An apparatus is being constructed which should be able to measure baselines up to 50 km long with a fractional uncertainty of about 5 x 10 to the -8 power. The instrument will measure both the optical length and the required correction due to the refractivity of the atmosphere, using three wavelengths transmitted in one direction over the path to an active receiver. The three wavelengths are 632.8 nm, 441.6 nm and 3.7 cm. The two endpoint instruments are synchronized using subsidiary return transmissions at 632.8 nm and another telemetry signal. The one-way nature of the system allows an increase in range over existing round-trip systems

Levine, J.

English

NASA Technical Reports Server

Multiple Wavelength Geodesy
Judah Levine *
Time and Frequency Division, National Bureau of Standards
Boulder, Colorado 80302
N79 21474
Abstract. We are constructing an apparatus
which should be able to measure baselines up to
50 km long with a fractional uncertainty of about
5 xiCT8. The instrument will measure both the
optical length and the required correction due
to the refractivity of the atmosphere using
three wavelengths transmitted in one direction
over the path to an active receiver. The three
wavelengths are 632.8 nm, 441.6 nm and 3.7 cm.
The two endpoint instruments are synchronized
using subsidiary return transmissions at 632.8
nm and another telemetry signal. The one-way
nature of the system allows an increase in range
over existing round-trip systems.
Geodetic measurements have important bearing
on many areas of tectonophysics such as plate
tectonics and earthquake processes. In particu-
lar precise geodetic measurements are needed to
understand how strain fields near plate bounda-
ries change with time and why there are stresses
in the interiors of plates large enough to cause
isolated zones of seismicity.
These questions are being addressed using
fixed geophysical instruments and portable
instruments. Although one instrument might be
used for all geodetic measurements, there may
be some advantage to considering different tech-
niques for the portable and fixed measurement
programs.
In the case of a permanent observatory,
weight and size are second order considerations,
and emphasis should be placed .on accuracy and
sensitivity.
Berger and Levine (1974) have estimated the
power spectrum of the random fluctuations in
strain over a wide frequency range. They con-
cluded that the power spectrum is inversely pro-
portional to the square of the frequency, and
that the power at 1 Hz is approximately 8 x10~28
(AL/L)2/Hz.
The important point is that they used two
very different instruments located 2000 km apart
in very different geologies. The two spectra are
essentially identical in spite of these differ-
ences. This suggests that both instruments are
limited by the same processes within 'the earth
and that their power spectra represent a lower
bound to what might be obtained using other tech-
niques .
Their results do not support the widely-held
beliefs that installations in mines or tunnels
present insuperable problems and that long (800
meter) baselines are a priori- better than shorter
(30 meter) ones. The instruments appear to be
limited by pier tilt, local effects, and, pos-
Fellow, Joint Institute for Laboratory Astro-
physics of the National Bureau of Standards and
the University of Colorado.
Proc. of the 9th GEOP Conference, An International Symposium an the Applications of
GeoJesv la Ceajviiamics. October 2-5.1978. Dept. of Geodetic Science Kept. No. 280. The
Ohio State Univ.. Columbus. Ohio 43210.
sibly, by drift in the wavelength stabilizer.
These are correctable, at least in principle, so
that it is not unreasonable to expect that a
carefully designed instrument of moderate length
(of order 100 meters) could be installed a meter
or two below ground level, and that such an in-
strument would be limited by earth noise for
periods shorter than a few years. Furthermore,
readout schemes are possible which would obviate
the need to operate the instrument continuously.
A strainmeter of this type would have only
two weaknesses. First, it would be impractical
to move to a new site since a significant frac-
tion of the cost of the system comes from site
preparation and installation. Second, it might
be influenced by local effects such as tilting
of the piers or shears within the ground in the
immediate vicinity of the piers.
These local effects were not a problem in the
Poorman Mine because it was a hard-rock site far
below ground level, but it is possible that they
will be the dominant problem at surface (or near
surface) sites even if the material appears to
be competent.
Berger.has studied these problems extensively
at the Pinon Flat Observatory. He finds sig-
nificant correlations between rainfall and
changes in strain rate and an anomalous shear
in the top few meters of the ground under the
pier (Berger, 1978). He concludes that the
only way to deal with this problem is to refer-
ence 'the endpoints to deeper, presumably more
stable, rock.
These sorts of difficulties will limit mea-
surements made with instruments of any length.
Anomalous pier motions on the order of milli-
meters represent fractional changes of parts in
108 even over 50 km baselines, so that such ef-
fects will make significant contributions to the
error budget of any instrument now in operation
or under construction. It is very important that
these effects be studied in detail. It would be
especially useful to compare measurements made
in the same area by instruments using very dif-
ferent length baselines.
Laser strainmeters are clearly unsuitable if
the instrument must be portable. In this case
we must use an instrument capable of measuring
distances through the atmosphere. There are
many instruments which have b'een designed to
perform such measurements (Slater and Huggett,
1976). Since all such instruments effectively
measure the transit time for some electromagnetic
signal, it is necessary to know the actual speed
of light in the atmosphere in order to derive the
distance.
The refractivity (the deviation of the index
.of refraction from unity) of the atmosphere is
about 3 x 10"1* for visible wavelengths. Since it
is desirable to measure distances with a frac-
tional uncertainty of less than IxiO"7, the
atmospheric correction is very important. The
refractivity is a function of atmospheric tern-
99
https://ntrs.nasa.gov/search.jsp?R=19790013303 2020-03-22T00:00:04+00:00Z
