IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 3, MARCH 2012 823

Frequency-Selective Seismic SensorEzzat G. Bakhoum, Senior Member, IEEE, and Marvin H. M. Cheng, Member, IEEE

Abstract—Recent trends in earthquake monitoring and predic-tion have focused on the monitoring of seismic frequencies thatare very close to the natural frequencies of buildings and otherstructures, such as bridges. This paper introduces a new type ofseismic sensor that is highly sensitive to vibrations at one specificfrequency. The sensor inherently rejects vibrations at all otherfrequencies. The sensor’s characteristic frequency must be tunedto match the natural frequency of the building or structure that isbeing monitored. The sensor is based on the fundamental principleof coupling an oscillating mass–spring system with an electro-magnetic transducer consisting of a space charge and a toroidalcoil. Analysis and experimental results show that the frequencyselectivity of such a vibration sensing mechanism is substantiallyhigh.

Index Terms—Building natural frequency, earthquake predic-tion, electromagnetic transducer, seismic sensing.

I. INTRODUCTION AND FUNDAMENTAL CONCEPTS

S TRONG earthquakes can be devastating for buildings.However, it is widely recognized that a building will

collapse only if it absorbs sufficient energy from the earth-quake at a frequency near its natural frequency [1]–[4]. At thepresent time, vibration sensors and accelerometers are usedextensively in earthquake detection and monitoring [5]–[10].The geophone was the classic earthquake detector for manyyears, but it has been superseded in recent years with piezo-electric and variable-capacitance transducers [11]–[19]. Veryrecently, new seismic sensors based on effects such as su-perconductivity or optical diffraction have been introduced[20]–[22]. An important feature in all those sensors, however, isthat they are inherently “broadband” sensors (i.e., they respondequally well to vibrations with a wide range of frequencies). Inmany cases, however, it is not necessary to evacuate a buildingor alarm its occupants simply because seismic vibrations havebeen detected. As long as the frequencies of the vibrations arenot sufficiently close to the natural frequency of the building,the building is not in danger of collapsing, as civil engineershave long recognized [1]–[4]. While it is theoretically possibleto use an electronic filter in conjunction with the sensor to filterout the unwanted frequencies, such a solution has proved to be

Manuscript received April 9, 2011; revised July 21, 2011; acceptedAugust 10, 2011. Date of publication October 17, 2011; date of current versionFebruary 8, 2012. The Associate Editor coordinating the review process for thispaper was Dr. Salvatore Baglio.

E. G. Bakhoum is with the Department of Electrical and Computer Engi-neering, University of West Florida, Pensacola, FL 32514 USA (e-mail:ebakhoum@uwf.edu).

M. H. M. Cheng is with the Department of Mechanical and AerospaceEngineering, West Virginia University, Morgantown, WV 26506 USA (e-mail:Marvin.Cheng@mail.wvu.edu).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIM.2011.2169610

Fig. 1. Fundamental concept of the new seismic sensor: A metallic disk withmass m is suspended with a spring that is attached to the building or structurethat is being monitored. A toroidal coil is also attached to the same structuresuch that the disk lies in the plane of the coil, as shown. An electrostatic chargeQ is applied to the surface of the disk. As the disk vibrates due to its inertia,a very small magnetic field is created inside the core of the coil. The magneticfield gives rise to an alternating voltage across the terminals of the coil, whichcan be detected with an amplifier.

quite impractical. The natural frequencies of most buildings arein the range of 0.2 Hz to 4 Hz. Unfortunately, a filter with acutoff frequency of a few hertz must be a substantially largefilter (larger than the sensor itself in most cases).

The objective of this paper is to introduce a novel newseismic sensor that responds only to vibrations with frequenciesthat are very close to the natural frequency of a building.1 Thesensor inherently rejects vibrations at all other frequencies. Thebasic concept of the new sensor is shown in Fig. 1.

