PREVERJANJE ZANESLJIVOSTI INSTRUMENTOV ZA BELEŽENJE HORIZONTALNO-VERTIKALNEGA SPEKTRALNEGA RAZMERJA MIKROTREMORJEV IZIDOR TASIC Ln FRANC RUNOVC o avtorjih Izidor Tasič Agencija Republike Slovenije za okolje Vojkova cesta 1b, 1000 Ljubljana, Slovenija E-pošta: izidor.tasic@gov.si Franc Runovc * Univerza v Ljubljani, Naravoslovnotehniška fakulteta Aškerčeva 12, 1000 Ljubljana, Slovenija E-pošta: franc.runovc@ntf.uni-lj.si * vodilni avtor Izvleček Nepreverjeni seizmološki merilni sistemi lahko povzročijo oporečno karto potresne mikrorajonizacije. Karta potresne mikro-rajonizacije, ki je namenjena potresno odpornemu načrtovanju, je lahko zasnovana - poleg nekaterih drugih postopkov - na podlagi analize spektralnega razmerja vodoravnih in navpične komponente mikrotremorjev. Mikrotremorje beležimo z modernimi seizmološkimi sistemi. Spremembe v prenosni funkciji seizmološkega sistema, če le-te niso zabeležene in upoštevane, vplivajo na rezultat in s tem tudi na interpretacijo meritve ter tako posledično na zanesljivost celotnega postopka priprave karte potresne mikrorajonizacije. Zato je potrebno seizmološke sisteme primerno verificirati. Razvili smo postopek, kjer s pomočjo dveh referenčnih seizmoloških sistemov preverimo vpliv prenosih funkcij testiranega sistema na krivuljo spektralnega razmerja mikrotremorjev, ne da bi vnaprej poznali prenosne funkcije kateregakoli od sistemov. Postopek smo prikazali na seizmometru Lennartz LE-3D/5s in na seizmoloških sistemu TROMINO, kjer smo za referenčna seizmometra uporabili širokopasovna seizmometra STS-2. Ključne besede potresna mikrorajonizacija, spektralno razmerje med vodoravnima in navpično komponento, vibracije tal, mikrotremor, prenosna funkcija seizmološkega sistema, kalibracija in zanesljivost seizmološkega sistema 16. ACTA GeOTeCHNICA SLOVENICA, 2010/2 HOW TO TEST THE RELIABILITY OF INSTRUMENTS USED IN MICROTREMOR HORIZONTAL-TO-VERTICAL SPECTRAL RATIO MEASUREMENTS izidor TASic and franc runovc About the authors Izidor Tasič Environmental Agency of the Republic of Slovenia, Vojkova cesta 1b, 1000 Ljubljana, Slovenia E-mail: izidor.tasic@gov.si Franc Runovc * University of Ljubljana, Faculty of Natural Sciences and Engineering Aškerčeva cesta 12, 1000 Ljubljana, Slovenia E-mail: franc.runovc@ntf.uni-lj.si * Corresponding author Abstract The reliability of a horizontal-to-vertical spectral ratio (HVSR) curve depends on the results obtained by a verified seismological system. Seismic microzonation provides the basis for a site-specific risk analysis and it can be evaluated using the microtremor HVSR method, where the data are recorded using modern seismological systems. Changes in the transfer function of seismological systems affect the HVSR curve and, consequently, also its interpretation, if these changes are not detected and taken into consideration while performing the microtremor spectral calculations. The reliability of the seismic microzonation performed by such a procedure becomes questionable. An algorithm is developed with a two references system, where the influence of the transfer function on the HVSR curve by the tested system can be evaluated without any a-priori knowledge regarding the transfer functions of any of the systems. This approach is applied to a Lennartz Le-3D/5s seismometer and to a TROMINO seismological system, where two Streckeisen STS2 seismometers are used as the reference systems. Keywords seismic microzonation, horizontal-to-vertical spectral ratio method, ambient vibrations, microtremor, seismic system transfer function, reliability and calibration of seismic systems 1 INTRODUCTION Seismic microzonation is the process of estimating the response of soil layers under earthquake excitations and thus the variation of the earthquake characteristics on the ground surface [1]. Microzonation provides the basis for a site-specific risk analysis, which can assist in the mitigation of earthquake damage [2]. The dynamic characteristics of a site, such as the predominant period, the amplification factor, the shear-wave velocity and the standard penetration test values can be used for seismic microzonation purposes. The shear-wave velocity measurement and the standard penetration test are generally considered to be expensive and are not feasible for a large number of sites for the purpose of microzonation. The microtremor measurement has become a popular method for determining the dynamic characteristics of a site and is being extensively used for microzonation. Microtremors are short-period vibrations resulting from coastal effects, atmospheric loading, the wind's interaction with structures and vegetation, and cultural sources. The microtremor horizontal-to-vertical spectral ratio (HVSR) method, initially proposed by Nogoshi and Igarashi [3] and later popularized by Nakamura [4], is widely used for microzonation projects in order to identify possible site effects [5], [6], or to identify the main frequencies of buildings and their vulnerability to earthquakes [7]. The main advantages of the HVSR method are the simple and low-cost measurements that can be performed at any time and at any location without any specific knowledge regarding the geological structure of what is beneath the ground. This