See the Latest Abstract on another page.
The paper on the new instrument is currently being revised and updated (as of 12 Feb 98); this is the original draft. If you want to create a good printout of the report using microsoft WORD,, download an .RTF format of it ( about 210K) and print it out. The HTML version here does not have the formulas in it. The figures and drawings are available at Figures, Schematics,and Drawings on another page.
But first, here are new photos of the Beta (January 1998) instrument. See the latest Broadband records on another page.
A WORD OF CAUTION ABOUT THE LEAF SPRING: WHEN IT IS BENT IN AN ARC AS SEEN IN THE PHOTOS AND DRAWINGS, IT IS DANGEROUS, AND HAS BEEN KNOWN TO GET LOOSE AND FLY ACROSS THE ROOM. BE CAREFUL WITH IT.
Look here for a photo of the original (April 1997) version of the vertical seismometer.
Look here for a photo (64k) of the Beta (January 1998) version of the vertical seismometer. More photographs of the Beta prototype follow.
Here is more detailed (128k) view of the Beta (January 1998) version of the vertical seismometer. Showing more detail of the spring, the damper, the clamping post, and VRDT geometry, mostly what is shown in the mechanical drawing in the figures page, accessed as: The Mechanical Drawing of the Vertical Seismometer.
Here for a photo of Overhead view of the Beta version of the vertical seismometer.
You want to see a source for getting parts to make this?
If you want printed info on the homemade leafspring broadband seismometer, send me email. The documentation is not yet complete enough to provide all the details to build an instrument, but I am working on it. I hope to provide most of the documentation, including updated photos here, within the next year or so. But the figures suffer in being scanned, etc., so if you want a printed copy of most of them and the latest version of the report, (but no photos) send me a return label accress and 6 33-cent stamps; I have envelopes.
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Here is a Photo of the Feedback Coil and Magnet , with the mass on the end of the boom. The coil and magnet are made from from a large 10" stereo speaker. The green windings barely visible above the main coils are the calibration and temperature compensation coils.
Here is a Photo of the Feedback Coil alone mounted on the aluminum channel, The green windings visible above the main coils are the calibration coils.
Here is a Photo of the VRDT displacement transducer with nanometer resolution. The coils are mounted to the base frame, and the sensing vane is attached to a brass rod attached to the boom above.
Here is a Photo of the HINGES taken from above the hinge support of the original prototype. Some detail of the lower leaf-spring flexure can be seen.
Here is a Photo of the Horizontal Seismometer boom and frame, with the vertical pull-push hinge arrangement. All the parts of the hinge post are epoxied together. The main transducer coil (speaker voice coil) is mounted near the end of the boom, below the mass.
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Some details of the pier and the insulation boxes:
The photos of the pier are from October, and of the prototype seis, so the spring damping is not present. The electronics box is the 12VDC power supply, the +,- 9V inverter/regulator, the VRDT electronics, etc. You can see some "extra" large NP capacitors hanging out of the integrator amp.
The styrofoam is cut with an extended break-off style razor knife, but without being broken off. It is actually four 1" sheets cut and glued together w. spray contact cement. I can always tell by the data when I fail to close it up. Notice the stepped fitting at the corners. It should probably be three times as thick. The concrete blocks of the pier are set in a thick grout in a form on the floor,and grouted together. Massiveness is the key here. A tombstone would make a great pier. The draft-tight inner box is prefab shelving, because it is square and can be screwed together. The front and lid are removeable, but restrained with brass latches and a thin foam weahterstrip for the top lid. An important detail is that the three feet of the seis go through 1" holes in the bottom of the inner box, so the seis sets on the glazed tiles directly. Thin (1/4") foam sheet fitted around the feet, inside the box, stop drafts. The box itself rests on a square of 1/4" weatherstrip rather than directly on the pier surface, so the seis is the only object making firm contact with the pier surface.
A High Resolution Broadband Vertical Seismometer Constructed from hardware store and consumer electronics components.
by Sean-Thomas Morrissey
Summary
A very sensitive broadband vertical seismometer is constructed with readily available hardware items and consumer electronic components. While the mechanical period of the sensor is 2 seconds, a displacement transducer allows the use of a multiple feedback configuration that allows the effective operating period to be 150 seconds or more. The transfer function indicates a velocity response that is flat (down 2db) from 100 seconds to 30 hz. Active electronic thermal and atmospheric buoyancy compensation is employed, with a PC providing digital recording.
