Miniaturized Gravimeter May Greatly Improve Measurements
J. M. Brown, T. M. Niebauer, B. Richter, F. J. Klopping, J. G. Valentine, and W. K. Buxton
A new miniaturized absolute gravimeter will greatly improve absolute gravity measurements in both dynamic and static applications. The new instrument is much smaller than previous absolute gravimeters and can acquire data at a much higher rate. The new rise&fall laser interferometric absolute gravimeter is capable of 100 repetitions per minute, with a measured noise floor of about 1 µGal/min.
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| Fig. 1. Comparison in size between the standard FG5 chamber, right, and the new rise&fall chamber, left. |
Applications using gravity data include detecting small crustal deformations that change over time owing to seismic motion, volcanic activity, and postglacial rebound [Sasagawa (a), 1995]. Gravity data is also used for petroleum and mineral exploration as well as geoid and tidal parameter definition.
The new absolute gravimeter offers geophysical researchers more accessible ways of studying the gravity field around the world. The instrument is just one fifth the volume and weight and, at 35 cm, one half the height of the FG5 dropping chamber (see Figure 1). It is highly portable, achieves a long free-fall time, and operates at a faster data acquisition rate than do current absolute gravimeters. As such, it is an ideal candidate for dynamic environments such as marine and strap-down airborne gravimetry, as well as short-occupation-time static surveys requiring a portable, field-worthy instrument.
The free-fall technique, based on the Michelson interferometer, has developed rapidly during the 20th century. Using fundamental standards of length and time, laser interferometric absolute gravimeters are capable of achieving ±1 µGal measurement precision [Niebauer et. al., 1995]. Absolute instruments also are much simpler than spring-type relative meters and provide independent information about the magnitude of the gravity field at a specified point, not the relative difference in gravity with respect to a known reference. Additionally, they do not suffer from tares, drifts, and calibration errors associated with relative instruments.
Many absolute gravimeters in use today are based on absolute gravity determination experiments conducted over 30 years ago [Faller, 1967]. Typical current free-fall laser interferometric gravimeters consist of three main pieces: an evacuated chamber with a free-falling test body, a reference test body (usually mounted on some type of isolation device), and a laser interferometer [Niebauer et. al., 1986]. Light is directed from a stabilized laser to a freely falling reflective test mass and also to a reference test mass held in isolation from nongravitational accelerations and other background noise. The light is combined with the laser reference to produce optical interference fringes. The optical signal is directed to a photo detector where the precise trajectory is sampled, resulting in many time and distance pairs. These data are then least squares fit by a computer to determine an absolute value for g.
Only a few years ago, a drawback of rise&fall instruments was thought to be their slow acquisition time [Marson et. al., 1986], but the new chamber is considerably faster and smaller than previous absolute instruments, whether drop only or rise&fall.
The new instrument is capable of a throw rate of over 100 cycles/minute and best-case single throw precision of ±4 µGal; this translates to about 3 µGal/ÖHz. Total free-fall time per minute of observation has increased by nearly an order of magnitude compared to past instruments.
The device's decrease in size and increase in data acquisition rate imply that dynamic absolute gravimetry can be seriously pursued. In dynamic applications the free-falling test mass acts as a satellite in orbit around the Earth. The test mass is precisely tracked by two well-known references, the stabilized laser and the atomic clock. One can imagine that in combination with georeferencing systems such as the Global Positioning System, the absolute value of the gravity field could be sampled much more rapidly and precisely than is possible with spring-type meters that require a typical filter length of 120 s or more.
The new rise&fall chamber's 35-cm height approaches the size of field portable relative gravity meters. Small isolation platforms are being developed and with laser and electronics technology continually decreasing in size, it will be possible to have a portable absolute gravimeter easily transported and operated by one person.
The majority of free-fall instruments, including the FG5 and other institutional meters, operate in drop mode only [Faller, 1988]. It is difficult to release a test mass smoothly into free fall, and so free-fall gravimeters, though simple in concept, offer substantial mechanical challenges in their construction. These challenges are even greater when considering the design and operation of a rise&fall meter. The optical system, although insensitive to rotations and translations, places severe limitations on acceptable levels for the test mass during free fall.
Because the initial velocity of the test mass at release is near zero in a drop-only instrument, small misalignment errors result in only small non-vertical initial velocity components. In throw mode, however, a high initial instantaneous velocity is needed to launch the test mass upwards. Therefore, even a small error can greatly influence the trajectory path of the test mass. The higher initial acceleration of the test mass also increases the recoil of the system compared to a drop-only instrument. Recoil must be minimized so that it does not interfere with the measurement.