From Fig. 1, it will be apparent that the mechanical mech-anism used in the new sensor (i.e., the mass–spring system) isthe same as the mechanical mechanism used in the geophone.The difference, however, between the geophone and the systemshown in Fig. 1 is the electromagnetic transducer. While thetransducer in the geophone is based on Faraday’s law, thetransducer shown in Fig. 1 is based on Ampere’s law (firstaction) followed by Faraday’s law (second action). The analy-sis and the experimental results presented in this paper will

1The natural frequency ω0 of any building can be calculated from a well-known formula [1]–[4].

0018-9456/$26.00 © 2011 IEEE

824 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 3, MARCH 2012

Fig. 2. (a) Frequency response of the geophone has linear dependence on thefrequency ω and is symmetric around the natural frequency ω0. (b) Frequencyresponse of the new sensor has quadratic dependence on ω and is symmetricaround ω0.

show that this transduction mechanism has substantially betterfrequency response characteristics. To understand qualitativelythe difference between the frequency response of the geophone(which can be made frequency selective to some extent) andthe frequency response of the sensor shown in Fig. 1, considerFig. 2. Fig. 2(a) shows the typical frequency response character-istics of the geophone [13], [14]. The voltage signal generatedby a geophone has linear dependence on the frequency ω and issymmetric around the natural frequency ω0 of the spring–masssystem. Fig. 2(b) shows the frequency response characteristicsof the new sensor. The voltage signal generated by the sensorhas quadratic dependence on the frequency ω and is symmetricaround the natural frequency ω0 [see (21) and the analysis inSection II]. As can be seen from the graph, the new sensoris highly sensitive to vibrations with frequencies that are veryclose to ω0 and is very insensitive to vibrations at all otherfrequencies.

It is to be pointed out that ω0 =√

k/m [23], [24], where kis the spring constant and m is the moving mass. This naturalfrequency must be matched to the expected natural frequencyof the building or structure that is under test. Table I lists thefour most important parameters of the new sensor: frequencyresponse, sensitivity, linearity, and noise level, as compared tothe other known types of seismic sensors.

Fig. 3 shows a cross-sectional view of the structure of theactual sensor that was built and tested by the authors. Fig. 4shows a photograph of the device.

Reference is now made to Fig. 3. Since it is practicallydifficult to inject and maintain a constant electrostatic chargeon the surface of the vibrating disk, a parallel-plate capacitorarrangement is used in which the vibrating disk constitutesone of the electrodes, as shown in the figure. A dc voltagesource that is connected to the two electrodes charges thevibrating steel disk positively while simultaneously charginga fixed aluminum disk negatively, as shown. The separationbetween the two metallic disks is approximately 3 mm in thepresent prototype, and therefore, the arrangement constitutes an

electric dipole [25]–[27]. An oscillating electric dipole createsan alternating electric field with a distribution as shown in Fig. 5[25]–[27]. The electric field, in turn, gives rise to a circularmagnetic field according to Maxwell’s equations and as furtherdescribed in detail in Section II.

As also shown in Fig. 3, the vibrating steel disk is mountedon a conductive rubber ring that conducts the electric chargeto the disk, in addition to serving as the “spring” in Fig. 1.As further shown in the figure, the lower aluminum disk hasa group of air pressure relief holes in order to allow the upperdisk to vibrate without a buildup of air resistance (see furtherthe detailed analysis hereinafter).

