Making My Own Seismometer
I have been asked about making a seismometer so many times that I have started to compile information. The topics include:
1.Historically significant seismometers.
2.Earthquakes, how much do they move the ground . Also, include the importance of building vibration and factors related to locating a seismometer
3. Basic mechanical designs. Including detains of the theory for the Lehman seismometer and gravity meter.
4. Basic sensor designs.
5. Recording systems, from ink to computer.
6.Calibrating my seismometer. The write-up given below.
7. Measuring earthquake magnitude.
8. Accessing other data. Provide a historical review of what seismologists had to do to get data. Give examples of a currently active data sources.
9. Data formats and programs.
Chapter 6. Calibrating My Home-Made Seismometer
Richterís classic textbook titled "Observational Seismology" defined a seismometer, as an instrument for which the constants are know well enough to determine ground motion. Richter struggled with a major difficulty facing all the early seismologists. Namely, the seismometers were individually constructed in the early 1900ís and there was little adherence to standards for constructing instruments and recording data. This situation is similar to that faced by amateur seismologists today when they construct their own seismometer or purchase a commercial instrument. Consequently, the sensitivity to ground motion of these early seismometers and the homemade instruments of today could differ widely. Many records of earthquakes exist now for which the instrument response is unknown. Calibration is essential for accurate measurement of earthquake magnitude, in particular, for measurements used for statistical studies and statistical comparisons of earthquakes in different areas. Even if the seismometer constants are known, the lack of computers in Richter's time would have made corrections to ground motion a difficult computational process. The Richter magnitude scale eliminated the uncertainty in instrument response by limiting magnitude computations to earthquakes observed on one particular instrument, the Wood-Anderson torsion seismometer, and by specifying itís gain, free period and damping. With digital data and today's desktop computers, calibration is not so difficult a task. This objective of this chapter is to explain how a homemade seismometer may be calibrated.
An important component in sharing data from a seismic station is maintaining a calibrated system. Calibration is essential if data from a seismometer are to be used for research, such as for computing magnitudes and for comparing the signals generated by the earthquake source. If everyone used identical instruments and did not change any of the settings or constants, records could be compared directly, but computation of the ground motion would still require calibration. The World Wide Standard Seismograph Network (WWSSN) which originally consisted of over 159 stations was installed in the early 1960ís. With the WWSSN instruments, calibration and design standards were prime concerns. Standard calibration signals consisting of a known acceleration function and the relevant constants were marked on each record. This calibration pulse and the associated constants contain all the information needed to define the seismometerís response. Coming as it did at the initial phase of the revolutionary ideas of the new global tectonics, the WWSSN facilitated significant advances in the understanding of crustal tectonics and the structure of the Earth's interior. The WWSSN data and much of the seismic data through the 1970ís were recorded photographically or on analog magnetic tape. Today, digital recording and the advent of low-cost seismometers that can record directly on personal computers has started another revolution in seismology, making possible more detailed images of the Earth's structure. Such instruments could take seismic recording out of the research laboratory and make seismic data widely available through open exchange over the Internet. For home-based systems to contribute to research, they will also need to be calibrated.
The seismometers of today record data in digital formats. Instead of using a portion of the record for a calibration pulse, as with the WWSSN data, the instrument calibration can be condensed and included in a separate file or as a header to the data file. The format of the header and/or data files is usually transparent to the user. In practice, the format depends on the recording system and the analysis system built for the seismometer. Problems can develop when attempting to convert data from one system to another, because the calibration information may be incomplete or expressed in different formats. However, when the calibration facts are complete, techniques borrowed from signal processing theory can be used to generate seismograms that look like seismograms recorded on any system. Only the noise and sampling rate for data recorded on the originating system limit the conversion of the appearance of a seismogram in one recording system to another.
