1u
u~
Q•
uh
>>
1“ä
**2*•2
•‘3
‘::3
1:6
:3-
••6
••
il
sI1
•*=
°1
1u
e:
ul:
6\a
6•a
6u
u1
Alu
1H
I1
-1-6
••6
-•
H6
BI
I•·•
.1
16
-•6
16
6U
OQ
I3
1Q
:Q
66
un
na
6.Q
,~••1
•¤a
§>
11
66
gu
-«••6•·•
6••·•G
56
61
1Q
-I0
<>
¢>
B6
QD
10
8:
1•••u
:1
11
1••Q
•\n
21
131*%1
66
U3
;N
60
QN
an
N6
06
Q,
u•<
1u
g.
•-••-•
1e
•e
•>
Q1
1>
ZQ
21
1sa"
Q11
11
-6:
1III
Ax:
g1
IU
I'
AE
1·
¥l•"
51
16
··•N
6N
u5
<Q
Q6
anN
d1
63
1IN
INQ
GQ
n•••
61
la1
••
J.I:
N8
N1
•••¢
'6
6I-•
I->
I-•>
IQ6
66
I-•1
1e
n-•
91
1~
•¢6
V1
::3nn
1g
a1
Qln
ä6
l1
r···•I··•3
Q'
12
>.
Q,,
..6
..-•6
nn6
n6
N6
:6
ue
!6
0Q
NQ
1u
6g
1N
MN
.1
Q:3
1:3
:hl
<Q
§•6
61
•e
•1
‘ä..„
1..5
gg
3“‘
SX
:.=3-2
16
00
6•~
6>
••
••
•e
ng
:N
NQ
•¤•0
6zu
11
06
N6
:N
1•••
611
:6
66
11
¤N
Q0
1B
US
11
Nnn
sf
•¤F
!1
•II
•nN
61
:0
::
N1-1
Q0
05
66
nn
FI
6n
1§
••6
0
11
*612*1
1•Z
11
gsi:
111
äfä
66
*1
QQZÖ
11
°’
.LC•—
L
ä4-P
w«•-P
d.!
1 'L
1
uä “
1
L.L
'
2:;
as'!
IL""
Q-;
pngn
"‘
*’
1*0
1-L
V
og
."’·¤
*^
'UL
Z
»-3
5-
So
I
¤•‘-
L
>~„:"’
1*
?""
..
gg
IV
'
4a
5
C
m
_:4
-!
'
>•
4-:
c
gg
gé°8
<~F°·’ *5'·‘·
12
signal is converted to a voltage which is proportional to the beam
position. The voltage is then filtered and transmitted to the chart
recorder. The analog chart is then digitized at 1 hour intervals for
subsequent analysis. The relative accuracy of values read from the
chart is generally better than 1 1 microgal.
Each Geodynamics tidal gravimeter is equipped with an internal
calibration system. It consists of a plate mounted near the beam, and a
circuit for applying a precisely controlled voltage to this plate. when
activated, it deflects the beam by an increment corresponding to a fixed
change in gravity. The value of this equivalent change in gravity can
be determined by operating the tidal gravimeter at a location where the
gravity field is varying by a known magnitude.
In some continental regions it can be argued that ocean loading and
anomalous geologic effects are small enough to neglect for purposes of
instrument calibration. By methods presented later, it can be shown
that the ocean loading effect on the lunar diurnal harmonic constituent
01 is very small in Blacksburg, Virginia. Because this site is in a
region of normal heat flow, the anomalous geologic effect should also be
quite small. Therefore, the tidal gravity factor found from thel
01 harmonic constituent should be 1.160 1 .005 at the Blacksburg,
Virginia observation site. The product of this value and the 01
constituent at the same location on a rigid earth determined from the
formulas given by Longman (1959) is the basis for the tidal gravimeter
calibration used in this study. The value of this product is 34.7
microgals for Blacksburg, Virginia.
13
All of the tidal gravimeters were operated at the Blacksburg,
Virginia site for calibration purposes. Using the record from each
instrment the amplitude of the internal calibration signal on the
analog chart was compared with the amplitude of the 01 constituent found
from the harmonic analysis. By adjusting the 01 constituent amplitude
to the known value of 34.7 microgals, the change in gravity equivalent
to the internal calibration signal was determined. Results are given in
Table 2 for three of the five gravimeters utilized in this study.
Weekly calibration signals were produced on each record for
detecting and adjusting any changes in instrument response. These
changes can result from different factors such as the slow tilting of
‘ the instrument from level orientation.
The North American Geodynamics gravimeters used for this study are
known to exhibit very complex characteristics resulting in a small
non-zero phase response to a given driving constituent. The simplest
rheological model that one might choose for Geodynamics gravimeters is a
two-parameter model. This model consists of the combination of a Hooke
and Kelvin body with one associated parameter to be determined for each
body. Ducarme (1975a) determined these parameters for 8 Geodynamics
gravimeters. Phase lags from 0.74 to 2.05 degrees for the M2A
constituent were measured with an average for all instruments of 1.28
degrees. Instruments used in this study are similar to those tested by
Ducarme. For lack of more direct evidence the phase shifting properties
of these instruments were assmed to be in the range given above.
14
TABLE 2
_ GRAVIMETER CALIBRATION PULSE GRAVITY CHANGE EQUIVALENTS ‘
Instrument Calibration Pulse Eguivalent
826 82.2 ugals
735 133.0 ugals
VPI-17 126.0 ugals
HARMONIC ANALYSIS
. The tidal gravity spectrum consists of more than 1,000 harmonic
constituents with periods known from the astronomy of the earth·moon-sun
system. Fewer than 12 of these constituents account for more than 95
percent of the strength of the tidal gravity field. Amplitudes and
phase angles of the harmonic constituents in Table 3 are of principal
interest for most studies of tidal gravity.
The method of Venedikov (1967) was used for harmonic analysis of
the tidal gravity records included in this study. This is the standard
method which has been adopted by the International Center for Earth
Tides, Brussels, Belgium. FORTRAN programs for implementing this
procedure are described by Venedikov and Paquet (1967) and Ducarme
(1975b). These programs compute amplitudes and phase angles of the
principal tidal harmonic constituents, and the corresponding tidal
gravity factor.
The Venedikov method begins with the separation of diurnal,
semi·diurnal, and ter-diurnal tidal constituents, and the elimination of
instrumental drift and very long-period constituents. For a given
· Species of tides, even and odd filters are applied on a sequence of 48
hourly readings. The diurnal filters have amplification factors that
are designed to accentuate the diurnal waves and eliminate the
semi-diurnal ones. The reverse is true for the amplification of the
semi—diurnal waves (Melchior, 1983).
16
The filters are constructed mathematically in such a way that they
eliminate the instrumental drift as an arbitrary combination of
orthogonal polynomials of order three. The filters themselves are
derived from matrix considerations involving the evaluation of
observational errors and particular constituent amplification needs.
The filters are applied to every continuous 48 hour record segment and
then the analysis is shifted to the next 48 hours, etc., thus ensuring
independent results and non-superposition of calculation effects. If a
gap occurs in the record, the filters are re-evaluated at the next 48V
hours data segment.
Next, the Venedikov filter acts on the 48 hour sequence of obser-
vations, producing a filtered number which is further processed as an_
observed quantity. A system of harmonic equations is then generated
such that through a least square process the unknown tidal parameters of
amplitude and phase are found from the solution of the system. The
system of equations to be solved has the mathematical representation of
. the observational equations as well as the theoretical equations needed
to represent the lunisolar tide on a rigid body. Instrumental drift is
eliminated by the Venedikov filters because the drift is considered
noise with a frequency lower than that of the diurnal tidal band.
In the process of solving the observational equations root mean
square (rms) errors are determined for each harmonic constituent. These
values are combined to obtain the rms errors for the combined diurnal
.constituents and the combined semi-diurnal constituents.‘ These rms
error estimates provide a basis for evaluating the record quality.
17
TABLE 3
PRINCIPAL TIDAL HARMONIC CONSTITUENTS -(Schureman, 1958)
Symbol Name Period Qhr)
M2 - Principal Lunar 12.421
S2‘
Principal Solar 12.000
N2 Lunar ellipticity 12.658
K2 « Lunisolar 11.967 _K1 Lunisolar 24.934
01 Lunar declination 25.819
P1 Solar declination 24.066
18
The original FORTRAN program of Venedikov and Paquet (1967)
included 79 constituents in the harmonic series used to represent the
luni-solar field. The program has since been upgraded by Ducarme
(1975b) who introduced the harmonic development of Cartwright. _. .
and Edden (1973) which consists of 347 constituents. Harmonic analysis
of the new tidal gravity records presented in this study, and thosek
obtained by Robinson (1974) were done with the upgraded program as well
as with the older program. Differences in the results of the two
programs are small enough to neglect for the purpose of this study.
Harmonic analysis of the individual records proceeded in the
following way. First, a moving window analysis was done to assess·
variation in record quality. This involved separate harmonic analysis
of one·month segments, advancing at weekly intervals through the record.
The rms statistics provided the basis for judging record quality.
Record segments of superior quality are indicated by combined rms error
values of less than 5 microgals for the diurnal or semi·diurnal groups
of constituents. Values between 5 and 10 microgals are considered
acceptable but those above 10 microgals are judged to indicate record
segments of poor quality.
By means of moving window analysis it was possible to locate short .
° segments of record, less than a week long, of poor record quality which
otherwise degraded superior or acceptable records. These segments were
then deleted, and the harmonic analysis was done on the remaining record.
Final results from the records edited in this way are in Appendix I.
19
Factors contributing to poor record quality include earthquake
disturbances and unusually high microseismicity, power failures which
lead to internal temperature change in the gravimeter, unexplained
responses of the instrument to sudden changes in atmospheric pressure,
and building or ground disturbances leading to instrument level changes.
Often, these factors may not be noted at the time of occurrence, and
come to attention later during record processing.
Although 15 constituents are tested in the harmonic analysis, only
the results for the lunar semi-diurnal constituents M2 were used in thisstudy. In the study area, this constituent has the largest amplitude,
and is the best separated from the other constituents of the harmonic
series.
M2 amplitudes, phase angles and corresponding tidal gravity factors
for the fourteen observation sites are given in Table 4. The measured
tidal gravity factors are seen to differ from a value of 1.16, indi-
cating that the combined effect of geology and ocean tidal loading on
tidal gravity can be measured.
. 20
TABLE 4
OBSERVEO M2 TIOAL GRAVIMETRIC FACTORS (Ä)
Phase (degree)Station Ampliitude Amplitude (not corrected +
Designation City, State (ugals) (6) 1.3 degrees forinstrument response)
*A Atlanta, GA 60.35 2 .24 1.160 2 .005 -4.01 2 .20
B · Blacksburg, VA 56.68 2 .09 1.1906 2 .0019 -2.074 2 .092
*BSL Bay St. Louis, MS 65.83 2 .17 1.184 2 .0035 -1.823 2 ?
C Columbia, SC 61.87 2 .24 1.1990 2 .0047 -1.559 2 .223
**0 Durham, NC 56.74 2 .32 1.920 2 .0067 -3.01 2 .32
**H Huntington, HV 52.60 2 .17 1.847 2 .0036 -1.57 2 .18
*J Jackson, MS 61.88 2 .48 1.160 2 .010 -0.2 2 .41
*KNX Knoxville, TN 55.29 2 .29 1.1668 2 .005 -1.67 2 .25
*M Memphis, TN 58.13 2 .29 1.163 2 .006 -0.2 2 .25
*R Ruston, LA 61.23 2 .29 1.153 2 .006 -3.4 2 .04
**T Tuscaloosa, AL 59.71 2 .39 1.1686 2 .0083 -0.28 2 .41
UVA Charlottesvil1e, VA 55.52 2 .18 1.1920 2 .0039 -1.18 2 .188
*N wooster, OH 50.03 2 .39 1.169 2 .0037 --·--
UVA Morgantown, HV 55.29 2 .24 1.2098 2 .0083 -1.208 2 .389
t A Phase angle of zero was assumed when no phase angle information was available.
* Older Robinson data and earlier Venedikov software.
** Older Robinson data processed by more recent Venedikov/Oucarme software.
Stations not labeled by an asterisk include new data and the latest Venedikov/Oucarme software.
THE WORLD OCEAN TIDE
The world ocean tide constitutes a temporally and spatially varying
load on the solid surface of the earth. This fluctuating load deforms
the elastic earth and perturbs the tidal variation of gravity. The
perturbation of the gravity field due to ocean tidal loading has long
been known to extend over continental areas (Kuo, 1970). If the
geologic effect is to be evaluated at a tidal gravity observation site,
it is first necessary to determine the effect of ocean tidal loading.
This can be accomplished by knowledge of:
1. The form of the ocean tide, and ·'
2. The elastic response of the earth to a surface load.
The form of the ocean tide can be described in terms of tidal
variations of sea level at points on a grid that extends over the entire
ocean. At each grid point the water level fluctuation can be resolved
into the harmonic constituents previously discussed. Direct measurement
_of the ocean tide is restricted mostly to coastal areas where tide
gauges can be operated. Very few deep water measurements have been made
because of the high cost and difficulties in operating the special
instruments required for this purpose. Knowledge of the ocean tide
comes largely from numerical solutions of a set of three partial
differential equations known as the Laplace Tidal Equations.
The basic Laplace Tidal Equations express the tidal motion in an
ocean of homogeneous, frictionless, incompressible water contained in a
rigid ocean basin with fixed boundaries. They relate the height of the
-21
22
tide (h) and the east (u) and north (v) tidal current velocity
components to ocean depth (z) which varies with colatitude (6) and
· longitude (A), the earth's angular rotation velocity (Q), radius R, and
gravity (9).
These equations can be written (Doodson, 1958) in the form:
%%·2s°zv cos9=%%
9V -· .....1 .9*L "ZQU C°S 6 °
_é1Slnö 81
1 .9. - 9 .-ün--....6 [3. <=··=‘··@>+ QT <=v>] Bt
where h' = h - h and h is the equilibrium tide elevations. Because h, u,
and v vary periodically, they can be expressed as
h = H cos hat - wh)
u = U cos hat - wu)
v =_V cos (ct - wv)
where ¤ and W are the angular frequency and phase angles of a tidal
harmonic constituent and H, U and V are the constituent amplitudes.
Efforts to solve the Laplace Tidal Equations to determine h, Wh, u
Wu, v, and WV are summarized by Schwiderski (1980). Early work con-
sisted of obtaining analytica] solutions for ocean basins of idealized
23
form. Application to the real ocean required the high speed computer
and bathymetric data that were not available until the 1960's.
Beginning then, finite difference methods and other schemes were
developed to solve first the basic equations given above, and then to
modify these equations taking into consideration friction, compressi-
bility, and non-fixed boundaries for the world ocean. Solutions
obtained by various workers revealed the main features of the ocean
tide. However, the ocean loading effects calculated by Robinson (1974)
from these various solutions were sufficiently different from one
another to preclude their use in adjusting tidal gravity records for the
purpose of subsequent identification of a geologic effect.