1. A leaf spring provides the suspension of the boom and mass for the vertical configuration. The leaf spring is the blade of a large drywall plaster taping knife.
2. The crossed hinge suspensions are made from bronze weatherstrip, and are glued in place. Most of the frame and boom are made from hardware store aluminum angle.
3. The displacement transducer is made from miniature audio transformers and simple electronics. It works as a variable reluctance sensor (VRDT) with nanometer resolution.
4. The main velocity transducer is made from the voice coil and magnet of a large stereo loudspeaker; it is the feedback coil of the broadband configuration.
5. Most of the 0.5 kg mass, which includes the main speaker coil, is of lead bar from the plumbing department.
6. A digital multimeter from Radio Shack, used with its' supplied software, allows 1 sample/second recording on a PC; digital seismograms are made with Mathcad. Of course, the digital recording possibilities with a PC are unlimited.
7. The usual noise sources associated with broadband sensors are readily obvious, including thermal variation of the mass position, buoyancy of the mass due to atmospheric pressure changes (storms, windy days, and the 3 to 10 minute acoustic gravity waves that indicate the passage of a weather front), local short period noise (it is in the basement of this farm house, 30 m from the street), and 3 and 6-second microseisms from hurricanes and low pressure storms off the east coast.
This is intended to be a simple descriptive narrative of this instrument as a home- hobby project, not a detailed recipe of how to reproduce it. The photographs, if available, are very helpful if studied in conjunction with this description. The author recognizes the necessity for the mixture of English and metric units and dimensions: American-made hardware is inherently non-metric. Also, since this is a "work in progress", the details here are based on the assembly of the prototype which was built as a "moment-of inspiration" activity. Assembly of a second vertical sensor (the beta vertical) is in progress; it is more compact and carefully designed so as to be documentable and reproducible. However, don't hold your breath waiting for detailed drawings and schematics.
First we need to consider an important point of the development of this Instrument:
A. Why a Fedback Seismometer ? ( rather than a basic velocity sensor ?)
A fedback seismometer can achieve a true broadband response because the parameters of the transfer function are determined primarily by four electronic components, which can be selected for the specific broadband performance desired, depending on the noise characteristics at the instrument site.
Very little of the mechanical system determines the sensor performance.
So almost any reasonable inertial or pendulum sensor will do if its' characteristics are within these approximate guidelines:
1. To (the mechanical period) is greater than 1 second.
2. The product of the mass (kg) and the period (sec) is greater than 1; the greater it is, the lower the noise.
3. The feedback transducer (which was the moving coil velocity sensor of the basic seismometer) has a low DC resistance but a very high force constant (Newtons/Ampere), of the order of 10x the mass (in kg). Seismometers designed for electronic amplification usually have a high resistance coil, and cannot be configured for feedback.
4. The displacement transducer has better than nanometer resolution with a similar noise floor; it is the source of the broadband output.
Minimal concerns for the mechanical sensor:
1. The mechanical dimensions; a smaller sensor can be sealed from the atmosphere, but other concerns may dictate a larger size.
2. In a vertical sensor, the spring constant and behavior need not be known; with feedback, there is minimal movement of the mass or boom and/or concurrent flexure of the spring.
It is important to understand the fundamental concept of this multiple feedback circuit. Simply put, the displacement transducer senses any slight movement of the mass with respect to the base or frame that is caused by acceleration forces acting on the frame, producing a voltage that is a function of the displacement. This voltage is turned into three characteristic currents that are fed to the feedback or force coil so as to attempt to prevent the mass from moving in response to the input acceleration. With this feedback taking place, the output of the displacement transducer becomes a voltage that is proportional to the input velocity of the frame. So when, and only when, the feedback is connected, the displacement transducer output is the very broadband (VBB) signal.
A further important point to note here is that there is no additional amplification or gain in the feedback circuit. The integrator amplifier operates at unity gain, so it has the same clipping level as the displacement transducer amplifier. There is nothing to add noise and limit the dynamic range of the output. So if the displacement transducer has a sensitivity of 1 volt/micron, and the noise level is 10 microvolts, or ten picometers, and the maximum voltage is 10 volts, the range is 106, or 120 db.
So a very broadband feedback seismometer has three feedback paths whose source is the voltage of the displacement transducer;
1: A proportional current, controlled by a fixed resistor Rp; this current also provides damping of the feedback; if it is omitted, the seismometer can actually oscillate at To.