The techniques used to calibrate new digital systems are the same as those used to calibrate simple systems of any age and design. A known force is applied to the seismometer mass and the response is measured. The simplest force is the gravitational attraction of a small test weight that is lifted off the seismometer mass. This is referred to as a weight lift test. The same effect occurs when the test weight is placed on the mass, but this is unreliable because variations in momentum of the test weight when it hits the seismometer mass cause variations in the signal amplitude. Alternatively, a force may be applied by an electromagnetic force, that is by a motor. The motor typically consists of a calibration coil placed near a magnetic portion of the seismometer and the force applied to the seismometer is proportional to the current sent through the coil. The signal generated when the small test weight is removed, or when a current is sent through the calibration coil, is the calibration pulse. The calibration pulse contains the information needed to compute the frequency response of the seismometer. The rest of the information, the gain, can be obtained either from a careful measurement of the mass and mechanical behavior of the seismometer, or by a comparison of two seismometers sensing the same signal. In this chapter the technique for computing the instrument response using a weight lift is given first, and the simpler comparison technique is given second.
The Weight Lift
In the weight-lift test a small test weight is placed on the seismometer mass. The force, F, applied to the mass is the product of gravitational acceleration, g, and mass of the small test weight, m. Then, by using a light thread attached to the weight or a lifting device, the weight is carefully removed. The change in force experienced by the seismometer mass is given by the removal of the gravitational attraction of the small mass. We do not use the weight drop method because the momentum of the small test mass can not be easily controlled or determined and the signal amplitude is unreliable. The resulting signal is recorded for analysis.
The mass in a seismometer may move with a linear motion or may rotate about a fixed axis. Most long-period seismometers have a mass that rotates about some pivot point. The most common short-period geophones have springs designed to allow only a linear displacement of the seismometer mass. The calculations for calibration of seismometers with linear and rotating masses are similar. However, the linear systems measure mass, whereas the rotating systems measure moment of inertia. Also, they differ in the treatment of the placement of the small mass used in the weight lift.
In the weight lift test the first thing to determine is the weight of the small test mass. It is possible to use standard scale weights, but often difficult to handle them because of their small size and inconvenient shape. A simpler technique is to weigh a sheet of paper or a long wire and then cut off a measured fraction to obtain a calibrated weight. For example, a common paper used in copy machines (for example, Cascade X-9000) lists its weight as 75g/m2. This is equivalent to 4.524 gm/sheet, or 0.0075 gm/cm2. The measured weight of a sheet of this paper was 4.55gm, or 0.00761gm/cm2. The difference may be explained by moisture content and normal variations in manufacturing processes. Then by cutting the paper in 1-cm wide strips, various weights can be generated by measuring off an appropriate length of the strip. The weight lift using a wooden stick is demonstrated in Figure 1. It was performed using a 6-cm2 strip of paper that weighs 0.0456 grams. We folded the strip into a V shape and placed it upside down on the mass and lifted it with a light wooden stick.
For linear spring systems, the location of the test mass is not important because its effect is independent of position. That is a vertical force placed on the system has the same effect when placed anywhere on the mass. However, for rotating systems the relevant force is a torque and its strength depends on the distance from the axis of rotation. In rotating systems the weight should be placed at a distance from the axis that is determined by the moment of inertia. If that position is not convenient, the torque can be corrected by measuring the distance from the axis of rotation. Then the mass is correct for the equations for an equivalent linear system. When the seismometer has settled down, the weight is carefully lifted using a gentle upward motion. The lifting device should be non-magnetic and should not cause the seismometer to move. Because the seismometer is extremely sensitive, the movement of a magnetized piece of iron, or any change in the magnetic field will contaminate the seismometer response. Also, care must be taken to avoid touching any part of the seismometer or the seismometer base because any movement there will also be sensed by the seismometer. Avoid generating wind disturbances by using slow motions because winds can also move the seismometer mass. Some seismometers protect the mass from wind with a case and utilize a remote system for lifting the weight. The object is to observe the response of the seismometer to the step change in acceleration (generated by removing the test mass) without introducing extraneous noise.