During the 1970's, improvements in the numerical technique and
supplementary bathymetric data made it possible to improve the accuracy
of solutions to the Laplace Tidal Equations. There is now a growing
consensus that results obtained by Schwiderski (1979) for the M2 consti-
tuent of the ocean tide are accurate enough to make the adjustments
required to begin the search for the geologic effect. These results
consist of amplitude and phase angles, relative to the Greenwich meri-
dian, specified at points on a 1 degree by 1 degree latitude and longi—
tude grid extending over the world ocean. These data are available on" digital magnetic tape from the Naval Surface Weapons Center, Dahlgren,
Virginia.
Numerical solutions to the Laplace Tidal Equations can be displayed
graphically by means of cotidal-coamplitude charts. The cotidal-coampli—
tude chart of Schwiderski (1980) shown in Figure 3 illustrates the time
24
and spatial variations of the M2 ocean tide. Cotidal and coamplitude
lines shown on the maps contain the equal phase values and tidal
amplitudes, respectively. By convention, the time of high tidal
occurrence is measured with reference to the Greenwich meridian. A
cotidal line of 3 hours connects those grid points where high tide
occurs three hours after the moon has passed directly above the
Greenwich meridian. Cotidal lines can be expressed in terms of degrees,
since for example, the tidal crest of a semi-diurnal wave moves by
approximately 30° per hour.
The tide can be viewed as a very long wave moving on the ocean.
Cotidal lines show the position of the wave crest at different times.
The points around which the tidal movement is centered are called
amphidromic points. Amphidromic points have a tidal amplitude of kero,
and exhibit a tidal crest rotating about them generally counterclockwise
in the northern hemisphere with clockwise flow rotation in the southern
hemisphere.
The tide model in Figure 3 does not include landlocked bodies of
water such as the Great Lakes and the Black and Dead Seas. Other
gridwise disconnected bordering waters not included are such bodies of
water as the Baltic, Irish, Mediterranean, Red, and Japan Seas. Gulfs,
such as those of California and Persia, as well as the Hudson and Korean
Bays are likewise not included. Similarly, many shallow (less than 5
meters in depth) and/or narrow waters such as the entire Barrier Reef
area, the Gironde Estuary, and the Fjords of Norway could not be
modeled. The combined effect of ocean tides in these waters has a _
25 _
negligible effect on tidal variations of gravity except at nearby
observations sites.
Ä:.g
äg
ää
a
—··
EI!&
g‘E
i§§
§--
S;
I‘·
Qämüflä
—~
I
:2
\gi
gw
l Avééääläää”'g?’mag%§@%m‘§g
gggg
Äf
Ö
EE
gigég„ä
ää
:
äéwaä
ä;
•= I
E :6g
8GJ 5;
66
’2 E
LOADING RESPONSE FUNCTIONS
Calculations of the effect of the ocean tide on tidal gravity
requires knowledge about how the earth responds to surface loads. It is
well known that a unit load acting at a point on the surface of a solid
body produces elastic deformation throughout the body. For the case of
a semi-infinite homogeneous body the elastic displacement Ü (r, 2) of a
point at distance r and depth 2 relative to the load is expressed in the
equilibrium equation
++ + .,, + -> _
(>„+2u)VV°S—pVxVxS=0
where A and u are Lame's constants. This is the classic Boussinesq
problem which has the solution (Farrell, 1972)7
u(rz)=—l—•4nuR 7.+},1 E2
2_ 1 2 A + r Z .1+ R- +liligf.
+ 2where u and v are the radial and vertical components of S, and R2 = r +
22. These expressions indicate that the elastic response diminishes in
approximate proportion with inverse distance from the load.
T 27
28
A much more difficult problem to solve is the response of a
self·gravitating sphere consisting of concentric homogeneous elastic
shells to a unit point load. Farrell (1972) reviews this problem in -
some detail, and presents series solutions for the radial and vertical
components of displacement and strain in the body. He combines these
results to obtain a Green's function that expresses the perturbation of
gravity produced at any point on the sphere by a load consisting of a
unit mass acting on a unit surface area. Such a Green's function
accounts for:
1. The gravitational attraction of the load,
2. The change in gravity resulting from elastic deformation
in the shape of the original sphere, andu
3. The change in gravity related to vertical displacement '
at any point on the sphere.
A gravimetric Green's function suitable for the purposes of this
study was calculated by Farrell (1972) using the elastic proportion of
the idealized earth model number 8734/06/06/68 which was obtained by
Backus and Gilbert (1970). This function is illustrated in Figure 4,
and numerical values for different geocentric distances are listed in
Table 5.
° 29
10-22
ZQ .E 10-2*< .¤¤izDAEäu.: ¤¤
{ Negative
O 10'zS Positive
Negative
1 2 5 10 20 50 100 200
· GEOCENTRIC ANGLE(degrees)
Figure 4: Gravimetric response function for solid earth model 8734/06/06/08 (Backus and Gilbert, 1970) calculated by N. E.Farrell (1972). Amplitude indicates gravity perturbationresulting from application of a 1 gram load.
30
TABLE 5
GRAVIMETRIC AND VERTICAL DISPLACEMENT RESPONSE FUNCTIONS(Farrell, 1972)
Geocentric Gravimetric Response Vertical DisplacementDistance Function Response Function(degrees) (gals) (cm)
1.0 -2.698 E-23 -1.243 E-171.2 ·-2.092 E-23 -9.573 E-181.6 -1.381 E-23 -6.246 E-182.0 -9.098 E-24 -4.451 E-182.5 -7.023 E-24 T -3.145 E-183.0 -5.227 E-24 -2.342 E-184.0 -3.165 E-24 — -1.425 E-185.0 -2.083 E-24 -9.486 E-196.0 -1.463 E-24 -6.789 E-197.0 -1.086 E-24 -5.168 E-198.0 -8.424 E-25 -4.130 E-199.0 -6.755 E-25 -3.421 E-19
10.0 -5.549 E-25 -2.907 E-1912.0 -3.927 E-25 -2.200 E-1916.0 -2.128 E-25 -1.365 E-1920.0 -1.149 E-25 -8.621 E-2025.0 -4.298 E-26 -4.484 E-2030.0 1.148 E-27 -1.167 E-20
- 40.0 4.518 E-26 1.937 E-2050.0 5.911 E-26 3.677 E-2060.0 5.504 E-26 4.164 E-2070.0 4.088 E-26 3.802 E-2080.0 2.147 E-26 2.899 E-2090.0 -1.240 E-29 1.694 E-20
100.0 -2.141 E-26 3.594 E-21110.0 -4.156 E-26 -9.825 E-21120.0 -5.970 E-26 -2.250 E-20130.0 -7.546 E-26 -3.385 E-20140.0 -8.849 E-26 -4.347 E-20150.0 -9.863 E-26 -5.110 E-20160.0 -1.057 E-25 -5.654 E-20170.0 -1.097 E-25 -5.968 E-20180.0 -1.105 E-25 -6.045 E-20
OCEAN TIDAL LOADING VECTORS
The perturbation of tidal gravity caused by the M2 harmonic
constituent of the ocean tide was calculated for each of the 14
observational sites. The M2 constituent of the ocean tide wasrepresented by the amplitude and phase angles obtained by Schwiderski
(1978) for points on a grid covering the world ocean. Each pair of
amplitude and phase angle values describes a vector which represents a
time varying load acting within a particular grid cell. For purposes of
computation, the real and imaginary parts of these vectors were
calculated from the corresponding amplitudes and phase angles.
Real and imaginary parts of the perturbation of tidal gravity at an
observation site were then obtained by convolution of the gravimetric
Green's function, described in Figure 4 and Table 5 and the real and
imaginary arrays representing the global M2 ocean tidal constituent.
More specifically, each grid cell of an array, bounded by latitude and
longitude coordinates occupies the area increment
dA = R2 smeaean
where R is the earth radius and d6, dp represent the 1° x 1° spacing of
latitude and longitude lines on the worldwide grid, with 6 as the
latitude of the center of the area increment. The load acting on dA of
the earth's surface is the weight of water in a volume equal to
the amplitude of the tidal constituent in that grid cell multiplied by
31
32
the area increment. The weight of water for each area increment on the
world ocean was calculated and assumed to be acting at a point on the
center of each of the 1° x 1° grid cells.
The individual perturbation to the earth's gravity field at an
observation site caused by a specific load in a grid cell was found by
multiplying real and imaginary parts of the load and the Green's
function value corresponding to the geocentric distance of the cell from
the site being considered. Summation separately of all of the real and
imaginary parts from the world ocean grid yields the total ocean tide
induced gravity perturbation vector at a given site, amplitude and phase
h angle of this vector were then found from the final summation of the
real and imaginary parts. The results of these computations are listed
in Table 6 for each of the 14 stations occupied.
In Table 6 two phase angles are given for each site. Because the
phase angles given by Schwiderski (1978) for the M2 ocean tidal
constituent are referenced to the Greenwich meridian, convolution of the
M2 ocean tidal arrays with the gravimetric Green's function yields phase
angles for the ocean loading perturbations of tidal gravity that are
also referenced to this prime meridian. To obtain the local phase angle
referenced to the longitude of each site the value of 2A was added to
° the Greenwich phase angle corresponding to that site. The factor 2 is
used because the M2 constituent is semi-diurnal.
‘33
TABLE 6
THEORETICAL M2 TIDAL LOADING
VECTORSGreenwich Amplitude LocalStation Amplitude Phase (gravity Phase
Designation City, State (gal) (degrees) factor) (degrees)
A Atlanta. GA 0.636x10°6 160° 1.1705 - .31
*8 Blacksburg, VA 0.993x10°6 165° 1.1773 · .57
BSL Bay St. Louis, MS 0.239x10'6 111° 1.1615 · .20
*C Columbia, SC 1.287x10°6 170° 1.1820 · .57*0 " Durham, NC 1.468x10°6 169° 1.1858 · .82
*H Huntington, HV 0.701x10°6 160° 1.1726 - .43
J Jackson, MS 0.245x10°6 121° 1.1624 359.81
*KNX Knoxville, TN 0.471x10°6 152° 1.1681 · .29
M Memphis, TN 0.275x10°6 133° 1.1637 359.80
R RuSt0n, LA 0.202x10°6 104° 1.1612 359.82
*T Tuscaloosa, AL 0.352x10°6 143° 1.1652 - .23
*UVA Charlottesville, VA 1.261x10°6 167° 1.1821 · .76
*UVA Morgantown, HV 0.889x10°6 164° 1.1763 - .57
* Utilizes updated Melchior potential development.
TIDAL GRAVITY ANOMALIES
The object of this study is to find indications of a geologic
effect on the tidal variation of gravity. Following Melchior and others
(1981) the search for such indications involves comparison of measured
tidal gravity with theoretical tidal gravity on an idealized earth model
subjected to ocean tidal loading. The resulting discrepancies must be
related to differences between the earth and the idealized model.
At a tidal gravity observation site the discrepancy ;Ibetween
measured tidal gravity ÄIand the theoretical tidal gravity T is:
+ + ->X=A-T „
where the theoretical value is found from the tidal gravity Ü on an
idealized earth model and the perturbation Ü produced by ocean tidal
loading:
The relationship between the vectors is illustrated in Figure 5.
Tidal gravity on an idealized elastic model is given by the product
of the luni-solar tidal force FIand the tidal gravimetric factor of the
model: I+ ->°
·. R=6F
34
35
For the M2 harmonic constituent the tidal force is given to a
first-order approximation (Melchior, 1966) by the expression:
FM2 Q 74.702 cosz W microgals
where W is the latitude. From a review of the properties of spherically
symmetrical models most closely representing the earth, Melchior and
DeBecker (1983) concluded that the tidal gravimetric factor corres-
ponding to the M2 constituent must be close to 1.160, and that the
response can be treated as being in phase with the tidal force (wahr,
1982). _
Therefore, the real part of the vector RM2 can be expressed to the
first order as:
real RM = 1.160 x 74.702 cosz W2
.and the imaginary part of RM is
imaginary RM2 = 0
Using these expressions together with values from Table 4 for the
vector El and values from Table 6 for the vector K, components of the
anomaly vector were calculated for all the observation sites. The
results are in Table 7. These vectors represent the tidal gravity
36
anomaly at each site. They should provide some indication of a geologic
effect on tidal gravity, if such an effect can be detected.
Phase shifts introduced by the tidal gravimeters were initially not
taken into consideration in the calculations. The non-phase corrected
values are designated ;' in Table 7. Based upon tests of similar
instruments reported by Ducarme (1975) an instrument phase shift of
-1.3° was arbitrarily assumed for the five gravimeters used in this
study, with an estimated uncertainty of :0.7°. This assumed instrument
phase shift was then subtracted from the tidal gravity phase angles
given in Table 4 to obtain values subsequently used to calculate a phase
_ corrected tidal gravity anomaly Y for each site. These results are also
included in Table 7.
The accuracy of the values found for Y depends upon the precision
of K, corrected for instrument phase shift, and the precision of Ü.
Differences in tidal gravity measurements made with the four gravimeters
at the same location in Blacksburg, Virginia indicate that the amplitude
of Ä is accurate to within : 1 microgal. Judging from these measure-
ments and those reported for other instruments by Ducarme (1975), the
phase angles adjusted for instrumental effects are accurate within
:0.7°. No attempt was made to assess the absolute accuracy of Ü, which
was calculated from the ocean tidal data of Schwiderski (1978). Because
the same data were used to determine E for each site, relative errors
between sites should be quite small and systematic, and should not
significantly distort any regional patterns of variation in Y within the
study area. The uncertainties in values of ifcan be estimated from the
37
error ranges for the amplitudes and instrument corrected phase angles
of
38
* BT{
a'r or T
A L
F
Ä;observed Mz vector }A: amplitude, az phase}.
lätidal vector for an elastic non-viscous earth with liquid core but oceanless }R: amplitude, zerophase}.
L-;ocean attraction and loading vector }L: amplitude, 7: phase}.
Tl'•=theoretical tidal gravity with ocean loading effects added }T: amplitude, 7:phase}.
geologic effect |X: amplitude, X: phase}.
Z=error envelope of observed M, vector.
The correct scale of this figure for the southeastern North America M: wave is approximately:
_l€·:Ä~?¤ 50-67 microgal Y= 0-3.5 microgal g
Ta 0.2-1.5 microgal Z = ; 1°; ;>_ 1.0 microgal
rr = 0-4° phase lag
Figure 5: Definitions and notati ons for the construction *0f the tidalgravi ty anomaly vector.