2: A frequency dependant differential feedback current, through a fixed capacitor Cp.
3: An integral feedback, where the output of the displacement transducer is integrated with an time constant TI, and applied as a current through a fixed resistor RI to the feedback coil. This current effectively keeps the mass centered at periods longer than the integrator time constant.
These three components essentially control the response of the seismometer, as indicated on the following description of the transfer function of this seismometer. Since these three feedback paths are of relatively high impedance, a single low resistance feedback coil can be used. In fact, if the coil has appreciable resistance, the response is unstable at the short period end, since Rf is a coefficient of the 4th order term.
For a detailed analysis of the multiple feedback configuration the thesis by J.M. Steim is required reading, followed by the paper by Wielandt and Steim where the configuration is changed to the current fully broadband output. This author has also been working on a review paper based on these two papers that attempts to explain and interpret the very broadband seismometer for non-engineers. It is about 30% complete.
a: Here is the formulation of the transfer function; the parameters are similar to those in the thesis of J. Steim and the Wielant and Steim studies where:
For the mechanical system: r = displacement transducer constant, volts/mm (range: 80 - 1000 V/mm) Td = Displacement transducer time constant (less than 0.06 sec) Rf = force transducer resistance, ohms (range 50 -500 ohms) Gn = force transducer constant, newtons/amp (range 10 -100 N/A) To = Mechanical free period of the sensor, seconds (range 1 -15 sec.) M = sensor effective mass, kg
For the feedback system:
Rp = Proportional feedback resistor, ohms (range 100 - 1000k) C = feedback capacitor, farads (range 1 - 36 uf) TI = Integrator time constant, seconds (range 10 - 1000 seconds) RI = Integral feedback resistor, ohms (range 200 -2000k) Tn = The resulting effective natural period, seconds (range 20 to 600 sec)(A table below in part II, section B-2, lists some of these values for some known broadband sensors)
b: In the transfer function, "G" is actually conventional "G" / M.
c: Expression for effective free period: controlled only by electronic components.
d: Expression for effective damping is determined by electronic components and the mechanical free period. If Rp is turned off, the system is effectively under damped, and will oscillate at Tn.
e: Complete transfer function: a fourth order expression.
Selecting the actual configuration using the transfer function is done with Mathcad. One can start with common values and iterate on variations of, for example, the value of the proportional feedback capacitor Cp, and see what it does to the response. And if the proportional feedback resistor RP is too small, the damping term zeta will decrease, and a peak will appear near the effective natural period Tn in the response curve. If in fact you disconnect the proportional feedback resistor Rp from the feedback coil, and other parameters allow minimal damping, the seismometer boom will actually oscillate at Tn, and if Tn happens to be 100 seconds, this would be shown on the recorder. The main values that are readily changed are the integrator time constant TI, and the three elements of the feedback loop, Rp, Cp, and RI. .
Mathcad worksheets with examples of various configurations are attached: see Figure 2.
A: A word of Caution:
The author strongly suggests that all proper shop practices be followed in preparing the hardware, especially the use of gloves and goggles where appropriate, and all the recommended guards for power tools. I find a small drill press is essential, and I use a 62-tooth carbide blade in a power miter saw and/or a table saw to make neat cuts of the structural aluminum. ALSO, be careful with the leaf-spring; when it is bent in an arc, it has a lot of potential energy, and has been known to get loose and fly across the room or fling all the loose hardware off the table.
The leaf spring is made from the blade of a large drywall plaster taping knife. The original plastic handle is easily removed. The blade is 12" long and 3.5" wide, and 0.018" thick. For use as a suspension spring, it is installed as an arc with the ends separated by about 12 cm. This provides a force of about 5 kg, which will support the effective mass at the end of the boom when the spring lifting point is about 15 cm from the hinge flexure point. The mounting for "zero length" behavior of the spring requires that the ends of the spring be allowed to flex with the curvature of the spring. Clamping the ends of the leaf spring is the wrong idea for this design, since a clamped end then involves the rigidity of the spring itself. Both ends of the leaf spring are restrained by flexure-type supports. This is an important contribution of this design. Details will be described later.