method produces an estimate of the site's geological conditions by providing the peak period of amplification from the HVSR. The amplification occurs where the ratio of amplitudes is greater than one [8]. However, the HVSR technique is not sufficient to characterize the complexity of site effects, in particular the absolute values of the seismic amplification [5]. In HVSR measurements, three seismic sensors that are perpendicular to each other, simultaneously measure 16. ACTA GeOTeCHNICA SLOVENICA, 2010/2 I. TflSIČ AND F. RUNOVC: HOW TO TEST THE RELIABILITY OF INSTRUMENTS USED IN MICROTREMOR HORIZONTAL-TO-VERTICAL SPECTRAL RATIO the ground movements in two horizontal and one vertical direction. A simple, vague recipe for the instruments in HVSR measurements that most people are applying is [7]: "Take whatever instrument you think is able to measure very weak ground motion, let it work on the site of your choice for the time you want, at the sample rate you prefer. Whatever A/D converter you use is fine. Aim for stationarity during quiet periods at night-time or, if you prefer, record heavy road traffic. Taper or not, filter or not, base-line correct or not, then perform an FFT, or some other time-domain/frequency-domain transform on separate components, then add averaging, to your taste. Before or after this last operation, take the ratio of the horizontal to vertical spectra, select the average of all the ratios (or the average plus the standard deviation) et voilà, site amplification is ready". This simple recipe should not be acceptable without hesitation, because a seismic instrument can have an influence on the HVSR calculation and finally on the result and interpretation. Seismic sensors are mostly based on the inertial principle, where the ground motion is measured relative to the inertial reference mass [9]. Modern seismic sensors convert ground motion into electric signals. In a conventional, inertial, short-period seismometer, the ground acceleration is first converted into a relative displacement between the seismic mass and the frame, and then this displacement or its velocity is converted into an electrical signal. Experience has shown that their eigenperiod and the attenuation may change with time up to several tens of percent, especially when these instruments are repeatedly deployed in temporary installations [9]. Changes of this order can cause imperfections in the HVSR measurements. When the ratio of the transfer functions is not 1, it can bias the H/V curve and consequently also its interpretation. Figure 1 shows the ratio between the horizontal and vertical transfer functions for a 4.5-Hz geophone, in the case when the eigen frequency, the damping coefficient and the transduction constant between the vertical and horizontal sensors differ by only 5%. For the same reason "Guidelines for the implementation of the H/V spectral ratio technique on ambient vibrations" [5] do not recommend the use of sensors that have their natural frequency above the lowest frequency of interest. Broadband seismometers use the negative force feedback to keep the motion of the mass small. Using this principle, the mechanical imperfections of the sensor are mostly avoided [10]. The feedback principle of a broadband seismometer also means that at some predefined frequency the sensors have a flat response and it also means that the transfer properties of the sensors in this frequency band are stable. Because of this, the producer of a seismometer guarantees the long-term stability of the seismometer's transfer function and they do not specify any corrections in the time period in their calibration certificates (e.g., [11]). These seismometers are not easy to use in the field for short-term experiments because of their relatively long stabilization time, as well as their sensitivity to temperature and pressure variations. When using broadband or short-period seismometers, it appears necessary to check or validate the instruments in the studied frequency band for an optimal analysis of the HVSR curve. The two following situations need to be checked: - Does the ratio of the transfer functions affect the HVSR curve? - Can the self-noise of an instrument affect the HVSR curve? The instruments can be checked with a reference seismological system using the ground noise, where both the reference and the tested system are placed next to each other - this is the most popular way [12], [13]. This technique was also used in extensive research work [14], where the influence of the instruments on the HVSR curve for ambient vibrations was investigated. These authors compared the differences between the HVSR curves of reference and tested systems for 18 sensors. The main disadvantage of using the difference between a tested and a reference seismometer to define the quality of the tested system is that the seismic signal is not canceled out: the difference is a function of the transfer functions and of the seismic signals. If the ratio of the HVSR curves between the tested and the reference system is used instead of the difference itself, the seismic signal is canceled out. But in this case we need to be careful how to interpret the results. Reference systems are usually