PhD Thesis Statement

CZECH TECHNICAL UNIVERSITY IN PRAGUE

DOCTORAL THESIS STATEMENT

Czech Technical University in Prague Faculty of Electrical Engineering Department of Measurement

Jaroslav Štrunc

ROTATIONAL SEISMOMETER ON THE CAPACITIVE PRINCIPLE

Ph.D. Programme: Electrical Engineering and Information Technology Branch of Study: Measurement and Instrumentation

Doctoral thesis statement for obtaining the academic title of “Doctor”, abbreviated to “Ph.D.”

Prague, July 2010

The doctoral thesis was produced in combined manner of Ph.D. study at the Department of Measurement of the Faculty of Electrical Engineering of the CTU in Prague. Candidate:

Ing. Jaroslav Štrunc Department of Seismology Institute of Rock Structure and Mechanics ASCR, v.v.i. V Holešovičkách 41 CZ-18209 Prague 8

Supervisor: Prof. Ing. Stanislav Ďaďo, DrSc. Department of Measurement Faculty of Electrical Engineering of the CTU in Prague Technická 2 CZ-16627 Prague 6 Supervisor-Specialist:

Ing. Milan Brož, CSc. Department of Seismology Institute of Rock Structure and Mechanics ASCR, v.v.i.

Opponents:

The doctoral thesis statement was distributed on …………… The defence of the doctoral thesis will be held on …………… at ……… a.m./p.m. before the Board for the Defence of the Doctoral Thesis in the branch of study Measurement and Instrumentation in the meeting room No. ……… of the Faculty of Electrical Engineering of the CTU in Prague. Those interested may get acquainted with the doctoral thesis concerned at the Dean Office of the Faculty of Electrical Engineering of the CTU in Prague, at the Department for Science and Research, Technická 2, Prague 6.

Prof. Ing. Vladimír Haasz, CSc. Chairman of the Board for the Defence of the Doctoral Thesis in the branch of study Measurement and Instrumentation Faculty of Electrical Engineering of the CTU in Prague Technická 2, CZ-16627 Prague 6

CONTENTS Contents .....................................................................................................................2 1

State of the Art ................................................................................................3

2

Aim of the Thesis ............................................................................................4

3

Methods ...........................................................................................................5

4

Results .............................................................................................................7

5

Conclusion.....................................................................................................13

References ...............................................................................................................15 Publications and Projects .........................................................................................18 Summary .................................................................................................................21 Resumé ....................................................................................................................22

2

1

STATE OF THE ART

Seismology is closely connected to the measuring technology. The second half of 20th century was influenced by spreading digitalization and time synchronization possibilities. Precise data records and accurate time identification enabled to use more sophisticated approaches for data analysis. Beside the localisation of the hypocenters, some new qualities from seismograms started to be studied. Seismic events have several specific features requiring cutting edge technology. No matter what event is measured, seismic signals are non-repetitive, broadband and highly dynamic in amplitude. Traditionally there were studied only three perpendicular components of movement – translations – despite the fact that there are the other three degrees of freedom – rotations. Fundamental theories about rotation movements were published about the year 2000, [70], and some rotations derived from seismic arrays were considered, [38]. The rotational movement measurement is most often considered as an additional functionality of device originally designed for some other purpose. The first calculations of rotations were deduced from seismic arrays. These dense networks are built out of independent seismic stations and their original role is to increase the SNR. Accurate time synchronization of them all is crucial. Array is in principle large in the horizontal plane and shallow in the vertical direction. There are many dense arrays operating all around the world but none of them performs routine calculation of rotational motion. The space intensity and necessity to know the transfer function of each sensor and to perform instrument corrections before analysis belongs among the most serious drawbacks of arrays. In addition, the calculated rotation means only an average value across the whole area. The first experiments on direct measuring rotation motion were carried out using modified classical seismographs. These sensors have a horizontal pendulum with seismic mass, spring and measuring and damping coils in a field of permanent magnet, [69] and [70]. The output signal is proportional to the velocity and its sensitivity is close to that of the original seismograph. The range of measured frequencies of motion is related to the eigenfrequency and the direct measurement of displacement is not possible. The algorithm for calculating the rotation movement, from separated signals, assumes the same or well known transfer characteristics for each couple of sensors. The maximal theoretical resolution expressed in angular velocity is assumed to be in order of 10-8 rad/s. The same principle as in the previous paragraph is used in the construction of roundel of geophones. It consists of even number of geophones, [7], mounted on the periphery of metal roundel. Each couple of sensors is placed in the opposite position. The geophones are in the corners of n-angle (polygon) shape. This type of sensor was created at the Institute of Rock Structure and Mechanics during the years 2008 and 2009 and is covered by the Czech patent, [7]. Measured signals are proportional to velocity and rotations are calculated by a dedicated algorithm that has to eliminate different characteristics of each geophone. Well known transfer functions of geophones means necessity of thorough tests and primary selection. Theoretically, this arrangement can achieve sensitivity up to the 10-8 rad/s. This sensor is currently tested within the local seismic network WEBNET. Systems for measuring rotational movement are also based on Sagnac’s effect, [15]. Nowadays there are two main types of optical systems used in geophysics – high 3

sensitive and robust system with mirrors, [57], and systems utilising fibre-optic coil, [41]. The first one, ring laser, was originally designed to determine small variations of Earth’s rotation. Measuring of rotations spread during earthquakes is only its additional feature. There are two places with such facilities in the world – in Germany and in New Zealand. Thanks to the perfect local conditions – linking to the subsoil, low level of noise – it is possible to achieve resolution up to the 10-10 rad/s. This sensor requires precise and stable placement – it cannot be relocated. Another version is based on fibreoptic coil. Generally, this type takes an advantage of using multiple turns of fibres on a coil. This means that even for smaller dimensions the same or higher sensitivity and resolution can be achieved. The theoretical resolution is in order of 10-8 rad/s. This sensor, as well as others based on Sagnac’s effect, suffers from low sensitivity at low rotational speeds – lock-in effect. Inertial systems as laser gyros used in navigation can be in principle applied in rotational seismometry. Unfortunately, their sensitivity is too low for seismological measurement. Naturally, they are primarily intended for use in aircrafts that change moving direction during the flight very fast. They also suffer from lock-in effect. The electrochemical sensor is probably the first one that is commercially produced for seismology, [19]. Some independent comparisons of its behaviour are available, [22]. According to datasheet it can achieve resolution in order of 10-7 rad/s, but with the self noise up to the 10-6 rad/s. This is clear from the principle – ions motion between anodes and cathodes causes steady noise level, [1]. As in the other sensor cases mentioned above its output is proportional to velocity so it does not allow to measure at very low frequencies, down to the DC. Sensors with piezo-electric layers are simple, small and cheap. Modern types are realized directly on the silicon die – MEMS. Measuring by piezo-sensors is similar to the array techniques but concentrated on small area. Sensors are supposed to measure signals with high SNR like motion in robotics etc. and their parameters are not suitable for rotational seismology.

