Multiple Wavelength Geodesy
*
Judah Levine
Time and Frequency Division, National Bureau of Standards
Boulder, Colorado 80302
Abstract. W
e are c o n s t r u c t i n g an apparatus
which s h o u l d b e a b l e t o measure b a s e l i n e s up t o
50 km l o n g w i t h a f r a c t i o n a l u n c e r t a i n t y o f a b o u t
5x
The instrument w i l l measure b o t h t h e
o p t i c a l l e n g t h a n d t h e r e q u i r e d c o r r e c t i o n due
t o t h e r e f r a c t i v i t y of t h e atmosphere u s i n g
t h r e e wavelengths t r a n s m i t t e d i n one d i r e c t i o n
o v e r t h e p a t h t o a n a c t i v e r e c e i v e r . The t h r e e
wavelengths a r e 632.8 nm, 441.6 nm and 3 . 7 cm.
The two e n d p o i n t i n s t r u m e n t s a r e s y n c h r o n i z e d
u s i n g s u b s i d i a r y r e t u r n t r a n s m i s s i o n s a t 632.8
nm and a n o t h e r t e l e m e t r y s i g n a l . The one-way
n a t u r e of t h e s y s t e m a l l o w s a n i n c r e a s e i n r a n g e
over e x i s t i n g round-trip systems.
G e o d e t i c measurements have i m p o r t a n t b e a r i n g
on many areas of t e c t o n o p h y s i c s such a s p l a t e
In particut e c t o n i c s and e a r t h q u a k e p r o c e s s e s .
l a r p r e c i s e g e o d e t i c measurements a r e needed t o
u n d e r s t a n d how s t r a i n f i e l d s n e a r p l a t e boundar i e s change w i t h t i m e and why t h e r e a r e stresses
i n t h e i n t e r i o r s o f p l a t e s l a r g e enough t o c a u s e
i s o l a t e d zones of s e i s m i c i t y .
These q u e s t i o n s are b e i n g a d d r e s s e d u s i n g
f i x e d g e o p h y s i c a l i n s t r u m e n t s and p o r t a b l e
i n s t r u m e n t s . Although one i n s t r u m e n t might b e
used f o r a l l g e o d e t i c measurements, there may
b e some a d v a n t a g e t o c o n s i d e r i n g d i f f e r e n t t e c h n i q u e s f o r t h e p o r t a b l e and f i x e d measurement
programs.
I n t h e c a s e o f a permanent o b s e r v a t o r y ,
w e i g h t and s i z e a r e second o r d e r c o n s i d e r a t i o n s ,
and emphasis s h o u l d b e p l a c e d on a c c u r a c y and
sensitivity.
B e r g e r and L e v i n e (1974) h a v e e s t i m a t e d t h e
power spectrum o f t h e random f l u c t u a t i o n s i n
s t r a i n o v e r a wide f r e q u e n c y r a n g e . They conc l u d e d t h a t t h e power spectrum i s i n v e r s e l y prop o r t i o n a l t o t h e s q u a r e of t h e f r e q u e n c y , and
t h a t t h e power a t 1 Hz i s a p p r o x i m a t e l y 8 x
(AL/L)2 / ~ ~ .
The i m p o r t a n t p o i n t i s t h a t t h e y used two
v e r y d i f f e r e n t i n s t r u m e n t s l o c a t e d 2000 km a p a r t
i n v e r y d i f f e r e n t g e o l o g i e s . The two s p e c t r a a r e
e s s e n t i a l l y i d e n t i c a l i n s p i t e of t h e s e d i f f e r ences. T h i s suggests t h a t b o t h instruments a r e
l i m i t e d by t h e same p r o c e s s e s w i t h i n t h e e a r t h
and t h a t t h e i r power s p e c t r a r e p r e s e n t a lower
bound t o what might b e o b t a i n e d u s i n g o t h e r t e c h niques.