The response of the seismometer in Figure 1 to a step in acceleration is shown in Figure 2. This seismometer is under damped and oscillates with a period that is close to its natural or resonant period, in this case 1.45 seconds. A heavier oil or larger damping vain could improve the response of this seismometer, but the under-damped system is used here for illustration. A system that has about 70% damping will just overshoot with a ratio of 14 to 1 for successive peaks. A damping coefficient of 70% (overshoot of 14 to 1) is ideal for a seismometer response because it yields the largest range of frequencies with a constant response. That is, for a wide frequency range, the seismometer amplifies all frequencies the same amount. The slight under damping increases the amplitude of the response near the natural period, counteracting the attenuation introduced by the damping. Critically damped systems do not over shoot. Under damped systems will ring for a long time. Some early systems were set to record as under-damped systems to give them higher gain. However, this is not desired because the ringing distorts the waveform and makes it difficult to observe individual phases. In Figure 2, the amplitude indicated for a test mass of 0.0456gm is 220 mVolts. Because the digitizing system was operated at high gain, the seismometer signal was a factor of 1000 smaller or 0.220 mVolt.
The free period is easiest to observe when the damping of the mass is minimized. Some seismometers allow removal of the damping mechanisms, such as the oil bath shown in Figure 1. The free period can be measured directly from the time between peaks in the weakly damped calibration response. Figure 2 shows a lightly damped signal. We measure the time between two successive zero crossings in order to obtain the fundamental period. In the example of Figure 2, the period is 1.45 seconds and was computed by counting the points plotted at the 20 samples per second digitizing rate.
The rotational systems and the linear spring systems can be shown to be equivalent for purposes of calibration. In the linear system, the frame moves with the ground and for displacement sensors the resulting displacement of the mass is the same as the ground displacement. For the rotational systems, the movement of the frame causes a rotation of the mass as well as a displacement of the frame from the mass. Hence, the actual displacement of the mass from the frame depends on the position of the measurement. In rotating systems where the mass is concentrated enough to be considered a point mass, the displacement is equivalent to that of a linear system for small displacements.
In seismometer analysis, the response is assumed to have a restoring force that is directly proportional to the displacement. This is a linear system. However, linear systems are difficult to design for systems with periods greater than 1.0 second. Long period response is achieved by increasing the mass or dimensions of the system. When this is impractical, non-linear systems are used. In non-linear systems the restoring force is nearly linear and small near the equilibrium position and increases with greater displacement of the mass. In non-linear systems, the period is dependent on the amplitude when it exceeds the small linear zone near the equilibrium position. Hence, in non-linear systems the linear zone should be large enough to accommodate the maximum displacement that is expected, 0.1 to 1mm. Non-linearity in the restoring force is an unavoidable consequence of techniques used to lengthen the period of a seismometer, but most systems are sufficiently linear over a 1 mm displacement to not introduce measurable errors. To test for non-linearity, the period can be measured at different amplitudes, starting with the largest amplitude expected for a large earthquake recorded at distance, about 1mm.
