When an amateur builds a seismometer, he is most likely to choose an instrument of the electromagnetic type developed in 1906 by Boris Borisovich Golitsyn, a physicist who was also a prince of the Russian Empire. A seismometer of this type picks up earthquake waves with a pendulum that supports a coil of insulated wire between the poles of a magnet rigidly linked to the earth. The relative motion between the magnet and the coil caused by tremors in the earth generates corresponding electric currents in the coil. The currents can be amplified to operate a pen recorder.
One unfortunate characteristic of the apparatus limits its performance. The electrical output of the coil is diminished by a factor of 1,000 for each factor of 10 by which the vibrations in the earth are below the frequency to which the pendulum is resonant. Ideally the period of the pendulum's resonant frequency should exceed 60 seconds. To be resonant at this frequency a simple pendulum would require a length of almost 900 meters.
The problem of improving the low-frequency response of the electromagnetic seismometer has defied all attempted solutions. Now, however, it has been sidestepped by Barry Shackleford and Jim Gundersen, who are electronics engineers with the Hughes Aircraft Company in Culver City, Calif. They make a hobby of seismology. Shackleford (7815 Kittyhawk Avenue Los Angeles, Calif. 90045) explains how he and Gunedersen developed a seismometer that not only performs much better then an instrument of the Golitsyn type put also is cheaper and easier to build.
"Jim suggested that instead of fighting pendulum's extreme lack of sensitivity below its natural period we should live with it and use electronics to compensate for the 'roll-off' of the pendulum. After six months of experimenting at home we succeeded in devising a seismometer that not only behaves as though the resonant period of the pendulum exceeds 60 seconds but also dispenses with the coil and magnet and replaces vacuum tubes with solid-state circuits [see illustration on opposite page].
"The instrument consists essentially of nine components. An oscillator generates high-frequency current that energizes an antenna in the form of a copper plate, which functions as the bob of the pendulum. Signals from the antenna are picked up by two adjacent fixed plates They are coupled rigidly to the earth.
"A detector converts the received signals into direct currents. The amplitude of the currents varies with the displacement of the pendulum from the vertical. The currents are combined in a summing amplifier and passed along to a signal-processing device known as an a.c. coupled integrator.
"Essentially the integrator functions as the 'electronics' to which Jim referred during our first conversation about the instrument. It compensates for the roll-off of the pendulum. After additional amplification the output of the integrator can be employed to drive a pen recorder. Advice on building two appropriate pen motors has been given in "The Amateur Scientist' [March, 1972 and January, 1975].
"The performance of the system is determined primarily by the integrator. This device includes four resistors, four diodes and three capacitors, and an operational amplifier in the form of an integrated circuit 'chip'. The combination of one capacitor and one resistor causes the gain of the amplifier to vary inversely with the frequency of the input signal. For example, if the amplitude of the input remains constant and the frequency is doubled, the amplitude of the output is halved.
"Moreover, if direct current (a signal of zero frequency) of constant amplitude is applied to the input of the integrator, the output increases steadily as a function of time. This accumulative property of integrators is the bane of people who try to design them. A constant voltage, however slight, applied to the input terminals of the integrator will in time cause the maximum voltage the amplifier can develop to appear across the output terminals. When the amplifier is in this states it is said to be saturated. Alternating current signals do not cause saturation.
"The integrator can be protected from external sources of direct current by feeding seismic signals into the device through a capacitor. Capacitors transmit alternating current but not direct current. When the input terminal of the integrator is coupled to the signal source through a capacitor and a resistor connected in series the lower frequency at which the response begins to drop of is equal to the reciprocal of the product of 6.28 multiplied by the resistance (in ohms) of the resistor and by the capacitance of the capacitor (in microfarads). For example, if the resistance of the input resistor is 10,000 ohms and the capacitance is 1,000 microfarads, the amplifier's response would begin to drop of at 1 / (6.28 x 10,000 x .001) = .016 hertz, a frequency that corresponds to a period of 62.5 seconds.
"The active element of the assembly is an integrated circuit known as the Type 741 operational amplifier. This device imposes a very small direct potential across its own input terminals, causing it to saturate automatically. The effect must be nullified by feeding some of the output current back to the negative input terminal of the 741 through a resistor. The amplifier, thus stabilized, is converted into an integrator by also connecting a capacitor between the output and the input.
"The gain of the integrator is determined by the ratio of the input resistor to the gain of the feedback resistor. Devices of the 741 type tend to be noisy when they have feedback resistors larger than 100,000 ohms. By fitting the integrator with an input resistor of 10,000 ohms, a feedback resistor of 100,000 ohms and a feedback capacitor of 100 microfarads, the circuit attains a gain of 10 at .016 herz.