39
TABLE 7
TIDAL GRAVITY ANOMALIES (X)
X ( al, degree) r (ugal)-
XcosxPhase (Q) No Phase (X‘) Phase (r) No Phase (r')
Station City, State Corrected Correction Corrected Correction
A Atlanta, GAE
2.37; 104° 3.61; 100° - .57 -.63
*8 Blacksburg, VA .67; 18° 1.61; 68° .64 .60
BSL Bay St. Louis, MS 1.14; 17° 1.90; 57° 1.09 1.03
*C Columbia, sc. .88; -21° 1.27; 51° .82 .80A
*0 Durham, NC .93; 73° 2.23; 84° .27 .23
*H Huntington, HV .59; -15° 1.25; 64° .57 .55
J Jackson, MS 1.31; 259° .42; 107° .25 .12
*KNX Knoxville, TN 1.34; 94° .01; 129° .09 -.006E
M Memphis, TN 1.23; 268° .03; 180° -.04 -.03
R Ruston, LA 2.23; 101° 3.47; 98° -.43 _ .48
*T Tuscaloosa, AL 1.22; -83° .17; 16° .15 .16
*UVA Charlottesville, VA .79; -53° .62; 42° .48 .46
H Hooster, OH 1.71; 264° .47; 249° -.18 -.17
*HVA Morgantown, WV 1.62; -22° 1.71; 23° 1.59 1.57
* Stations with potential derived empirically for Melchior results and inputedin ocean-loading program.
‘ DISCUSSION OF RESULTS
Regional geologic effects on tidal gravity have only recently been
recognized. Yanshin and others (in press) and Melchior and Deßecker
(1983) suggest patterns of regional variation that are evident from
their analyses of tidal gravity measurement at 178 sites in Eurasia and
Africa. At most locations they found the tidal gravity anomaly
amplitudes to be on the order of one microgal, as are the results in
Table 7 for this study. This is close to the measuring precision of
most tidal gravimeters and the precision to which ocean tidal loading
effects can be determined. Therefore, they suggest the most practical
way to establish meaningful correlations is by means of grouping and
averaging values from many sites rather than attempting to interpret
individual values.l
Yanshin and others (in press) obtained their clearest correlations
between tidal gravity anomalies and geotectonic environment from
.analysis of the real part of the vector, real Y. They recognized a
tendency for relatively large positive values of real Y to occur in
geotectonic environments characterized by a shallow asthenosphere and a
tensile stress state. Here the earth could be viewed as more mobile and
responsive to the tidal gravity force. Further, they noted that large
negative values of real Z tend to occur in geotectonic environments
where the asthenosphere is relatively deep and a compressive state of
stress exists. Small values of real Zloccur in environments inter-
mediate to these two extremes.”_
40 -7
41
The clearest confirmation of this global pattern found by Yanshin
and others (in press) is the correlation between real ; and heat flow.
Values of real ; from sites where reliable heat flow data were available
are plotted in Figure 6. The results indicate a relationship between
the tidal gravity anomaly and heat flow.
The fourteen sites available for this study are too few to justify
an attempt at recognizing tidal gravity anomaly patterns within the
study area. However, treated as a single group, the values in Table 7
are found to be consistent with the global pattern of Yanshin and others
(in press). Regional heat flow in the area, estimated by the method of
silica geothermometry (Sass and others, 1981), is consistent with
conventional heat flow measurement patterns shown in Figure 7. Judging
from the contours over the study area, the heat flow at all of the sites
appears to be in the range of 1.0 to 1.6 HFU, or 42 to 67 E; . The
squares in Figure 6 encompass this range, showing that the relationship
between real Z and heat flow in the study area falls within the global
pattern.
Histograms in Figure 8 show the distribution of real { values in
different ranges. The distribution without regard to sign, lreal ; I,
is similar to that of Yanshin and others (in press). The distribution _
with regard to sign indicates a weak positive value for real I in this
area.
42
Tap-YansNn,M¢ld1io1,a¢•doth¢rs1-5 vcwhs cl r values vs. Heat flcw for•
• Europe.
ä• • =
• •E '
• ••t C Ö . •
•
·
·Ü • 0
• ••
-0.S • ‘ •
8 -1.5 °Ge °
‘2·’ ‘ suxors
-3.5
-1) -10 5 10 ' S0· 4-0
• HEAT "'ow (‘*‘umm lattdnv-Yanshln, Melchoir, andma ••h•n' results of r values vs. Heat. Flowfordnwuddwkhscuelseasaem
Nocdnhnuiavalussuperinuposedas square
2'°·
• •U
•~
9 · ¤ _ .° °•
E 0 s·° ' 'i
•
g- gu ° •8 on ' ° •
Ge •·
·Z ugl • • ° ° WÖRLÜ
-2.0 - . '
-40 0 40 80HEAT FLOW (¤ *ü-Y EP!)
0Hpn6:
Non: luc H•a¤·F|0w unus han conupond so S23my
43
3"*%•‘%j'
„ :.4
f'=iCOSXV
‘l’op—Hls¤ogran• ol lvl values in microgals.
110 5 1 1.5 2.0 rnicrogals
l‘ lreal flMiddle-Histogram ol r' values with positive and negatlve microgal values.
1 111 In 1
-1.5 -1 -0.5 0 0.5 1 1.5 2 micogals
real YBottom-Different histograrnatic represenution ol r' rnicrogal values.
ll 1-1 0 1 2 microgals
real ll-
All above histograms contain phase•cotre¤ed r' values.
figureI:_
CONCLUSION ‘A geologic effect on tidal gravity has been detected in south-
eastern North America. Here the measured tidal gravity anomalies on the
order of one microgal are consistent with global patterns reported by
Yanshin and others (in press) and Melchior and DeBecker (1983). The
amplitudes and directions of the tidal gravity anomaly vectors group in
the range expected for a geotectonic environment in which the
asthenosphere is at an intermediate depth and existing stress is not
excessive. The accuracy of the tidal gravity measurements used in this
study is between 0.5 and 1.0 microgal, and similar accuracy is estimated
for calculated gravity perturbations produced by the ocean tide. In' view of these limits of accuracy the tidal gravity anomalies are too
small to support further speculation about the geotectonic environment.’
The important results of this study is that the existence of such
anomalies has been confirmed.
l 45
BIBLIOGRAPHY
Alsop, L. E., and J. T. Kuo, The characteridicnumbers of semi-diurnalearth tidal components for various earth models. Ann.‘Geophysics, 20(3), 286-300, 1964.
Backus, G., and F. Gilbert, Uniqueness in the Inversion of InaccurateGross Earth Data, Phil. Trans. Roy. Soc. London, Ser. A, 266,123, 1970.
Cartwright, 0. E. and A. C. Edden, Corrected tables of tidal harmonics,Geophy. J. Roy, Astro. Soc., Vol. 33, pp. 253-264, 1973.
Doodson, A. T., Oceanic Tides, Advances in Geophysics, 5, 117-152, 1958.
Ducarme, B., A fundamental station for trans-world tidal gravityprofiles, Physics of the Earth and Planetary Interiors, 11,119-127, 1975a.
Ducarme, B., The Computation procedures at the International Centre forEarth Tides (ICET), Marees Terr. Bull. Inform., No. 72,4156-4181, 1975b.
Farrell, N. E., Deformation of the Earth by Surface Loads, Rev. Geophys.'and Space Phys., 10(3), 761-797, 1972.
Garland, G. D., Introduction to Geophysics-Mantle, Core, and Crust, 420pp., N. B. Saunders Co., Philadelphia, 1971.
Kuo, J. T., Jachens, R. C., white, G., and M. Ewing, Transcontinentalgravity profile across the United States, Science, 168,
_ 968-971, 1970.
Lonman, I. M., Formulas for computing the tidal accelerations due tothe moon and sun, J. Geophysical Research, 64(12), 2351-2356,1959.
Melchior, P., and M. Deßecker, A discussion of world-wide measurementsof tidal gravity with respect to oceanic interactions,lithosphere heterogeneities, earth's flattening and inertialforces, Physics of the Earth and Planetary Interiors, 31,27-53, 1983.
Melchior, P., The Tides of the Planet Earth, Pergamon Press, New York,1983.
46
47
Melchior, P., Moens, M., Ducarme, B., and M. Van Ruymbeke, Tidal LoadingAlong a Profile Europe - East Africa - South Asia - Australiaand the Pacific Ocean, Physics of the Earth and Planetary' Interiors, 25, 71-106, 1981.
Melchior, P., The Earth Tides. Pergamon Press, New York, 1966.
. Robinson, E. S., A Reconnaissance of Tidal Gravity in SoutheasternUnited States, Journal of Geophy. Res., 79(29), 4418-4424,1974.
Sass, J. H., Blackwell, D. D., Chapman, D. S., Costain, J. K., Decker,E. R., Lawver, L. A. and C. A. Swanberg with contributions byBlackstone, D. L., Brott, C. A., Heasler, H. P., Lachenbruch,A. H., Marshall, B. V., Morgan, P., Munroe, R. J., and J. L.Steele, Heat Flow from the Crust of the United States, Chap.·13, Properties of Rocks and Minerals, Ho, Editor, 1981.
Schureman, P., Manual of Harmonic Analysis and Prediction of Tides, U.S.. Coast and Geodetic Survey, Special Publication No. 98, 1958.
Schwiderski, E. W., Global Ocean Tides, II, The semi-diurnal principallunar (M2) report, Naval Surface Weapons Center, Dahlgren,Virginia, 1979.
Schwiderski, E. W. On Charting Global Ocean Tides, Rev. of Geophy. andSpace Phys., 18(1), 243-268, 1980.
Schwiderski, E. W., Global Ocean Tides, Part I: A Detailed Hydro- .dynamical Interpolation Model NSWC/DL TR-3866, Naval SurfaceWeapons Center, Dahlgren, Virginia, 1978.
Venedikov, A. P., and P. Paquet, Sur l' application d'une methode pourl' analyse des marees terrestres a partir d'enregistraementsde longueurs arbitraires, Marees Terr. Bull. Inform. 48, pp.2090-2114, Observ. Roy. de Belg., Brussels, 1967.
Wahr, J. M., Body tides on an elliptical rotating elastic and oceanlessearth, Roy. Astron. Soc. Geophy. Jour. 64, 677-703, 1981.
Wilson, D. C., Ocean Tidal Loading in Southeastern United States, M. S.Thesis, Virginia Polytechnic Institute and State University,1978.
Yanshin, A. L., Melchior, P., Keilis-Borok, V. I., Deßecker, M.,Ducarme, B., and A. M. Sadovsky, Global distribution of tidal
. gravity anomalies and an attempt of its geotectonicinterpretation, Proceedings of the Tenth InternationalSymposium on Earth Tides, Madrid, in press.
APPENDIX I”
RESULTS OF TIDAL GRAVITY HARMONIC ANALYSIS
FOR BLACKSBURG, VA, COLUMBIA, SC,
MORGANTOHN, NV AND CHARLOTTESVILLE, VA
48
QIIOOBQNM.
NSI\I
II
=Q
55
ä
°ä
ää
·Ü
MM
OQ
IMN
NO
OM
MO
M•·R
RQ
QÜ
Ü—
IQQ
OO
.M
M|~§M
ON
NO
ON
NM
MM
MM
MN
NM
MM
MM
MQ
MI
•I••MM
•~•~•••~•~••MM
••uI~
•?T
•!N••••
••
QI
IIIIIIIIII
III¤
•¤lII
IIQQ
IIII
hl:
—U
II
II
JM
•••M
M•n
n••••••••~
•~••
IIMIQ
QO
OM
MII
MM
I•
l!QO
OQ
Q•«
••••••••••••v•-••••«
•••••
••
¤IIIIIIIIN
NIIO
IO
MIIN
NIIQ
QII
OO
8M
‘un
QM
{U
IP
PO
OM
QM
MO
IOO
NN
·O
OM
OM
MM
MQ
QM
MI
M•!N
r~•~
•QM
M••••n
••n•Q
MM
•nn
••tQ••=
••
•I
•O
ON
NO
OM
ON
NIIM
OIN
Nh
h¢
OI*|
IIIIH
Q[
••••••••••••••
••••••••••••
••
P••Ü
•„nä
II
hä
·M
I!n
•n•s•~
••MM
••I•M•¢
••N•~!M
•••••~•=MM
PP
Q\I
M•
•~•~
•••••nQ
•~••••N
NÜ
NÜ
ÜQ
QIIQ
00
MMI
•2
'§
BIO
NN
IIOO
OO
OO
MM
UIU
INN
NN
OY
IIO
OP
g••••••••••••••
••••••••••••
••
Qun
Inn•••n¤n•••n•n«•••~•~M
MO
OQ
QN
NM
MM
MQ
QII
=dP
—I
IIIIIIIIII
IIIIIIIIIIIIII
IIU
IB
P•
)P*
=M
DO
NO
O•
IQ
I!•
••
u~
MM
••••••••~•~
MM
¤••M
•••~•~
••••••~
•~M
•I
[M
MIIM
MQ
QIIh
I~M
MQ
QN
NIO
OO
IINN
M:
IIP
•IO
OIIIIO
IIIIIOIIIIIIIQ
IIII
IQ
Q••••••••••••••
••••••••••••
••
IIIIIIIIIIOO
IIOOIIIM
IIOIIIMI
OIM
MO
!M
MN
NO
OI
UI-
PIQ
hs•nQM
MM
MQ
OM
MM
MN
NM
I:MO
fMM
MM
Q•
QI
3N
NQ
QM
MIIN
NQ
•Q
gg
Q4
=
••••••••••••••
••••••••••••
••
Q
M•
-!h
lg-
••I
IIl!
‘•
IIQIN
NN
IQQ
II
•I
QP
UIQ
••••••••••••••
••••••••••••
••y;
IOIIIM
IIOIO
IIO
IOO
IOIIO
IIII
QI
IO‘
H\
•P
IO
INN
MQ
IIMM
IOP
PIIM
OO
OO
MM
OO
hh
SS
S‘S
'“•"
s;.:„:•:„;;;.:.:•:•:.:.:....**.:.2
*'.2..;•§•Z~i666
.I
MM
QO
n•n•==N
NI
:Q
QI
PI
‘
==
sl!
IQ.
•Q
Q
ä=
IC
CIO
SS
IIMM
HW
I:N
N8
=2
§•!Q
MM
II$
2=
S°
eln
ug
an(
I••••Q
Q•••~
s•
MM
•~•~MM
MM
••••IO
••••
Q==N
NM
M•n•nQ
QM
MN
=M
MO
OM
MM
MQ
QN
NQ
QI
pQ
••
••
••
g•
••
••
••
g(d
ÜsP
P:M
MM
OM
hX
OO
IDI
=_
!M
anne•
I•
•~••~
•Mu
•••I••~••
MM
IOM
MO
QIh|~I•
II
:•••¤•n
Mnn
IIM
•n•n•Qn••n•M
n••n••QIN
MN
INM
NO
NR
NIM
=Q
ltP
ISP
B>
UIIM
IOIIIIM
IIII
BIM
IMIO
IIIOI
IIIn
OM
QN
NM
MIO
QIs
gQ
UII
SQ
••M:!•~
•MM
••Q:•~
NI
•MQ
•MM
••M•~
••~IQ
n•,
·-PQ
IUQ
UP
Man
MÜ
QIQ
IIQ
|nM
•~N
IN•|I•N
•QIQ
MO
°50
äE8.
Q.
ä.
EtE3'Q'8
ai
§Q§
FES5
:55
fa-
aäV
§=§
51
nIIäInIN.