II. THEORY OF OPERATION

A. Magnetic Field Inside the Core of the Coil

The electric field intensity of a stationary electrostatic dipoleis given by [25]–[27]

�E =Qd

4πε0r3

(2 cos θ r̂, sin θ θ̂

)(1)

where Q is the magnitude of the charge, d is the distancebetween the two charges, r is the distance from the dipole tothe point of measurement, r̂ is a unit vector in that direction,θ is the angle between r̂ and the vertical axis, and θ̂ is thecorresponding unit vector in the spherical coordinate system.If the dipole is oscillating, the distance d is simply replaced byd0 + dmax sin ωt, where d0 is the fixed separation between thetwo charges, dmax is the maximum displacement, and ω is theangular frequency. The electric field is then expressed as

�E =Q(d0 + dmax sinωt)

4πε0r3(2 cos θ r̂, sin θ θ̂). (2)

The electric field described by (2) is shown in Fig. 5. We shallnow consider only those points in the vicinity of the dipolethat are located along the core of the toroidal coil. At thosepoints, the angle θ = 90◦, and the electric field intensity will begiven by

�E =Q(d0 + dmax sinωt)

4πε0r3θ̂. (3)

To calculate the magnetic flux density �B (which will be di-rected along the axis of the core), we invoke Maxwell’s fourthequation

∇× �B = μ0μr�J + ε0μ0μr

∂ �E

∂t(4)

where μ0 is the permeability of free space and μr is the relativepermeability of the iron core inside the coil. Since there isno current inside the iron core, the current density �J = 0. Bymaking use of (3), (4) is then written as

∇× �B = ε0μ0μr

(Qdmaxω cos ωt

4πε0r3θ̂

)

=μ0μr

4πr3Qdmaxω cos ωt θ̂. (5)

BAKHOUM AND CHENG: FREQUENCY-SELECTIVE SEISMIC SENSOR 825

TABLE ICOMPARISON OF THE NEW SENSOR TO THE OTHER KNOWN TYPES OF SEISMIC SENSORS (SEE [13] AND [14])

Fig. 3. Vertical cross-sectional view of the actual structure of the sensor(drawing not to scale).

Fig. 4. Photograph of the sensor. The diameter of the toroidal coil is 15 cm.The diameter of the steel disk is 4.5 cm.

In spherical coordinates, ∇× �B is given by [25]–[27]

∇× �B =1

r sin θ

(∂

∂θBφ sin θ − ∂Bθ

∂φ

)r̂

+1r

(1

sin θ

∂Br

∂φ− ∂

∂rrBφ

)θ̂

+1r

(∂

∂rrBθ −

∂Br

∂θ

)φ̂. (6)

As we can conclude from (5), only the second term exists alongthe axis of the core. Furthermore, since there is no dependenceon the circular angle φ (due to the circular symmetry), weconclude that

∇× �B = − 1r

∂

∂rrBφ θ̂. (7)

Fig. 5. Electric field lines around an oscillating dipole.

Hence, from (5) and (7)

− 1r

∂

∂rrBφ =

μ0μr

4πr3Qdmaxω cos ωt (8)

or

rBφ = −∫

μ0μr

4πr2Qdmaxω cos ωt dr. (9)

Hence

Bφ =μ0μr

4πr2Qdmaxω cos ωt (10)

where the constant of integration must be assumed to be equalto zero since there is no permanent magnetic field inside the ironcore. Equation (10) describes the circular magnetic flux densityalong the core of the coil. The peak, or maximum value Bmax,can be written as

Bmax =μrμ0

4πr2ωpmax (11)

where pmax = Qdmax is the maximum transient dipole mo-ment. To find that dipole moment, the system consisting ofthe oscillating mass and spring can be modeled as a forcedharmonic oscillator. The force driving that oscillator is

F = Fmax sin ωt. (12)

From the standard solution of the problem of the forced har-monic oscillator, the amplitude of vibration is given by [24]

d(t) =Fmax sinωt

m(ω20 − ω2)

+ d0 (13)

826 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 3, MARCH 2012

where ω0 =√

k/m is the natural frequency of oscillation.Details about the natural frequency of oscillation of thespring–mass system in the present device will be given in thefollowing section. The maximum transient dipole moment willbe now given by

pmax = Qdmax =QFmax

m (ω20 − ω2)

(14)

and hence, Bmax in (11) will be alternatively given by

Bmax =μrμ0

4πr2

ωQFmax

m (ω20 − ω2)

