ALTHOUGH no one has learned how to predict when an earthquake will occur, Japanese investigators have suggested that in some instances the surface of the earth may tilt slightly along a fault line somewhat in advance of a seismic event. Various seismologists are exploring the idea with an instrument known as a tiltmeter. In one of several possible forms the sensing elements of the device include two cylindrical cups of mercury spaced a few feet apart on a rigid, horizontal base. The cups are interconnected at the bottom by a length of metal pipe. The air spaces above the mercury are similarly interconnected by plastic tubing.

When the assembly tilts like a seesaw, some of the mercury drains from the upper cup into the lower cup. The relative change in the level of the mercury is measured continuously by an electrical circuit in which the surfaces of the metal in the cups function as the movable plate of a differential capacitor. One simple version of the instrument can detect a tilt of only .002 second of arc, which is about the angle that would be subtended by a dime at a distance of 500 miles.

A tiltmeter of this kind can also function as an inexpensive seismometer. The device is particularly sensitive to earthquake waves that vibrate in the direction of the tube that connects the cups of mercury. The acceleration of the tube and the cups causes metal to flow from one cup into the other. In effect the mercury reacts mechanically like the pendulum of a conventional seismometer, but it is far more stable and easier to adjust. For these reasons it is ideal for amateur use. The construction of such an instrument and some of the seismic effects it is designed to measure are discussed by William W. Gile, a research engineer on the staff of the Seismological Laboratory of the California Institute of Technology.

"In southern California the San Andreas fault is mentioned more frequently in daily conversation than the weather, although we can control the behavior of neither. On the seaward side of the San Andreas fault the crust of the earth appears to be creeping northward at a rate of about two inches per year. The underlying rock bends in response to the movement. Ultimately it snaps and the San Andreas fault lurches.

"The readjustment, in terms of feet and inches, can be impressive. For example, in 1857 a circular sheep corral about 20 feet in diameter straddled the fault near our part of the state. On January of that year the accumulated stresses at the sides of the big crack reached the critical limit. Somewhere a rock fractured. When the dust settled, the sheep corral had the form of the letter S. During the subsequent 116 years stresses have again accumulated. If the relative motion along the crack in our vicinity is indeed two inches per year, the slabs of rock must now have a bend of about 19 feet.

"For such reasons earthquake prediction has become a focus of attention in many branches of geophysics and seismology. A number of prediction techniques have shown promise. It must be emphasized that although no technique exists for predicting earthquakes, the present findings do not exclude the possibility of developing one. It is this real but slender hope that continuously renews the enthusiasm of those of us who work in the field of seismic instrumentation.

"The effort has been rewarded in recent years by the development of some remarkably sensitive apparatus. For example, strain gages now routinely measure forces equivalent to those that would be developed if the width of the U.S. were increased by the thickness of a human hair, and temperature probes for use in deep holes can measure thermal variations across fault lines that amount to less than .001 degree Celsius. Finally, we have long-baseline tiltmeters that can detect angular changes as small as 10 radian, which is about the angle that the period at the end of this sentence would subtend if it were placed on the moon and viewed from the earth.

"Some of the devices are relatively inexpensive and easy to adjust and to maintain. The short-baseline tiltmeter [see illustration, right] is an example. We have operated versions of the instrument on the island of Hawaii to measure changes in the tilt of the earth's crust caused by the eruption of Halemaumau volcano. The instrument also works well as a sensitive seismometer. When it is combined with an appropriately adjusted pen recorder, it can also be used for monitoring earth tides: the daily rise and fall of the crust in response to tidal forces exerted by the moon and sun. The low cost of the apparatus and its ease of construction, together with its high stability and sensitivity, make the instrument ideal for both amateurs and professionals.

"Conventional seismometers of the pendulum type depend on critical adjustments that, following seismic disturbance, determine the rate at which the pendulum swings, the number of oscillations it completes before coming to rest and the position at which it stops. Although the mercury of the tiltmeter is analogous to a conventional pendulum, the instrument does not require these tedious adjustments. The period of its oscillation and the damping (the rate at which it stops oscillating after a disturbance) are determined by the physical properties of the mercury, together with the size of the cups and the interconnecting tubing. These dimensions do not change significantly with time. Accordingly the instrument is stable.