2

AIM OF THE THESIS

The main objective of this Thesis is design, development, manufacturing and verification of measuring system for newly emerging discipline of geophysical sciences – rotational seismometry. The final result will be a prototype of sensor that could be used in routine seismology in local or regional distance. The system should fulfil following requirements 1. Capability of both autonomous and network operation. System should allow to work as a part of seismic network. This feature enables signal comparison among different types of sensors. 2. Continuous form of the primary signal from the sensor. 3. As simple mechanical construction as possible. 4. To have attributes of smart sensors. 5. Digital form of all output signals suitable for direct monitoring and further signal postprocessing. 6. Maximum possible suppression of movements in vertical direction on horizontal angle of deflection (cross-sensitivity). 7. The system architecture similar to the absolute sensor based on a seismic mass. 8. Architecture, dimensions and design allowing absolute mobility of the instrument. 9. Ability to work in field conditions. 4

10. To measure an angle deflection in horizontal plane with sensitivity in order less than 10-5 rad. Expected rotational events are very weak in sense of whole range ±5 mrad. 11. Contactless method of angle measurement. 12. Linearity of transfer function angle-output signal better than 0.5 %. This has to be achieved by transforming mechanical movement into electrical quality. 13. Frequency range: lower frequency as close to zero as possible, upper frequency around 20 Hz. 14. Adaptability of the system to variation of parameters affecting transfer function. 15. Digital form of information about angle as close as possible to the front--end system. 16. Diagnostic tools for checking correct operation of the whole system.

Clearly solution of these tasks represents a multidisciplinary complex problem. Accept this challenge will lead to qualitatively new system, suitable for basic research as well as practical application. All work can be divided into four parts 1. Theoretical consideration of rotational move and possibility of their implementation for events observed in seismology. 2. Designing mechanical part of the sensor. seismological 3. Design of data acquisition module for continuous measuring in sense of seismo requirements. 4. Conceive and implement algorithm for efficient data evaluation.

3

METHODS

All current methods of rotational motion measuring are based on derivative principle, i.e. they do not provide any information about the DC component. This fact causes many difficulties in weak and slow signal measuring, near the noise level.

Absolute sensor of angular vibrations

Figur e 1 On model o f rot at ional seis mo me t er

Assume an angular deflection sensor designed according to the figure 11. In this model static (stator) and rotational (rotor) parts are represented as their equivalent masses. They are coupled by bond with two parameters – rigidity k and damping b. Damping is proportional to the velocity. Angular deflection ϕy effects on the stator and the rotor mass mr. Flexible element – bond, e.g. represented by a spring – transfers this move to angular deflection of the rotor ϕx. The movement equation is:
  

    

 

 

      0

(1)

Angular position (specified as ϕz) of mass point mr with respect to the reference plane is combination of initial time independent component ϕz0 and time variant components ϕx and ϕy (2). Rewriting (1) using (2) and assuming zero initial conditions we get a normalized form (3). 5

    

       

 

 







  

(2)     

(3)

In fact the rotor might have complicated shape and mass distribution and instead of term mr*r2 the moment of inertia J should be used in equation of motion. Measured harmonic rotation (4) causes in this linear system also harmonic response but generally phase-shifted by angle α (5).     ! ∙ #

%$   & ! ∙ # $% '(

(4) (5)

Figure 2a shows the dependence of characteristics on normalized damping B. For frequencies substantial higher than ω0 phase shift is close to 180° (figure 2b) b). It means that the deflection of the rotor mass is stable and equal to the initial angle ϕz0. This is typical feature of absolute angular deflection sensor – mass mr stays steady and behaves as a seismic mass. α

Figur e 2 Magnit ude a) and phase b) charact er ist ics o f rot at io nal seismo met er (aft er [16]))

Capacitors with pre-calculated capacitance Measuring small angular movements in seismology has to be performed by a sensor with specific features – high sensitivity, linearity and immunity against parasitic effects. Excellent candidates to fulfil these strict demands are sensors working on the principle of capacitors with pre-calculated capacitance. All theoretical formulas for calculating capacitance from dimensions are valid only in case when parasitic capacitances are equal to zero or have negligible effect on the main capacitance. The important source of parasitic capacitances is a deformation of electrical field on the boundaries between electrodes and outside space, known as fringe field [16]. Guard ring

Kelvin had proposed a method of eliminating parasitic capacitances by using the third electrode – guard ring (figure 3). It is remarkable that the capacitor has the same value of capacitance no matter which one of the two active electrodes is grounded. However the field is homogenous only in case when the island and electrode and the guard ring are on the same potential (figure 3b) b) and according to often occurring claim, only in this case, capacity is supposed to be calculated from dimensions. On the basis of the previous analysis Heerens defined the rules of thumb for design capacitors with pre--calculable capacitance: 1. For the deviation from linearity δ ≤ 1 ppm and precision of calculation of capacitance from dimensions ons using theoretical (ideal) formula the minimum dimension causing the change of overlapping area of planar electrodes must be >5d,, where d is the air gap – distance between electrodes. Based on this rule the dimension of active electrode can be chosen. 6

2. The minimum guard area dimension g (e.g. width of guard ring) satisfying inequality g ≥ 5d guarantees that the relative deviation of accurate and calculated capacitance δ will be less than 1 ppm. 3. The difference between true and calculated capacitance will be less than 1 ppm, provided that width of insulating gap s between active electrodes and guarding electrodes fulfils the condition s < d/5. The boundaries of active electrodes can be found in the centre of these gaps. 4. If two electrodes – that are situated on both opposite electrode carriers and which are forming together the properly guarded capacitor – have fringe field effect then accuracy of calculation better than 1 ppm is achieved if the side-way distance y between fringes is equal to 5d.

Figur e 3 Kelvin’s guard r ing cap acit or, a) 1…act ive elect rode-island, 2…gu ard r ing, 3…oppo sit e elect rode, b) capacit or wit h ho mogenous fie ld, c) cap. wit h inho mo g eneo us field ( fro m [16])

4

RESULTS

Modern seismic sensors are designed to be mechanically as simple as possible. This tendency should be preserved for designing a new portable sensor for rotational seismometry. All requirements on the mechanical part can be fulfilled by capacitor mounted on a seismic mass coupled by crossed flat springs to the axis located on the desk fixed to the place where rotational movement is measured. Rotational seismometer is in fact system with angular movement of seismic mass around initial position. The final design of the sensor is in the figure 4. By solution of equations similar to those from the previous chapter using Laplace’s transform where the input variable ϕy(t)
Y(p) and the output variable ϕx
X(p) transforms we get the transfer function F(p) of the sensor (6). )* 

+, -,



.,

, '/,'%0

(6)