. (15)

According to Newton’s second law, the force Fmax = ma,where a is the maximum acceleration acquired by the vibratingmass. Hence

Bmax =μrμ0

4πr2

ωQ

(ω20 − ω2)

a. (16)

Finally, the flux Φmax through the core of the coil will be equalto Bmax multiplied by the cross-sectional area A of the core.Hence

Φmax =μrμ0QA

4πr2

ω

(ω20 − ω2)

a. (17)

B. EMF Generated by the Coil

According to Faraday’s law, the electromotive force [(EMF)or voltage] induced in the coil will be given by

EMF = NdΦdt

= Nd

dtΦmax sin ωt = NωΦmax cos ωt

(18)

where N is the number of turns in the coil. The rms EMF willbe therefore equal to

EMFrms =1√2NωΦmax. (19)

From (17) and (19), we have

EMFrms =μrμ0QAN

4√

2πr2

ω2

(ω20 − ω2)

a. (20)

The following are the physical parameters of the presentsensor:

1) μr of the iron core (electrical steel): ≈ 4000;2) charge Q on the steel disk: 4.7 × 10−9 C;3) cross-sectional area A of the iron core: 1.1 × 10−3 m2;4) number of turns N in the coil: 100 000;5) mean radius r of the coil: 5.625 cm;6) natural frequency ω0 of the spring–mass system: ≈ 2π ×

3.3 rad/s, where f0 = 3.3 Hz is the natural frequencyin hertz (note that the natural frequency can be adjustedby varying the mass of the vibrating disk and the springconstant, which are 14 g and 6 N/m in the present device,respectively).

Fig. 6. Minimum detectable acceleration as a function of frequency(2.6–4 Hz).

By substitution in (20), the rms EMF can be expressed as

EMFrms = 4.62 × 10−8 ω2

(ω20 − ω2)

a

= 4.62 × 10−8 a

|(f20 /f2 − 1)| . (21)

III. PERFORMANCE DATA AND EXPERIMENTAL RESULTS

A. Frequency Selectivity and the Dynamic Range of the Sensor

The minimum voltage that can be detected with a field-effecttransistor (FET) amplifier is about 1 μV (i.e., coil voltages thatare less than 1 μV cannot be detected, and this is a naturallimit on any FET amplifier). By using this figure in (21), theminimum detectable acceleration can be expressed as

a = 21.65∣∣(f2

0 /f2 − 1)∣∣ m/s2 (22)

or, in units of the gravitational acceleration g (9.81 m/s2)

a = 2.2∣∣(f2

0 /f2 − 1)∣∣ g. (23)

Fig. 6 shows a plot of this equation for the frequency range of2.6–4 Hz.

It can be clearly seen that the sensor is very selective forthe range of frequencies that are very close to the naturalfrequency of 3.3 Hz. Theoretically, (23) indicates that thespring–mass–coil system will be responsive to an accelerationof 0 g at the exact frequency of f0. Practically, however, damp-ing and other inefficiencies prevent that theoretical limit frombeing reached.2 As the figure shows, the minimum accelerationthat was actually detected was about 0.01 g. It is to be pointedout that a number of other commercially available sensors offer

2It is important to point out that damping was ignored in (13). The effectof damping is to limit physical quantities like displacement and acceleration atthe natural frequency ω0. The effect of damping is otherwise very small as theresults in Figs. 6–8 show (i.e., the differences between the theoretical and theexperimental results are negligible).

