An Analog Circuit Technique to Improve a

Geophone Frequency Response for Application as

Vibration Sensors
Navid Hakimitoroghi Rabin Raut Mehrdad Mirshafiei Ashutosh Bagchi
Department of Electrical and Department of Electrical and Sensequake Department of Building, Civil,
Computer Engineering Computer Engineering and Environmental Engineering
Concordia University Concordia University Concordia University
Montreal, Canada Montreal, Canada Montreal, Canada

Abstract—Vibration sensors find use in monitoring and mea-

suring vibrations of buildings, bridges and in seismological
sciences. Geophones are one of the commonly used sensors for
such applications. However, geophones have a natural frequency
response like that of a high-pass filter. In the past, several
innovations have been introduced to extend the −3 dB corner
frequency of the geophone to capture the natural frequencies of
a building around 1 Hz. These involved modifying the physical
construction of the geophone, and/or introducing digital signal
conditioning which is cost intensive. We investigated several
analog circuit techniques such that the overall electrical response
of the geophone approximates to a low-pass filter response. In
one approach the device is followed by a cascade of an ideal
integrator and a lossy integrator. This eliminates the zeros of the
device while preserving the natural low-frequency pole of the Fig. 1. Geophone mechanical structure
device. It is desirable to create a low-frequency pole independent
of the natural pole of the geophone. In order to achieve this goal
we used multi-loop feedback method which affords to a low-
pass characteristic where the pole frequency becomes different Due to the mechanical arrangement of the mass-spring
from the natural pole frequency of the geophone. In the following structure, the lower −3 dB corner frequency of the geophone
theoretical foundations for two techniques are presented. Validity could be only around 8 Hz [3]. In certain structural health
of the multi-loop feedback technique has been established by
numerical simulations and verified by lab-bench experiments. monitoring (SHM) applications frequencies down to about
Index Terms—Seismic sensor, geophone, frequency response 1 Hz are of interest [1].
compensator, multi-loop feedback. In the past, several innovations have been introduced to
extend the −3 dB corner frequency of the geophone to
I. I NTRODUCTION capture the natural frequencies of a building around 1 Hz.
Dynamic response of structures, fluids and/or other systems These involved modifying the physical construction of
due to an excitation is routinely studied by modal analysis the geophone [4], [5], and/or introducing digital signal
technique [1]. In structural engineering, modal analysis uses conditioning [6], [7]. Since analog circuit techniques quite
overall mass and stiffness of a structure to find the natural often lead to less expensive solutions in terms of power
frequencies at which the structure resonates. This information consumption, and substrate area from an integrated circuit
is not available for all the structures especially for older or system perspective, we investigated several analog circuit
buildings. Therefore, structural engineers use vibration sensors techniques to compensate for the poor low-frequency response
to extract the natural frequencies. An array of such sensors can of the geophone in [8] and [9]. One of the techniques is
produce the vibration characteristics along different directions the use of multi-loop feedback [10] principle to realize an
in a three-dimensional space [2]. overall transfer function with a bandwidth beginning from
The common component in all types of the vibration sensors is DC (or very low frequencies) to a specified low-pass corner
an element which can measure either velocity or acceleration frequency. The presented work in this article is an extension
and generate a physical variable related to the intensity of the of [8] by the same authors. Also, It should be declared
motions. One of the commonly used sensors is a geophone. that this paper reuses some content from thesis in [9] with
The internal structure of a typical geophone (i.e., GS-11D from permission.
Geospace [3]) is shown in Fig. 1.

978-1-7281-3320-1/20/$31.00 ©2020 IEEE

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 Based on the above motivation, we looked for possible
analog circuit techniques to pull the low-frequency response
of the geophone device toward DC (i.e., zero frequency). It
was considered possible to work with the frequency response
characteristics of a typical geophone and figure out ways
to modify the frequency response to conform to a low-pass
characteristics. Consulting the data sheet and application notes
of an industrial standard geophone became necessary for this
purpose. For our work we used GS-11D series of geophone
from Geospace Technologies Inc. in this work. Full component
characteristics of this device is available in [3]. Fig. 2 shows
Fig. 3. Proposed geophone model
the geophone response versus frequency for two different
loads; graph in A for open circuit and graph in B for 1.74 KΩ.
A. Lossy and ideal integrator cascade technique
The expression in Eq. 1 has two zeros, i.e., s = 0, s = −
Rg
Lg .Combining Eq. 1 with a lossy and an ideal integrator
function will lead to:
Rg
s2 + s
Lg K1 K2
He (s) = ∗ ∗ (2)
2
R g 1 1 C 2s
s + s( ) + s +
Lg Lg Cg C1 R1
Which is equivalent to a second order low-pass transfer
R
function under the arrangement Lgg = C11R1 . A schematic
circuit arrangement to accomplish the above is shown in Fig.
4.