Capacitive sensor Only variable area sensor fulfils requirement of linear transfer characteristics within types of capacitive sensors. To avoid the basic drawback of this configuration, i.e. influence of air gap variation, the differential type of sensor can be used. Universal multi-electrode capacitive sensor of position

This design is composed of the four-electrode vertical capacitor. Two electrodes, the bottom and the upper one, are fixed. The third and the fourth, the middle two, are mounted on a seismic mass and can move within a small horizontal range between the others, figure 5. This type is used as a special kind of differential arrangement of capacitive sensor which in ratio-metric measuring circuit is independent on the vertical displacement of the middle electrode, [16]. The outline of all electrodes is the same – sector of a circle. Electrodes are angular rays, going from the centre of a circle, made on each board. The electrodes are connected by a bus at the inner periphery. Words stator and rotor are used in sense of stationary and rotationally part respectively in the further text. 7

Figur e 4 Fina l design o f rot at iona l seis mo met er

Stator electrodes are marked E1 and E2 and the rotor ones D1 and D2. Both sides of the rotor are used for electrodes with the angle shift the same as the electrode’s width is. The stator electrodes are identical and face each other. All the other conductive parts are used as shielding. According to the Heerens’s rules the effective shielding must be 3 to 5 times wider than the electrode, [26]. In the ideal zero position electrodes D1 and D2 overlap in the middle of the E1 and E2, figure 5. The rotor move causes changing the overlapping area ∆S and consequently it increases the capacitance of one couple, e.g. D1-E1, and decreases the capacitance of the second one, e.g. D2-E1. The main features of this configuration are following: a) linear dependence between overlap area change ∆S and angular move, b) c)

differential measuring enables sensitivity increase and disturbances reduction, set of n parallel electrode couples D1-E1, D2-E2 can increase SNR.

Figur e 5 Front view (alo ng t he arrow in t he figure 4) on vert ically p laced elect ro des

There are seven basic configurations of electrodes interconnection. To measure the angle of rotation the option, where E1 and E2 are interconnected, stator shielding is grounded and capacitances CD1E1E2 and CD2E1E2 are measured, is uses. All electrodes were made by PCB technology. The basic requirement was to achieve as high accuracy as possible because the spaces between electrodes have to be the smallest feasible. From mechanical reason the air gap distance d cannot be less than 1 mm. The full scale of angle was chosen to be ±2.5 mrad i.e. the angle width of electrode is a = 5 mrad and guarding segment width is 4a = 20 mrad. The critical issue is sensitivity to vertical movement (i.e. variation of d). Vertical vibrations are primarily reduced by the mechanical construction. Nevertheless, the suppression of vertical movement can be further improved using ratio-metric measurement method. Capacitance between D1 and interconnected E1 and E2 is a sum of particular capacitances between D1–E1 and D1–E2 (i.e. CD1E1 and CD1E2). At the initial position the overlapped area is equal to S0 and air gap is equal to d0. Rotation in 8

horizontal plane changes the overlapping area of the stator and the rotor electrodes by ∆S. The unwanted vertical move modifies air gap by x. The influence of general movement divided into horizontal and vertical component affects capacitances as follows. The factor V means the influence of an air gap d on the capacitance. 12343  5 5

60 '∆6 0 . 

; 1234  5 5

123434  12343  1234  2 ∙ 5 5

60 '∆6 0

60 '∆6

(7)

0 ' 

 

∙ : .3 ; :  1  < = 

(8)

The ratio-metric measurement method gives results proportional to the relative change of electrode overlapping area caused by rotation in the horizontal plane. Design supposes usage of n parallel electrodes. Main advantage of such configuration is n-times enhancement of useful signal (proportional to ∆S) and so increase of SNR. >?@A@A.>?A@A

>?@A@A'>?A@A



∙B B0 ∙C D@ ∙60 '∆6.60 '∆6∙0D@

∙B0 B ∙C D@ ∙60 '∆6'60 .∆6∙0D@



∆6 60

(9)

Measuring Circuit The measuring circuit is implementation of commercially available capacitance to digital converter (CDC), AD7746. It has two independent channels so that it can measure two single-ended capacitances or one differential capacitance. It is an autonomous system. CAPDAC is used for initial common-mode capacitance compensation and lock-in detector for following small changes of capacitance. The fullscale (varying) capacitance range is ±4.096 pF and resolution down to 4 aF.

Figur e 6 Funct ional b lock diagram o f CDC AD7746 ( fro m [2])

The designed sensor requires to measure capacitance higher than 40 pF. An elegant way how to extend the measuring range is to use both excitation outputs, EXC1 and EXC2 (with opposite phase), resistor divider and precise operational amplifier. DAQ CDC Module

The work on the specific data acquisition module with features suitable for seismic measurement – DAQ CDC Module (DCM) – started after verification of CDC features. The DCM was designed to increase measuring capabilities and to fulfil the requirements of typical seismic measurement. Seismic records have to be mutually comparable, so it is necessary to assign an accurate time to each measured sample [60]. This is achieved by synchronizing with the global time reference – GPS. Current seismic stations operated within the IRSM use the data-logging system called RUP. It was designed and composed by the author of this Thesis, [62]. The key features of DCM as designed are: a) b) c) d) e)

single-ended measuring of CIN1 or CIN2, continuous single-ended measuring of CIN1 and CIN2, continuous, simultaneous, differential measuring, continuous, synchronizing digital input for GPS, independent power supply, 9

f)

two-board design – the first, main, with the micro-computer and the second, detached, with the AD7746 located as near as possible to the electrodes.

Despite the fact that CDC can sample capacitance with discrete frequencies up to 90 Hz it is applicable for single channel measuring only. Continuous mode with simultaneous sampling both channels is not possible by default by CDC. One-chip micro-computer controling directly values in registers of AD7746 had to be used. This is the only way to provide nearly simultaneous measurement of two single-ended capacitances connected alternatively to CIN1(+) and CIN2(+). The input circuit configuration of AD7746 (small internal resistance of excitation voltage source and virtual zero at the input of current to voltage converter) reduces substantially the effects of leads’ parasitic impedance. The single-ended to differential configuration and vice versa is switched over internally. The leads connection is shown in the figure 7. The CDC measuring range can be extended by jumper setting at the board located close to AD7746.

Figur e 7 Connect ion o f cap acit ors t o CDC

DCM is plugged in the host system USB port. Communication is performed by ASCII commands in query-answer mode. The main emphasis was placed on the possibility of the maximal configuration variability. There are three command groups: a) b) c)

configuration – reading and setting registers of AD7746, single measuring – reading of current capacitance value, continuous measuring – start/stop type of measuring.

Figur e 8 DCM - det ached board wit h CDC and ranging and main- bo ard wit h co nt ro ller

The simultaneous measuring is the main feature of the device. As mentioned switching between channels is performed via changing the register content only and is automatic. It is possible to achieve almost 90 samples for both channels which means the sampling about 45 Hz for each input. Nyquist’s frequency is slightly above 20 Hz.