"A normal rule of thumb in seismic instrumentation is that the period of the pendulum-the interval required for the pendulum to make one full excursion in both directions-must exceed the period of the longest seismic wave that is to be observed. The necessity for the long period is explained by the role of the pendulum in measuring the length of seismic vibrations. In effect the bob of a pendulum will stand still, even though the framework from which it is suspended vibrates, if the period of the pendulum is long with respect to the period of the vibration. In other words, the stationary mass of the bob serves as a reference for measuring the relative motion of the earth's crust. The principle can be demonstrated by an interesting experiment.

"Make a pendulum by tying a foot or so of string to any small weight. Hold the string in one hand. Dangle the weight about 10 inches below the point where you grasp the string. Jiggle your hand back and forth an inch or so at the rate of about five vibrations per second. Observe that the weight stands fairly still. If your hand were the earth and the weight were the bob of a seismograph pendulum, the earth's relative motion could be observed just as readily. .

"Now decrease the rate at which you shake your hand to about one second per cycle. Within a very few vibrations of your hand the weight will be swinging back and forth violently. The reason is that one second is about the period at which a 10-inch pendulum vibrates naturally, that is, one second is the frequency of vibration to which the pendulum is resonant. If the pendulum of a seismograph were tuned to the period of the earth's vibration, it would yield a grossly exaggerated measurement of the seismic event.

"Stop moving your hand. Observe that the pendulum continues to swing for a time but with diminishing amplitude. It is said to be poorly damped. The damping effect results from the suppression of a pendulum's motion by the loss of energy through friction. A pendulum that comes to rest after about one vibration is said to be critically damped. Good seismographs of the type that employ mechanical pendulums must be fitted with adjustable gadgets for dissipating unwanted energy.

"Finally, move your hand back and forth slowly, at a rate of about 10 seconds per cycle. Observe that the motion of the weight follows the motion of your hand. If the pendulum of a seismograph were similarly adjusted, it would be insensitive to seismic vibrations of long period. Indeed, in the case of a displacement seismograph, as is illustrated by this experiment, sensitivity declines at the rate of 12 decibels per octave for seismic vibrations of lower frequency than those of the freely vibrating pendulum. That is to say, each time the seismic period doubles, the pendulum moves only a fourth as much with respect to its motion at the free period.

"The earth has one free period of about 53 minutes per cycle. This is the frequency at which the earth 'rings like a bell' following a big earthquake. A conventional pendulum of this period would need to be more than 1,500 miles long. The period is equal to , in which l is the length of the pendulum in feet and the period is in seconds.

"As I have mentioned, the mercury of the short-baseline seismometer is analogous to a pendulum. Its free period is determined by the inside diameter of the cups and of the interconnecting tubing and by the distance between the cups. To find the period in seconds, divide the inside diameter of the cups as expressed in feet by the inside diameter of the tubing and multiply the quotient by 6.28. Next divide the center-to-center distance between the cups by 64. Find the square root of the quotient. Multiply the square root by the product of the preceding calculation to find the period. The procedure is expressed by the formula , in which T is the period in seconds, = 3.1416, D is the inside diameter of the cups, D is the inside diameter of the interconnecting tubing, L is the center-to-center distance between the cups and g, the acceleration of gravity, has the value 980 if lengths are expressed in centimeters and 32 if they are expressed in feet.

"An instrument of convenient size and excellent performance that is particularly appropriate for amateur construction would measure two feet from center to center of cups having an inside diameter of two inches. The cups would be interconnected by a stainless-steel tube with an inside diameter of 3/32 inch. The period of the recommended seismometer can be calculated by substituting these dimensions in the formula: seconds.

"Why not make the cups wider with respect to the diameter of the interconnecting tube and thereby achieve a period of an hour or more? In theory the period could be thus increased without limit. As a practical matter, however, the mercury moves less in the end tanks as the ratio of diameters is increased. The sensitivity of the instrument to long seismic waves does not increase with the period. Instead its sensitivity decreases to vibrations of shorter period.

"It is useful to know the method of calculating the damping factor of the pendulum. As I have mentioned, the term damping suggests the tendency of a pendulum to vibrate at a diminishing amplitude after it has been set in motion. The amount by which a pendulum is damped is expressed by a factor h that approaches zero in the extreme case of an undamped pendulum and unity at the other extreme when the pendulum returns to its equilibrium or mid-position in exactly half the interval of its free period [see illustration, left].