"The copper plate that serves as the bob of the seismometer pendulum is two inches square. It is made of circuit board, which consists of sheet plastic whose sides are coated with cooper foil. (The material is normally used in the construction of printed circuits.) We refer to this plate a the transmitting antenna. It is free to vibrate between the two adjacent fixed plates, which are of the same size and construction. Essentially the combination constitutes a differential capacitor. Alternating current at a frequency of five megahertz is fed to the transmitting antenna by a solid-state, crystal-controlled oscillator mounted on the lower part of the pendulum arm. Although the oscillator is small and comparatively light, it adds mass to the pendulum (as does a permanent magnet that, in combination with a solenoid, is used for damping the pendulum).
"When the seismometer is in operation, the vibrations of the earth cause the frame of the pendulum assembly (and therefore the receiving antennas) to oscillate. The pendulum stands relatively still, as does the transmitting antenna. Hence one receiving antenna moves closer to the transmitting antenna and picks up more energy. The other receiving antenna moves away from the transmitting antenna and receives less energy. After detection the amplitude of the total potential difference across the receiving antenna varies with the displacement of the pendulum and therefore with the displacement of the earth's surface.
"Each receiving antenna is connected to a tuned circuit and a simple diode detector. One detector produces a positive voltage, the other a negative voltage. The outputs of the diode detectors are connected to the summing amplifier. A displacement of the pendulum of less then .01 inch can cause the output of the amplifier to change from +15 volts to -15 volts, a total change in potential of 30 volts.
"The oscillator is conventional. Its frequency is not critical, Almost my quartz crystal ground for 160 kilohertz or more will be satisfactory.
"The 2N2222 transistor should be fitted with a heat sink. Not having any heat sinks on hand I soldered a penny to the top of the case. The soldering should be done quickly and with care to avoid damaging the device.
"My technique, which proved successful on the first try, was to sand both the penny and the transistor until they were shiny bright. I melted enough solder in the center of the penny to form a small mound. A similar was applied to he top of the transistor case. I reheated the mound on the penny and thrust the transistor into the center, keeping the tip of the iron off to one side. As soon as the solder solidified I cooled it with water. Notwithstanding my success in this improvisation, I strongly recommend the purchase of a heat sink specially designed for the TO-18 case.
"The construction of the pendulum is left to the ingenuity of the experimenter. Gundersen and I use a vertical suspension that consists of a small metal shim that is attached to both the frame and the pendulum by metal clamps. Not having any shim stock on hand I put in a piece of stainless-steel erasing shield. Aluminum foil is too flimsy, but a piece of metal from a frozen-food pie tin would do. I built the oscillator in a small box made of copper-clad circuit board, supporting the components with tiny standoff insulators. The radiator plate is soldered to feed-through insulators at the bottom of the box.
"In making the receiving plates of circuit board I arranged matters so that one side of the board served as a receiving antenna and the other side was the ground. The experimenter should keep in mind that l/16-inch dual-sided circuit board has a capacity of 19 picofarads per square inch This capacity will affect the frequency of the tuned circuit. A two-inch-square plate will have a capacity of 76 picofarads and so will require an inductor of approximately 13.4 microhenries to resonate at five megahertz . It is good practice to tune the circuit to resonance with a variable inductor.
"To tune the receiving circuit, cover the transmitting antenna with cellophane tape to prevent the output of the oscillator from coupling directly into the receiving plate. Then wedge the transmitting antenna against one of the receiving plates and adjust the inductors for peak output of the diode detector. Repeat the process for the other plate. I start with both receiving plates about a quarter of all inch apart and then adjust for the desired sensitivity. I was able to find the inductor I needed at a store selling television parts. It was part of a 4.8 megahertz sound trap.' The inductor had a 75 picofarad capacitor in parallel with it, which I removed.
"If a variable inductor is not available, use a 10-microhenry fixed inductor and add a trimmer capacitor (variable from eight to 33 picofarads) across the inductor to tune the circuit. The resonant frequency of a parallel LC circuit is f = 10e6 / 6.28 X (LC)1/2, where f is frequency in kilohertz, L is inductance in microhenries and C is capacitance in picofarads. If L is 10 microhenries and C is 101 picofarads, 10e6 / 6.28 X (10 x 101)1/2 = 10e6 / 199 = 5,025 kilohertz. The difference between the capacitance of the circuit board and the capacitance required for the circuit to resonate at the desired frequency is supplied by adjusting the variable trimmer capacitor.
"The entire pendulum assembly including the oscillator was mounted on a piece of aluminum half an inch thick, about five inches wide and one foot long that I bought from a scrap dealer for a dollar. Any sturdy metal frame can be substituted. Wood should be avoided because of its tendency to warp with changes in temperature and humidity. An enclosure is essential to protect the pendulum from air currents. I put a grounded metal enclosure around the metal base to eliminate the radiation of stay radio interference.