Experimental verification of sensor parameters In order to verify sensor parameters several experiments using CDC evaluation board were performed. An example waveform of the response to force is in the figure 9. The spectral analysis of the response shows two side-bands around main frequency. This is typical for amplitude modulation (AM). It seems like some kind of AM with the carrier equal to the resonant frequency of the sensor is present. More likely the waveform is a result of beats of oscillations with two near frequencies ω1 and ω2. This fact leads to the hypothesis that the two modes of oscillations – the main-mode and the 10

side-mode exists. Existence of the side-mode can be explained by uncertainty of the fixing point locations of the flat springs. Thus the oscillation condition is fulfilled for two modes reflecting complexity of spring geometry.

Figur e 9 Response t o t he force imp ulse app lied int o t he senso r’s base; T s = 11 ms

System Identification Generally, measured signal is modified by a system’s transfer function. Ideally, output signal should be a copy of an input stimulus. This is the case for flat magnitude and linear phase transfer function. As it is evident from figure 2 these conditions are approximately fulfilled for normalized damping B between 0.5 and 0.7. The other values lead to the harmonic distortion of measured signal. Presented sensor is defined by transfer function specified in Equ. (6). There are several parameters that can be calculated from material and mechanical attributes of the sensor or measured as a response to a test input – model based calculation. This method of identification is intuitive, simple, less accurate but fast, feasible with basic equipment and works well with simple input stimuli. Using the response to a test input for identification is more convenient as it can involve time variability of the system features and adapts transfer function to them. Estimating based on Least Mean Square criterion

LMS based estimating of parameters utilises minimization of sum of mean square differences between the measured system output data and the output signal of searched system model. This approach of estimating belongs among the most emerging and used techniques in measurement. It is based on the knowledge of input signal and supposed model of examined system. Transfer function F(p) of the continuous system as inferred in (6) is used as a model of the sensor. LMS estimating is specific by using statistical data processing respecting existence of noise and perturbance. It leads to substantially improved accuracy of model parameters. Identification methods comparison

There is no available facility for generating as short testing angular movement (e.g. Dirac’s pulse shape) as presented sensor would require. Generally, the stimulus looks like a short pulse of sinusoidal shape and such pulse of force was used in case of identification by LMS method. Parameters obtained using impulse response (model-based) and by LMS are almost the same (table 1). Despite the fact that the input stimulus is not exactly known the LMS algorithm can be used for periodic estimating of parameters. These parameters are then employed at the deconvolution process and it is feasible to get the right shape of the input mechanical signal (stimulus). 11

Table 1 P aramet ers co mp ar iso n list

model LMS factor chapter 7.1 chapter 7.3 f0 1.91 2.00 δ 0.67 1.26 Q 9 5.0 B 0.1 0.1

Approximate Deconvolution The input stimulus shape can be formally accomplished by deconvolution process – multiplication of the sensor’s measured output, X(p), by the inverse transfer characteristic 1/F(p). Ideal transfer function does not depend on frequency. The seismic sensor is typically characterised by a transfer function of the second order without any time delay. Unfortunately in case when F(p) has zeroes at zero frequency (p = 0), the direct deconvolution is not possible as it would require division by zero. The approximate deconvolution (ApDc) proposed in Thesis can be then used. The zeroes of F(p) are removed by multiplication of F(p) by the term (10). The price is acceptable slight distortion of the input signal at very low frequencies. 3

E*  3',F

(10)

I GH 

Here m is the order of zeroes at zero frequency of F(p). The inverse value of τcor determines corner frequency of m-order low pass filter and should be chosen to be smaller than eigenfrequency ωo. For frequencies where inequality (11) is valid approximation of D(p) can be used (12). *JKL ≫ 1

E* ≅ EO *  ,F

(11)

3

(12)

I GH 

Then the multiplication F(p) by Da(p) causes removal of F(p) zeroes. Now assume the second order transfer function (6). Then the ApDc process consists of multiplication of measured input stimulus as X(p) by expressions as given in (13). 3

E, *  3',F

GH 

I

∙ *  P*  ! 

(13)

The equivalent transfer function between the input stimulus Y(p) and the output from ApDc block is (14). )* ∙ E, * 

.,

, '/,'%0

3

∙ 3',F

 GH 

∙

, '/,'%0 3

,

  3',F

 GH 

(14)

The final shape of transfer characteristics depends on the position of all zeros and poles. The examined rotational sensor has two zeros so the order of correction element is m = 2 and τcor = 0.1 s was chosen. Its eigenfrequency is 2.2 Hz. Waveform in the figure 10 proves the right function of ApDc. The input stimulus derived by approximate deconvolution is shown as green line and the measured signal is the blue dashed line.

Figur e 10 Inp ut st imulus (green) found by deconvo lut io n fro m measured dat a (blu e)

12

The approximate deconvolution procedure can eliminate the distortion of signal caused by the real system transfer function F(p) even if the ideal deconvolution is not feasible due to the existence of zeroes at the zero frequency. In case of exact knowledge or estimation of the transfer function, the deconvolution can be used as an alternative to transfer function modifications by complicated electromechanical means like e.g. direct or feedback damping. The sensor without damping elements can have substantially simplified mechanical construction. Such simplification is a newly emerging way due to possibilities of performing easy and fast signal post-processing.

5

CONCLUSION

The original structure of absolute sensor for measuring angle in horizontal plane was designed, created (chapter 4) and experimentally verified (chapter 6). The mechanical part of the sensor uses the balanced rotor mass (seismic mass) bonded to the stator part via flat crossed springs (chapter 4.1, appendix A). Vertically oriented flat springs minimize the sensitivity to vertical motion and balanced mass of the rotor eliminates translational movement influences (chapter 4.1). The angle deflection sensor based on the capacitive principle was found as the optimum solution as its resolution is not inherently limited by the principle but only by properties of measuring circuits (chapter 4.6). The negative effect of stray fields was simulated by FEM and eliminated using Thomson-Lampard’s theorem approach (chapter 3.2.2). The universal version of the novel type of multi-electrode capacitive sensor using modified principles of pre-calculated capacitance (Heerens’s rules) was designed (chapter 4.2.1) and verified experimentally (chapter 6). The main attributes of the original capacitive sensor are following: a)

b)

c) d)

e)

f)

The output signal from the sensor is proportional to the angle of deflection, while existing types of sensors used for rotational seismometry generate a signal proportional to angular velocity (chapter 1, chapter 6.4) Resolution is limited only by noise of measuring circuit. In case of coherent demodulation (lock-in detection) based measuring system, resolution is inversely proportional to the value of the corner frequency of demodulator low pass filter. CDC converter AD7746 presents this feature. Using it as a core of measuring circuit allows reaching resolution down to the 10-9 rad. Recommended sensor for rotational seismometry in [22] is a velocity type and has sensitivity 10-7 rad/s (chapter 1.4). Linearity is better than 0.5 % even when preserving small dimensions of the sensor (chapter 6.4). Substantial reduction of sensitivity to the vertical movement and theoretically absolute elimination of it when the ratio-metric measuring method is employed was achieved (chapter 4.4). Possibility to measure DC component of angle, i.e. the sensor can also be used for tilt measurement. This feature can be used easily as diagnostic information (checking the signal when sensor’s base is tilted from horizontal plane, chapter 7.4). Simple and cheap production technology (PCB) is used for manufacturing mechanical part of the sensor and electrode pattern (chapter 4.2.3).