"In the case of the mercury pendulum the damping factor h is equal to , in which u = .01554 (the viscosity of mercury in poise units), T is the period of the pendulum in seconds, d = 13.55 (the density of mercury in grams per milliliter) and D is the inside diameter of the interconnecting tube in centimeters. The damping factor of the recommended seismometer can be calculated by substituting appropriate quantities in the formula: . The pendulum is somewhat overdamped, which is to say that it stops oscillating in less time than is required for it to complete one full cycle of vibration.

"The proportions of the instrument can be varied to alter both the period and the damping factor. The damping factor of most professional instruments ranges between .7 and 1. Calculations indicate that a period of 25 seconds and a damping factor of .73 can be achieved by interconnecting the two-inch cups at a center-to-center distance of four feet with stainless-steel tubing of 1/S inch inside diameter. Experimenters can manipulate the dimensions to achieve still other characteristics.

"The cylindrical cups can be made of clear plastic. If the experimenter does not have access to a lathe, the cups can be fabricated of flat stock and of tubing with a thick wall [see top illustration on opposite page]. The cups must be cylindrical in form, not rectangular, to prevent the development of nonlinear turbulence. Nonlinear turbulence is not canceled differentially. Therefore it adds to the 'noise' of the system.

"Stainless-steel tubing interconnects the cups. This material was selected to provide an electrical contact with the mercury while avoiding an amalgamating reaction at the ohmic contact. The second tube, which is situated above the mercury level, equalizes gas pressure in the tanks. This tube can be of plastic.

"I flood the tanks of long-baseline instruments with nitrogen to prevent the mercury surface from oxidizing. Incidentally, the mercury cups of larger instruments have baselines of 30 meters (98.4 feet). They are interconnected by butyrate plastic. The coefficient of thermal expansion of this material approximates that of mercury. Electrical contact with the metal is provided by stainless steel fittings that couple the plastic tubing to the cups.

"A fixed electrode in the form of a polished disk of stainless steel is supported above the surface of the mercury in each cup by a threaded shaft that passes through the center of the lid. These electrodes constitute the fixed or sensing plates of the mercury-pendulum capacitor. The surface of the sensing electrode that faces the mercury must make a true right angle with respect to the axis of its supporting shaft.

"The shaft also functions as a screw for adjusting the gap between the surface of the electrode and the surface of the mercury. The threads must be as fine as the experimenter can cut. I use 80 threads per inch. If you do not have access to an engine lathe, have the rods threaded to this pitch by a local machine shop.

"If the cover of the cup is made of slab of half-inch plastic and drilled about .001 inch narrower than the diameter o the thread, it will not be necessary to tap the hole. The rod will cut a shallow thread of adequate strength in the plastic. The base, provided with leveling screws for supporting the instrument, can be improvised from any rigid aluminum section, such as the rectangular aluminum tubing that is commonly used as door framing in office buildings. Adequate lengths of the material are usually available at low cost from dealers in aluminum scrap.

"An electronic transducer, which I refer to as an 'inverse' discriminator, converts the displacement of mercury into a correspondingly varying signal voltage. The voltage can be used to operate a pen recorder of the kind previously described in this space [see "The Amateur Scientist, SCIENTIFIC AMERICAN, March, 1972]. Essentially the transducer consists of a circuit similar to the one used in radio sets for detecting frequency-modulated signals. Such circuits are known as discriminators. The circuit of a conventional discriminator includes a fixed capacitor and a coil that help to detect signals carried by a variable frequency. My device works in reverse: an electric current of fixed frequency helps to detect 'signals' that are represented by the minute motion of a differential capacitor-the mercury pendulum.

"Discriminator circuits are essentially; resonant systems. They are analogous to pendulums, the strings of musical instruments and similar mechanisms that vibrate at maximum amplitude when they are tuned to a preferred period. The basic principle is illustrated by an electrical circuit consisting of a capacitor and an inductor. A circuit of this kind is naturally resonant at some frequency When a quantity of electrons is deposited on one plate of the capacitor, they immediately flow through the inductor, pile up on the other plate of the capacitor and return to the first plate for another round trip, just as a pendulum, when it is given a push, vibrates continuously at a characteristic rate and for exactly analogous reasons.

"The inductor of such circuits usually consists of a small coil of insulated wire. Assume that the capacitor and the inductor are connected in series to a source of current that alternates at a frequency lower than the frequency at which the circuit is resonant and that the frequency of the source is gradually increased until it is higher than the resonant frequency. Assume also that a method is provided for measuring voltage that appears across the coil. The experimenter will observe that voltage across the coil is minimum when the frequency of the imposed current is lower than the resonant frequency of the circuit, that the voltage becomes maximum at resonance and that it declines as the frequency of the source exceeds the resonant frequency of the circuit [see left].