T h e i r r e s u l t s do n o t s u p p o r t t h e widely-held
b e l i e f s that i n s t a l l a t i o n s i n m i n e s o r tunnels
p r e s e n t i n s u p e r a b l e problems and t h a t l o n g (800
m e t e r ) b a s e l i n e s are a p r i o r i b e t t e r t h a n s h o r t e r
(30 m e t e r ) ones. The i n s t r u m e n t s a p p e a r t o b e
l i m i t e d by p i e r t i l t , l o c a l e f f e c t s , a n d , pos"Fellow, J o i n t I n s t i t u t e f o r L a b o r a t o r y Astrop h y s i c s o f t h e N a t i o n a l Bureau of S t a n d a r d s and
t h e U n i v e r s i t y of Colorado.
Proc. of the 9th GEOP Conference, AII liileriiiitiuiid .Sviiipu>iiiin 011 rhr Applicoriaiis of
Giwdrs! roCeo~l?~iamic*.
OcrobrrZ-5. 1978. Dept. ofGeodetic Science Rept. No. 28O.The
Ohio State Univ.. Columbus. Ohio 43210.
s i b l y , by d r i f t i n t h e wavelength s t a b i l i z e r .
These a r e c o r r e c t a b l e , a t least i n p r i n c i p l e , s o
t h a t i t i s n o t unreasonable t o expect t h a t a
c a r e f u l l y d e s i g n e d i n s t r u m e n t o f moderate l e n g t h
(of o r d e r 100 m e t e r s ) c o u l d b e i n s t a l l e d a meter
o r two below ground l e v e l , and t h a t such a n i n s t r u m e n t would b e l i m i t e d by e a r t h n o i s e f o r
p e r i o d s s h o r t e r t h a n a few y e a r s .
Furthermore,
r e a d o u t schemes a r e p o s s i b l e which would o b v i a t e
t h e need t o o p e r a t e t h e i n s t r u m e n t c o n t i n u o u s l y .
A strainmeter o f t h i s t y p e would have o n l y
two weaknesses. F i r s t , i t would be i m p r a c t i c a l
t o move t o a new s i t e s i n c e a s i g n i f i c a n t f r a c t i o n of t h e c o s t o f t h e system comes from s i t e
p r e p a r a t i o n and i n s t a l l a t i o n . Second, i t might
b e i n f l u e n c e d by l o c a l e f f e c t s s u c h as t i l t i n g
of t h e p i e r s o r s h e a r s w i t h i n t h e ground i n t h e
immediate v i c i n i t y o f t h e p i e r s .
These l o c a l e f f e c t s were n o t a problem i n t h e
Poorman Mine b e c a u s e i t w a s a hard-rock s i t e f a r
below ground l e v e l , b u t i t i s p o s s i b l e t h a t t h e y
w i l l b e t h e dominant problem a t s u r f a c e ( o r n e a r
s u r f a c e ) s i t e s even i f t h e material appears t o
b e competent.
B e r g e r h a s s t u d i e d t h e s e problems e x t e n s i v e l y
a t t h e Pilion F l a t O b s e r v a t o r y . H e f i n d s s i g n i f i c a n t c o r r e l a t i o n s between r a i n f a l l and
changes i n s t r a i n r a t e and a n anomalous s h e a r
i n t h e t o p few meters o f t h e ground u n d e r t h e
p i e r (Berger, 1978). He concludes t h a t t h e
o n l y way t o d e a l w i t h t h i s problem i s t o r e f e r e n c e t h e e n d p o i n t s t o d e e p e r , presumably more
s t a b l e , rock.
These s o r t s o f d i f f i c u l t i e s w i l l l i m i t m e a s u r e m e n t s made w i t h i n s t r u m e n t s o f any l e n g t h .
Anomalous p i e r m o t i o n s o n t h e o r d e r of m i l l i meters r e p r e s e n t f r a c t i o n a l changes of p a r t s i n
l o 8 even o v e r 50 km b a s e l i n e s , s o t h a t s u c h e f f e c t s w i l l make s i g n i f i c a n t c o n t r i b u t i o n s t o t h e
e r r o r budget of any i n s t r u m e n t now i n o p e r a t i o n
o r under c o n s t r u c t i o n . It i s v e r y i m p o r t a n t t h a t
t h e s e e f f e c t s b e s t u d i e d i n d e t a i l . It would b e
e s p e c i a l l y u s e f u l t o compare measurements made
i n t h e same area by i n s t r u m e n t s u s i n g v e r y d i f ferent length baselines.