Despite the complications in constructing such a device, the advantages of rise&fall gravimeters outweigh the difficulties in producing them. For example, the symmetry of rise&fall measurement offers obvious benefits in terms of cancellation of many classes of errors [Marson et. al., 1986]. Among others, air resistance and magnetic field errors will cancel on the rise&fall portions of the trajectory. Frequency-dependent errors in the system electronics are also eliminated.
Two additional advantages of rise&fall have been neglected in past literature. The first is the possibility to reduce the size of the free-fall chamber. The equation of motion shows that in order to obtain a 200-ms measurement period, the drop-only meter must be at least 20 cm tall. In fact, including mechanical parts, the FG5 chamber is nearly 75 cm tall. In a rise&fall instrument, the distance necessary to achieve the same free-fall time can be reduced by a factor of 4 to 5. This is a considerable advantage in terms of size and volume reduction.
The second is its ability to increase measurement time or duty cycle. One important parameter that defines the quality of an absolute gravimeter is the precision obtained in a single free-fall measurement. For example, the FG5 has shown a best-case precision of about 4 µGal/drop. However, all absolute gravimeters utilize averaging over many drops to increase precision. Thus, the repetition rate directly affects the precision measured in µGal/ÖHz. Clearly, this quantity is improved by reducing the amount of dead time where the test body is not in free fall.
A drop-only gravimeter typically spends a relatively large amount of time gently lifting the test mass, letting it settle at the top, and then waiting for it to gain an acceptable initial velocity to begin measurements. At the end of the measurement the object must be caught and stopped in a gentle fashion. The FG5 operates at a best-case rate of one drop every 2 s (in usual operation it takes one measurement every 10 s). The best-case duty cycle of this instrument is therefore .2s/2s or one tenth.
In contrast, rise&fall instruments accelerate the test mass upwards very quickly, measure on both sides of the rise&fall trajectory, and finish at the initial starting point. No need exists to return the test mass slowly to the beginning of the measurement cycle. Therefore, a much shorter duty cycle can be easily realized.
Only a few different rise&fall interferometric instruments have been developed to date. The first successful symmetric rise&fall gravimeter was developed at the Bureau Internationale des Poids et Mesures (BIPM) and is described by Sakuma [1986]. Nearly a decade later, a more portable version of the Sakuma instrument was developed jointly by BIPM and a commercial company, Jagger, for the Instituto di Metrologia (IM) [Cerutti et al., 1974].
A modernized version of this instrument is now used at the IM [Alasia et al., 1982; I. Marson, personal communication, 1999]. The semiautomatic device uses a human-assisted placement and triggering mechanism. The instrument launches the test mass at a maximum rate of once each minute. Stated accuracies are ±10 µGal per throw at a quiet site.
The Ukrainian State Scientific Industrial Association has produced a fully automated rise&fall instrument [Bondarenko et. al., 1996]. That instrument achieves ±100 µGal precision after 120 throws over 30 min. In the course of 2 days of observation, measurement accuracy is reported as ±14 µGal.
The new rise&fall chamber was developed as an alternative to the current FG5 dropping chamber. The FG5 dropping chamber mechanism produces a 20-cm vertical free fall that the test object traverses in 0.2 s. The dropping chamber is capable of ±5 µGal single-drop precision at a quiet site. One of our primary design goals was to produce a chamber competitive with this number. For portability, it was also desirable to create a chamber substantially smaller than the FG5.
Interest exists in using absolute gravimeters for dynamic airborne and marine applications. Relative spring-type gravimeters used on moving platforms typically store a filtered sample at 1 Hz. Thus, it was desirable that the new chamber throw at or better than this standard 1-Hz rate. To achieve these design goals, the new chamber uses some of the FG5 features, including a motor-driven mechanism for throwing, and a cofalling, dragfree chamber around the test mass to shield it from air resistance and electromagnetic forces. To obtain a smooth launch, we increased the symmetry of the throwing mechanism and kept the design simple and robust.
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| Fig. 2. Oscilloscope trace of the rise&fall trajectory. The parabolic trace is the dragfree cart path. The box-type trace shows the tracking signal between the cart and the freely falling test mass. |
As seen in Figure 1, an added benefit of the smaller chamber is the reduction in size of the ion pump used to maintain the 10-6T vacuum environment. This results in a smaller magnetic field generated by the magnets used to evacuate the chamber, which in turn reduces possible systematic effects.