A digression here regarding spring constants and what "zero-length" means (see Kisslinger); do these with mathcad: k = m*g / ( l - l0 ) and k = 4 * pi**2 * M / T**2 in an oscillating system
There is, of course, a three-way trade-off between the size of the mass, the strength of the main spring (and the spring contribution of the hinges themselves), the location of the boom support point, and the resulting mechanical period. The various possibilities have only been briefly explored with this leaf spring configuration. The major consideration here is a sort of "rule of thumb" (see reference 1, pg 2357) that requires that the product of the mass (kg) and the period (sec) be greater than 1 kg*sec for reasonable noise figures. Also, the transfer function needs a mechanical period greater than 1 second for reasonable component choices to properly damp the feedback system. So for the prototype a mechanical period of 2 seconds was realized with an effective mass of 0.5 kg. Lighter hinges in the beta vertical provide a Tn of 3 to 4 seconds.
One would intuitively think that a velocity transducer for a seismometer should have a coil with as many turns as possible to maximize the output, and in the age of electronic amplifiers, high impedance coils have been the norm. (In fact, some seismometers have coils with such high resistances that they cannot be used for damping.) On the other hand, the transfer function for a multiple feedback seismometer has a problem with a large DC resistance in the feedback coil, which causes instability. In commercial fedback sensors, the feedback coils have resistances of the order of 100 ohms. So consideration of a very low impedance stereo speaker as the transducer is not obvious, except that the speakers have very strong ceramic magnets. They are also plentiful and relatively inexpensive. So a large Radio Shack speaker was selected; the 10 inch unit has two 4-ohm coils and a 20 ounce ceramic magnet with a specified flux density of 7.5 kilogauss.
The force transducer constant of the speaker coil is easily determined by using the assembled seismometer displacement detector as a null position indicator. First the boom is centered, as indicated by the VRDT. Then a convenient test weight is applied above the centerline of the coil above the magnet, and then a small DC current is applied to the main coil and adjusted until the boom is raised up and exactly centered again, as indicated by the VRDT. With the original instrument, a 1 gram weight required 0.775ma to balance it, which calculates as 12.654 Newtons/Ampere. This is actually a very reasonable figure compared with other sensors; see the table below.
To confirm this value, the speaker coil was examined and determined to have 162 turns at a mean diameter of 39.5 mm. Using the formula G = B * L *10-6 N/A (or V/M/sec), where L is the total length of the winding in cm, and using B = 7500 gauss, a constant of 15.08 N/A was calculated. Since the constant determined by the force balance is less, it indicates that not all the winding is within the magnetic field, which is the case.
That this is a reasonable value for a feedback force transducer is supported by the data in the following table, which includes data on existing and prototype broadband sensors. This homemade sensor is labeled "8-ohm", and the data is for the 150-second configuration; 20,40, and 90 second variations have been implemented.
Name or model Unit 8-ohm STS-1 STS-2 S-5k S-6k S-7k GDMG Effective Period sec. 150 360 120 600 30 120 40 Effective Mass Kg 0.5 0.6 0.3 11 0.5 1.14 ? Mechanical Period Sec. 2.0 6 4 15 0.5 1.5 ? Displacement Xducr. V/mm 370 800 570 400 520 740 ? Feedback Coil Res. Ohms 8 200 50? 469 120 50 ? Feedback Xducer N/A 12.65 24 50 83 35 29 ? Integrator time Sec 240 1036 80 400 20 100 ? Integrator R M.ohm 0.1 0.32 0.60 0.41 0.12 0.27 ? Proportional C ufarad 24 4-8 7.8 6.3 10 13.4 ? Proportional R M.ohm 1.4 3-9 1.7 2.1 6.7 3.0 ? Effective damping zeta 0.87 0.91 ? ? ? ? ? Output, VBB V/M/s 1600 2400 ? ? ? ? ?