Digital measuring system using C/D converter AD7746 by Analog Devices as the core element has been designed and experimentally verified (DCM). The system allows to measure nearly simultaneously sum and difference of the sensor capacitances as required by ratio-metric method (chapter 5.2.3). This measuring system fulfils requirement of mobility and contains several attributes of smart sensor (chapter 5.2.3): 13

a) b) c) d)

Digital measurement and processing by means of two microcontrollers. Adaptability – after repeated identification in given intervals the modified transfer function could be used for correcting the output signal by deconvolution. Signal arising by tilt of the sensor’s base can be used for diagnostic purposes or even calibration. Duplex digital communication between system and host computer or data-logger.

Procedure of the system identification using the LMS criteria has been developed and verified. It can be used for estimating parameters of the sensor despite the uncertain knowledge of input stimulus (chapter 7.3). Mechanical construction of the sensor was significantly simplified because commonly used and quite complicated electromechanical part for setting the correct damping factor B is replaced by a novel procedure of deconvolution. The new method called Approximate Deconvolution (ApDc) was developed (chapter 8.1). This process enables correction of systematic errors due to non-ideal shape of the sensor transfer function. The ApDc reduces problems when classical deconvolution cannot be used for system with transfer function containing zero for zero frequency in numerator. This is often the case of seismic mass based sensors. The ApDc method was verified and brought positive results, e.g. explanation of “mouse effect” occurring in the record of signals from Güralp sensors. The paper describing this method has been sent for publication to the Studia Geophysica et Geodaetica Journal in May 2010, [66]. The novelty of the sensor is proved by its admission for patenting in the United States (see appendix E and [72]). The basic description of the sensor was also provided to Analog Devices as an illustration of C/D usage, [64]. Summary of conclusions

All objectives defined in the aims of Thesis were fulfilled. The novel sensor has been designed specifically for rotational seismometry and has better properties (e.g. resolution larger by two orders, measuring of static deflection) than any known sensor (of angular velocity) used for the same purpose at the present time. Future prospects

There are three main objectives concerning accurate testing, application in the field within the framework of seismic network and mechanical improvements flowing from the experiments for the future. Rotational seismometer developed in terms of this Thesis has potential for further improvement as far as resolution and cross-sensitivity are concerned. Resolution is limited by the required dynamic properties of system, namely by sampling frequency. Nevertheless, using the double sampling method could allow suppressing distortion caused by possible aliasing effect when sampling frequency is above the Nyquist’s limit. Even in the ideal case when limits of resolution given by measuring system will be reached, the principal problem separating pure rotational movement in horizontal plane from the other components has to be concerned about. Naturally, the problem of cross-sensitivity was taken into consideration during the whole process within this Thesis. The special design of fixing crossed springs proves it. As preliminary experiments show there are good reasons for reaching necessary level suppression of cross-sensitivity by this rotational seismometer. However the quantification of crosssensitivity is difficult task because of the lack of appropriate test facility and instrumentation – testing bench. The only known testing equipment was designed and realized in mid-1990’s by common effort of Union Scientific Research Institute 14

(UNIIA) of the Ministry for Atomic Power Engineering of Russia in collaboration with the U.S. Geological Survey. The cross-sensitivity reduction problem will be addressed in the future research either under the auspices of IRSM ASCR and/or in the frame of Czech Science Foundation grant project that I have proposed for together with my supervisor and colleagues. My vision is to improve or redesign the mechanical structure of the sensor, namely by better balancing and shaping the rotor body, finding optimal construction of flat crossed springs and creating simplified test bench for cross-sensitivity evaluation. There is certain possibility to use testing bench in the laboratory of Prof. Evans at the University of California in Los Angeles, USA (UCLA). The first visit at UCLA is planned for November 2010. An alternative or parallel way to decrease cross-sensitivity might be implementing compensation principle by measuring unwanted movement components and remove them from the output signal of rotational seismometer numerically.