BAKHOUM AND CHENG: FREQUENCY-SELECTIVE SEISMIC SENSOR 827

Fig. 7. EMFs generated by the coil and detected with the amplifier versusfrequency (acceleration = 0.4 g).

even higher sensitivities at the present time.3 However, all thosesensors are inherently “broadband” as was indicated earlier. Itis generally recognized that a modern well-constructed buildingcan be in danger of imminent collapse if the seismic vibrationsat the natural frequency of the building reach or exceed 0.4 g[3], [4] (this corresponds to approximately 6.5 on the Richterscale). Vibrations with frequencies close to f0 and magnitudesthat are less than 0.4 g are therefore very useful predictorsof imminent danger. As Fig. 6 clearly shows, vibrations withmagnitudes that are less than 0.4 g will be detected by the sensoronly if the range of frequencies is 3–3.6 Hz or within ±10%of the natural frequency f0. Vibrations of similar magnitudesthat are outside this frequency range will not be detected bythe sensor, which is the desired outcome since those vibrationsshould not be a cause for alarm.

To obtain the results shown in Fig. 6, the sensor was mountedon an electrodynamic shaker (from Data Physics Corporation,San Jose, CA) and exposed to sinusoidal forces at differentfrequencies. At each frequency, the minimum acceleration thatresulted in a voltage appearing at the terminals of the coil wasrecorded. To confirm the measurements, another commerciallyavailable sensor (Model 7600B1, from Dytran Instruments,Inc., Chatsworth, CA) was mounted on the electrodynamicshaker together with the present sensor and was used to confirmthe value of acceleration at each different frequency.

Concerning the upper value of the dynamic range, the sensorwas found to be sensitive to accelerations up to 5 g, in whichcase the range of applicable frequencies is indeed very broad.

B. EMF Generated by the Coil

Fig. 7 shows a plot of (21) for an acceleration a = 0.4 g.Fig. 8 shows a plot of the same equation for a = 0.01 g. Asexpected, no voltage was detected outside the frequency rangeof 3–3.6 Hz when a = 0.4 g. This once again indicates that, for

3The sensitivity of the prototype described here can be increased by increas-ing parameters such as the number of turns in the coil, the charge on the movingmass, etc. The objective of this paper is mainly to demonstrate the frequencyselectivity of the sensor.

Fig. 8. EMFs generated by the coil and detected with the amplifier versusfrequency (acceleration = 0.01 g).

Fig. 9. Signal-to-noise ratio versus frequency, for a = 0.01 g.

a substantially high seismic acceleration that is likely to destroya building, the sensor is very selective (response range is within±10% of the natural frequency f0). As Fig. 8 further shows,for a very faint acceleration of 0.01 g, the sensor is extremelyselective: Only the vibration with frequency f0 was detected(it is to be pointed out once again that a very narrow bandwidthis, in fact, the characteristic feature of this sensor, and it is to befurther observed that the 0.01 g is the frequency resolution ofthe sensor).

C. Signal-to-Noise Ratio

The thermal noise power in the coil is given by the well-known Nyquist equation [28]

〈V 2〉 = 4kTBR (24)

where k is Boltzmann’s constant, T is the temperature indegrees Kelvin, B is the bandwidth in hertz, and R is the total

828 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 3, MARCH 2012

Fig. 10. Measured coil voltage versus temperature, (a and b) for a fixed acceleration of 0.4 g and (c and d) for a fixed acceleration of 0.01 g. Each figure showsone complete cycle, starting at 25 ◦C. Only one frequency was used in the testing: f0.

ohmic resistance of the coil. From (21) and (24), the signal-to-noise (S/N ) ratio will be given by

S

N(dB) = 10 log10

(4.62 × 10−8a)2

4kTBR (f20 /f2 − 1)2

. (25)

The resistance R of the coil was found to be approximatelyequal to 10 Ω in the present device. Given a bandwidth ofinterest of approximately 0.6 Hz4 and a room temperature of300 ◦ K, Fig. 9 shows a plot of the S/N ratio for a = 0.01 g.5

Clearly, even at the bottom of the dynamic range, the S/Nratio in this transducer is excellent.