To dismantle the speaker use a sharp Xacto style knife; carefully remove the cone by cutting around the outer edge and around the lower support diaphram. The central dome is also removed. Cut off the leads near the underside of the cone. Very carefully remove the coil assembly: if it gets damaged, it won't fit back into the magnet gap. Then cut away all but the last 1-2" of the cone. I then cut a square notch in both sides of the remaining cone to fit a 1/2h x 3/4"w x 6"l aluminum channel to the coil, carefully fitted so it rests directly on the inside end of the coil, epoxied to both the end of the coil and the base of the cone on both sides. Drill a pattern of mounting holes in the aluminum channel first, though, so it can be mounted to the boom. So the coil assembly, which is still attached to about 2 cm of the central part of the cut away speaker cone, is glued to the aluminum channel that is fitted between the original coil lead attachment points of the speaker cone, flush against the end of the aluminum tube form of the coil. A miniature terminal strip (a 16-pin IC socket) is also glued to the channel as a place to connect the output leads to the coils. Additional coils are wound above the main coils for calibration and the dynamic temperature compensation. These are well away from the intense magnetic field that the main coils move through in the poles of the magnet, but there is more than sufficient magnetic fringing field to make them quite effective. The three auxiliary coils are 1 turn and 5 turns for calibration, and 25 turns for the temperature feedback; they are wound with # 36 magnet wire.
This whole coil assembly is attached to the underside of the free end of the boom with threaded spacers. The output leads are lightweight phonograph arm wires that are led down the inside of the main boom channel to the hinge assembly, where they are looped lightly to the hinge support frame and fastened with tape. These may be a source of noise, and may be replaced with the more conventional seismometer output arrangement of very fine magnet wire loops to conduct the signals around the hinges.
To prepare the magnet, first tape over the annular gap and the 1/2 inch holes through the pole with heavy tape (like duct); you don't want magnetic filings in the gap. Then cut away the steel cone frame just above the magnet face; I have used metal shears as well as a hacksaw. The metal shears leave a ragged appearance, as on the prototype. The hacksaw makes lots of filings that have to be pulled off of all parts of the magnet with sticky tape. I eventually overwrap the outside of the magnet with stretched tape to keep the remaining filings trapped. Remove any filings from the annular gap with tape.
The speaker magnet is mounted with a 3/8 " aluminum or stainless threaded rod or bolt through a convenient hole through the central magnet pole to a stacked pair of 4" aluminum outdoor electrical box which is fitted with wide flanges that rest on the seismometer base frame. The magnet is easily removed to transport the seismometer without risking damaging the coils; to do so, either the vane or the coils of the displacement transducer must be swung out of the way to free the boom. To install the magnet, it is positioned below the coils and gently moved until the coils start to drop into the magnet gap. As this occurs, the magnet must be moved slightly toward the hinges to accommodate the arc of the coil movement. The fine positioning of the magnet is very important; the alignment can visibly be determined when the clearances of the coils in the gap are symmetrical on all sides, and freedom of movement can be determined by observing free oscillations with an analog meter or an oscilloscope. The magnet is clamped down to the baseplate via the aluminum flanges of its' mounting box or the 3/8" bolt through the base.
The vertical position of the coils in the magnet gap is controlled with the trim masses on the boom, a coarse 20 gram brass weight, and a 1 gram slider made from a piece of the hinge material. Having about 3 mm of the coils visible above the magnet poles seems to be satisfactory, and places the auxiliary coils close enough to the magnet to be effective; at this position the sensing vane should be centered in the displacement transducer. With the displacement transducer moved out of the way, the boom or coils should freely move vertically about 2 mm either side of the rest position. The mechanical period should be about 2 seconds.
The heart of a broadband seismometer is the displacement transducer; it is the sole source of the output signal. Without the multiple feedback electronics, its' output is pure displacement; when the feedback elements are connected to the feedback coil, its' output is the full broadband velocity signal. So it is critical that it has low noise, high dynamic range, and is linear over the range of the feedback integral.
Two types of displacement transducers are usually used in fedback seismometers, the LVDT and the capacitive bridge. This is not the place to go into real details about these; see D. C. Agnews' excellent discussion. However each has its' drawbacks, so neither is used in this seismometer. The LVDT's main disadvantage is the need for the critical alignment of the moving sensing core inside the fixed coils; the clearance is less than 0.1 mm, and any non-linear or lateral movement of the seismometer boom or mass will cause the core to touch and drag on the coils. It is also quite difficult to construct. The common solution is to use a capacitive bridge transducer, where a moving vane moves between two fixed plates that form a capacitive bridge that is unbalanced by the movement of the vane. With proper geometry, these can be very sensitive and linear over a range of several hundred microns. However, they are difficult to construct and have a working gap of less than a millimeter, and are prone to off axis sensitivity. They usually operate at relatively high frequencies, from khz to mhz, which complicates design and implementation problems.