Laser strainmeters are c l e a r l y u n s u i t a b l e i f
t h e i n s t r u m e n t must b e p o r t a b l e . I n t h i s case
we must u s e a n i n s t r u m e n t c a p a b l e of m e a s u r i n g
d i s t a n c e s t h r o u g h t h e atmosphere. T h e r e are
many i n s t r u m e n t s which have been d e s i g n e d t o
perform s u c h measurements ( S l a t e r and H u g g e t t ,
1976). S i n c e a l l s u c h i n s t r u m e n t s e f f e c t i v e l y
measure t h e t r a n s i t t i m e f o r some e l e c t r o m a g n e t i c
s i g n a l , i t i s n e c e s s a r y t o know t h e a c t u a l speed
of l i g h t i n t h e atmosphere i n o r d e r t o d e r i v e t h e
distance.
The r e f r a c t i v i t y ( t h e d e v i a t i o n of t h e i n d e x
of r e f r a c t i o n from u n i t y ) o f t h e atmosphere i s
about 3 x
f o r v i s i b l e wavelengths. Since i t
i s d e s i r a b l e t o measure d i s t a n c e s w i t h a f r a c t i o n a l u n c e r t a i n t y o f l e s s t h a n 1x l o V 7 , t h e
a t m o s p h e r i c c o r r e c t i o n i s v e r y i m p o r t a n t . The
r e f r a c t i v i t y i s a f u n c t i o n of a t m o s p h e r i c t e m -
p e r a t u r e , p r e s s u r e and humidity s o t h a t making
the corrections using meteorological data is
cumbersome b u t p o s s i b l e . For optimum r e s u l t s
t h e atmosphere must b e sampled a l o n g t h e p a t h ,
u s u a l l y u s i n g s e n s o r s c a r r i e d by a n a i r p l a n e
(Savage and P r e s c o t t , 1973).
Methods which d e t e r m i n e t h e r e f r a c t i v i t y of
t h e atmosphere by measuring i t s d i s p e r s i o n ( i . e . ,
t h e a p p a r e n t d i f f e r e n c e i n d i s t a n c e between measurements made u s i n g d i f f e r e n t wavelengths) have
been proposed f o r some y e a r s (Bender and Owens,
1965).
The u s e of two o p t i c a l w a v e l e n g t h s , f o r example, e n a b l e s one t o d e t e r m i n e t h e d r y - a i r cont r i b u t i o n t o t h e r e f r a c t i v i t y , b u t does n o t c o r rect f o r t h e r e f r a c t i v i t y due t o water v a p o r ,
s i n c e t h e r e f r a c t i v i t y of water vapor i s almost
n o n - d i s p e r s i v e a c r o s s t h e v i s i b l e spectrum. The
a d d i t i o n of a t h i r d measurement a t a microwave
frequency allows n e a r l y p e r f e c t d e t e r m i n a t i o n of
t h e i n d e x e x c e p t f o r a small term which can a l most always be determined u s i n g t e m p e r a t u r e measurements a t t h e e n d p o i n t s . An a n a l y s i s by
Thayer (1967) of such a three-wavelength system
s u g g e s t s t h a t b a s e l i n e s up t o 50 km l o n g could
b e measured w i t h f r a c t i o n a l u n c e r t a i n t i e s of
3x
and t h a t t h e main l i m i t a t i o n on t h e
a c c u r a c y o f such a measurement would come from
t h e d i f f e r e n c e i n t h e p a t h s t r a v e r s e d by t h e two
o p t i c a l wavelengths due t o t h e v e r t i c a l g r a d i e n t
i n t h e r e f r a c t i v i t y of t h e atmosphere.
I n s t r u m e n t s which measure t h e r e f r a c t i v i t y of
t h e atmosphere u s i n g m u l t i p l e wavelength methods
have been d e s c r i b e d by S l a t e r and Huggett (1976)
and by o t h e r s (Wood, 1971). The one shortcoming
o f t h e s e i n s t r u m e n t s i s t h a t t h e y can measure
o n l y r a t h e r s h o r t b a s e l i n e s ( u p t o 1 5 k m ) . These
i n s t r u m e n t s a r e l i m i t e d by s p r e a d i n g a n d a t t e n u a t i o n of t h e beam i n t h e atmosphere and by a n
i n a b i l i t y t o t o t a l l y d i s t i n g u i s h between a true
r e t u r n s i g n a l and l i g h t s c a t t e r e d backwards from
t h e e x i t o p t i c s of the transmitter.