Q2
Q2
U=J
J5
5S
55
UIIn
•~
IIU
••n
nII
Un
en
nIIü
IO
OIO
N„.
„„=:.3
„3
ugag
77••• •
ag°°
77777:
än.777%
I‘
IIIIII:
IIII
S6
••S
22
22
2.
2*
22
22
22
2*
22
22
IInn
nn
••nJn
nIIII
.e
•¤•••
00
en
n‘
nI
L•.
IIIII
LI
IIIr~
•~n
I•••n
=N
nI
III:
I_
Äg
··:·:·:·:QQQ
g222222
'Qg
2222=
iN
NIIII
a•In
n•¤
•eJ
nn
III
•I
{L
U2
J5}:
Q2
.222222
Q2
.222222
Q2
.SQ22
,.5,
.'..:2
;,,
{22
22
22
2.,
{2:
22
22
22
.,{2
:2
.22
II
LI
IL
In
nI
=v~
QQ__2
__2
•77777__
2'
77••__
"27777
US
I•,•ü
I
2u
Qi
222'6••Q
6222222
Qi
2222I
sbg
•IIIIII
•n
nIIII
•IIII
gg_
Q.....•
_
Q.•..••
_
Q...•
Jo
•EEL
IIIIIII
IIIIIII
IIIIn
na
nI
nII
e1
=U
••I••
IIIIII!
•n
z•~
••II•
IIII
.„,
.„a
,„
E-2-:-:-: ..
„SE
Q.··:Q·:·:
SE··:··:·:·:
\N
•:
={
Ob
••_L
nn
nn
nn
•~L
nn
nn
nn
••L
nn
nn
•7;°Ö
••••••••us
°•;••••••
°•Üe
JJ
I••
••
•nu
•n
nu
un
n••
••=
••••=
'°•
:::2Q
psg
ne
Q.•
•..•
.Q
.•••••
•Q
IIIIII
IIIIIII
IIII
IJ;
{=
IIIISS
2=
IIIIII:g
=IIII
IIIIII
IIII
•••
3‘2
2°'
· 666666°'
•i•i666’
°'666
°§
=Q
‘IIII
II
III:
II
gII:
II
.I
b2
Q"
232
•••
Q22
•«
222
QJe
nI
nU
«n
n8
eU
Un
n3
.n
Uls
bI
II
III!
II
In
en
ne
ni
ne
nn
en
§n
en
eE
zb
Ie
IIIILL
IIIILL
IIII
Q•
•U
‘U
•I
••
II
IIi
III
I-I
I••••¤•e
Uxn
nn
nn
nU
Inn
nlle
In
Ug
en
eJ
nh
läh
IIIIII
IIIIIII·
IIII
I•I•
Ib
NIIO
NIII
IüO
Nh
¤Iü
ON
·
_I¤
dß
ßä
InIn
InIn
Inü
Ie
InIn
IInIn
|••
IIILLe5NIäE
=’·
EU
¤ß
U
=n
n•I
3
E3
3ä
.II
IIIIII
IIIIII
UIIIIO
OI
55
·5
55
55
55
55
55
5”
55
55
55
5L
LL
UIIIII?
LU
IIOY
IIL
IINN
RI
IlT
T!
II!I!
el:IIIIII
LL
•—
•L
LIIII
•—
•IIL
LII
IIII00
I{
Y!
"2"2'Z'£'2'1Q
"*!""'!€.•‘
'€'°'2
'“"'!'
II
IIIIII
IIIIII
IIe
eII
nn
An
n·
0O
0
=•
NIIIL
L=
•IIIIO
I=
•IIIIII
II
II
II
IN
NI
·•·2ä
2•e€*I·:·:
·°“2
···:¥•'?€’:»*
2·:’~F‘·'··’:":
=II
IIIIII
nn
IIIIn
eII
I0
00
0I
UIIII
IU
IIII
III
g8
•IIII:=
=I
•0
08
8::
SI
•II0
0=
N3
'2'Z,,
{2!!'!"!'!1
S{1*
"!"!'€'€'£'£.,it
'€'!'£
!!'!'!
IU
II
LII
LB
IIIIII
IL
NI
III
IIIIII'·
..
.n
eI
NN
ÜÜ
LL
IIIÜ
IL
LI
IIIIn
nI
:3•
IIOO
II•
IIIIII
•IIII0
00
{-•-••III
II~
•~
••II
IIIIIII
I,
II
•IIIO
II
•IIIIII
•IIIIII
IQ
••
_
Q••••••
gg
-Q
••••••
.•••••
•
JII
IIIIIII
IIIIII3
IIIIIII
:=•·
IIIIII
•sn
e0
0IU
•IN
ee
IIU
I0
255
$33355"
"•-R3„'•L‘$"3
"*2
222222•
ne
In
en
ne
nI
ne
nn
en
IN
uhtüenI
Q••
Q••••••
Q••••••
Q••••••
•n
en
LL
ne
nn
en
LL
ne
nn
en
LL
ne
nn
en
e
nL
Ln
nL
z°•Ü
•n••••••°•Ü
an
••°•;
uu
•••
I=
ne
ne
e-·
~n
ee
e=
=n
e•
Ilhkü
ze
IU
Q••
•Q
••••••
•_
Q••••••
•g
••••••
••
II
Ii
IIIIIII
iIIIIIII
né
IIIIII
II
II
gB
IIII00
g=
Ilen
hd
L¤
IIII0
0ä
II
SIIO
OL
LIIIIII
=X
XIII}
''
"'°
'55
5"'
55
55
5°
"5
5’‘5
'5
0°
S'}
••
·°°••••••·
••
{new
s•
•5
5•$
•5
IL
nn
ne
n°
Ö=
Ö••
=II
äe
II
II
II
II
nn
nU
In
ee
UU
nn
nU
Un
nII
III
III
III
äLL
dIIIIL
Ld
IIIILL
3IIIIL
L0
0I
IIII0
0I
IIII0
0I
IIII0
0L
II
ä=
0IIII
IS
OIIII
I0
0IIII
05
Ü'
55
w5
55
S5
55
II
=I=
IO
II
IIIIO
II
IIIIO
II
IB
In
Ug
en
au
ee
U=
eL
eIe
nU
=n
IeIn
I?
I.I
·
I.?I.?
!‘I
·
I.?I.?
I.I
•I.?
I-?I-L
IÖ
ÜC
NL
IIIIN
Le
IIIN
Ln
0C
In
NI:0
=I
nI~
IIIOII
nN
I=0
III
·
0n
LE
In
nL
IeIn
0n
LD
In
0n
L
Q00LV
_
b•¤•
.N
03
•2
32
20
an
..ä
¤u
Ues
¤e
••an
••.•
§S
7ä
äS
äIO
IOQ
hh
hh
lü•~
••••I•
•!
•••~•¤
••¤•••
••n•~
N••
06•B•£•5•I
Jéeäui-3°
•§J«G«i-Z-S«£•£•Z•i•i«3
JJ'é•£•£
6IIB
QIN
N6
|•¤••¤•|•
II••••
•¤••••|•¤
•••|||•
•••¤
••-
·I
II
OI
II
II
Ild
hh
hh
lllhh
hD
IIOO
OO
OIN
NN
I!Q
••••••¤•
Otlllllll
•\•\•~•~
NN
t•u•••¤
•••=:
Q•••••
••••••
••••••
••••••
••••••
••¤
•NQ
••••N
NN
NN
N•••••¤
••••¤•
••••••••••
•••!H•¤
•••0
00
00
00
hh
OQ
•=s••Il•¤
••¤•
NO
hslll
•¤•¤
•••NN
00
00
00
Ofh
hll
00
00
00
hI
nvtlte
eQ
OO
IIIINM
00
00
00
00
00
00
00
00
00
0Il
OQ
NQ
00
00
0O
O3««•„.
33••-$**3•-•--7•«•Z-'§
•--$27-*2*-:223833
3'!!!'!'2
*!'Y"!"!'!'€
"!"!'t't'!"!"!"‘!"!"!'!'!
*'!*'!'!*'£"!'!9
0N
MR
HN
IIDN
NN
NN
N—
al
0O
•··E
:=
:E
VO
QO
NH
0O
IGIIIQ
•Ilh
hü
h0
00
00
00
00
00
00
00
00
00
00
•¢
••••••O
•U
IIINN
OO
-•~
••~•¤
•NN
•Ilh
lhh
•0
00
00
0a
n•¤
•¤•N
N•IQ
0•¤
••¤••••C
00
00
00
0••
••«
••••
an
•¤••
fffff
·"2'!!!€
!{E
ffi!
ffifff
ffffff
EJ
00
00
0=
00
00
00
al0
00
00
0an
00
00
00
=0
00
00
0al
0h
•••••••••••~
•¤•••
••I\I\••
••••N
N••••••I•
l0
00
00
00
00
00
00
IIQS
00
00
00
00
00
00
00
00
00
00
00
OO
h•~
O0
00
00
0N
kü
nu
nO
1••¤
••¤••¤
••¤••••¤••••¤••¤•
•n•••¤
••••¤•••
•••¤••¤••¤•¤•••0
||•••••
·••••••
••••••
••••••
••••••
•I:
¤•••¤••••S
•••¤•¤••••¤••••
•¤••¤••••¤••¤•••·- •
•¤••¤••¤••¤••¤••¤•_
•¤••¤••••¤•••••
·
an0
•~0
0N
0!~
N0
08
00
00
00
00
00
0sü
ß0
0~
•2:2-««
2-
87•••3'63
'€-„„„-••
„-
3•'6
•••.*3
"!.*:.*:2-22
•-
2Q
••••«
•q
••••••
•q
••••••
•;•
••••••
•q
••••••
•q
•ä
00
00
0Q
••••••••¢•
=0
00
00
0Q
00
00
00
an_
00
00
00
H0
00
00
00
00
00
00
00
00
•~:7
’·*’:••"=.F
e••ee¥F
·?·:·:·:eeF
1v:·:·:·:F
·e•·2··°“:·:E-' •‘
0U
IQB
IIGO
OIIG
IIMO
IIIIIIG0
00
nn
ah
hd
z"°
7·
77
°°
SQ"
Sg·"
S"I
Sg"
Sg‘*'
NN
00
NN
Hä
NN
NIn
E_
Ilgg
ü·.
Iga
zll
--”
88
22
0N
Qh
lllläH
hh
llüh
üI!
••G
IWIQ
ItllllhIIIIU
IOO
QUIO
OII
OO
IIIIOO
IIU
==
IIlIQO
IIIII
II
I‘
{J
;‘
II
II
II
II
Iä
I.
OI
O·
OO
•II=p
=_
•OIII|•~•~
OO
I\I\I~=
_
lQ|\I\b
=
_
IOI\I\s
E_
ON
lhh
ßIIN
¢N
•~~
*|N
INh
N||N
lN••N
IININ
MII
UI
*-7*-7*-S
7*-7*-7*-S
7*-7*-'^*-
27*-7
*-7*-E"
7*-7*-7*-2
7H
¤••••••
51
N•••¤
•I\•ä
OII•¤
••¤•J•Q
Ä{M
an
ue
ll!\
Q•••¤
••¤••\•
\O
OG
OÜ
§d
QO
ÜÜ
UIE
QO
ÜR
GE
Il
Qfü
ßü
h1
Q
·N
INO
NI
|~N¢N
OU
CM
NIH
ON
OI~N
INO
NO
hß
lülü
II~
III3I
••anIN§IEILIN
NII
7332*ä
II
IT—
•¤•IIh
••4
•~•~
•~u
H
·
••
••
•I•\¤
•••¤•
Q:2::::••••¤
•l•lI‘
I'
IIIII
••.
anI•~
••I••••••~•u•••••••••••••II
'•
ÖÄ
ÄÖ
ÄI
I•
II
I_
IL
N1IIIÜ
III
••••n••
•_¤
•••¤••¤
•••
·•
iiiii
JIIIII
=•
2££2°..
„„„.„:E
NI~
IN•¤
•••Q
••
••
•••
•¤••¤••¤••¤••¤•
:3E
•· :22ß
ßR
'!•
••
••
••
@•
IIOII
Nä
‘
I•¤
•IIIIIn
äA
IIIIINI
\I
nd
S?•
Sg*2
••_§§:=••
•—2
•••·••••••••n
äOIIUIGO..
..&
III
n••••••••~•••••••N
IIä
·~?
••T••
=I¤
•
g::::2
Qzg
,N
OH
INI
S··
3§
Zs
S•¤••¤•R
RQ
QR
RQ
OQ
QR
RQ
R•¤:••Q
(R•Q
•¤•••hO
ON
NN
NO
UIO
OO
NN
NN
OO
OO
IO
OO
Q1
•7•||I•;••;••••¤
••¤•|•
TT
IIII•I•
I••
OR
R{
55
·':"!':':"!'2
!"!'!€'1
"2'1
"!'!'1
'!!!'£"2
°:‘!'!.
.E
!O
OO
OO
OO
ON
NO
OO
OO
OO
ON
OO
OIIIQ
OO
OO
III
uO
OO
OO
‘N
NN
NO
OO
gQ
'!{2
S5
$222-‘•!„••••«•«•$¥•‘•!•'Q3
3••••2
2••{{
{•'2
Si
•••¤:•¤••••RQ
Q¤••¤:Q
QR
•Q
OO
OO
OQ
ON
NO
I!R
Qnn
·
=R
•••s•~•••••••••¤
••~••
OO
MO
OO
OO
IIOO
RR
Q\!
‘•
OO
QIO
OO
OO
FIOO
OO
RR
•••~•~•¤••¤••R••
OOI
NO
NN
O1'•
••••••••••
77O
H8
BJ
•D
h*
=ä
QU
•N
N•v
••••RR
•v••
hI~OO
•¤I••O!|O
ON
Na
nR
•sl!
§8
NN
••RR
•¤•¤
•••RR
••O
O•••I•~
••I•••¤•
susO
I-:•
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
OO
••••••••••••••
••••••••••••
••
RO
'*
S.·:¥=¤
E.:s
:::::-;:::::::2:=:„z==:¤;3::
2:-.ä
••••
••u••••
(••~
•~
••••R
R••••R
uu
•~
•~
••••
~••
NN
RO
(•
anI
=•••¤••~••¤•~•••¤••••¤••¤•R•~~
•¤••••¤••¤•••••u|l•••¤••••¤•nun
•'“
SS
'“82
.-3;"
O•I-
N:8
I•
se
eR
II•
hI
(•
•In
IO
OO
OO
OO
OO
N•
{E
ISS
;2
••O
OO
OO
NN
OO
OO
OO
OO
NN
OO
OO
‘{
6ä
ät
2-2
E'2-:°·?‘“·%%%·%•·¥=-2%
%%%%%%%%€’•Ü%¥%%
:"
Q••'?°§2
'°•
Q"‘¤‘•2•"•""2L"•$'3""""'
""'2233"""3$'°"'°
••
•n•h•¤••
·••
¤•
gan
••I-
I(
e=
RR
SO
O|
:
_
U,
•¤••¤
•••••·~¤
•§E
¤¤
—_
Ng
ßN
NN
NN
=R
OO
OO
OO
OO
OO
OD
•-=
:2Q
a5
*ä::
'°°•”·.„:„:„:;··
,;;.:*.6.;
-:2*
••I-¤•In
llR
¤••¤
•¤•••¤R•¤•I•¤Q
•¤•R
~R
NR
N¤
N¢
|lI•HIR
ul¤|
·OD
gE
§asä
··§E
*z:·„:=z=·„::=:::z:
:=:==:„·=:=:=:::2
E5
_P
JOB
O8
PIO
O
NIIIOll2Lö.