For this seismometer, a sensor similar to the capacitive sensor is used, called a variable reluctance displacement transducer, or VRDT. Here a ferrous vane moves between two inductors that are part of an inductive bridge. They are commonly used in pressure transducers, where the moving element is the sensing diaphragm and the coils are imbedded in the housing. To construct one, small 500-ohm audio transformers are dismantled (by heating the wax that holds the ferrous laminates together), and the cores are reassembled in an "E" pattern that is open on one side. Two such coils are epoxied to notches cut into small (1/2" x 1/2") aluminum channel, with a gap of about 2 mm between them. A drawing of the assembly is attached. The sensing vane is made from the laminate of a larger transformer, and has about twice the area of the coil pole faces. The electronics consists of a stabilized sine-wave audio oscillator operating at about 5 khz (the commercial electronics), or 600 hz (the recycled tiltmeter electronics), the reference bridge, a synchronous demodulator ( a DPDT cmos switch driven by the oscillator), and an output amplifier. It is calibrated with a differential micrometer in 10 micron steps, and is linear over 500 microns (it can also be calibrated with the mechanical sensor acting as a beam balance). Its' output is around 30 to 50 mv per micron, depending on the width of the gap and the amplification. For the feedback electronics, a further gain of 10X to 20X is needed for a value of around 500 000 volts / meter. The electronics for the VRDT can be purchased as module from the pressure transducer company, or assembled with common parts. It is essential that the displacement transducer time constant Td be short with respect to the seismometers' high frequency response. But when using the commercial VRDT electronics module, which has a response to 1 khz, the feedback system will oscillate at a few hundred hertz, which causes an audible hum of the sensor. A passive low-pass filter corrects the problem.
Common amplifiers (op-amps) can be used for the voltage gains needed, since we are not pushing any gain-bandwidth figures. Ideally only three are needed: one for the additional displacement transducer gain (10x to 20x), one for the integrator, which is essentially a one-pole low pass filter, and one for the output line driver, to provide an additional 10x or more gain to the recorder. The LM308a amplifier is preferred over the common 741 op-amp because with its' FET input it has of low noise near DC and low input offset voltages. Another selection would be to use the OP-177 or a similar unit. The pictorial drawing of the sensor shows the simplest configuration of these. In reality, each amplifier is two stages, one for the low-pass filtering, and a follower for the voltage gain. The integrator uses the classical three amplifier instrumentation amplifier configuration to present a very high impedance to the integrator capacitor so its' leakage current doesn't cause DC drift and noise.
The broadband output signal is coupled to the recorder or DAC through the line driver amplifier, which has a large input capacitor and resistor (1000 uf into 1 meg-ohm) to block the near DC mass-position signal from the recorder, which commonly would have limited dynamic range, and if it is a helical drum recorder, the traces would cross each other with temperature and earth-tide meanderings. If you happen to have a 24-bit digitizer, this, of course, is not necessary. Also, for a monitor drum recorder, a twin-T 6- second notch filter is advisable to reduce storm microseisms.
Other electronic monitoring ................... Mass position, VBB, etc .....tba
The base or frame of the sensor is made of structural aluminum channels and plate. There is nothing special about it other than it is rigid and has a large thermal inertia. In form it comprises an inverted channel about 20 cm in width and 60 cm (24") long. The original base is a laminate of six aluminum plate and angle extrusions "pop-riveted" together; this appears to be a mistake in that thermal expansion causes step-like noises. The beta version is only three pieces, and only 18 inches long. A single large extrusion would be preferable.
Everything possible is made of aluminum for thermal considerations; however most of the smaller hardware is non-magnetic stainless steel. No magnetic materials are used in the construction. The principal problem here is that the main (speaker) magnet is not shielded at all, ...yet. Even the displacement transducer, with its' ferrous cores and vane, must be located at least 10 cm from the large magnet.
At one end of the base is a rigid vertical support about 20 cm high to support the hinge mount for the boom. It is bolted to the base with 1/2" aluminum bolts. The fixed side of the hinge assembly is bolted to this stand and the boom is bolted to the hinged side, At the other end of the base is the support for the main magnet, consisting of a cast aluminum box mounted with provision for fine lateral positioning of the magnet. The base frame has leveling feet about 2 cm long finished with 3/16" stainless steel cap nuts. These protrude through the floor of the covering box, which is made of pre- made shelf boards. The cover must close and seal tightly because drafts blow the mass around. Some provision for dense outer insulation is also helpful.
