The LaCoste and Romberg gravity meter is made of metal parts. It is far more rugged than meters made of fused quartz glass. Because the thermal expansion and contraction of metals are generally greater than quartz, the L and R meters must be accurately thermostated. Since metals creep when thermally expanded or contracted, it is best to maintain the L and R meters at their constant thermostated temperature whenever practical.
The design of the meter allows it to be very sensitive to small changes in gravity. The simplified diagram of the meter shows a mass at one end of a horizontal beam. At the other end of the beam are a pair of fine wires and springs that act as a frictionless hinge for the beam. One purpose of the hinge springs is to help eliminate damage to the meter from all but the most severe impact.
The beam is supported from a point just behind the mass by a "zero length" spring. The spring is at an angle of approximately 45 degrees from horizontal. The meter is read by nulling the mass position, that is, adding or subtracting a small amount of force to the mass to restore it to the same "reading" position. This is accomplished by lifting up on the top end of the zero length spring. This must be done with great accuracy and is accomplished with a series of levers. In turn, the levers are moved by a highprecision screw which in turn is rotated by a gear box with considerable reduction.
The lever system and screw are accurately calibrated over their entire range. Calibration factors depend only on the quality of the lever system and measuring screw, not upon a weak auxiliary nulling spring as are used in other meters. For this reason the calibration factors of the L and R meters do not change perceptibly with time. This eliminates any need for frequent checks of the calibration.
The moving elements of the meter are restricted from movement of more than a few thousands of an inch (less than a tenth of a millimeter). Thus, if the meter sustains a severe impact it would be difficult for the movable parts to attain enough momentum to damage themselves. For further security and to minimize irregular instrumental drift, the beam can be clamped when not in use.
When the beam is clamped, it is pushed down against the bottom movement limiters or "stops". This would elongate the main spring and induce creep in the springs metal. To eliminate this creep, the beam also is pushed backwards upon clamping. Thus the length of the main spring in the clamped position is exactly the same length as it is when unclamped and at the reading line.
Few ferrous metal parts are used in the meter. The meter is demagnetized or compensated, then installed in a double metal shielding to isolate it from magnetic fields.
Changes in air pressure could cause a small apparent change in gravity because of the buoyancy of the mass and beam. This is prevented by sealing the interior of the meter from the outside air. As an additional precaution, should the seals fail, there is a buoyancy compensator on the beam.
When the meters are new, their average drift is less than one milligal per month. With a few years of aging, their average drift is usually less than half a milligal per month. This small drift is true drift, not a large drift compensated to a small value by a clock and microprocessor.
In the early days of earthquake seismology, long period horizontal motions could be measured with the horizontal pendulum seismograph. As the axis of rotation became closer to vertical, the period became longer. Theoretically, if the axis is vertical, the period is infinite.
Dr. Romberg posed the question to his student, Lucien LaCoste, how to design a vertical seismograph with the characteristics as good as the existing horizontal pendulum seismograph.
In the illustrated suspension, there are two torques: gravitational and spring. If these two torques balance each other for any angle of the beam, the system will have infinite period. The smallest change in vertical acceleration (or gravity) will cause a large movement.
The torque due to gravity is:
Where W is the mass and d is the distance from the mass to the beam's hinge.
The torque due to the spring is the product of the pull of the spring and the springs lever arm, s.
The length of the spring is r and by the law of sines:
If the spring constant is k and the length of the spring without force is n, The spring force is illustrated by this graph.
The torque due to the spring is then:
The total torque is:
This equation would yield zero torque and would be satisfied for all angles of q if:
For n to equal zero, we must have a "zero length spring". That is , a spring whose forcelength graph passes through the origin or, at least, points toward the origin. The turns of a helical spring of zero unstressed length would bump into each other before the spring actually reached zero length. By making a helical spring whose turns press against each other when there is no force on the spring, a "zero length spring" can be made.
There are several ways to make a zero length spring. A simple zerolength spring is a flat spiral spring. The mechanical properties of a spiral spring are not as convenient as a helical spring.
To make a zerolength helical spring, the spring wire can be wound onto a mandrel. As the wire is wound, it can be twisted.
Another method is to hold the wire at an angle and with tension while winding it on a rotating mandrel.
Still another method is to "turn the spring inside out".
The actual spring used in the L and R meters are "negativelength". The spring wire is large enough and stiff enough that the spring would not act like an ideal spring if the spring were to be clamped at both ends. Thus, a very fine but strong wire is attached to the top end of the spring and another to the bottom of the spring. The top wire is clamped to the lever system and the bottom wire is clamped to the beam. The effective length of the spring is the combined length of the helical spring and the two fine wires. That combination is "zerolength". The helical spring by itself is "negativelength".
A mechanical nulling technique is normally used to read the LaCoste and Romberg Model D and G land gravity meters. In this technique, the downward force of gravity on the mass is balanced only by the mechanical force of the spring pulling up on the beam. A precisely calibrated system of levers and measuring screw allow the force exerted by the spring to be measured very accurately.
A different method of reading the gravity meter has been used in the "U" series of underwater gravity meters. This method, called electrostatic nulling, allows a faster reading time than possible with "H" series meters, as well as the ability to automate the reading process under computer control.
The electrostatic nulling technique combines the effects of two forces, one mechanical and the other electrostatic, to balance the force of gravity. The following diagram shows the relationship of these forces within the gravity meter.
The underwater meter uses a Model G gravity meter with a capacitance plate on the end of the moving beam. This plate is used in the land meters as part of the Capacitance Position Indicator ( CPI or electronic readout ) system to sense the position of the beam. Two fixed plates are located above and below the beam plate. An electrostatic force can be applied to the beam simply by applying a DC voltage between the beam and one of the fixed plates. This DC voltage is commonly called CHEAT VOLTAGE and abbreviated as C.V. in many places in the system software. This terminology comes from the "Cheater" switches available as part of the variable damping option for the land gravity meters and used in situations requiring high damping.
The electrostatic nulling system requires an accurate knowledge of the relationship between the electrostatic force produced by the Cheat Voltage, and the mechanical force measured in counter units. This Cheat Voltage calibration is obtained by making a series of measurements in which the Cheat Voltage is increased by small steps, and the mechanical force is decreased just enough to keep the meter beam in balance.
To read the meter, the mechanical force is first adjusted to be near the null point (within about 2 milligals ) by turning the measuring screw. Then, the Cheat Voltage is adjusted to complete the balancing with electrostatic force. The reading will be in two parts, one in counter units and one in volts. The counter units are converted to milligals using the meter calibration table as is done with the land gravity meters. Cheat Voltage is converted to milligals from the Cheat Voltage calibration described above. In actual use, the computer program performs the above calculations and reports a final relative gravity value in milligals.