InOI\OSCI-
PI2LP.
ID§IOI _
CL
InIn
83
¢·Q
G•~Il•n
II
nGn
g•
In
I\
•
=
•~n
Gä
72I
nv
hä‘
=?
ln
'!‘
‘IP.
ä2;
·b
=L•y
.n
e(n
l'{SE
S:2:
D
C•II•s•••3Q2nud
2ä
SI
.-
••J$JJ«Ä
pu}
IRSSZÄn
u::7
7'°
ä7
77
77
7•·•
aD‘;‘1'°
'' ‘
73
77
§e
••
-
°I
C•
IIB
Qum
.••
7•
==•~r~••Q
,}====••••
S'$
"!{{Q
••·•·•......
SU
I!
C—
•·•u
uU
eu
lU
N5
•n
d!
nq
q2
·•g
•-·,;
:22
•.':.•ä
•-2
,-:::2
-•••~••~•
•Q
.•••••••--•
•"S
.{...
S··•·
Ü°
gs
*ß
äiiié
7•••***
i7
77
72
•·33
-7"
nO
O*
U""7
7O
5••n
nO
nU
20
•F
'“"""2
Qi}:
S':=
·'=
~••••;•;
3"¢
gg
11*1*2‘
7g
gü
.!''
"gf-;.}-Ä
ÄÄ
Qg
n•¤••¤••-•7
•ä
„§=
‘*2
77
77
77
77
••
•.•n
••
N!
‘_
b
~Ü
7.8 ä gg!
•U
-,
Q;}
•q
nn
hh
72
226
••~~
~g
Q222232
i3
;::¢
,,•
-•-==
:•ä
Q••·••-•=
=.
••••
3•
‘••{
==
••••°
{{{{
..
•·•I
·•''
iQ
bg
—
-
••
••
••
=
_
·gQ
QV-
_···
QNQUU
g••••••
3_
NUN-Ü
Ü•
~•••••••
8•••~•~
2‘°S
”!·-E
-2-:2.::2.
....sR3•••*
""
·—·•
..J
-·:....„•
.::2.:
•§
—--—
S.•
•»u•·••*'
,2.--••••
•{....•
nN
U.--,_
-_,·
55
ee
nn
nä
=5
**,:
•_
5n
en
ne
eF
I·~
Q3
Ü•
••
Qe
aO
••
U•
dg
QN
OO
=•
FÜ
!O
O••d
!*V
"qO
°":"}"}‘7
—·
••
IBO
g••••••
°,
O‘
••
=p
nn
ne
nn
I
••••°
V"
••I
••••Nä
ä'°
>;_•§=*
z8
333==
•g
,_%
°:'!"!'!‘!{
•-_;_;;ä
.
‘O
.•
••
•••
=•
ä{{2233
••
Qn
•'•'•'•**
{ä
°°.
·'
_
ne
•••2
äE
=§
"g·•
-··•·
:3=
••:3
:2
Su
Q•S **7-5=
E=····„=::
2:::2:..
ä1
3::ä
g7
7::
Q,.
2g
.••••••
ED
$=
==
:=Q
ä'
••~•~
•d
‘*"“O
OO
OO
OÜ
E.
,._
.•sa
u;
*ä
Q,
..
8°
,,,
nu
,.
U•
••¤
31
ägg.,.-·
Es..
.2¤
••;
•·.=
„••'1
,„-::2
.g
nu
n:}
I3=
U••
•¤•gf
}1'“7
=7
7>
?'_
f‘,...
••'§'5•'J•
>:•.$
'.'!".•
-7-•
'I
{••••••
„U
,••
Qn
•N•~
¤U
gn
O
•·-•·
!{
2$‘•"‘3'33-•
••••;g3;•„,,
..,...2...••
«•u
•·•*°
·.
QC
.
-IIIISbGID
.GI\\
II
II
:n
nn
nI
II
I_
UII
UII
33
3"
"g
E§
GG
ÜIIIIO
ON
IIO
OII
OO
¤•¤
•GG
GG
GG
II•Z•i
Q ’633633
Q336633
333i•§•·¢•ü663346
hh
hG
GO
OII
hG
GIIII
IGG
IIN
NII
IIIIIIII
?|IIII
TT
YY
OI
PI
IG
G=
•G
GIIG
G=
•Q
OIIII
I•I•I•I••=IIG
GII
In
nU
e•••¤
••III
Ue
NG
IIGG
IIOO
Nh
hIIG
GQ
33
Q3
33
33
3Q
33
33
33
33
33
33
33
33
33
II
IIIIII
gIIIIII
nn
uß
nn
IIIN••n
n—
UU
8:
=•
II~•~
nn
=•
GG
NN
GG
NN
s•~
nn
NN
NN
II=
I•~
••~•~
•••I
=I
==
II•~••
•••••¢I•
IIIIII
NI
•II•
¤•n
nn
•Iu
nn
IIn
n!III
IIn•¤
•N
II3
3Q
3•••3
3Q
••••3
••3
••3
•3
33
33
33
II
éIIIIII
an
nIIII
IIIIII
IIIIII
I
GG
NN
I33
Q3
.333322
Q3
.$$3333
333333333333
GG
gb
IIBR
IIa
bIIG
GII
IIIIhh
GG
GG
II••
Q|,
33
33
33
33
33
33
33
33
33
33
33
33
III
IIn
IIIIII
IL
Gn
nn
nN
IIIIIII
Illnn
uß
II~
CIIIIII
NC
IIIIII
IIIIII
IIIIII
’N
b.
O3
•n
GO
OG
GO
II
IIII
3Q'!
2233333
•333333
333332-
333333I
nn
IIIIG
GIIII
NN
IIIIn
nn
IIIIII
•IIIIII
•IIIIII
IIIIII
IIIIII
33
_
Q3
33
33
3n
Q3
33
33
33
33
33
3II
IIIIIIIIIIII
IIIIIIIIIIII
NIIIIG
GIO
NN
NN
II¤
•IO
OI
IO
OIIG
=O
OIIII
IIIINN
GG
IOh
•~
II••
IIßh
GG
GC
CG
GIIIIII
nn
In
dn
un
nI
nn
nn
nd
Iun
nn
nn
nn
nn
nQ
33
Q3
33
33
3Q
33
33
33
33
33
33
33
33
33
3I
nu
hb
••¤¤
¤n
¤h
b•l¤•¤•¢¤d
nn
nn
nn
~n
nn
nn
nb
O,
h·
hä
IIIIIII
IIhh
GG
IIIII••~
•~••
IG
IIIGG
In
nQ
•n
nn
nn
n•
nn
nn
nn
Gn
nn
nn
nII
•n
nn
nn
n.
..
._
gg
......
.S
;......
.......
...,
II
Na
IIIIII
In
EIIIIII
GIIIIII
NIIIIII
GG
333
g3
333333*3*"
3223333
333333"
333333=
33sp
33
33
33
gp
GG
IG
Q
nnn
nIn
nnn
Innn
?(
II
IG
IHI
GB
Unn
nMU
nnan
UI
nn.
In
ugG
I2
:S
;,
nn
nn
zn
8li
bb
JIIIIb
b
=
IIIIbb
ä8
8IG
*I
GG
°••••••¤•
•••••••••ä
333
Qä'
$$33333
E3*
$$33333
333333ä
E333333
•U
••
3•
3.
33
33
33
3•
•¤•II
nII
I2.* Q
QJ'
·E:§:§Q
E„
-5:SsSQ
szzzzzä„‘·
=z:=·.:„·:Q
I?—
I?
IYI?
I>
FIT
IT
Ig
:-·QS
Sz=·.•···~-·Q
SS
.2.:::::Q:===„·=:Q
:.:2:::::·
•=••
•••·•====••
=••••¤•••n•••
•~•~
•INII
I•~••I•~•I••
Il'
IIIIILII•
-InIS
II
IS
aa
a=
·«•
eu
gS
Sä
'„'99
99
99
99
99
99
99
99
99
I•h
=III
IIhI•N
NIIIIII
Y?
II?IIIIII
?IN
II
II
II
IIT
?IT
TP
IIINIA
G¢
III=IIIIII
IÖ
NIIÜ
GIIIIN
•••~
•~
IIp
••••••
••••••
••••••
,II—
~ä
dIIN
In
eIIÜ
ÜII
IIÜÜ
ISIIÜ
GIÜ
IIIIII‘
ee
IIIIIe
eIO
ee
Ilbe
ee
e9
99
99
.9
99
99
99
99
99
98
IIIIII
IIIIII
ee
IIIIe
IINII=
IIIIII
IIIIII
IIIIU
IIIN
NIQ
IIIIII
IIIIII
IIIIII
IIIIII!
IIIIIII
IIIIII
IINN
INIIIIII
IIIIII
IIIII
•·E
E=
ES
IIIN
NN
UI
IIIINH
IIIIIII:
I•IIIIII
•O
OIII:
•IIO
OI
•e
nn
IIII
en
eIII
nI•IH
II•¤•e
e9
99
99
99
99
99
99
99
99
9g
=IIIIII
slIIIIII
=IIIIII
=IIN
Nh
•~
IIe
eh
hh
••IIe
eä
IIIIII
IIIIII
I~h
IIIIIIIIII
IIIIII
IIIIII
ne
ee
ee
ee
ee
ne
uu
ne
ee
q••••••
••••••
••••••
Ie
ee
ee
ee
ee
ee
en
ee
nn
e•
Ia
hh
E'
II
Ie
••8
Ie
OI
I•IIIe
e•~
IIIIII
N(IIIIII
IQ
I•
ee
ee
ee
I•
ee
ee
ee
•Q
MN
NII
•·
g•q
••••••
•_
••••••
•q
••••••
•—
·
EI
IIIIII
HIIIIII
IIIIIII
I';
IIIIIII
ee
•I
ee
IIII
nI
QF
·:·:e~e·2·2F
2·e·e2€¥F
Fre
ue
F;
eII
II
nII
Ie
ne
II
e•
aä
uu
•$$••=
n$=••
•
=••%
‘°°°••ä°°°°
nä
"“••äz
|a
lN
·I
F··§
"„·=
"„
SS"E
5Q
_G
ääää__
§§§!«••_
¤§2§««_•
·I
•~•~
IIIIe
h•IIII
I•~
•~IIII
nä
I••
IIIIII!
eIIIIII
NIIIIII
II
II
IIa
J•7
•7J
J•!
66
-3•!
•I6
J=
•II••••I•II••=
I•II••••N
IN•~
II
l|NIIh
IIIIII
IG
1"-7'-7"-
G?'•?'•7"-
G?'-?'•?'•
G-
}•N
nn
II\
I•••¤•¤
•II\
•I•¤•••II
sIO
III•s
nIIIIII
nIO
III•~
n
·
Ih
NIN
INI
hN
IIINI
I•IIIINI
QQQQQSQQ\5Q
OQ
ä-
Q=
Q5
u5
=e
••e
5S
SS
‘Ü
OO
OQ
PP
ÜQ
GD
QO
OO
GQ
OO
NN
OO
ä‘;"••;;"•••‘
••••••••••••••
an
••Q••I•¤••¤••~•~Q
SQ
•T
‘1"i'1"?""""1'1"i°'I'
""‘?7
''
T?P
•¤•Q
hh
I•
QU
INN
OO
OO
••••••••••••••
••••••••••••
••
QN
={
Ü 'Q
-.
O•
QP
NN
HO
QO
PQ
•O
HH
!!NN
I\I\QQ
Q=
•I
O•
BQ
OO
NN
NN
OO
NX
NN
OO
Üh
hQ
Q••••••••••••••
••••••••••••
••
_=
3é
QIIQ
QI\Q
:=•Q•¤••¤•
_•
SO
!Q
\II
•G
IIQQ
QÜ
ÜÜ
OO
QP
ÜQ
QO
••••~••Q
•~•~
•••¤••¤•
Q_
;„
2.„
ät
•!··:1·e·:··:•:•:·2•e·2•e1~e·2e·':·¤!·s·e11•2•·s
et
•·Q
Qgun
OO
-OÜ
ÜÜ
ÜC
OQ
QC
QN
NO
OD
ÜN
NJP
··Q
III!
IIIIQQ
IIII
III!
IIQ
III.
S•
EP}Q
F:O
Q•
NN
b•~N~Q
QO
OQ
=Q
QO
OO
IIIUQ
QO
Il•
SU
8!!Q
QhQ
QN
NN
NN
NN
OO
Qh
g~
Q„
NN
·
ÜQ
Q••••••••••••••
••••••••••••
••
gäi
EQSQ
QQQQQQQQQQQQQQQQQQQQQQQQQQ
OOO
O!
OQ
GH
QN
DD
QB
WN
dl)
PIll!
IIQ
NN
!!Q••N
¤Q
Üd
•Q
QN
NQ
Q•
¢Q
S\Q
••••••••••••••
••••••••••••
••Q
UP
I:S
IQ
=Ü
äQ
OO
OO
OQ
NO
QO
O=
Q0
IQ
u•
NQ
NN
NN
QN
NN
¤III••Q
•¤•••
an
•Q
Q•p
=|—
¤[
••••••••••••••
«•••••••••••
•••
OQ
OQ
OQ
CQ
Q•
8:
HQ
IIOO
QO
QP
QC
5"
3‘•¥
"JJA
°««° °•%•¢éJ•5•i•S•Z
-2-2-J•S•§•3••••°Zi °é•S
66
Q„
PO
D:
·ä—
=5,!—-=5
--55
--,,.·
5-l
gE
ÜN
UN
DP
A
5c
•-5S
__5
555522i.':55=•'="•S8••«522!:!‘„•••••5
:2S
8R
Q$
Q!!O
¢Q
QS
Sä
ui
E555533=23$5555
••••55••••«•„„-«••••
E§
ä!
••
••
••
p•
••
••
••
QS
GQ
ÜQ
QP
RQ
OQ
ÜO
QO
NÜNOQ
OQ
QO
IIQO
OQ
QPPP
IQ
I!|IQ
Q•¤•:••Q
•¤•Q•¤•Q
•¤•OQ
QN
QN
IINQ
QIQ
•P
ISP
)D
IM!
IQ|$
|?|?
|Q
OQ
IQIQ
IQU
OI
IIQ
Pllll
I~*
I•I•I•O
•I•••
O•••|•
|••|•
|•:•I
·-5
5:
•--••
-•I•9Q
Q••
QIÜ
Q
61
N••••ä3GO\•~O\83•¤IunILä1
{.
ä3••«••
LI!••
.•¤•
8
ä•
‘:1
E3•
0
=I!