The hinge flexures are made of thin 0.005" tempered brass or bronze strips, 0.75" wide (half that wide in the beta unit). The material, used for weatherstripping, can be purchased at any "True-Value" hardware store. Rather than making a clamping arrangement to retain the hinge flexures, they are simply glued with quick-set epoxy to the 1.5" x 1.5" x 0.125" aluminum angles that form the classical crossed hinge assembly. Clearances are maintained where the flexures cross so the epoxy doesn't flow in.
The boom is a 50 cm length of 1" wide by 0.5" high aluminum channel. The boom needs to be this long not only to achieve the mechanical period needed but mainly to provide a somewhat linear movement of the coil in the magnet gap. As it is, a range of 4 mm of the coil is possible before it jams in the magnet because of the curvature of the arc of its' motion. The circular gap is only about 1 mm wide. In commercial seismometers, a much larger magnet gap of several mm is used, with machined plastic coil forms.
The mass consists of about 0.35 kg of solder bars from the plumbing department. Two short 4 cm lengths of a "5 pound" bar are bolted (with a stainless steel eyebolt) above the end of the boom. The total effective mass, which includes the coil assembly and the slider "trim" masses, is about 0.5 kg.
For coarse mass adjustment, the heavy (about 20 grams) brass hex clamps that are used for setting a "T" square for cutting stairsteps are used; they slide along the edges of the boom channel, The fine mass position trim masses are made of short lengths of the brass hinge material formed as an inverted U to slide along the boom.
The design of the prototype was done with little consideration of physical temperature effects of the boom support structure on the mass position, other than to observe mechanical symmetry where possible. Certainly a careful study of the mechanical system might lead to a determination of where most of the differential thermal expansion takes place and suggest design changes that would reduce it. However most of the thermal effect seems to be from the leaf spring itself, which becomes more rigid with decreasing temperature, raising the mass. The effect is of the order of 100 microns per degree C, or about 5 volts at the integrator output. Once a second sensor is constructed, this problem can be investigated.
The best offense here is a good defense, namely to protect the sensor from thermal variations, especially within the passband of the feedback system. A remote corner of a basement room is vary advantageous, and a multi-layer, tight-fitting styrofoam enclosure at least 4" thick will reduce variations at the diurnal level, especially those caused by the air conditioning system. Further long-term thermal protection can be achieved by more thermally massive protection, such as an enclosure made from 6 layers of drywall plasterboard with styrofoam between each layer. But longer term, up to seasonal, effects will remain, which seem to require the boom to be recentered. There is also a slow relaxation of the spring or other structure of the prototype sensor which so far (after 4 months) requires it to be recentered about every two weeks. ( A motor-driven centering weight on the boom is being considered).
A temperature sensor acting in a separate feedback system of the seismometer has the potential of being a serious noise source, causing more noise than it eliminates. It also must assume that the mass position change with temperature is linear, which may be true for gross thermal variations. Since the noise problem with the prototype instrument was a real problem when it was running on the garage floor, it was worth trying. It does work, but is an additional electronic complication. Relocating the seismometer to an insulated concrete block pier in a corner of the basement greatly reduces the thermal problem.
Dynamic temperature compensation: describe: Sensor, reference voltage, LP filtering, insulation of sensor Adjustment
Barometric noise, affecting the bouyancy of the mass in the atmosphere, is the major problem with broadband vertical seismometers. A formula from Sorrels et al, 1971, describes the problem: Wa = Describe the experiment: Equip a compensated aneroid (dial) type barometer with the VRDT. High-pass (gt. 1000 second) connection to an auxiliary coil.
A: Displacement transducer: borrow a differential micrometer, or use the seis as a beam balance, or use shim stock to introduce small displacements at the VRDT. Details later.......
B: Main velocity / feedback coil: see above.
C: Calibration coil: how to use it to use the FFT of a step pulse to get the response. Basically, a small current introduces a step in displacement of the sensor. This results in a transient pulse in the VBB output as well as a small DC offset. The FFT of the voltage produced by the transient pulse is divided by omega2 to get the velocity response, which is compared with the transfer function. This produces good results well away from the nyquist period (1/2 the sample rate), but can be quite noisy at short periods. See figure 12 below. The generator constant of the calibration coil can be determined as in B above, and multi-frequency sine wave calibration can also be done.