Seismometer Mass or Moment of Inertia
In rotating seismometers, the moment of inertia should be computed and used in a calibration. However, it is convenient to convert the equations and parameters to those of an equivalent linear system. The moment of inertia of a rotating system, C', where the rotation is about a point separated a distance d from the center of mass is Cí = Md2 + C where C is the moment of inertia about the center of mass and M is the total mass. If the mass is concentrated enough to be considered a point mass, then the moment of inertia is small about the center of mass and the moment of inertia for the point mass can be approximated by Md2. If the mass is not a point mass, then the moment of inertia needs to be computed from its shape of the mass and its supporting elements. Examples for computing moment of inertia for solid bodies of various shapes can be found in most physics textbooks. For example, the integral form for computation of the moment of inertia,
for a thin rod of length L and mass M gives a moment of inertia at its end of C=ML2/3. For a seismometer mass like the AS_1 that can not be approximated by a point mass, the moment of inertia is found by finding the mass of each component and approximating each (for example) as either as a rod or a point mass. For a system of connected components, the total moment of inertia is the sum of all the individual contributions. The computation may be easier if one uses the relation C'=Md2+C given above. First the center of mass is found. Then the moment of inertia, C, about the center of mass is computed. The moment about an arbitrary point can be found from the equation for C' above. In order to use the equivalent relations for a linear system, an equivalent distance de for the total mass is needed. We obtain the equivalent distance from Mde2= Md2+C = C', and thus de=Sqrt(C'/M)
The position of the weight is important in systems that rotate. The torque applied by the test mass is the force applied perpendicular to the line from the axis of rotation, and is proportional to the distance from the axis of rotation. If the line from the axis of rotation to the test mass m makes an angle of a and the test mass is a distance dm from the vertical, the torque is given by [dmmgSin(a )], where g is the acceleration of gravity. In most system designs, the test mass can be placed on a level with the axis of rotation and the torque simplifies to dmmg. It can be seen from this that the force applied is a function of distance from the axis of rotation. A weight lifted close to the axis of rotation will have much less effect than one lifted off the center of mass. To correct for the distance from the axis of rotation, we use a force defined by dmmg/d e. For linear systems, the applied force is given simply by mg.
In the seismometer shown in figure 3, the portion of the swinging arm sensitive to vertical movement consists of the main block, the coil and connecting rods. The main block has a density of 1.9 gm/cm3, which was computed by measuring the dimensions and weight of a small sample. The measured dimensions of the large block and its density give a mass of 250 grams which we assume to be a point mass at its average distance. The coil weight was measured prior to installation and has a mass of 74gm. The small rods were also weighed prior to construction and have a mass of 85gms for the longer support pieces and 25gm for the position sensor rod and the damping vane. The effective seismometer mass can be approximated by the sum of the mass at its average distance. The moment of inertia is computed and added to the moment of inertia for the support rods. The equivalent distance and total mass are then computed. The total mass is 395gm, when the small weight used to center the mass is included in the total and the equivalent distance indicated the position to place the test weight.
The Calibration Coil
The calibration coil provides an electronic substitute for the weight lift. The force applied to the seismometer mass is proportional to the current in the calibration coil. The motor constant for the calibration coil is the constant that allows conversion of the current to its equivalent acceleration. Many seismometers are manufactured with both a sensing coil and a separate calibration coil. If the seismometer lacks a calibration coil, one may be added if there exists sufficient space and easy access to the sensing coil. On the AS-1, the sensing coil is mounted on the base and is easily accessible. A calibration coil can be added by winding and securing 10 to 25 loops of wire around the outside of the sensing coil.
A constant current that is sent through the calibration coil is equivalent to a weight sitting on the mass. As with the weight lift, the removal of a constant current is more reliable than putting a current into a coil. Electrical transients associate with starting the current load could affect the signal, whereas when stopping a current, the calibration coil effect can be shorted to eliminate other signals. Most calibration coils are too small to affect damping of the seismometer when shorted. In order to calibrate a seismometer using a current in place of a mass, the relation between current and mass must be established. This is the motor constant of the calibration coil, expressed in mAmp/m/s2. In order to do this we place an ammeter in the calibration coil circuit and measure the relation between current and calibration pulse amplitude. The arrangement is shown if Figure 3. The current is 5mAmp coming out of the current relay box. The height of the calibration pulse, that looks just like the pulse in figure 2 is 0.437mVolts for a 5 mAmp current.
The motor constant can now be computed from the relation
______(Cal. Pulse current)*(Wt Lift height)*(Seismometer Mass)_____
(Cal Current pulse Height)*(Test Mass Weight)*(gravitational Accel)
A worksheet can be set up as shown below for this computation.