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[44] Large Laser Gyroscopes for Monitoring Earth Rotation, Online: http://www.wettzell.ifag.de/LKREISEL/G/LaserGyros.html (as of November, 2007) [45] Lennartz electronic GmBH (1986), LE-3D General Description, Rev. 01, Product Manual, Tübingen, Germany [46] Linda M. (2010), DAQ C/D Module – design and production documentation, internal document, cdc_cdu_v100.pdf, Tedia s.r.o., Pilsen, Czech Republic [47] Low G, iMEMS Accelerometers, Analog Devices, Online: http://www.analog.com/en/mems/low-gaccelerometers/products/index.html (as of June, 2010) [48] Maxwell J.C. (1873), A treatise on Electricity and Magnetism, Vol. I, Clarendon, Oxford [49] Melton, B.S. (1981), Earthquake seismograph development: a modern history - part 1, EOS, 62(21), 505-510 [50] Melton, B.S. (1981), Earthquake seismograph development: a modern history - part 2, EOS, 62(25), 545-548 [51] Norsar, Array Processing, Online: www.norsar.no/c-83-Array-Processing.aspx (as of April, 2010), Kjeller, Norway [52] Pancha, A., Webb, T.H., Stedman, G.E., McLeod, D.P., and Schreiber, U. (2000). Ring laser detection of rotations from teleseismic waves, Geophys. Res. Lett., Vol. 27, 3553-3556 [53] Precise Monitoring of the Earth Rotation by Ring Lasers, Online: http://www.wettzell.ifag.de/LKREISEL/CII/precise.htm (as of November, 2007) [54] Ring Laser Group, Uni. of Canterbury, New Zealand, Online: http://www.ringlaser.org.nz (as of May, 2010) [55] Ring Laser Project Webpage, Fundamental Station Wettzell, Online: http://www.ringlaser.org.nz/content/gross_ring_facility.php (as of May, 2010) [56] Simandl M. (2000), Adaptivni systemy, University of West Bohemia, Pilsen, Czech Republic, ISBN 80-7082-678-9 (in Czech) [57] Schreiber K.U., Stedman G.E., Igel H., Flaws A. (2006), Ring Laser Gyroscopes as Rotation Sensors for Seismic Wave Studies, in [71], pp. 413-438 [58] SMART2, Small Aperture Array – Shape, Taiwan, Online: http://www.earth.sinica.edu.tw/cdr/IASPEI/data/smart2/smart2.html (as of November, 2007) [59] Stejskal V. (2005), Ostaš, situation map, not published material, IRSM ASCR, Prague [60] Strunc J. (2005), RUP2004 – Seismic Apparatus, Complete User Manual, Rev. 1.2, internal document, published on web-site, IRSM ASCR, Prague, Czech Republic, in Czech, Online: http://www.irsm.cas.cz/RUP2004/RUP2004.pdf (as of June, 2010) [61] Strunc J., Broz, M. (2006), RUP2004 - High Definition Apparatus for Standalone, Network and Micro-Array Applications in Seismics, Transactions of the VSB - Technical University of Ostrava, Civil Engineering Series, v. 6, no. 2, VSB-TU, Ostrava, ISBN 80-248-1187-1, ISSN 1213-1962 [62] Strunc J., RUP – solution for seismic monitoring; web presentation, IRSM ASCR, Prague, Online: http://www.irsm.cas.cz/RUP2004 (as of June, 2010) [63] Strunc J., Buben J., Dado S. (2005): Rotation Component of Seismic Signal; Poster, EGU 2nd General Assembly, Vienna, Austria, SM1-1TU2P-0037 [64] Strunc J., Dado S. (2008): Capacitive Sensor for Rotational Seismology, 16th IMEKO TC4 International Symposium, "Exploring New Frontiers of Instrumentation and Methods for Electrical and Electronic Measurements", September 22 - 24, 2008, Florence, Italy, ISBN 978-88-903149-3-3, p. 513-516 [65] Strunc J., Dado S., Malek J., Brokesova J., (2009), Grant project solving and final summarization, Registration number of project: 102/07/0794, Name of project: Sensor of Rotational Movement around Vertical Axis for Seismology, Acta Research Reports, No. 18, Prague, ISSN 1214-9691 (in Czech) [66] Strunc J., Dado S. (2010): A simple way of elimination of distortion caused by transfer characteristic of seismometers, Studia Geophysica et Geodaetica, ISSN: 0039-3169, submitted [67] Takeo, M. (1998), Ground rotational motions recorded in near-source region of earthquakes, Geophys. Res. Lett., Vol. 25, 789-792 [68] Takeo, M., Ito, H.M. (1997), What can be learned from rotational motions excited by earthquakes?, Geophys. J. Int., Vol. 129, 319–329 [69] Takeo, M., Teisseyre, R. (2006), Design of Rotation Seismometer and Non-Linear Behavior of Rotation Components of Earthquakes, Earthquake Source Asymmetry, Structural Media and Rotation Effects [70] Teisseyre, R., Suchcicki, J., Teisseyre, K.P., Wiszniowski, J. and Palangio, P. (2003), Seismic rotation waves: basic elements of theory and recording, Annals of Geophysics, Vol. 46, N.4 [71] Teisseyre R., Takeo M., Majewski E. as Eds. (2006), Earthquake Source Asymmetry, Structural Media and Rotation Effects, Springer, ISBN: 3540313362

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[72] Texas Institute of Science (2010), IP of the Month: Capacitive Sensor for Slow Rotational Movements in Horizontal Plane, Online: http://www.txis.us/txis/about/press/NewsLetters/NewsLetter_May2010.htm (as of May, 2010) [73] Texas Institute of Science (2010), Available IPs: 01054 Capacitive Sensor for Slow Rotational Movements in Horizontal Plane, Online: http://www.txis.us/txis/technologies/ips.aspx (as of July, 2010) [74] Thompson A.M., Lampard D.G. (1956), A new theorem in electrostatics and its application to calculable standards of capacitance, Nature, Vol. 177, p.888 [75] Vejdelek J., Dado S. (2003), private unpublished calculations, FEL, Czech Technical University in Prague [76] Wiszniowski, J. (2006), Rotation and Twist Motion Recording – Couple Pendulum and Rigid Seismometers System, in [71] [77] Zahradnik J., Plesinger A., (2005), Long-Period Pulses in Broadband Records of Near Earthquakes, Bulletin of the Seismological Society of America, Vol. 95, No. 5, pp. 1928–1939

PUBLICATIONS AND PROJECTS Works relating to the doctoral thesis Projects Sensor of Rotational Movement around Vertical Axis, 2007-2008, Czech Science Foundation, project no. 102/07/0794, Main Investigator: Jaroslav Strunc Modification of Sensor of Rotational Movement on Capacitive Principle, 2010, Institute of Rock Structure and Mechanics ASCR v.v.i., Main Investigator: Jaroslav Strunc

Referred Journals Strunc J., Dado S. (2010): A simple way of elimination of distortion caused by transfer characteristic of seismometers, Studia Geophysica et Geodaetica, ISSN: 0039-3169, submitted Strunc J., Dado S. (2010): Rotational Seismometer on the Capacitive Principle, being prepared for Measurement Science and Technology, ISSN 0957-0233 (Print) ISSN 1361-6501 (Online), Section „Sensors and sensor systems”

Patents Brokesova J., Malek J., Strunc J. (2008): Rotational Seismic Sensor System, Generator of Rotational Seismic Waves and Seismic Measuring Set, Faculty of Mathematics and Physics, Charles University in Prague, Date of Application: October 30, 2008; Patent Granted: November 2, 2009, (in Czech) Brokesova J., Malek J., Strunc J. (2008): Generator of Rotational Seismic Waves, Rotational Seismic Sensor System and Seismic Measuring Set, Faculty of Mathematics and Physics, Charles University in Prague, Date of Application: October 30, 2008; Patent Granted: November 2, 2009, (in Czech)

Patent Application Strunc J.: Capacitive Sensor for Slow Rotational Movements in Horizontal Plane, Intellectual Property specified in Application for a Patent was submitted to the U.S. Patent and Trademark Office by means of Texas Institute of Science

Journal Strunc J., Dado S., Malek J., Brokesova J. (2009): Sensor of Rotational Movement around Vertical Axis for Seismology, Grant project solving and final summarization, Acta Research Reports. No. 18, pp. 67-74. ISSN 1214-9691, IRSM AS CR, Prague

International Conferences Strunc J., Broz M., Dado S. (2010): Rotational Seismometer and its Possible Usage for Oscillation Measurement of High Towers of Historical Buildings, ESC2010, 32nd General Assembly, September 6-10, 2010, Montpellier, France, admitted for presentation Strunc J., Dado S. (2008): Capacitive Sensor for Rotational Seismology, 16th IMEKO TC4 International Symposium, "Exploring New Frontiers of Instrumentation and Methods for Electrical 18

and Electronic Measurements", September 22 - 24, 2008, Florence, Italy, ISBN 978-88-903149-33, p. 513-516, oral presentation Strunc J. (2008): Mobile sensor of rotational movement for seismology, The 33rd International Geological, Congress, Oslo, August 6 - 14, 2008, oral presentation Strunc J., Buben J. (2005): Rotation Component of Seismic Signal; EGU 2nd General Assembly, Vienna, Austria, SM1-1TU2P-0037, poster

Software RUP2010/ROT - Application for recording of continuous seismic data from rotational sensor. Software uses Data Acquisition Capacitance to Digital Converter Module that enables to measure two capacitances simultaneously.