D. Temperature Hysteresis

Fig. 10 shows the temperature hysteresis curves that wereobtained for an acceleration of 0.4 g (a and b) and for anacceleration of 0.01 g (c and d). The acceleration functionapplied with the electrodynamic shaker was amax sinωt, where

4The 0.6 Hz is the combined bandwidth of the coil/amplifier assembly. Thisis where detectable voltages are present.

5The exact frequency f0 is not represented in the plot.

amax was either 0.4 g or 0.01 g. Only one frequency was usedin the testing: f0. As the figures clearly show that the maximumtemperature hysteresis error is about ±7% full-scale output forthe temperature range of −10 ◦C to +80 ◦C (this rather largetemperature hysteresis error is quite typical for accelerationsensors). The temperature hysteresis is believed to be totallydue to variations in the spring constant of the rubber membraneas the temperature is cycled.

E. Sensitivity of the Sensor to External andStray Magnetic Fields

Testing was conducted to determine the sensor’s sensitivity toexternal and stray magnetic fields. It was found that static (non-time-varying) magnetic fields, such as the magnetic field of theEarth, have no effect on the operation of the sensor. In addition,a time-varying field that is perpendicular to the plane of the coilhas no effect. Circular time-varying magnetic fields (i.e., fieldsthat are oriented along the core of the coil), however, can veryseriously degrade the performance of the sensor. Fortunately,such fields are very unusual (except in the presence of somespecial types of machinery), and the sensor therefore shouldnot be operated near such fields.

BAKHOUM AND CHENG: FREQUENCY-SELECTIVE SEISMIC SENSOR 829

IV. CONCLUSION

The new frequency-selective seismic sensor introduced inthis paper is highly sensitive to vibrations with frequenciesthat are very close to the natural frequency of the spring–masssystem used in the sensor. The sensor inherently rejects allother frequencies. The natural frequency of the spring–masssystem must be matched to the expected natural frequency ofthe building or structure that is being monitored. Unlike othersensors that are currently used for earthquake prediction andwarning, a voltage is obtained from the sensor only when thereis a genuine possibility that the seismic vibrations detectedmay lead to the collapse of the monitored building or structure,thereby preventing false alarms to the occupants of that buildingor structure. The theory behind the device is a straightfor-ward application of the principles of electromagnetics, andtesting has shown a very good agreement between theory andexperiment.

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Ezzat G. Bakhoum (SM’08) received the B.S.degree in electrical engineering from Ain ShamsUniversity, Cairo, Egypt, in 1986 and the M.S.and Ph.D. degrees in electrical engineering fromDuke University, Durham, NC, in 1989 and 1994,respectively.

From 1994 to 1996, he was a Senior Engineerand a Managing Partner with ESD Research, Inc.,Durham. From 1996 to 2000, he was a Senior Engi-neer with Lockheed Martin/L3 Communications,Inc., Camden, NJ. From 2000 to 2005, he was a

Lecturer with the Electrical Engineering Department, New Jersey Instituteof Technology, Newark, NJ. He is currently an Assistant Professor with theUniversity of West Florida, Pensacola, FL.

Marvin H. M. Cheng (M’04) received the B.S. andM.S. degrees in mechanical engineering from Na-tional Sun Yat-Sen University, Kaohsiung, Taiwan,in 1994 and 1996, respectively, and the Ph.D. degreein mechanical engineering from Purdue University,West Lafayette, IN, in 2005.

From 1997 to 1999, he was an R&D Engineerwith the National Synchrotron Radiation ResearchCenter, Hsinchu, Taiwan, where he developed a real-time monitoring system for high-energy emissionsystems. From 2006 to 2010, he was an Assistant

Professor of mechanical engineering technology with Georgia Southern Univer-sity, Statesboro. He is currently an Assistant Professor of mechanical engineer-ing with West Virginia University, Morgantown. His current research interestsinclude mechatronics, controller synthesis with the consideration of finite wordlength, precision, motion control, fast imaging of atomic force microscope, andembedded controllers.