Fig. 2. GS-11D frequency response [3]

In section II we present the theoretical background of

the analog conditioning techniques utilizing the frequency
response characteristic of the geophone mentioned above.
Section III presents the experimental set up and the results
for the multi-loop feedback method. Section IV contains
the conclusion, followed by acknowledgment and a list of
references.
Fig. 4. Geophone (equivalent circuit) followed by lossy and ideal integrator
compensation
II. P ROPOSED A NALOG C IRCUIT T ECHNIQUES
The above technique is very straightforward and effective
Using curve fitting technique and a second order
except for the fact that the low-pass pole frequency remains
approximate model to the graphs in Fig. 2 we could
the same as that of the original geophone device. In some
arrive at the equivalent circuit model for the geophone, as
cases this may not be desirable. A low-pass pole frequency
shown in Fig. 3. The transfer function of the circuit in Fig. 3 is:
independent of the pole frequency of the geophone could be
created by using the multi-loop feedback method [10]. This is
Rg presented next.
s2 + s
Ig Lg
Hg (s) = = (1) B. Multi-Loop Feedback (MLF) Method
Ii Rg 1
s2 + s( )+
Lg Lg Cg In this technique the electronic circuits together with the
geophone is rendered to produce a specific low-pass transfer
In the transfer function, the values of elements are calculated characteristic to compensate for loss at low frequencies as well
as: Rg = 380 Ω and Cg = 91.0507 µF , Lg = 2.7820 H. as attenuating unwanted high-frequency signals. To achieve
Based on the simulations, this transfer function agrees with this objective the equivalent circuit model of Fig. 3 is used in
the graph B in Fig. 2. Fig. 5. Our aim is to realize the unknown impedance function

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 io
Z(s) such that the transfer function T (s) = ii has a first order
low-pass characteristic. Thus:

Fig. 5. Geophone cascaded with an unknown impedance Z(s)

Rg + sLg K0 Fig. 6. Schematic of T (s) analogue of Y (s) in Eq. 5

= (3)
Rg + sLg + sC1 g + Z(s) s+a

where, a is the new low-pass corner frequency. It is desirable

that the overall LP response be independent of the electrical
characteristic of the geophone. Our goal now is to find the
unknown impedance function Z(s). From Eq. 3 we can derive:

s3 Lg Cg + s2 Cg (Rg − Lg (a + K0 )) + sCg Rg (a − K0 ) − K0
Z(s) =
sCg K0
(4)
The impedance function in Eq. 4 can be realized by adding Fig. 7. Admittance converter
the outputs of several functional blocks, such as differentiators,
and integrators. Use of a differentiator is not favorable, since
this accentuates high-frequency signals (esp. noise). Therefore, placed on a cardboard covering the conical opening of the
we decided to implement the inverse of Eq. 4. This will be an loudspeaker. The output response containing leakage of har-
admittance function. Thus: monic signals was monitored via a data gathering module
(DC2222A from Linear Technologies [11] in our experiments).
sCg K0 Numerical values of the uncompensated geophone response
Y (s) =
s3 Lg Cg + s2 Cg (Rg − Lg (a + K0 )) + sCg Rg (a − K0 ) − K0 and the compensated response are presented in Table. 1. The
(5)
values are numerical value of the stars in Fig. 9. The response
The admittance function in Eq. 5 can be connected in a
feedback loop to realize the impedance function of Eq. 4.
TABLE I
Fig. 6 shows the schematic of the system which uses MLF FREQUENCY RESPONSES FOR COMPENSATED AND UNCOMPENSATED
technique to realize Y (s) ∗ R as a voltage transfer function, CASES
T (s), R being an arbitrary scaling resistance. The active Uncompensated Compensated
building blocks are operational amplifiers used as inverting Freq. (Hz)
Geophone (v/v) Geophone (v/v)
summing amplifiers, and integrators. The output of the system 1 <0.01 0.9873
in Fig. 6 is to be fed back to the node X (see Fig. 5) via a 2 0.1450 1.0147
4 0.4342 1.0216
transconductance device so that the functionality of Z(s) is 6 0.6105 0.9764
restored. The system in Fig. 7, finally converts the admittance 8 1.1230 0.9646
to the impedance function as in Eq. 4. In the following, we 10 1.0920 0.9612
12 1 0.9785
present experimental results to validate our theoretical work. ... ... ...
80 1.1153 0.8951
III. E XPERIMENTAL R ESULTS 96 1.1650 0.7736
To validate the proposed method, we used numerical simu- 100 1.2452 0.8235
120 1.2950 0.1177
lation and lab bench tests. Both K0 and a in Eq. 3 have been
set to have −3 dB frequency at 100 Hz.
The lab bench test setup is shown in Fig. 8. We used a values over the frequency range 1 Hz to 120 Hz only are
low frequency shaker in the lab since a shake table with included to demonstrate the ability of the proposed MLF to
very low frequency (∼ 1 Hz) was not available. The shaker compensate for the poor response (column 2 in Tab. 1) of the
was made from a loudspeaker supplied with low frequency geophone over this low frequency range.
pulse signals from a signal generator. The geophone was Fig. 9 shows the experimental results in a graphical form.