QÄ
Q•¤
•0
26
•G
O\
80
•IG
°Q
'!‘
=?°I"'2
.
~•.
.E
nä••
N8
Qt
-e
8D
.s
Esä
D
OOOO.
OOOOOOOO3O.
OO
Oä
==
=O
llO
B"
Q3
I-ll
VM·
Ss
äO
OO
OO
OO
OO
OO
OO
OO
OO
O6
66
66
6"
66
66
66
"‘6666
OO
OO
OO
OO
OO
OO
OO
OO
;O
OO
On
nn
II
II
nn
nI
In
5•
II
•I
IO
OO
OO
NN
nn
nn
nn
OO
OO
nnO
Onn
On
nn
OO
UU
OO
I}Q
'I:n
nn
n•
SO
OO
OO
NN
SO
-O
OO
O••
On
nn
nO
IU
IIN
NO
ON
NO
OO
O••n
nO
OJ
n•¤•OO
OO
éO
OO
On
O•
SO
OO
OO
OO
OO
OO
OO
OO
OO
OII
OO
OO
O\I
OO
•n
nO
u\O
IIO
•O
vtnn
•*„ää
..ä
ttu
ev:
..ä
t@
@1221
..ä
t•1•e~e1
Oa
nO
Sn
Ou
uu
nn
OO
nO
OO
OO
OO
Ln
nn
nn
OO
TT
II
II
_O
II
II
_O
IIII
IISO
O•
Db
äOlb
OO
OO
ON
NN
OO
OO
OO
OO
OII
•O
ON
NQ
O•
OO
=:O
OO
SO
8nnN
N•¤•••
8N
NO
OO
OO
llnn
MIn
g•
nn
OO
OO
•O
OO
OO
O•
OO
OO
tg
QI
=•ISOOOOOOO
OOOOOOOOOO
e3
Q.•
Zgää"·
ä3!•'!2•"
*=323232
""§
3322•
OI
OO
On
nn
nO
Ou
nn
nn
On
nn
nQ
••••••
Q••••••
QUI-
SS
nnnnnul••
Snnnnnn
SS
nnnnO
•g
dO
OO
OO
OO
OO
OO
MM
OO
OO
O3
9{
$7
--si
YY
YY
Y!
'1sg
"!"Z'2"Z'€'f'T
sg
'f*£"!"!\
OO
OO
OO
•O
OO
OO
OO
•O
OO
OO
OO
•O
OO
OO
NN
OO
OO
OO
OO
Q2
Qsäßä
I3
2""'!"£'2'Z
i,.
"!"'*'tO
OO
OO
OO
P:
OO
OO
OO
OO
IOO
an
nn
nO
On
n8
nO
l!n
nn
II{S
OP
DO
OD
OO
DI
OQ
On
nn
nn
nn
nn
nn
nn
nn
nO
OO
OO
OO
OO
OO
OO
OO
OS
UO
IIO
OO
OO
OO
OO
O(
OO
OO
OO
OO
OO
OO
OD
UO
OO
OO
OO
OO
OO
OO
OD
OO
OO
OS
g5::
°°’·°§„;„z
;§§
„.„z
„;·§=
„sa
O·-
6*
'“3*2727
"*
'“37**727
"*
ä3727
{PO
I!S
I•I•
nO
OO
OO
UO
ON
OO
OO
OO
NO
OO
OO
ON
O=
O
·
-I•
OS
nO
•~•In
••n
•n
InS
On
nn
tn
I•O
n••
.
NIIIIIIIIan0Ig.
2I
II
I,
U*
22
2=
•••
E-•
jE
22
••ä
II0
0I•
~0
0II
IIIIII0
0-••-IIII
I"
·'°
°'°
'2
°'6666666662
6II
II•¤
•••II
00
NI
0I
277
22
7722;;2
äI
2277222
äI
;;;;22
••
•
"••
•°'°
•°'°
an
an
•_
••
••
I
·6
6-g
IIIIII
IIII•-•¤I
IIIIII
I8
88
•¤•F
l*5
_-
II0
IIIIII
02
26
2222222
6222222
26
IIOO
IO2
*='
******
j2
22
22
2i
22
22
22
2•I
Ö;
2ÄÄÖÖÖÜ
é••••••••
é••••••••
u•~
Ian
II
IIIIIII
III
IIIIII
IU
•-•-IIII
••I
IIn
hI
22I
:6222222
222
2222222
22222222
2•
JJÜ
zi:•F•••ÜS6
Ü;•-•
••••2•2••
•,=••••••••••
••=
II
-
II
II
I_
II
I_
II
II
_
II
IIIO
OÜ
IÄ
NN
00
••••Ä
II
=•~•~3
II
I•
NN
OO
NN
•IIII•
¤•••
•N
N:
hh
22
-8
8·•-¤
••¤•••
§8
•¤••¤••¤•••••••8
II==
==
2II
éIIIIII
_é
IIIIII
_
inun
••
II
IIIIIII
IIIIIII
IIIIIII
Iä
II
•••••~•~
NI
I"
2JI
2222222
J2222222
262
2222222
=I-
uu
••
In•¤••·•00•¤••¤•
•=
32
22
S2
22
22
23
S.
.22
22
2......
.a
nI
I•¤
••¤•••••••••
I-I
•-•¤••¤••¤••¤•••I~
I•••••••¤••¤••¤•
an
=°
°°
°••«
•••Ji
I••••¤•••
•I22
2*2
2222222
*2=
=II0
02
.=
=IIII
22
266
622
6666666
6666666
6666666
6E
222
2-222222
22
2222222
~222222
22
'°S
"66
'°66.
5666666
"666666
6.
22•
•==••
••
__¤•••••
•2
••¤••••
••.
••
-«•
••••0
I-•-an
0I-
•••¤•:
I-55
55:55:
55:-5
:5:
••••••••-••·•
EQ
§=
==
II=J
V§
Ji
IIIIIIV
0I
IIIII0
0I
I•••••0
II
••••••
vs00
I000000
II
000000000000
••
••
°'•
••
·
••
•I
I-U-
II
IU-
=I
IE
=I
I•••
••••0
O55
·5
2555555
55
2555555
•··· 2
::-:5-.=·.1· •‘:
„|
II
•I
•I
5-*Q5
55:2555;*Q
55
éééézéQ
55
:5•·:::Qz
§=
I•¤•I•¤•0•¤•h
Ia-I•¤•0•¤•I-
I•-=••0•¤•I
nIIIIIIIIIII2I.
sI
II
II
8n
nn
nn
II
II
III
III
IN
=«•
:•I
:•I
'8U
IIIII.
In
nn
II
IIIIII
IIIIII!
IIIIII
I6
''6
66
66
66
66
66
66
66
66
66
66
66
66
66
IIN
NII
NN
IIII
IIIIN
NIIIIII
I,
IIII
IIII
IIIIIIIIII
IIIII?_
I••s••II
IIIIII
nn
•••nII
IIIIII
IIIII:
II
•~
IInII
IIIIII
IIn
nII
IIIIII
NN
III
Ig
•••••
••••••
••••••
••••••
••••••
•IN
NII
IINN
nn
nn
nn
nn
IInn
NN
nn
nn
nn
I
IIIII
IIIIII
IIIIO
OIIIIII
IIIIII
nIn
nII
IIIII:
'•~
•~•••~
IIIIIIII!
nn
IIIIN
'ifi!
f'°"'f"!.
""f"!"£!
"2""'fif
"'°
f'°f
"I
NIIII
IIIIII
IIIIII
IIIIII
IOIIN
NN
2n
IIn
nO
OIIII
IIIIII
.n
nIIn
nIIIIII
I'
IIIII
IIIIII
IIIIII
nn
IIn
nIIN
NN
Nn
ffii!
fffff'2ifffff
fififi
{ffii!
iI
IIIII
IIIIII
nn
II
IO
ON
NN
Nn
IIII
IIIIII
.--71
.IIII':-T
I?IIIIII
NI
In°
I·—
z:
sa
E=
IINN
IIIIIII
III•
s••II
IIIIIn
nI
IInn
nn
II
IIII
•IIO
OII
•n
nn
nn
n•
nn
•II=
•N
N•~
•~II
•I
33322"
333333"
333333"‘
223336"
233333"'
3§
66666=
666666=
666666=
666666=
666666=
6IIIII
IIIIII
IIIIII
nn
III=IIIIII
NIIIIII
IQIIN
NIIIII
IIIINN
IIII
IIIIN
Nn
nn
nn
nII•••~
II
IIIIII
IN
NN
IIN
NN
N•:•=
NN
NN
IIN
NN
NII
ut3
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
32
33
33
'N
II
NIIIIII
II
IIIIII
NIIIIIII
NN
IIIIIn
GII
N•IIIIII
I•
nn
nn
nn
n•
NN
NN
NN
I•IIIIII
n•
•gIIIII
III
II
IIII
On
nI
5I
IOIIn
nII
nIIIIII
n••••IIn
nn
n•¤
•II
nI
§=
nn
==
?IIIIII
IC
CIIII
IN
NIIO
II
IN
NI
IN
NN
NN
NI
NN
NN
II
IIII
IN
NN
NI
nn
:IIN
=I
sn
n••N
NI
·\
nn
I•N
=I
\:=
•~
•N
NI
\n
nIIN
=I
\n
_I
Iui
I;
I•+•
I=
II
I22
"'2ä
"22
"°2ä
"22
"N
NN
NN
NN
NN
‘6
22266__
2:226N
::2262N
22226222262
N2
In
nn
nn
nn
•~•~
nI\n
nn
nn
nn
nn
n5
IIIIII
IIIIII
II(IIIIII
II2
IIIII!
•IO
IIIIOO
IIz
OI
II
II
II
II
II
II
II
II
II
II
II
II
·I
IIIIII:
IIIIII:
IN
INN
NI
YIN
INN
NI
ININ
NN
IIN
ININ
'IIN
INN
NI
IIIIII
IIIIIII
IIIIIII
IIIIIII
IIIIIII
II
•I•I•
I|•I•|•
II•I••
I•I•I•
I‘I•|•I•
II
Nn
nII
INn
nIII
\IIIIII
\I
In
In
•~
IIIn
nn
••
nIIIIII
IItn
nn
uI
IQ
n|•n
In
I’
NIN
INI
ININ
INI
NN
ININ
IIN
ININ
IN
NIN
INI
N
ÜOOOCInO!GhÜC\|~.
äÜ
!!OO
A•
••
A·
Q
hu
i!
II
II
PO
ÜÜ
BR
{'£
'!Y'2
'EO
NN
DG
.
l!
E„:==:
CO
IIGN
N!
Nh
hu
u—
_.
1
ÜN
NÜ
Üe
••Q
Q
€'!'£
"!"!I
he
ul!
OI
II
I-
ul
s8k
!!!!!
Qn
ssu
u•
•••••A••
uO
IOO
OÜ
OO
OO
O
=8
ÜÜ
ÜÜ
Üä
lNN
ÜÜ
uu
uh
O
E—C
O!
ÜÜ
=3
t6•
=O
OIIO
O6
O••O
•h
ul
Q"fif
TSh
l=S
««¤•
T:
UI
uu
=7
ll
223*2
s333322
~"‘l!
.·
=„=•:gä
5.
..
.¤O
OO
OO
lllbh
NIN
BN
u•I
•I
•ll-
3N
uulhä
\äO
hlh
uu
,R
OH
ON
B
CCCCCCCCCCC2CC
CC
8*2
"2
UU
„d
du
l
SS
SS
IIC
CC
CP
PC
CC
CR
PO
ON
NN
IIIIQN
NQ
••••••••••••••
••••••••••••
••
Q~I••Q
Q•••¤•
QQ•II~••¤••¤•I
IQQ
IIIIQQ
QY
II
•••¤••:••;••••••••¤•¤••¤••¤•••
II
I•¤••¤••:•7I
PC
Cd
C•
P•~QQ
Q•I\II•¤n•¤•Q
:Q
QC
PQ
QM
CIIIIIU
NQ
Q(
•u
uQ
QP
PM
IIOQ
MM
MIIN
MM
NQ
PP
CN••
CC
CC
CC
CC
CC
CC
CC
CC
CC
NN
CC
NN
CC
CC
8M
In
1:
Eg
2E
CC
•C
CC
CC
CC
CC
CC
CP
PC
CC
CC
CC
CC
CC
CC
CN
•Q
M••••~
•~••~
•~••M
I•N•n
••~•••N
~••N
•••u
u•
QI
•Q
•••·•~•~
•¤•••II••Q
••I•~
•••¤••¤
•uN
~•••••IIII
MM
MQ
[••••••••••••••
•••••••••«
••
••
CN
CC
QC
Cln
BC
UC
CC
CC
IICC
CO
OC
CC
CO
CC
CC
CC
Cäh
IICCCCCCCCCCCOCCCCCCCCCCCCC
CCP
•Q
dQ
••••••••••••••
••••••••••••
••
CC
CC
CC
CC
PP
CO
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
C=
-·d
b_
CII
CC
IIIIII
IIIIII
Z·
·· *2:2—
‘„.
•C
CC
CC
PP
NN
CC
NN
PP
•Q
Qu
l•
••I••••Qu
~~
•~•v
~•~
•I\••••v•¤
•«
••Q
QN
NQ
U•
SU
{C
IICC
CC
NN
CC
NN
CC
NN
NN
CC
CC
CC
CC
Ph
QC
Ps
•C
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
C•¤•••
gg
Q••••••••••••••
••••••••••••
••
U•I
I=
d&
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
•‘C
CC
CC
CC
CN
NC
CN
CC
CC
CC
CC
CC
CC
CC
CP
UJ
CC
CC
CC
CC
CC
CC
CC
CIIC
CC
CC
CC
CN
NO
OC
d•IU
PP
III\CC
CC
•~P
CC
CC
C=
CC
CC
CC
CC
CC
CC
CC
CC
gn•
CC
CC
CC
CC
CC
CC
CC
C•
Q(Q
Qg
Q••••••••••••••
••••••••••••
••
Q·
anP
QU
P3
I•¤•¤••¤••••¤••••¤••••••¤••¤••••¤•••
•••••¤••¤••¤••¤••••¤••¤••¤••¤••¤••¤••¤•
;2
9äS.•.„
•¤•II
llgg
‘• •
an•
‘C
CJC
CC
CC
CC
CC
CC
CC
CC
CO
CC
CC
CC
CC
NC
I;I
CC•
CQ
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
Can
•Q
ass
PQ
QM
\Q
•)•
IIII••••Q
IIQ
QIIIIII
•¤•••¤••¤•
3"
8‘§•'i°•
°°Q
IIII•¤••¤••Q
CIIC
CN
CQ
L•¤•
MQ
PC
•-•C
CC
CU
UC
Cs
Utl!