A: Recycle an old drum recorder by converting it to use a hot stylus on fax paper; it has the advantage of possibly providing an accurate clock and additional amplification and low-pass filtering. For the prototype sensor operating in the basement of the farm house here, the noise of cars on the street about 30 meters away needs to be heavily filtered above 5 hz, while causing little attenuation of 1hz data from regional and global earthquakes. This particular recorder was designed for micro-earthquakes, so it did not have a response to long period data; a minor modification of its' filters to pass DC signals corrected the problem so it would record broadband data.
B: Digitizing the data with a PC
1: Using the Radio Shack digital multimeter for 1 sample/second LHZ data: This is a multi-function digital multimeter that functions as a "plug-and-play" digitizer; the resolution is 12 bits, so the 200 mv scale is used, providing 0.1 mv resolution. It comes with data logging software for DOS and Windows that writes *.txt files that almost anything can read. Most of the output file is useless verbiage, and amounts to about 3 megabytes per 24 hours, so the disk space has to be cleaned up regularly. Quick editing makes it palatable to Mathcad, so graphic plots, spectral analysis, etc., are readily done. Samples of "digital seismograms" are attached.
The digital meter (RS 22-168) battery lasts only about 72 hours, so a modular AC-DC, 9 volt "cube" style adapter is needed for continuous operation.
The major short coming of this digitizer is that it uses the PC clock for its' time reference. The clock in this PC varies from true GMT by as much as 10 seconds, so accurate time picks are not possible. However, this is not a major concern, since it is not anticipated that this data would be used as part of a network for earthquake location.
2: Plan B: ..........tba.........the 12 and 16-bit...DACs in use by the PSN..........EMON, in its' various adaptations, etc .......Software available for downloading ..
3: There are innumerable commercial/ industrial PC-based digitizers available starting at about $100, and lots of software options for logging the data..
C: ideas for making a simple drum recorder: Use a speaker for "pen motor"; Thermal recording: FAX paper; Rolling log drum
1. Aluminum angle, nuts and bolts, miscellaneous hardware: $80 2. The main transducer (10" speaker), sale price: 40 3. Electronics parts, VRDT transducer coils, amplifiers, etc. 120 4. A decent 12VDC power supply, DC-DC converter 50 5. Enclosure (shelf boards, hinges, etc) and insulation 50 6. Digitizer: e.g: RS 22-168 digital multimeter, sale price 110
A prototype has been assembled: the vertical hinge
A WWNSS-type LP vertical successfully operates at an effective period of 600 seconds using an almost identical feedback system. The WS-5000, as it is known, has a high quality factor (15 seconds X 11 kg mass), and the 500 ohm coil will work for the feedback. (see table B-2 above, where it is designated the S-5K). The lingering problem in extending the response to very short periods is the massive coil spring, which rings, especially laterally, raising the mass slightly, causing bumps in the output when someone tromps down the stairs that the vault is located under. The large steel case does not provide protection from barometric noise, but the large mass helps. Acoustic waves of 10 to 60 minutes are seen on the recorder.
1. Block diagram of the leaf spring vertical sensor, showing the basic configuration of the mechanical sensor and the feedback electronics.
2. The Mathcad worksheet showing the parameters of the transfer function, and the resulting VBB velocity response.
3. Drawing of the details of the displacement transducer (VRDT) construction.
4. Schematic of the VRDT oscillator.
5. Schematic of the VRDT bridge, AC amplifier, demodulator, and amplifier
6. Plot of the VRDT output, showing its' sensitivity and linearity.
7. Schematic of the instrumentation amplifier used for the integrator
8. Schematic of the general-purpose two channel line driver amplifier which is used for additional gain for the VRDT, and for amplifying the high pass of the VBB output for the recorder/ADC. (along with a table of component selections for various gains)
9. A block diagram with details of the electronics, feedback, and monitoring system, with suggestions for options, like remote centering.
10. Samples of data: LHZ digital seismograms of events, comparing the waveforms at the same scale with data from regional broadband stations:
a:
11. Noise studies, comparing the PSD with that of regional broadband stations
a:
12. Results of a calibration step: comparing the response recovered from the FFT with the response predicted by the transfer function from 2 to 1000 seconds.
13. An assortment of photographs, each worth a thousand words.
Geophysical Instrumentation Consultant
(since 1969)
Seismic Instrumentation Engineer at
St. Louis University,
Department of Earth and Atmospheric Sciences
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