I f t h e s e systems are c o n v e r t e d t o one-way
o p e r a t i o n by r e p l a c i n g t h e r e t r o r e f l e c t o r by a n
a c t i v e r e c e i v e r and a second t r a n s m i t t e r , t h e n a
l a r g e increase i n returned s i g n a l w i l l r e s u l t .
The i n c r e a s e i n r a n g e r e a l i z e d by c o n v e r s i o n t o
one-way o p e r a t i o n i s a t l e a s t a f a c t o r of two
( i f t h e signal-to-noise r a t i o is limited prim a r i l y by a t t e n u a t i o n ) and may b e c o n s i d e r a b l y
more t h a n t h a t .
The s i m p l i f i e d s c h e m a t i c diagram of such a n
i n s t r u m e n t i s shown i n F i g u r e 1. L i g h t from t h e
s o u r c e i s s e n t through t h e l o c a l m o d u l a t o r , trav e r s e s t h e p a t h , and t h e n goes t h r o u g h t h e f a r end modulator b e f o r e d e t e c t i o n . A f t e r b e i n g
twice modulated t h e l i g h t a t t h e d e t e c t o r w i l l
show v a r i a t i o n a t t h e d i f f e r e n c e frequency
f b = f l - f 2 ( t h e o t h e r , h i g h e r , f r e q u e n c y components are n o t d e t e c t a b l e ) . I f two d i f f e r e n t
o p t i c a l wavelengths are s e n t t h r o u g h t h e system
s i m u l t a n e o u s l y , t h e two s i g n a l s a t t h e f a r end
w i l l show a phase d i f f e r e n c e p r o p o r t i o n a l t o t h e
If a third light
r e f r a c t i v i t y o f t h e atmosphere.
s o u r c e s e n d s l i g h t backwards t h r o u g h t h e system,
i t w i l l a r r i v e a t t h e o r i g i n a l end w i t h a phase
proportional t o t h e t r a n s i t t i m e along t h e path
and t h e v a r i o u s o s c i l l a t o r o f f s e t s . I f a second a r y l i n k i s used t o t r a n s m i t s y n c h r o n i z i n g i n f o r m a t i o n between t h e two ends t h e n b o t h t h e
d i s p e r s i o n and t h e d i s t a n c e may b e determined.
T h i s l i n k i s most c o n v e n i e n t l y done u s i n g a
microwave c a r r i e r , i n which case t h e phase s h i f t
of t h e microwave c a r r i e r p r o v i d e s i n f o r m a t i o n
47~fZD
1
C'
Fig. 1. P r i n c i p l e o f two-way o p t i c a l d i s t a n c e
measurement. Note t h a t t h e measured phase depends o n l y on t h e frequency of t h e o s c i l l a t o r a t
t h e end where t h e measurements are made.
100
I t is p o s s i b l e t o u s e t h e p r i n c i p l e s of t h e
m u l t i p l e wavelength system t o c o n s t r u c t a t h r e e
wavelength r e f r a c t o m e t e r . Such a n i n s t r u m e n t
would measure t h e i n d e x of r e f r a c t i o n of t h e
p a t h b u t would n o t measure t h e d i s t a n c e .
Although such an i n s t r u m e n t would u s e e s s e n t i a l l y t h e same hardware a s t h e distance-meas u r i n g i n s t r u m e n t , t h e e l e c t r o n i c s a r e measurably
s i m p l e r and no r e t u r n t r a n s m i s s i o n s a r e n e c e s s a r y .
Such a n i n s t r u m e n t m i g h t p r o v e u s e f u l as a n
adjunct t o e x i s t i n g geodetic instruments.
T h i s work i s s u p p o r t e d i n p a r t by NASA Grant
No. NSG-7344 through t h e U n i v e r s i t y o f Colorado.
a b o u t t h e c o n t r i b u t i o n of a t m o s p h e r i c w a t e r
vapor t o t h e r e f r a c t i v i t y .