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 this problem and improved geophone response using an analog
conditioning circuit. Application of analog circuit technique
for this case is new. With slight changes in the proposed MLF
circuit, the conditioning system can fit different geophones
with different frequency response characteristics. Experimental
results confirmed the effectiveness of the proposed method of
Fig. 8. Laboratory experimental setup compensation.
ACKNOWLEDGMENT
The financial support of the NSERC (Natural Sciences
and Engineering Research Council of Canada) is gratefully
acknowledged.
R EFERENCES
[1] J. Havskov and G. Alguacil, Instrumentation in Earthquake Seismology.
Springer International Publishing, 2015.
[2] F. Mirshafiei, M. Mirshafiei, and G. McClure, “A new three-dimensional
seismic assessment method (3d-sam) for buildings based on experimen-
tal modal analysis,” Computers & Structures, vol. 180, pp. 125–137, 02
2017.
[3] GS-11D geophone specifications. [Online]. Available:
http://www.geospace.com/geophones-gs-11d/
[4] C. Collette, L. Fueyo-Roza, and M. Horodinca, “Prototype of a small
low noise absolute displacement sensor,” IEEE Sensors Journal, vol. 14,
no. 1, pp. 91–95, Jan 2014.
[5] A. Preumont, Mechatronics: Dynamics of Electromechanical
and Piezoelectric Systems, ser. Solid Mechanics and Its
Fig. 9. Frequency response of compensated geophone vs. geophone Applications. Springer Netherlands, 2006. [Online]. Available:
https://books.google.ca/books?id=b753Dr4X0cAC
[6] R. Brincker, T. Lagö, P. Andersen, and C. Ventura, “Improving the classi-
cal geophone sensor element by digital correction,” in The International
The gray solid graph is the theoretical frequency response of Modal Analysis Conference. Society for Experimental Mechanics, 2005.
the geophone while the gray dots are the normalized response [7] Y. Zhang, Z. Zou, and H.-w. Zhou, “Estimating and recovering the
low-frequency signals in geophone data,” in Society of Exploration
of the uncompensated geophone placed on the shaker. The Geophysicists, 09, 2012, pp. 1–5.
values were normalized with respect to unity. The black solid [8] N. Hakimitoroghi, R. Raut, M. Mirshafiei, and A. Bagchi, “Compen-
line is the theoretical response of the compensated geophone sation techniques for geophone response used as vibration sensor in
seismic applications,” in 2017 Eleventh International Conference on
with the target to be a low-pass filter with −3 dB cut-off Sensing Technology (ICST), Dec 2017, pp. 1–5.
frequency at 100 Hz (refer to Eq. 3). The black dots are [9] N. Hakimitoroghi, “A study on vibration sensors with application in
the response of the compensated geophone placed on the structural health monitoring (shm),” August 2018. [Online]. Available:
https://spectrum.library.concordia.ca/984322/
shaker. The values were normalized with respect to unity. The [10] R. Raut and M. Swamy, Modern Analog Filter Analysis and Design: A
component values for the experiment were selected to have Practical Approach. John Wiley & Sons, 2010.
1
S for three integrators in the circuit in Fig. 6. For inverting
[11] LTC2508-32 demo board — 32-bit over-sampling
ADC with configurable digital filter. [Online]. Avail-
amplifiers, the components were selected based on the gains able: http://www.analog.com/en/design-center/evaluation-hardware-and-
in signal path [10]. Also, three potentiometers are responsible software/evaluation-boards-kits/dc2222a-b.html
to zero the offset of the integrators.
Clearly, the geophone setup with the frequency response
compensator followed the transfer function of a first order low-
pass filer as we presented in Table 1. However the −3 dB
frequency of the system is 96 Hz due to the tolerance of
the real components versus calculated value resistors and
capacitors in the circuit of Fig. 6. For this setup, the −3 dB
cut-off frequency of the system can be adjusted by changing
the components in circuit in Fig. 6.
IV. C ONCLUSION
Use of geophone in vibration sensing (especially in SHM) is
preferable to other types of sensors due to its higher sensitivity
in comparison with micro-electromechanical system (MEMS)
accelerometer and its lower price in comparison with a piezo-
electric accelerometer. The main drawback of the geophones is
their response at lower frequencies. In this study, we addressed

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