The other works Referred Journals Malek J., Broz M., Stejskal V. and Strunc J. (2008): Local Seismicity at the Hronov-Poříčí Fault (Eastern Bohemia). Acta Geodynamica et Geomaterialia, Vol. 5, No. 2 (150), pp. 171-175, IRSM AS CR, ISSN 1214–9705, Prague Malek J., Kolinsky P., Strunc J. and Valenta J. (2007): Generalized average of signals (GAS) - a new method for detection of very weak waves in seismograms, Acta Geodynamica et Geomaterialia, Vol. 4, No. 3 (147), pp. 5-10, IRSM AS CR, ISSN 1214–9705, Prague

Journals Broz M., Malek J., Valenta J., Stejskal V., Stepancikova P., Strunc J., Kolinsky P. (2009): Hydrogeological effects of seismicity in the Hronov-Poříčí fault zone area, Acta Research Reports. No. 18, pp. 61-63. ISSN 1214-9691, IRSM AS CR, Prague Broz M., Strunc J., Svatos J. (2008): Monitoring of seismic impact on historical buildings and their damage during building the tunnel Blanka – especially influence on the stability of historical buildings in the Prague Castle area, 2nd.Traditional International Colloquium Geomechanics and Geophysics, Ostravice, May 22 – 23, 2008, ISBN 978–80–86407–36–4, Ostrava Sosna K., Broz M., Strunc J. a realizační tým projektu 1H-PK/31 (2007): Laboratorní stanovení hydrodynamických a migračních parametrů granitových bloků a jejich vztah k šíření seismických vln – informace o řešení projektu, Sborník vědeckých prací Vysoké školy báňské - Technické university Ostrava, Řada stavební, česky Broz M., Strunc J. (2007): Anomální seismické účinky při některých těžebních odpalech v kamenolomech a povrchových dolech, Trhací technika a pyrotechnika - zpravodaj 3/2007, Český svaz vědeckotechnických společností, Společnost pro trhací techniku a pyrotechniku, Praha Ostrava, česky Strunc J., Broz M. (2007): Seismické přístroje pro lokální měření a monitorovací sítě, Trhací technika a pyrotechnika - zpravodaj 3/2007, Český svaz vědeckotechnických společností, Společnost pro trhací techniku a pyrotechniku, Praha - Ostrava, česky Broz M., Stejskal V., Strunc J. (2006): Local Seismological Network Ostas, Transactions of the VSB - Technical University of Ostrava, Civil Engineering Series, v. 6, no. 2, VSB-TU, Ostrava, ISBN 80-248-1187-1, ISSN 1213-1962, in Czech Strunc J., Broz M. (2006): RUP2004 - High Definition Apparatus for Standalone, Network and Micro-Array Applications in Seimics, Transactions of the VSB - Technical University of Ostrava, Civil Engineering Series, v. 6, no. 2, VSB-TU, Ostrava, ISBN 80-248-1187-1, ISSN 1213-1962 Broz M., Strunc J., Tesitel M. (2006): Monitoring of Seismic Effects of Blasts at Quarries and Mines, Blasting Technic and Pyrotechnic 2006, Czech Association of Scientific and Technical Societes, Association for Blasting Technology and Pyrotechnics, Prague, ISBN 80-0103547-6, in Czech Rudajev V., Buben, J., Broz M., Malek J., Strunc J., Zanda L., Zivor R. (2006): Experimental determination of acceleration decay of seismic vibrations in the Bohemian Massif, Acta Research Reports. Vol. 3, No. 15, pp. 49-56. ISSN 1214-9691 19

Horalek J., Broz M., Novotny O., Svancara J.; vedecti spolupracovnici: Fischer T., Plesinger A., Sileny J., Bouskova A., Babuska V., Psencik I., Jedlicka P., Spicak A., Mrlina J., Safanda J., Cermak V., Pek J., Cerv V., Praus O., Malek J., Strunc J., Zanda L., Jansky J., Nehybka V., Havir J. (2006): Comprehensive Geophysical Research of the Seismogenic Western Part of The Bohemian Massif, Grant project of the Grant Agency of the Czech Republic No. 205/02/0381, Acta Research Reports, No. 15, 57-67, Prague, Institute of Rock Structure and Mechanics AS CR, ISSN 1211-1576

International Conferences Broz M. Strunc J. (2009): Seismological measuring systems for monitoring heavy works at subterraneous buildings and basements of engineering structures, 32nd Polish-Czech-Slovakian symposium on mining and environmental geophysics, May 20-22, 2009, Piechowice Strunc J., Broz M. (2009): Response of Historical Buildings on Induced Signal with Exactly Defined Frequency Spectrum, EGU2009, General Assembly, April 9-14, 2009, Vienna, Austria, EGU2009-11364, oral presentation Stejskal V., Strunc J., Stepancikova P. (2005): Intrasudetic Basin (Czech Republic) - Complex Regional Geodynamical Study, EGU 2nd General Assembly, Vienna, Austria. SM3-1TU3P-0042 Broz M., Malek J., Strunc J. (2005): Interpretation of the seismic events at the underground gas storage Háje-Příbram, 30th Polish-Czech-Slovakian Symposium on Mining and Environmental Geophysics. Ladek-Zdroj 6-8 June 2005 Strunc J., Broz M., Valenta J. (2004): Determination of correct times of quarry blasts and properties of surrounding rock for measurement on seismic profiles, 32nd International Geological Congress, Firenze, Italy, oral presentation Broz M., Brokesova J., Malek J., Novotny O., Strunc J., Zanda L. (2003): Determination of the upper crustal structure using seismic waves from quarry blasts, EGS-AGU-EUG Joint Assembly, Nice France, April 6-11 2003, poster

Handbook Strunc J. (2006): RUP2004, seismická aparatura, kompletní manuál (rev. 1.2), IRSM AS CR, online publication (http://www.irsm.cas.cz/RUP2004/RUP2004.pdf), Prague, in Czech

Software (selection) RUP2009 – Seismological Monitoring System, RUP2004/RUP2009 is a PC-based recorder for continuous seismic monitoring. Depending on specification it offers wide dynamic range of data resolution (from 14-bit up to 28-bit). High dynamic range is very important for scientific measurements. The resolution of 14-bit is suitable for monitoring of strong technological events such as quarry blasts but is also useful for temporary measurements. (http://www.irsm.cas.cz/RUP2004) gse2txt – Seismological Data Format Converter, Software for conversion from GSE2(int) data format to mSEED or ASCII (Jiri Malek’s specification) format. It can convert data produced by RUP station and thus prepare input for other systems. Nevertheless it can be used for any GSE2(int) data. slowDAQ – Data Acquisition System for Slow Measurements, Data-logging system for measuring of analog and digital signals of slow processes with alarm and telemetry capability (GSM, Ethernet). MicroDAQ – Data Acquisition System for Slow Measurements, Simple data-logger for PC that uses ISA A/D converter and stores averages of continuous recording for specified blocks. GPStime - Accurate time synchronization (with GPS) via receiver connected to serial port. Excel Template for Seismology - visualization of time-series and frequency series of velocity and acceleration of ground movement recorded by BR3 or RUP.