"The alternating potential across the coil can be converted to unidirectional voltage at the output terminal of the device by inserting a diode in the circuit, and it can be further converted into a reasonably constant potential by connecting in the circuit a second capacitor that acts as a filter. This simple device is known as a slope detector. It was used in inexpensive radio and television sets for detecting frequency-modulation signals. In that application the slope detector was tuned to a point such that the center frequency of the radio station was located about halfway up the resonant characteristic of the circuit, as indicated by the X on the graph of the detector. Excursions of the imposed frequency from the midpoint appeared as proportional excursions of voltage at the output of the slope detector. The voltage and the linearity available at the output of the device can be improved by connecting two of the circuits back to back.

"My inverse discriminator works in reverse. Alternating current of fixed frequency is imposed across a circuit of variable resonance. The signal consists of the movement of a differential variable capacitor in the form of the mercury pendulum. I tune the transducers to 50 percent of the peak resonant output. For an input potential of one volt peak to peak the peak output of each transducer is about 30 volts. The outputs of the transducers are detected, filtered and combined through three resistors to provide a single-end output. Note that in the practical circuit each transducer circuit is shunted by a trimming capacitor of the piston type. Minor variations in the characteristics of the coils and stray capacitances can be compensated for by adjusting the trimmers.

"The constant frequency is generated by a crystal-controlled oscillator. In this circuit one can use any silicon transistor that is rated for a collector-to-emitter potential of 45 volts and a dissipation of .3 watt. The collector should be rated at .05 ampere or more, and the small-signal, common-emitter current-transfer ratio should be about two at a frequency of 30 megahertz. Surplus catalogues list many transistors that meet or exceed these specifications. Experimenters who are not familiar with the techniques of constructing resonant circuits and transistor oscillators may want to enlist the cooperation of a radio ham.

"Install the completed instrument on a solid foundation in an environment of the most constant temperature available. Our seismographs and tiltmeters operate in tunnels several hundred feet underground and are provided with servomechanisms that automatically compensate for temperature changes. Nonetheless, an instrument of remarkable performance can be installed in a good basement, particularly if it is insulated in a styrofoam box with thick walls. Use clean mercury of National Formulary grade or better. About six ounces of mercury will be required for an instrument 24 inches long.

"Lift one end of the instrument about a foot to flush air bubbles from the mercury in the interconnecting tubing, and lower it quickly. Adjust the base to the horizontal position as accurately as possible with the aid of a bull's-eye level. Rotate the piston-type trimmer capacitors of the transducers to minimum capacitance. Install a jumper between the junction of the three one-megohm resistors and the common point.

"Switch on the power supply to the oscillator. By means of the adjustment screw decrease the air gap between the mercury level and the sensing plate of the capacitor until the corresponding meter indicates approximately half a microampere. Similarly adjust the other mercury cup.

"Adjust the piston-trimming capacitors to the point where each meter indicates 3.5 microamperes. Replace the jumper with a high-impedance voltmeter. The meter should indicate zero volts. If the meter indicates an offset voltage, rotate either one of the sensing capacitor plates to the point of zero indication. At this adjustment the instrument is essentially balanced.

"Finally, rotate one of the sensing-capacitor plates a full turn. The voltmeter should now indicate a potential of 17.36 millivolts. If the output exceeds this potential, the sensitivity of the instrument is too high. Increase the air gap in both cups between the surface of the mercury and the sensing plates. Next increase the capacitance of the piston capacitors to the point where the meters again indicate 3.5 microamperes. If the output voltage is less than 17.36 millivolts, which indicates inadequate sensitivity, reverse the procedure. If the instrument is to be used exclusively as a seismometer and the highest possible sensitivity is wanted, adjust the piston capacitors to minimum capacity and the sensing capacitors to maximum."

Bibliography

ADVANCES IN GEOPHYSICS: VOL. II. Hugo Benioff in Earthquake Seismographs and Associated Instruments. Academic Press, Inc., 1955.

ELEMENTARY SEISMOLOGY Charles 11. Richter. W. H. Freeman and Company, 1958.

SCIENTIFIC AMERICAN BOOK OF PROJECTS FOR THE AMAATEUR SCIENTIST C. L. Stong. Simon and Schuster, 1960.

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