"The damping device on the pendulum is needed to suppress fee oscillations. I made the damping mechanism by cementing one end of a bar magnet to the lower part of the pendulum arm. The magnet was partly surrounded by a solenoid, which was mounted on the supporting frame of the pendulum. The solenoid is a coil of 1,000 or so turns of fine magnet wire that I salvaged from a miniature synchronous motor. The coil is connected to the output of the summing amplifier through a 500 ohm rheostat in series with a 50-microfarad capacitor. If the pendulum starts to oscillate when the power is applied, reverse the solenoid connections. Push the pendulum slightly and then adjust the rheostat to the point where the swing is damped out within about two vibrations.
"The output of the summing amplifier is coupled to the integrator through a l,000-microfarad capacitor and a 10 kilohm resistor in series to the input terminal of the integrator. In addition to compensating for roll-off of the pendulum the integrator transforms the output signal so that its amplitude varies with the pendulum's velocity rather than with its displacement. When we were debugging this instrument, we found that, at least for amateurs, a seismometer based on a velocity response is more convenient than one based on a displacement response.
"During significant seismic events earth waves of a broad spectrum of frequencies are generated. Assume that the waves all have roughly the same amplitude. As the distance between the observing station and the epicenter of the earthquake increases, the waves of higher frequency are attenuated more than the lower frequency. If a signal that varies with the pendulum's displacement is desired, the gain of the seismometer must be large to resolve the high-frequency pressure waves. If the frequency response extends down to .01 hertz or so, the amplitude of the long waves (which is not attenuated as severely as the amplitude of the higher frequency pressure and shear waves) will saturate the instrument. If velocity output is the basis of operation, the amplitudes of the various sets of waves will be more or less comparable.
"Another practical consideration for an amateur, who is unlikely to have an underground room where he can mount his seismometer far from sources of manmade vibrations, is the thermal noise of the building where the sensor is located. This noise is easily identified because it can be correlated on a 24-hour cycle, although the timing of the noise varies from structure to structure. The cause of thermal noise is the expansion, contraction, tilting and so on that result from the uneven heating and cooling of the structure over a period of 24 hours. The noise can show up as a series of sharp spikes indicating sudden small releases of stress or as slow rolling one-minute waves from five to 10 times larger in amplitude then the ever present six-second microseismic waves that are recorded during quiet periods.
"I previously operated a Golitsyn sensor with a resonant frequency of about eight seconds. Therefore I had not encountered the phenomenon of thermal noise until my new sensor reduced the frequency response to the one-minute range. If a second integrator were added to the new circuit, the output would vary in amplitude with the displacement of the pendulum. The thermal noise would be enough to saturate an instrument that had been made sufficiently sensitive to record the microseisms of higher frequency.
"Gundersen and I used electrolytic capacitors to couple our alternating-current circuits. Because the capacitors are polarized, two would normally be connected back to back to make a nonpolarized unit appropriate for alternating polarity. This scheme, however, would cut the capacity in half. Here we resorted to a little trick. We adjusted the tilt of the seismometer to the point where positive potential appeared and remained at the output terminal. It was then possible to connect the sensor buffer to the integrator with a single polarized electrolytic capacitor. A tilt that generates an output of about +5 volts is adequate. The integrator is likewise biased by a source of reference voltage (a Zener diode), so that one polarized feedback capacitor and one polarized coupling capacitor to the output buffer stage will suffice in the circuit.
"Because of the extreme sensitivity of the instrument a fine leveling adjustment is required. I used a machine screw with 72 threads per inch. To support the screw I soldered two nuts onto two small pieces of brass that I cemented with epoxy to opposite sides of a piece of 1/8 inch aluminum.
"The entire assembly was attached to the bottom of the baseplate and provided with a shaft and knob so that adjustments could be made easily. The screw rests in the lubricated drill dimple in the bearing plate. One full turn of the screw raises or lowers the end of the platform approximately 350 microns.
"Assuming a base length of about a foot between the rear leveling screws and the front adjustment screw, the tilt of 350 microns corresponds to an angle of about 1,150 microradians. (A complete rotation amounts to 6.25 radians; one second of are is equivalent to about five microradians.) Less than one full turn of the adjustment screw will drive the output buffer (which has a gain of 10) from negative saturation to positive saturation. This amount corresponds to a tilt sensitivity of less than 30 microradians, or six seconds of arc, per volt of output from the buffer.
"Experience showed us not only that the pendulum must be shielded by a housing from air currents in the room but also that the free space inside the housing must be filled with a thermally inert material such as Styrofoam. The idea is to minimize the effective mass of free air within the enclosure. The convective movement of the trapped air will otherwise be communicated to the pendulum and will appear in the output signal as noise of significant amplitude at a very low frequency.
"All of this leads up to a final challenge to amateurs who build the instrument: the measurement of tides in the solid earth. From what I have read I gather that such tides typically cause a tilt of less than .1 microradian. I suspect that the measurement will not be easy because few of us are specially equipped to solve problems of thermal noise, man-made noise, temperature drift of the electronic components and so on. On the other hand, it is just these annoyances that make amateur seismology so much fun."