-V'
perature, pressure and'humidity so that making
the corrections using meteorological data is
cumbersome but possible. For optimum results
the atmosphere must be sampled along the path,
usually using sensors carried by an airplane
(Savage and Prescott, 1973).
Methods which determine the refractivity of
the atmosphere by measuring its dispersion (i.e.,
the apparent difference in distance between mea-
surements made using different wavelengths) have
been proposed for some years (Bender and Owens,
1965).
The use of two optical wavelengths, for ex-
ample, enables one to determine the dry-air con-
tribution to the refractivity, but does not cor- •
rect for the refractivity due to water vapor,
since the refractivity-of water vapor is almost
non-dispersive across the visible spectrum. The
addition of a third measurement at a microwave
frequency allows nearly perfect determination of
the index except for a small term which can al-
most always be determined using temperature mea-
surements at the endpoints. An analysis by
Thayer (1967) of such a three-wavelength system
suggests that baselines up to 50 km long could
be measured with fractional uncertainties of
3xlO~8, and that the main limitation on the
accuracy of such a measurement would come from
the difference in the paths traversed by the two
optical wavelengths due to the vertical gradient
in the refractivity of the atmosphere.
Instruments which measure the refractivity of
the atmosphere using multiple wavelength methods
have been described by Slater and Huggett (1976)
and by others (Wood, 1971). The one shortcoming
of these instruments is that they can measure
only rather short baselines (up to 15 km). These
instruments are limited by spreading and attenua-
tion of the beam in the atmosphere and by an
inability to totally distinguish between a true .
return signal and light scattered backwards from
the exit optics of the transmitter.
If these systems are converted to one-way
operation by replacing the retroreflector by an
active receiver and a second transmitter, then a
large increase in returned signal will result.
The increase in range realized by conversion to
one-way operation is at least a factor of two
(if the signal-to-noise ratio is limited pri-
marily by attenuation) and may be considerably
more than that.
The simplified schematic diagram of such an
instrument is shown in Figure 1. Light from the
source is sent through the local modulator, tra-
verses the path, and then goes, through the far-
end modulator before detection. After being
twice modulated the light at the detector will
show variation at the difference frequency
ft, = fi - f'2 (the other, higher, frequency com-
ponents are not detectable). If two different
optical wavelengths are sent through the system
simultaneously, the two signals at the far end
will show a phase difference proportional to the
refractivity of the atmosphere. If a third light
source sends light backwards through the system,
it will arrive at the original end with a phase
proportional to the transit time along the path
and the various oscillator offsets. If a secon-
dary link is used to transmit synchronising in-
formation between the two ends then both the
dispersion and the distance may"be determined.
This link is most conveniently done using a
microwave carrier, in which case the phase-shift
of the microwave carrier provides information
Modulator
D
-*«•
4?rf2D
c1
Fig. 1. Principle of two-way optical distance
measurement. Note that the measured phase de- :
pends only on the frequency of the oscillator at
the end where the measurements are made.
100
about the contribution of atmospheric water
vapor to the refractivity.
Figure 2 shows a block diagram of the complete
instrument. The dispersion measurements are made
using 441.6 nm, 632.8 nm and 8.1 GHz. The red
(632.8 nm) signal is sent back along the path for
the distance measurement.
Figure 3 shows the calculated range of the
instrument, and compares it with a retroreflect-
ing instrument using similar technology. The
lower three curves are for the retroreflecting
instrument and the upper ones for the two-way
design. Both systems are assumed to use 5 mW
lasers with 1% overall detection efficiency.
The range is defined to be the distance at which
shot noise limitations allow a measurement with
an uncertainty at 1x10~8 in 10 seconds. We
feel that an angular beam spread of 10 arcsec-
onds is probably realistic for a typical atmo-
sphere. .
An instrument designed according to these
principles is currently under construction. This
instrument can be easily broken down into pieces,
the heaviest of which weighs about 60 kg so that
it can be assembled by two people at.any location
accessible by a four-wheel drive vehicle or a
helicopter.
It is possible to use the principles of the
multiple wavelength system to construct a three
wavelength refractometer. Such an instrument
would measure the index of refraction of the
path but would not measure the distance.
Although such an instrument would use essen-
tially the same hardware as the distance-mea-
suring instrument, the electronics are measurably
simpler and no return transmissions, are necessary.
Such an instrument might prove useful as an
adjunct to existing geodetic instruments.
This work is supported in part by NASA Grant
No. NSG-7344 through the University of Colorado.
References
Bender, P.L. and.J.C...-Owens, Correction of opti-
cal distance measurements for the fluctuating
atmospheric index of refraction, J. Geophys.
Res.. JO, 2461-2, 1965.
Berger, J., private communication, 1978.
Berger, J. and J.^Levine, The spectrum of earth
strain from 10~8 to 102 Hz, J. Geophys. Res.,
79, 1210-4, 1974.
e= 12 20. 70 Hz
50 km
Fig. 2. Block diagram of the prototype system.
"UHF" is a low bandwidth telemetry channel. The
various phase measurements are identified with
subscripts r for red (632.8 nm), b for blue
(441.6 nm) and vi for microwave (8.1 GHz).
101
Visibi l i ty (km)
50 35 20 10
0 0.1 0.2 0.3 0.4 0.5 0.6
Attenuation (km~1)
Savage, J.C. and W.H. Prescott, Precision of geo-
.dolite 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., 81. 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, EOS. 5_2_, IUGG17-21,
1971.
Fig. 3. Calculated range of one-way (upper
curves) and retroreflector EDM instruments as a
function of optical beam spread and atmospheric
attenuation.
102


Multiple wavelength geodesy

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