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SUMMARY Rotational movement measuring belongs among emerging parts of seismology. This Thesis presents a novel approach based on the direct measuring of rotations. It is achieved using sophisticated mechanical transmission of ground movement into a change of capacitance between electrodes of capacitor. It enables to construct small and portable sensor for field measurement. The other current methods for studying seismic rotations depend on the indirect measuring. Most often it is provided by means of sensor matrix requiring careful in-situ planning. Additionally all so far manufactured sensors work on the derivative principle while the presented one measures position. The aims of the Thesis are theoretical study of optimal construction and measuring principles, and finally creation of a prototype complying with all seismic requirements. Mechanical part of the sensor is based on a movable seismic mass coupled by crossed flat springs to the basis. This solution enables angular deflection in the horizontal plane and primarily suppression of vertical disturbances. The four-electrode vertical capacitor performs measuring that is based on the principle of changing overlapping area. Such configuration provides linear dependency of capacitance on the angular deflection. Capacitor’s dimensions have to fulfil specific rules for fringe field elimination. Around the active electrodes are shielding elements. Two electrodes, the bottom and the upper one, are fixed. The third and the fourth, the middle two, share the same board that is mounted on the seismic mass which can move within a small horizontal range. That is a special kind of differential arrangement of capacitive sensor which in ratio-metric measuring circuit is independent on the vertical displacement of the middle electrodes. Therefore reduction of the vertical move influence on the measured horizontal one is provided by a combination of mechanic and electronic components. A specific data acquisition module fulfilling requirements of seismic measurement was developed around commercial capacitance to digital converter AD7746 with two input channels and resolution down to 4 aF (10-18 F). This measuring circuit and its software plug-in for seismological data-logging system RUP, previously composed by the author of this Thesis, allows usage of the sensor within the regular seismic network. The sensor as designed is not equipped with damping element. Only internal friction in the flat springs is present. The shape of input stimulus i.e. seismic event can be reached by deconvolution of the measured signal by means of the inverse transfer function. This approach assumes knowledge of system parameters. Estimating them is performed by the least mean square algorithm which gives satisfactory results even if the shape of testing input is not known exactly. Nevertheless, the system transfer function is of the second order with two zeros at zero in numerator. Simple inversion is impossible because of division by zero. Approximated deconvolution is proposed as solution of this matter. In case of exact knowledge or estimation of the transfer function, the deconvolution can be used as an alternative to transfer function modifications by complicated electromechanical means like e.g. direct or feedback damping. The sensor without damping elements can have substantially simplified mechanical construction. Such simplification is a newly emerging way due to possibilities of performing easy and fast signal post-processing. The output of this Thesis is prototype of sensor for measuring position of angular deflection which thanks to the approximate deconvolution is mechanically very simple and that can be employed in the framework of basic seismological research. 21

RESUMÉ Měření rotačních pohybů patří mezi perspektivní oblasti v moderní seismologii. Cílem této práce je zcela nový přístup založený na přímém měření rotací. Toho je dosaženo pomocí mechanického přenosu pohybu na změnu kapacity mezi elektrodami kondenzátoru. Díky tomu je možné konstruovat malá a přenosná zařízení vhodná i pro terénní podmínky. Současné metody studia rotačních seismických pohybů jsou založeny na nepřímém měření, nejčastěji na tzv. husté síti. Navíc všechny doposud uvedené sensory pracují na derivačním principu, zatímco zde popisovaný měří polohu. Cílem této práce jsou teoretické studie optimální konstrukce a měřicích principů, jejichž výsledkem bude tvorba prototypu vhodného pro seismické účely. Mechanická část sensoru je postavena okolo seismické hmoty spojené se základnou křížovým závěsem tvořeným dvěma vertikálně orientovanými plochými pružinami. Toto řešení umožňuje pohyb v horizontální rovině a primárně potlačuje vliv rušivých vertikálních složek. Měření výchylky je realizováno čtyř-elektrodovým kondenzátorem s vertikální strukturou založeným na změně plochy překrytí. Taková konfigurace poskytuje lineární závislost měřené kapacity na úhlové výchylce. Rozměry kapacitoru musí splňovat pravidla pro eliminaci rozptylových polí. Okolo aktivních elektrod jsou tedy i elektrody stínící. Horní a spodní elektroda je nepohyblivá. Třetí a čtvrtá elektroda jsou každá na jedné straně téže desky, která je připevněna na seismické hmotě a může tedy v malém rozsahu rotovat. To představuje určitý druh diferenciálního uspořádání kapacitního sensoru. Ve spojení s poměrovou metodou měření dosáhneme nezávislosti na změně vertikální polohy prostřední desky. Redukce vertikálních rušení je tedy dosaženo jak mechanicky, tak elektronicky. Pro splnění požadavků kladených na měření seismických signálů byl vyvinut a vyroben modul postavený na komerčním převodníku kapacita-číslo AD7746, který poskytuje dva vstupní kanály a rozlišení až 4 aF (10-18 F). Tento měřicí obvod a softwarový modul pro registrační systém RUP (již dříve vyvinutý autorem této práce) umožňuje použití sensoru v rámci seismické sítě. Sensor je navržený bez tlumení. Jediné tlumení existuje jako vnitřní tření v křížovém závěsu. Původní tvar vstupního signálu neboli seismického jevu je výsledkem dekonvoluce měřeného signálu a inverzní přenosové charakteristiky. To předpokládá znalost parametrů systému. Jejich odhad je realizován metodou nejmenších čtverců, která dává velice dobré výsledky i v případě, že testovací signál není přesně znám. Nicméně, přenosová funkce systému je druhého řádu a obsahuje dvě nuly v nule. Prostá inverze není možná, protože by znamenala dělení nulou. Z toho důvodu je navržena metoda přibližné dekonvoluce. Ta v případě, že je známa přenosová funkce, může být obecně použita jako alternativa k modifikacím realizovaným pomocí přímého nebo zpětnovazebního tlumení. Sensor bez tlumicích prvků je velice jednoduchý a následný post-processing signálu je snadno realizovatelný. Výstupem této práce je prototyp senzoru polohy úhlové výchylky, který díky použití přibližné dekonvoluce je mechanicky velice jednoduchý a může být nasazen v rámci základního seismického výzkumu.

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