IQ
••~•~
•M
I••~••M
•••I••••
QIn
s*(•IO
CP
P=
CC
CC
Ch
BC
CC
CC
=C
M•¤•••Q
Q:I
Q•~•I~•M
I~I•Q~•I\•~•Q
CC
CO
CC
OC
CP
PC
IQ
PP
C•¤•
IIM
•¤•••¤••¤Q••M
•¤•Q•¤•~t•¤•
QN
IINQ
IIIINQ
MP
NIC
•I
•P
SP
CI
CIC
IOIC
ICIC
IYI
PIC
ICIC
ICIC
III
C:P
M•u
P!}
|•|•|•|•I•I••
|•I•|•
I•I~
I•
|•=
eg
„Q
S';*"
-•S
¤2•*982•¤*;'2$"•'!§!$2•'!$'SS23!'•!$!
2:
•-Q
__P
•••„u•¤
•Q
uP
QIII
M
67
23Cä-
E3.
ES.
>
E23E·-E2
Q':
ai
3:22
:22”
6°
E'}
5;:sg
6§=ä
••0000ä0N.
0N.
0S_v0
02
=2
23
33
33
=0
00
00
00
00
00
00
0I•I••••¤••¤••¤•
••••0
0N
N:
00
I~h
00
00
00
00
•¤••¤••••••¤•¤••¤•••
II
IIn
nI
I—
6_
II
II
II
II
¤•
00
•¤••¤
••=0
0I••~
¤•
•~•~_
‘"
55
gd
"!'!'i't€.
22
21
22
*22•
0
2°"""2
22.*:2222
2"Y
00
00
00
•¤••¤•••0•h
h•E
:'$‘•·2
::::22::2.::·
:2..'
•°:22;2
22"!"£'!'1'!'f
222222'!"!"
00
00
00
00
22
it::*2
77..77••1"I'••
•••¤•
JJ
00
8*
Öß
•>
••00
00
00
00
00
00
NN
00
•0
Q•
00
•¤•¤
•hI~
00
00
00
00
0•
•Q
•¤•••
'°::,*3
,.,5
.°2
'!2!
22
22
22
"2"2ä
=Jb
00
00
00
00
00
00
00
02
22322
.12222225
22222222
•J
JU|¤
I•l•
00
00
00
00
00
00
00
0'
••
¤•3
=•0¤•¤••¤••¤•
•¤u••¤••¤•¤••¤=0
06
==
2=
SL
•••¤••••••••¤••¤••¤•¤•••¤•••
nun
=0
••
SJ
0N
U8
•~
hIR
00
00
00
00
00
0N
0S
:••••••
••••••
••g
gg
J0
00
00
02
g. ·:§§
;_a
g2.:.:::
....2:::
2,-:*
222Bü': •
.g
••::2::2
::::···· .
.2:Q
•••••¤•
••¤
••¤•0
an•\
NO
In•¤••¤•
O?
00
Ü·
äs=§.ä
== =2·
2222
2--2
•-'
22223
22
22222;22222«•
222
5"
unIS
J0
00
00
00
00
••00
00
00
Ph
*E
=2:„§
°-··
g.....„
=„.„„
..g
3,§
>g
:_,g
·~:·.•s
0J
0§
XX
00
00
00
_
|\¤•¤
•0n
g0
00
00
00
00
0h
I•I
:‘
•••¤•••¤•
U=•¤•N•¤•l\•¤•
nu
nvsv
=•
-"-·h
-’
I•T
•I
•Jlh
g‘
„2.:2
-·§_¥*
::·2:::::::2
2: ..gz:•¤•
,-=
p.•5
9•¤
•Q
•••••¤
•=•¤
•••¤•
•~•••N
•••In
dl
0
Q3••
ME36M••
•I
==
\Q
-·—
ÜÜ
"e
QI
EÜ
Ü.
·;Q
5ä
QI._
q0
•••u
0····
666666.5
66
••••6
ul
==$G
_gg
•~••II•~
I~Ü
Ü,6
ag
•6•••¤••·•25
•¤••¤••¤•••IIQ
aÜ
°I•¤•
ggp
•:•
IIIINÜ
Q;
$=
::::Ü
Ä=
=••
40
•“¢
fiiiii•
·····•‘s
6666>
Q‘
3‘g
••••••S
••••••—
•
•Ü
_
.Ü
QII
gä
U•¤•
Q—
•u
nf?
I•¤•
"g
pl
•Ü
Ü"'“•
QIO
NN
"0
••'*
Q$
$::6
65
0vvvvgg
Q,
,,,,,,,,63
,·g
=N
gg•
••••
g.
..
••
·ag
e3
3*3
3;
=s666666
,;g
g••
d•
00
•••.
0Q
Q3
•~3
•¤••
U-••0
0N
Ü""""
Q5
Isg
0II
*"
DO
NN
=°
:::5::
ÜS
6::3
:::E
EQ
'BY
Y’
*"2"!'2
..
•.•
u····'
'-
5-
6••~••••
ég
gg
;=
EE
-_°°T
Y·
‘=7
77
77
7M
-
•••
NN
gé
·Q
EÜ
EÜ
_•
'__
··6
00
00
ÜÜ
ÜÜ
U*
"“"°°
0Q
:*'*
**
fÜ
Ü==
6ue
•••
'•'•*"3B
z•••--•••
.6
66
6·
zuQ
‘"'°=
=••
g·
•'°
"'
6M
···••
QD
°€
Y..•
•n
I••'°
".
••••
kU
s:
·••••••
I••••••
=
U'
”""‘ß
•ID
NN
OO
'Q'°'“'“‘
U5
•••¤•N
•·••'•S
-•-«•u•••~kU
••""""“
ä3
ß!
•·-•!
$$3333"
"··,-4
:::::•
gg$$33
QJU
PÜ
Ö,
Q•
°'
°
..
„-•=
gg
}€
."!.„•nu
3_
;_;•|'„..;
,,5
••••
'•§
2'*‘„2
6•~
••••·•··•••·••‘“"
"'*
M°•
Säge
:••
I--.°•;
MM
IIUI8
°6gggggg
3ffii
gd
•Iu
2'
....„•
•:8
•·•°"
Q„
«M
00
Q•
~F
IIIIII
IQ
Q•‘··
0I„•
B'°
'ääsä•·
g3
.:23'£$$S
B•--•-•-••;
B=
•\:=
gQ
Q_
.....•
•k
{M
M==
·••••••
{0
0••
I•
ÜI
¤~
~¤
¤•
{6
0••
I•
•¤
.ga
rts
_..
·~
¤•
.„.
•p
.g
Q•6•••¤•
Q•.
••••0
F·g
•0
„•N
'•,
6u
e•
Q.,
...„6
uu
-•
5{g
s:
*{
:2::::
E{
••••5••
J*•
sF
=·=
;uS
{••••••
ÜI
••••••
!S
SS
:;
5U
kgE
..
•ä
u-
•„
5=
·ä•
N:
*•8
**·¤
•:•
=Q
I•\U
'==
Q=
ggsq
gg
n”
”::=
°0
Ug
.•••
gQ
•„,„
e|
Ian
M0
•••
“Q
QIF
«0
••••
*6
-Üq
nn
F¤I
ua
I“
6¤
6¤
•¤F
pI
••IU¤
ÜU
".
‘j
Q
NDCOOLONCNÜ
O=B
OC
B3
2“
22
ÜÜ
ÜÜ
=d
dul
d
1=S
SS
‘Q
äL
NQ
UQ
Qll
ÜO
LD
ÜO
OO
ÜÜ
11
L
222
222222•
u2
2„„
2u
••««
•••
15
L1
11
17
71
27
71
11
aß
11
77
LQ
1Q
1Q
1N
N¤
•O
RO
OLL
Q•
hL
1llN
NQ
•Q
QIIQ
Q‘
•*
2*
€':':'Z
'!'!2
*ffiiff
2*
'1'1"!"£'!"2*1
·h
bD
O11O
O1
1B
B1
1B
D1
11
11
11
‘1
00
01
11
äN
QL
•N
NQ
QL
•Q
Q11Q
QL
•Q
QL
OL
LQ
OO
·••Q•••
Q•
OO
•=I••II
U•
OO
QII
ä•
OO
LL
OO
-„
..:6Q
.6.:6666Q
666666Q
666666.;
-R1
11
OÜ
NO
ÜO
OL
NN
OO
RIL
NN
CB
Dg
LO
OO
O11
2L
OO
••LL
••
gg
••••••
,gg
••••••
Qg
••••••
•L
:B
DD
BQ
L:
TQB
BC
O~
QL
:1
1”1
1Q
1N
QN
LO
OO
OO
OO
NN
OÜ
GO
OO
OO
55g
E::55::
Qe
::::55g
e.2:::::
:1
111
„2
fffii!=
29
!!!::=
2QQQQQQ
QC
BO
BO
OC
DC
OD
BC
11
NN
OM
OL
LO
BO
s··
5-*5
555555·
-*.5::55:5
S-*.5
::::5.::
O2
:Q
·-O
OO
CC
D.
Q1
11
1Q
2Q
Q1
11
1N
Q••
Q••••••
Q••••••
Q••••••
•Q
11
LL
CD
11
11
LL
11
11
11
LL
11
11
11
1
R=
.·
Ü·D
NN
L1
O_
.,•
•S
g••••••
•Q
••••••
•g
••••••
••
11
1N
NO
OO
OO
OO
PO
OO
NN
O
=O
O=
LL
Q•=
=3
3Q
:Q••
=C
=B
B11
Q2
66"
•i•i•Z•Z$°J'E
uU 'éJ•Z•ZE
Jédééj••
=S
H=
OB
HO
BB
HO
OB
S22
S"
"‘222
‘""
"‘222
"'“2
221
11
11
11
E22
Q=
{222222
{{
22222;S
{••••;;
2°O
OI
OO
BO
OO
IQ
QO
OI
OO
L
QII
NQ
Q1
II1
N1
01
Q27
"2
27$"?••1‘"
">
27'•'I'••'I'2
2. ••
«••;•
|•••|•
g•••|•
¥
l•I•|•
g:—.··§
SS
2.::-:::S
S::•:::
§..
S·
O:
LÜ
1=
10
1L
I•1
=1
01
LQ
1•••1
O1
L
IIIII(IIN.
INS•¤•\I
II
II
'5
55
55
=n
••••
••Ln
«I
LI
ul
eLn
I_
IIQ
Iz
25
‘I
IIIII
IIIIII
III5
•l•
IIIIIII
IIIIII
ll•iJJ•I•I
°••••'°JJJJ•IJ•i«{•7•Z
-JJJJJJ
JJJJJJ
JIIIII
NN
IIIIIIII
IINII•••¤
•IIIIIIII
III7
7IIII
IIIIII
IIIIII
PIIIIII
IIIIII
nn
nn
nn
II
II
OO
(IIIII
IIIIN
NIIN
NII
II==
•¤••I
=g
•••••
•••••·•
••••••
••••••
••••••
,u
nn
ßß
IINN
NN
II==
IU•
IINN
NI
IIIIII
I
IIIII
•I•¤•N
NII
IIIIII-!
IINN
•¤••¤•n
••NN
IOI
IIIII
IIIIn
•¤
IIO
IIU
II
IIIIII
NN
IIOO
IQ
~n
nII
IIIIII
nn
55
nn
1Q
I•N
O1
NN
Ifn
••
5
=••IIII
•••¤•IIII
IIIIII
•¤•¤
IIIIIIIIII
II
IIIII
IIIIII
IIIIII
IIIIII
IIIIII
lla
I•II=IIIIII
Iblln
nn
nIIIIII
IINN
ÜI
On
nI
QIIIQ
QIIIIII
11
II•~
5IIIIII
NI
Inn
IIIIIYIIIIII
CO
NN
IIN
NÜ
ÜII
II
IIII
III
NN
II••••
IIIIII
•¤
•¤
•IIII
In
·I
II
II
I5
NI
nI
UI
15
••~
I1
31
IIIIII
IIIIIII
IIIIIII
IIh5
•¤••¤
•I
nn
OO
NN
IM
IÜÜ
UII
•IIIIII
•IIIIII
•IIIIII
•n
nn
n1
1•
5N
IIIIn
NN
IIIIn
NN
I=n
NN
IIIIn
IIIIII
nn
IIIII
IIIIII
IIIIII
IIIIII
•••¤
•IIII
IU
IIIII
=IIIIII
=IIIIII
anIIIIII
=IIIIII
'al
In
nN
~Q
QN
NIIII
xn
INN
IIN
NN
NII
I•~n
n1
1n
IIIN
N5
5n
nII
IIN
NII
IIIÜN
XIIIIII
IIn
nn
nN
HN
NII
IIIIII
nn
nn
nn
nn
uu
nn
Nq
•••••
•«
••••
••••••
••••••
••••••
•M
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
nn
•I
II
II
IN
In
II
NO
II
0I
IIIII
II
IIIIII
II
nn
nn
lillI
nIIIIII
hIIIIIII
II
IQ
Mn
nu
hI
•N
hü
un
nN
•IIIIII
I•
NN
NN
NN
I•IIIIII
Q•
ng
•••••
•Q
••••••
•·
••••••
•·
••••••
•g
••••••
•Q
•
ÄIIIII
IIIIIIII
IIIInn
2IIIIIII
1n
nn
nn
ntz
IIN
N1
nIIIIII
nIIIIn
nn
NH
IIII
nn
nn
nQ
Qn
QIIIIII:
8IIIIII
IIIIII
IIIIIII
II
8JJJJJ
LJJ
'°«i•i
LJJJJJJ
L66-6666
L666
'äuiL
J••III~
••II
s••«•==«••
I\
•¤•nQQ
•••II
=IIIN
NI
\•-••••=••••
I\
¤•I
nI
nI
In
In
29
99
99
uu
Sn
Nn
M‘
nN
NS
•¤•u
sI
n
-°5
IIII
nIIIIII
I5
5IIIII
35
5IIII
I5
5Iu
II•I
Q5
IIIIII
UI
IIIIII
IIIIIIIII
IIIIIII
US
IIIIII!I
II
II
II
II6
IIIIII:
IIIIII
IIIIII
·IIIIll5
hI
•••••~•5
•••I
••••••I~••~
I~I
••••~••u
5••
I¤
•IN•I•5
II
.U
ININ
IHI
IIIII
•¤•IIIIII
llIIIIII
llIIIIII
IIIIIII
•¤II
~I~
I¤=
lI•I•
I•II•I•I•
lI•I•I~
II•I•I•
II
Nn
nII
s1
~n
nII
\1
Nn
nII
\1
N••n
II\
1N
nn
II\
1n
IOIIII5
nIIIIII
•¤•IIIIII
••IQ
IIIIUI5
nI
NIN
INI
ININ
INI
ININ
INI
INIIIN
IIN
ININ
II~
••••LQQ•Q•SSIEEL*%
*22
QO
O•=
=••
••¤
¤_
••ä
hh
hb
§G
EWYY
Idd
ne
n
ll\•••••¤•
••‘
Effi!