broadband seismometers, with a similar or better quality level than tested systems. But the comparison with this type of reference systems is often wrongly equated with a calibration. In a calibration procedure, the reference system needs to be periodically (at least annually, unless otherwise justified or required) calibrated by a higher-level standard or by an external reference, and all the procedures and changes of the reference instrument need to be traceable. The trace-ability is defined, in this case, as an unbroken chain of comparisons to national or international standards with stated uncertainties at each step. Broadband seismometers usually come with a so-called "certificate of calibration" provided by producers. But after that, these seismometers are very rarely, if it at all, compared or calibrated using higher-level standards. 18. ACTA GeOTeCHNICA SLOVENICA, 2010/2 I. TflSIČ AND F. RUNOVC: HOW TO TEST THE RELIABILITY OF INSTRUMENTS USED IN MICROTREMOR HORIZONTAL-TO-VERTICAL SPECTRAL RATIO The reason for this is very simple. A high-quality broadband seismometer, such as the STS-2 from Streckeisen, the Trillium 240 from Nanometrics or the CMG-3T from Guralp, which can reach the price of a mid-level car, are usually permanently and precisely installed at a seismic station, with the main purpose being to detect seismic signals. Because of the known long-term stability of seismometer's transfer function (e.g., [11]), a periodic de-installation, transportation to an institution where the calibration is performed, and once again installation at the seismic station, may cause more problems than are solved by a regular calibration: it is difficult to place the seismometer exactly as it was before; the out-of-operation time of the seismic station can be prolonged; after the reinstallation, the seismometer needs days to be stabilized again [15]; and there is always a risk that the instrument will be damaged during the transport. These types of seismometers are usually just periodically controlled with test (or calibration) signals, which are built in acquisition units. (Using test signals from acquisition units is often wrongly equated with calibration. The test signal sources are also not periodically calibrated by higher-level standards or by an external reference.) Only in cases when the response of a seismometer to the test signals is unusual is the seismometer returned back to the manufacturer for verification. Situations where broadband seismometers are used as reference units are very rare and are more or less coincidental. Because of this we need to be aware that when using a broadband seismometer as a reference unit, the parameters of the tested systems are only defined or estimated relative to this particular, non-calibrated reference unit. By using two broadband seismometers - of higher quality than those of the tested system - at the same time as the reference units, the uncertainty of the measurement results can be minimized. The purpose of this paper is to present a simple test to check the reliability of the instruments used in the HVRS method by using two reference systems without any a-priori knowledge of the transfer function of any of the systems. This approach will be applied to a Lennartz Le-3D/5s [16] and to a TROMINO seismological system [17] where two Streckeisen STS-2 seismometers [15] are going to be used as the reference systems. 1.1 1.05 I " 0.95 -0^=2^.5 py=0.7071 °i)h=ccbv &r1-05Pv Eh=105Ev -CCbv=2#5 Pv=0.7071 G*)h=1-05CQ)v Ph=ft, E h=105Ev -CCbv=2#5 Pv=0.7071 0*>h=105G})v Ph=1.05Pv Eh=1.05Ev 0.9- 0.851—■_■_i_i i 11_i_i_i_i_i i i 11_i_i_i_i_i_i i 11_L 10"1 10° 101 frequency [Hz] Figure 1. An electrodynamic seismometer, also called a geophone, converts the motion of a mass into an electrical signal using an electromagnetic velocity transducer. The frequency-dependent complex response functions depend on the eigen frequency wg , the damping factor j and the transduction constant E [18]. The plot depicts the ratio of the transfer functions for a 4.5-Hz geophone in two-dimensional space (vertical and horizontal), when the difference between the eigen frequencies, the damping coefficients and the transduction constants of the vertical and horizontal sensor is only 5%. 18. ACTA GeOTeCHNICA SLOVENICA, 2010/2 I. TflSIČ AND F. RUNOVC: HOW TO TEST THE RELIABILITY OF INSTRUMENTS USED IN MICROTREMOR HORIZONTAL-TO-VERTICAL SPECTRAL RATIO 2 MATHEMATICAL MODEL We present the model in two-dimensional space, using the horizontal and the vertical directions. The measurement is performed by seismological systems with two similar sensors with a linear transfer function, being orthogonal to each other and set up one in the vertical and the other in the horizontal direction. First, we will assume that both the vertical and horizontal sensors detect the same (seismic) signal x. The output yh of the horizontal sensor can be written as the convolution of the input signal x with the sensor's transfer function h^ yh = hh ® x , (1) Here, the symbol <8> denotes the convolution. Similarly, the output yv of the vertical sensor is the convolution of the input signal x with the sensor's transfer function hv: = hv Ä x (2) We assume here, that there is no internal