F i g u r e 2 shows a b l o c k diagram o f t h e complete
i n s t r u m e n t . The d i s p e r s i o n measurements are made
u s i n g 441.6 nm, 632.8 nm and 8 . 1 GHz. The r e d
(632.8 nm) s i g n a l i s s e n t back a l o n g t h e p a t h f o r
t h e d i s t a n c e measurement.
F i g u r e 3 shows t h e c a l c u l a t e d r a n g e o f t h e
i n s t r u m e n t , and compares i t w i t h a r e t r o r e f l e c t i n g i n s t r u m e n t u s i n g s i m i l a r technology. The
lower t h r e e c u r v e s a r e f o r t h e r e t r o r e f l e c t i n g
i n s t r u m e n t and t h e upper o n e s f o r t h e two-way
d e s i g n . Both s y s t e m s a r e assumed t o u s e 5 mW
lasers w i t h 1%o v e r a l l d e t e c t i o n e f f i c i e n c y .
The r a n g e i s d e f i n e d t o b e t h e d i s t a n c e a t which
s h o t n o i s e l i m i t a t i o n s a l l o w a measurement w i t h
a n u n c e r t a i n t y a t 1x lo-* i n 10 s e c o n d s . We
f e e l t h a t an a n g u l a r beam s p r e a d o f 1 0 a r c s e c onds i s p r o b a b l y r e a l i s t i c f o r a t y p i c a l atmosphere.
An i n s t r u m e n t d e s i g n e d a c c o r d i n g t o t h e s e
p r i n c i p l e s i s c u r r e n t l y under c o n s t r u c t i o n . T h i s
i n s t r u m e n t c a n b e e a s i l y broken down i n t o p i e c e s ,
t h e h e a v i e s t o f which weighs a b o u t 60 kg s o t h a t
i t c a n b e assembled by two p e o p l e a t any l o c a t i o n
a c c e s s i b l e by a four-wheel d r i v e v e h i c l e o r a
helicopter.
VHF
References
Bender, P.L. and J.C. O w e m , C o r r e c t i o n of o p t i c a l d i s t a n c e measurements f o r t h e f l u c t u a t i n g
a t m o s p h e r i c i n d e x of r e f r a c t i o n , J. Geophys.
Res.,
2 4 6 1 - 2 , 1965.
B e r g e r , J . , p r i v a t e communication, 1978.
B e r g e r , J. and J . L e v i n e , The s p e c t r u m o f e a r t h
s t r a i n from
t o l o 2 Hz, J. Geophys. Res.,
79, 1210-4, 1974.
E,
I
3E>
8.1 GHz
3E
3€
4
2.7 GHz
cPrb
+tL
E
4416
63288,
6320A E
E
\
H
~=1220.70
Hz
50 km
Fig. 2 . Block diagram o f t h e p r o t o t y p e system.
"UHF" i s a low bandwidth t e l e m e t r y c h a n n e l . The
v a r i o u s p h a s e measurements are i d e n t i f i e d w i t h
s u b s c r i p t s r f o r r e d (632.8 nm), b f o r b l u e
(441.6 nm) and 11 f o r microwave ( 8 . 1 GHz).
101
Visibility
20
50 35
10
I
I I
Savage, J.C. and W.H. Prescott, Precision of geodolite distance measurements for determining
fault movements, J. Geophys. Res., 78, 6001-8,
1973.
Slater, C.R. and G.R. Huggett, A multiwavelength
distance measuring instrument for geophysical
experiments, J. Geophys. Res., E, 6299-6305,
1976.
Thayer, G.C., Atmospheric effects of multiple
frequency range measurements, Technical Report
IER 56-ITSA 53, Environmental Science Services
Administration, Rockville, MD, 1967.
Wood, L.E., Progress in electronic surveying,
U. S. National Report, E , 52, IUGG17-21,
1971.
(km)
I
100
\
90
80
70
60
E
Y
v
& 50
'
c
40
30
20
~
'0
0.1
0.2
0.3
0.4
0.5
0.6
Attenuation (km'l)
Fig. 3. Calculated range of one-way (upper
curves) and retroreflector EDM instruments as a
function of optical beam spread and atmospheric
attenuation.