Data for 6/6/00 8:53
Seismometer Mass (M) = 395grams
Test Weight Mass (m) = 0.04566grams
Acceleration of gravity (g) = 9.79m/ss
Height of weight lift Pulse "a" = 250mVolts (see figure 1)
Height of Calibration Current pulse "c" = 437mVolts
Current of Calibration Pulse "b" = 5MAmp (use meter to measure)
Test Mass acceleration = mg/M = 0.00113m/ss
Motor constant = (b*a/c)*M/(mg) = 2531mAmp/(m/ss)
The CHEAP SEIS AD unit and associated programs make it possible to compute the frequency response of the seismometer. The data logging program "LOG1CH20.exe" includes a calibrate option. This option initiates a calibration pulse sequence and writes the recorded signal and calibration input to a separate calibration file. Approximately 4 minutes of data are collected. The calibration pulse is turned on, then after a set length of time the pulse is turned off by the computer program. Operation is automatic (after pushing "R"). This program used a single pulse. Additional pulses may be added in order to boost the calibration energy at the higher frequencies. The computation of instrument response is independent of the character of the input, so long as it does not contain frequencies with zero energy. The calibration pulse satisfies this criterion.
The CHEAP SEIS AD unit is designed to draw its power from the parallel port. This is convenient in that no additional power supplies are needed. However, this arrangement does not provide sufficient power to directly drive a calibration coil at a reasonably high level for computing response in areas of high noise. The CHEAP SEIS Calibration Relay Driver provides the needed extra power from a separate internal 9v battery. It uses the signals from the computer, through the parallel port, to trigger a relay switch for the calibration current.
Procedure for Calibration using the Data Logger
The seismometer, CHEAP SEIS AD unit, CHEAP SEIS Calibration Relay Driver and ammeter need to be connected as shown in the wiring diagram in Figure 4. The Ch. A. and the adjacent ground should be connected with a twisted pair to the signal coil. The calibration terminal and its adjacent ground should be connected directly to the corresponding input terminals on the Calibration Relay Driver. Be careful to attach the grounds together. Connect the output of the Calibration Relay Driver ground directly to the calibration coil. Route the output signal through an ammeter. A resistor may be needed to reduce the current below 4.0mAmp for more sensitive calibration coils. Use a 20000 to 100000 ohm trim pot for optimal adjustment at low amperage levels.
The Calibration Relay Driver comes with a variable resistor (2500 ohms) mounted on the top of the case for easy adjustment. The switch turns off the 9v internal battery when the unit is not in use. The battery should be changed if its voltage drops below 6 volts, the voltage needed to trip the relay. The purpose of the relay is to isolate the calibration circuit from the computer power supply and to minimize interference with the recorded signal.
The CHEAP SEIS AD unit has only one adjustable part. That is the jumper that selects either high gain or low gain. The CHEAP SEIS AD unit has an internal 1000 gain amplifier for recording low-level signals such as signals from sensing coils like those in the AS-1. To change the setting, open the box and locate the 4 jumpers.
When the wires are hooked up and ready to record, plug the parallel cable connector into the parallel port of your computer. Data is acquired by program LOG1CH20.exe. This is a DOS operating program that will also run under windows. Requirements are given on the specification sheet for the instrument. The program is menu driven. Files of one-hour duration are saved with file names following the PEPP file name notation. The files have a separate header file listing what is in the file. The data and header files are written in ASCII so that they can be viewed using EXCEL, the DOS TYPE command, or read in directly to a simple basic program.
Before starting the program, create a directory "c:\seisdata". This is where the data are stored and where the calibration file is stored. The program starts like any other DOS program. When it is running and you are recording data, turn the calibration pulse on and off. Use the calibration pulse on/off keys ("C" is on, "V" is off) switch to set a convenient calibration pulse height. The calibration pulse height should be about 50% of full scale or about 250mVolt (actually 0.25mVolt operating in high gain) for optimum signal to noise.
The calibration sequence is initiated by pushing the "R" key. After pushing R, a calibration pulse should appear on the trace and a counter will begin indicating progress of the calibration sequence. Approximately half way through the sequence you should see another calibration pulse. When the calibration record is complete (when the counter is no longer seen) a file called "CALFILE.HDR" and "CALFILE.DAT" will be saved to the "c:\seisdata" directory.