The new chamber successfully launches an object into the air and gently catches it upon its return. Figure 2 shows an oscilloscope screen with two traces. The top trace depicts the rise&fall of the cart, which carries the reflecting test mass. The bottom trace is the liftoff signal between the dragfree cart and the freely falling object. The upper left-hand corner of the scope shows that free fall lasts approximately 225 ms. This time is greater than with the FG5. This is an important advantage because a longer free-fall time results in a greater sampling of the gravity field.
Tests on the instrument were conducted at the Table Mountain Gravity Observatory north of Boulder, Colorado. Operated by the National Oceanic and Atmospheric Administration, the observatory is away from traffic and industrial sites and is seismically quiet. Its absolute gravity value is well known [Sasagawa (b), 1995].
The small chamber was designed to be backwards compatible with previous FG5 chamber tripods. Our first experiment was conducted with first-generation FG5 electronics and interferometer. The system uses a stabilized HeNe laser and a rubidium time standard and is capable of recording 150 zero crossings of the fringe signal.
The first data set represents an uninterrupted 24-hour run. We programmed the instrument at 30-min intervals to observe a set of 100 drops. At the selected 1-Hz throw rate, each set is 100 s in duration. The electronic system was scaled to sample the zero crossing at every 1000th fringe. From either side of the apex, 95 samples (a total of 190) were fit to a parabolic trajectory. In the least squares fit we solved both sides of the parabolic trajectory simultaneously. The resulting g was then corrected for Earth tides, ocean loading, polar motion, barometric pressure, and vertical gradient, with software identical to the FG5.
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| Fig. 3. Typical residuals from a single throw. RMS value is less than 0.5 nm. |
Figure 3 displays typical residuals from a single throw. RMS values for the fit are below 0.5 nm. The gap in the middle is a dead zone around the apex. Because of its high-pass filter, the photo diode does not track the fringe signal efficiently at slow speeds, introducing a gap at the apex. This gap is not a significant disadvantage because the derivative of the position of the object at the apex is small. It is more important that the clock is still advancing throughout the rise&fall measurement. This is borne out by the resulting single-throw standard deviation of ±7 µGal or better throughout the 24-hour data set.
This number is very competitive with the current large FG5 dropping chambers and exceeds all previous rise&fall meters. Average single set standard deviation is 1.49 µGal. This value is very competitive with the precision of the FG5. The final number is within statistical agreement of the known value.
In addition to progress in size reduction, the cycle time between throws is considerably shorter than for previous absolute instruments. Our rise&fall chamber is capable of making 100 throws per minute. The duty cycle is .2 s /.6 s or one third, a factor of 3 better than the drop-only FG5 chamber.
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| Fig. 4. One hundred drops taken in 1 min. Set standard deviation is ±1.4 µGal. The final value is within statistical agreement of the known number. |
Figure 4 shows the results of a 1.67-Hz series of 100 throws. Set standard deviation is ±1.7 µGal, and the final number is within statistical agreement of the known value. The benefit of a rapid throw rate becomes even more obvious as time progresses. For example, in normal operations, the drop rate for the FG5 is 10 s. During this time, the object is in free fall for 200 ms. The new chamber throws the test mass at 1.67 Hz or 100 times each minute. With 225 ms of air time each throw, this implies that in a 60-s interval, the test mass is in free fall for 22.5 s, significantly longer than all other drop-only or rise&fall chambers.
The new throwing chamber also appears to be more rugged than the FG5 dropping chamber. Recently, we disassembled a small throwing chamber after more than 500,000 measurements and observed very little mechanical degradation. This promises to increase the field worthiness of new instruments that use this launching mechanism.
We would like to thank R. Bilson and G. Broeder of Micro-g for their assistance in developing the new chamber. We would also like to thank the National Oceanic and Atmospheric Administration for use of its Table Mountain Gravity Observatory.
J. M. Brown, T. M. Niebauer, B. Richter, F. J. Klopping, J. G. Valentine, and W. K. Buxton
For more information, contact John M. Brown, Micro-g Solutions Inc., P.O. Box 636, Erie, Colorado 80516 USA; E-mail: freeheel@compuserve.com or see the Micro-g Solutions Inc. Web site at http://www.microgsolutions.com.
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