OO
OO
Ln
$228*.
wwneiO
••••¤•N
N•
IIIII
'°an
LNL
¤IN
N•••¤
••
BQQOO•
—«
•••O
Ian
:3238Q
'•••••
8••••¤
•¤•—
•I~
88
°Q
••Q
Q
=TTTÜ
ÜY
i•Ö
•••••
Ng
*28888
33i
.:· us-:.2.:
·I
\OQ
nl
="'Q
8*2
«u
hQ
S_
s::::„
si·
5a
•:· §
Za'
s::sS„
·IO
OO
On
ä•|
•••
II-
Nnnllß
\äO
vllln
s•¤•
·
NQ
MQ
NO
U
1IIII5IE1OBI\Q§Q
II
BB
BI
II
IIÜ
ÜI
••I
eE
2'°
SB*
ää
UIIIIn
•e:
QIn
n:II
Inh
IQO
OU
IIN
NIIN
NIs
,I
IIÜ
ÜO
OIB
IYIIII
INIQ
ab
nee••n••1•?I
IIT
?I
Ih
QB
dIIIIn
nN
NN
NII
II
(Ü
•d
OO
IOII
IQIIU
IÜÜ
ÜQ
3Q
••
•«
••
••
••
••
••
IIIIII
ÜÜ
ÜN
BÜ
QI
•B
••Iu•
äG
IIOO
IIQO
INN
IIN
N•
"2
L',3
g2
22
22
22
22
22
22
2'°
ÜB
9Q
—h
\=Ü
ÜN
NIIIQ
IIIIII
II
n\In
I•
IIÜÜ
IQII
Ilb
·•IIIIII
OO
IQIl
II
sn
IIn
QIIQ
IQÜ
ÜB
IÜÜ
IT=
=/nÜ
ge
l-~
_
II
II
II
II
I(Ü
ÜS
Os
dä•
>••=~•
3I
Isl
•~
Ing
NO
(ÜI
NN
OO
ÜÜ
IIQQ
IIh
h•
Q(
UIII
e"B
BR
1IIIIII
II
ß•
•g
lä
IIn
ne
-IIN
NC
ÜIB
Inn
ISS
!$
S•
-•i
92
29
29
92
99
92
22
8:
I=1Q
Ü_
QIQ
IQI
IQIQ
QC
IQ=
UId
dü
bh
PO
OIIIIÜ
IIIIII
ÜUI
I•
•In
II
1B1¢
nnuuanenIII
•:
;3
**8:
•s
„..:.:.:.;.:..2
.2.;.:.:.:.;.2.:
'•I
In
II
5S
'5
5**
"•-
«••5
Oct
IIII
•IIIU
IÜÜ
NN
NN
NIB
•I•
I•Il•l|I1
1=
SQ
•••••«
••••••
••g
_-
}2:
2Ja
zz:2
3„.
99
22
22
22
22
22
-:2·:·••
anI
nI
Inn
nII
ÜI
III
II
I2I
2I
InI
Ute
Int
IIIIIII
InnnnnnII
nenaä
=Iu
u:u
>IIIIII
OQ
OÜ
ÜO
YO
Q§
gIn
Q•
••
••
••
[e
ag
te
IIn
=II
III
¤I
an.
Innennt
IIIIII
IIIIII
Ia
In••n
nII
RB
NB
ÜB
ÜN
INR
NII
ä•|
l•3S
PQ
>IO
IÜI
IIIIII
II1
SIIII
bg
!••I•
I~I•
I•I•
I•1
8Q
-2•
SS!"
-282-"•"$'3:
$$555252
2-5
:·
-••I
usu
nQ
DIn
••In=
n•n
I~I~
•IIIIIÜ
nIQ
nIIII*.
.
II.
nIIEEI
II
n=
nß
«5
=J
JJ
n.3
ää
IN
IIIIP
DIO
OO
II
PP
‘"-S-.2•I•Z¤¢•I
66-Z-¥«i«SJ6
III;
II|||In•¤
lIIIIII
II
IR
nn
nn
II
II
nn
•__:
_I
II
II
IIIIIN
NIN
ND
GI
~IIII•~
I~=
OII=
=N
Iä
pg
gg
••••••
•-••„•
••
·=
IInn
NI
IInn
••MII
8S
EIE
EI
I•
NN
IINN
II•~•~
•vI
nn
II
IIIIII
NN
IIIIIO
On
nh
I~II
IIIIIII
nn
I•
OO
IIIIn
nIIII
II
SI
nn
IIs
I—
naäI
IIIIIIII
nn
IIIIn
n•\I
SI
•II•~
••I••~
•~IIII
NN
II
IN
NA
RII
IIIIO
III
P3
,•-••••
•„••••
••
I3
*nI
nIIn
nIN
IInn
IYP
PI
InI
II
II
II
II
I°°
JFn°:=
°°•
II
>I
NII:
•zu
I•IIIII
I•III•
•••
•¤•~
II•••~II
•I
III
•I\I\III\n
nIIP
IU
II
II
I•
Bg
uI
IInn
nn
III•n
nII
nn
ZS•-•
iifffif
fiffff
"!"!O
III
OJS
232232$$23-Z'!
-3•
QJ0
•¤••
I-IIn
nn
n•~
•~IIII
IOI
I•
nI
I2
nn
nn
nn
nn
nn
nn
hh
•Q
Q.
t·
IsI
nn
nn
nn
nn
nn
nn
II
U.I
•J
III
3J
III
•IIIIIIII
IIIIUIIN
nn
•I
•~
gg
g—
_Q
••••••
••••••
••Q
nQ
nI
ÜZ
ÖÜ
IID
MIIIO
II
In\
•>
IIIn
n•~
ßIIIO
nn
II
I••
|
gI
__
III!
nn
IIINI
.n
II
nI
•-'
I‘
IJ
••II
•••
I,
IIS·
‘?
••
gig
:2
"''“!
33-.- ·°":•'
II
Nn
umI
IU
zu
IIIIIII
IIIIIIIIIIg
gg
p¤
••
••
•_•
•ß
•&‘
{(
äN
;H
XI
II
II
ll.
*
Inn
IIIIIII
IIII•~•~
I:
.••••n
nII
:n•u
nIn
UIN
INR
NI
">
5-7-°*'•-°
’.*-7*-7%
7*.7*-7*-7*-
3*;-g
S·- ::2ä
-·SS
S::·2::
:2:::::::
Sgz:
,-I¤
IJIO
nIO
••In
InIn
RN
ININ
IIII
IO
DDDDDDIIDQ.
NN\D
D
=n
n=
S3
S=
6•6•
,6P•¤•D *
33
3D
DD
NIIM
OD
Dll
DD
QO
fD
IISvg
äan
••6
aa7?T7
ugE
::77
—
·=
•P
PO
OD
D
_
=N
NN
NN
·
_
•Q
66
66
66
-
,,
,,
nn
NN
III\n
nN
N•III
nn
••g
DIl
tlnn
g0
00
DD
DU
sB
•O
OP
PIb
IIIIINN
L•
nn
qI
II\IIO
t==
I·••
DD
Q2
'·*2
::1:::
2,5
°'2
**22=
gé
DD
DD
DD
én
en
nn
niO
D-
“•
LL
II
P(
DU
DD
DÜ
ÜD
U.6
63.6
Q3
•Q6.6666
S3-
333333Q
3-
3333D
DQ
IIDam
DD
DD
DD
gl
PP
DD
·
-56
66
66
6J
g6
66
66
6J
gb,,,,
~P
IL
nIIN
NU
IUI
IL
nIIIIN
NI
Ln
nn
II
DP
ND
PD
IIII
DIII!
D•¤
••I|I°°
33
Gag°°
"'*
D•
IP8
ID
=D
•6
6P
O(Ü
DN
NP
PD
D:
E„.···
g,5
2:::::··
2::25:5
g2
*2**·
DB
•D
DD
DD
D•
•¤•¤DD
DD
•g
e
5Q
:.66.33
"666666
ä‘
6666663
‘6666
‘D
NN
NN
DD
:·
;:.,:.2
3::::::
·· JE255äE:
E-Ԥ"""
\||_
Q•••••6
Q6
66
66
6Q
66
66
ilg’
UP
LL
nn
nn
nn
LL
nn
nn
nn
LL
nn
nn
D•
'~
‘'°
°•€••••••••
••°°
°°•
Jn
n
35
3’s-'ää
QS
F333333
Q3
333333Q
3:333
=
PI\(Il
P6
66
66
6p
66
66
66
p6
66
6••
•-•¤•I
L
=:;:6
.6
Q"3
33
36
6Q
**33
33
66
{**3
33
.35
53
33
”33
33
333
=•
6••¤•P
Illl!
.n
nS
UN
nn
·a
llÜ;
Dd
DD
DD
DD
DD
DD
DD
DD
DD
,-6B
UIIIID
all
8D
_D
DD
DO
OD
DD
DD
DD
D(
ZD
DD
D_—
OO
IIDD
U•|
Pll
66
66
66
66
..2„
..Q
53
BPP:63
6S
"636563
3S
"636563
3S
"6365
••Pn
UIn
Ua
nu
nn
nI
•¤•ll
DD
DD
DI
nll
Qn
un
ulI
II
TIQ
I2
E·· ::22
-22
2::-2::
22
::-2::Q
22
::•·‘‘
nD
UP
P(
llnxn
fnP
P
N000_
0l•0G0Q.
0SNQ3
22
-3
35
_B
«•«•
-•_
d
*ä
55
EY
'!'£"!'€'!"!!
'QN
YYYY$911%
%a
nd
RU
IOO
00
00
00
hh«••¤•I
II
II
I•¤l•¤•I
II
II!
NQ
00
00
00
h0
GII
NU
nu
tte
nC
IOC
ÜB
¤••••I••••••¤
•
0O
lhh
dl
llüß
hlh
hO
UIIH
IIGe
g0
00
00
0IO
•¤••¤¤NNN
NO
OQ
Q.
'I.
'2'€"!'!'t't!'!€
'!'t't!€
""¢'!"!
=0
0•••¤
•¢O
•lN
NO
OO
ON
IIOO
OO
hh
UID
IIGIIO
OIO
ON
N••¤
•III|¢¢
Rh
f••¤••¤¤¤••¤•••f••N
•=•••••••~
hO
f
·
I!I|•••¤•Q
O0
00
Hd
d8
88
80
0O
INN
UIG
N8
8‘
3"‘
20
0Q
OQ
QB
G0
00
00
00
3I•N
N•=
0I:
I••~I~
•Q•
00
00
00
•0
00
00
•0
•••¤••••¤
••¤•
•¤•l\I••••¤
•¤•
•¤•v•••¤
••¤•
ang
eO
IQO
QO
IQQ
O0
00
00
0
ä0
00
00
00
0=
00
00
00
=0
00
00
0=
00
00
00
00
UIM
IIIIQS
00
00
00
an·„:.·:
2.::::::E
sass:.ä
:::2::ä
00
NN
NN
NH
•¤••¤••¤••¤••¤••¤••·••¤
•~I••N
NQ
••
••••••
••••••
••••••
Ü0
0Q
ää
iäé
Qä
äd
äi0
”0
N0
••
=an
00
00
00
80
DD
¢••••
0O
OU
CN
N0
038
3R
••
••••••••••••\•~
~G
O•••|••
•n
nu
uu
u~
••
g•«
•••••••
•·
••••••
•_
•••«
••
•~
Qä
00
O0
00
00
0Q
00
00
00
I0
00
00
0(
•8
8••I•I••
••u
gO
IOO
NQ
?_;
Illn
zn
kg
00
0•¤•
00
00
OO
OO
UIO
O
2$2
T··
7?
•a
nN
:an
uu
••M
Md
ä2
:N
hlg
gzü
=I•I8
8.
ES
l8
80
0
=~
88
22
00
-O
Oh
hllß
äü
'•~sl•I\0
HIIU
IUIII
IbO
OO
OU
IIIOO
IIII
ll•Z
6•I
'ä
6•Z
•I°
°•I
•!°'
°C
Q•O
||IIh=
IOI\I•
h=
—•O
I|I\h=
_
an
nu
nh
su
n•••••••~u~••
nu
lu
su
1l
I.I,
I7I
I.N
sn
ON
•¤••¤
•I••\
•N•••¤
••••\
•N•·••¤
•l\•s
OO
•OIIII!|•~
anQ
OIIIII••~
anO
fhllllh
•¤•O
l!I~N
DN
ON
ON
ND
NO
NO
BN
IRO
NO
•00000L
-00NN\
00
03
““
3ä
II3
3‘
30=
SS
SN
00
NN
00
NN
00
00
00
Q••••••
••••••
••
•ug
33333333233*
330
RLII II
III?00
I-Ä
•¤•
·
IQ
•0
00
00
00
00
00
00
00
•Ile
NN
00
00
00
00
00
-00
Qg
••••••
••••••
••
00NN
NN
003
2Q
8E
‘N
N0
0sL
.00
0••0
0••
00
00
NN
NN
•"
5't'°""Y
'€"!"2
"!"'“'tN
'!'
==
i0
00
00
0N
N0
00
0"
2•
LI
h0
NN
00
00
«•
•23333•••3
$3
«3•
g8
A2;..:1-
'!'!'I'I"!'!111111
11•·
00
L0
0N
N0
00
0=
zé
—=
77
II
l TIT
•¤•N
III0
LS
•>
l•3N
N•
UI
Q0
>=
00
N0
00
00
00
00
00
00
NN
0II
II•
00
00
00
00
00
00
00
0I
••••-••••••~|•••••••¤•
••
enan
g_
i0
00
00
00
00
00
0N
N•
••
••
••
••
••
•§
=•!L
00
00
00
00
00
00
00
00
=l!
0U
zls
•=••••••!=
0•••0
0nun
I•
•~l!
e•••••
~••••¤•¤•
¤••¤•0
••0
••U•••-
00
00
00
••••••••
•••¤••l
07
=\s
••¤••¤••¤••¤••¤•0
NN
NN
NN
00
J=
¥sätn-
¤L
000000000000
00
0~
••.
0I
IIN
-=00•~•~00
00
0N
0=
0ll!
•0
00
00
00
00
00
0•
0•
Qyg
gg
g••••••
••••••
••g
gg
ä~
0a
z!-0
i0
00
00
00
00
00
00
00
0•
N0
00
Ina
\0
_0
00
00
0·
00
00
00
00
0*
hh
00
00
00
00
00
00
00
=
_0
00
00
00
0N
N0
=•
gi
3=
2=
==*
·?•
0IIN
N4
"is"
••>
.$3
nä-•
"'¢'•I
)N
{0
00
00
0N
=2§N
I-0
0—
:00
00
00
LL
80
03
*N
I:N
0=
S0
00
00
0I~
s00
00
00
l-0;
ä=
SU
B·_
E0
00
00
00
00
00
00
0.•
•¤•„
L•
§*•<
!.•~s••••
SS
SS
SS
inn
.-0
00
00
I0
00
00
00
00
00
0I•~
•-0
0II
=•¤•N•¤•0•¤•0N
ON
•~NI0
el
•I-Iä
h>
IOIO
I0
IOIO
IIl
00
:>0
l!I•
I•l•
I•l•
l•I•
=•!8
I-g
„"
ZS"'
„333*333
3$¤'•S•'22E:
•-‘.!Q
·
—l-
00
I-I
00
00
00
•~NO
NO
NI0
02
0
The vita has been removed fromthe scanned document