In order to observe the calibration curves, the program "CALSPC20.EXE" is run. This program expects to find the "CALFILE" files in the "c:\seisdata" directory. The screen from this program is shown if figure 5
On screen commands will switch the display from particle velocity response to particle displacement or particle acceleration response. The spectra of the input signal and trace can also be displayed. Figure 5 is a screen dump, created by using "print screen" and using the paste command to insert it into a graphics program. You may need to copy the program and the "CALFILE.DAT" to a WINDOWS operating system to do this. If the curve is too high, or too low, it can be raised or lowered in 3dB increments. In this example, the velocity response has a slight peak at a period of about 1.2 seconds, close to the natural period of the seismometer. This is expected for the calibration pulse shown in figure 2.
In the CALSPEC program, the frequency response of the seismometer to an impulse in acceleration is computed in the frequency domain by using the fast Fourier Transform. The frequency response is the ratio of the Fourier Transform of the output signal (expressed as mVolts, or microVolts if using high gain) to the Fourier Transform of the input signal in its appropriate units. The current in the calibration coil is directly proportional to the acceleration applied to the seismometer mass. Therefore, by recording the time variations in the input current, the time variations in the acceleration applied to the seismometer mass are known. The conventional calibration function is a boxcar, a signal that at time zero rises instantly to a constant value and at a later time returns to zero. We have arbitrarily set the amplitude to 100 in our LOG1CH10.exe program. The CALSPC20 program uses this value when the calibration current or motor constants are unknown. For absolute calibration, the calibration current and motor constant need to be read into the CALSPC20 program. The amplitude of the acceleration applied by the calibration coil is found by measuring the current (5 mAmp in our example) and converting this to m/s2 by using the motor constant, which for our instrument is 2531 mAmp/m/s2. The motor constant converts the mAmps measured with the ammeter to m/s2. The resulting amplitude of the input acceleration time function is given by the ratio of the calibration current to the motor constant, or 5 mAmp/2531 mAmp/m/s2 = 0.002 m/s2. The program CALSPC20 has the option of either using the default 100 value for relative calibration, or reading in the calibration coil current and motor constant for absolute calibration. In the program CALSPC20 we take the Fourier Transform of the output signal (mVolts) and divide it by the scale corrected input signal (m/s2) to get the seismometer frequency response in mVolts/m/s2. On high gain the response is in microVolts/m/s2. We actually compute it from the Log of the spectra in the frequency domain from an equation that looks like:
Log[accel(f)] = Log[Out(f)]-Log[In(f)]-Log[Cal.Current mAmp]+Log[Motor constant].
Where this is zero, it is plotted at 0 dB (for a high gain recording add 60dB). For the velocity response we add the Log[2 p f] and for the displacement response we add Log[4 p 2 f2] to the acceleration response. The response can be shifted up or down to keep it on the screen. The acceleration response is in units of mVolts/m/s2, the velocity response is in units of mVolts/m/s and the displacement resonse is in units of mVolts/m. For the high gain recording each of these is in terms of microVolts, not mVolts.
Shake Table Calibration
A shake table is designed to move with a prescribed motion. In theory, one places the seismometer on the shake table, and measures the output for the programmed input. The principle difficulty with a shake table is that well-calibrated movements at low levels of seismic signals are difficult to simulate outside a well-equipped professional laboratory and at higher displacements where most shake tables are designed to operate, the seismometers are saturated. A simpler procedure on a shake table is to compare a previously calibrated seismometer with the seismometer under test. This can actually be performed by shaking any rigid surface on which two seismographs are mounted. Usually one shakes at a prescribed frequency and compares the output to calibrate the unknown seismometer relative to the seismometer with a know response.
Additional topics to be completed later:
Shake table construction.
Use of tilt table in calibration.
Details for Comparison with seismometer of known response.