noise. These equations translate into the frequency domain as: Y = Hh X, Yv = H v X , (3) (4) where Yh, Y , X, Hh and Hv represent the Fourier transforms of yh, y , x, hh and hv. Assuming that both systems are linear and noise-free, the output power spectral density (PSD) can be expressed by: Phh = H h H hX P = H H,,*P„ (5) (6) The symbol * denotes the complex conjugation, and Pxx = XX* is assumed to be the coherent ground-motion power spectral density. The horizontal-to-vertical spectral ratio HVSR is defined as HVSR= F^ . (7) P When the same seismic signal x is detected by both systems, the HVSR ratio is affected only by differences in the transfer functions of the used sensors. The ratio of the square magnitude of the transfer functions of the tested seismological system reduces in this particular case to: ^hMjhL=HVSR2 = ^ (8) HvHv* Pw The instruments where this ratio is 1 are trustworthy and can be used in the HVSR measurements. Under real circumstances, the signals of the horizontal and the vertical components are very rarely equal. A more realistic case is that we have different seismic signals in the horizontal and the vertical directions. Equations (5) and (6) are now rewritten: Phh = HhHh*PxhXh (9) P = HH ,*P„ (10) The expression P = XhX'h is assumed to be the coherent ground-motion power spectral density in the horizontal direction and Px x = XvX* the coherent ground-motion power spectral density in the vertical direction. A simple procedure to check the reliability of the HVSR of particular instruments involves putting it close to a reference seismological system with an equal or better quality class. The output PSD of the reference instrument can be expressed by using the index V: Phrh, = HhHh/PxhX„ (11) Pv.v. = Hv.Hv, *Pxx (12) where Hh and Hv represent the Fourier transforms of the references sensors' transfer functions hh and hv . Let us presume that the reference system is not calibrated, as written and defined in the previous section. In this case, the ratio of transfer functions of the reference systems lHh |/[Hv | is unknown. If, for testing purposes, we use the difference of the HVSR curves of a tested and of a reference system, a function of both transfer functions and also of a seismic signal is obtained: IPxx xhxh |HhHh* (Hh Hhr * ¡Px,x, V HvHv * Hvr \ A=HVSR - HVSR, = f (Xh, Xv ,Hh,Hv,HvHvr) ,(13) where the index r represents the reference system. Because this expression still includes the unknown seismic signal, equation (13) cannot be applied to uniformly evaluate the influence of the transfer function of the system under test on the calculated HVSR ratio. The ratio of HVSR between the tested and reference system caused the seismic signal to be canceled out. If the reference system is ideal, meaning hh = hv , the information about the transfer function can be evaluated: HhHh* H,H * 1 HVSR. (14) Using a non-calibrated reference system, the ratio of HVSR between the tested and the reference is still an unknown function: 18. ACTA GeOTeCHNICA SLOVENICA, 2010/2 I. TflSIČ AND F. RUNOVC: HOW TO TEST THE RELIABILITY OF INSTRUMENTS USED IN MICROTREMOR HORIZONTAL-TO-VERTICAL SPECTRAL RATIO V HhHh* HH 1 HyHv * Hh Hhr HVSR. (15) In the case where only one non-calibrated reference system is used, there is no information about in which frequency band or if at all, the calculation is trustworthy. A more promising procedure to check the reliability of the HVSR of particular instruments is by putting it close to two reference seismological systems, where both references system have much better characteristics than the tested one. We will assume that these two seismological systems are composed of two high-quality broad-band seismometers, which have the manufacturer's "certificate of calibration", but were never calibrated again after that. The first step is to define the frequency interval where the two systems can be used as a reference. The frequency interval where the two systems can be used as reference units is defined by: HVSR HVSR. - = 1, (16) JHh H HVSR +HVSR. 2HVSR HVSR. (18) Another possibility is to calculate the average value for the square ratio of the transfer functions first, and then to take a square root of the complete expression: iHh H P„, HVSR2 +HVSR2 2HVSR2 HVSR2 (19) The third possibility is to estimate the ratio of the transfer functions by using a simple mathematical manipulation. First, equation (13) is rewritten in a different form: HhHh* H ,H hNhc P xhxh Hv Hv * vr1 v1 ) - = ^ - HVRS2 P„, r1 (20) At this point we will assume that both reference systems are ideal and the ratio of the transfer functions of the reference systems are equal: H^ H^ * =Hw Hw * for i=1, 2. The left-hand side of equation (20) reduces to: where the indices r1 and r2 refer to the first and second reference systems. In reality, this is almost never true. While seismometer manufacturers certainly attempt to build their instruments with equal characteristics, in practice there will almost always be some difference, at least in the mechanical alignment of the two systems and in small deviations in the transfer functions and generator constants. Considering this, equation (16) needs to be adjusted by: HVSR HVSR --1 |HZI |HZI " |Hn|y — j ; 10 Frequency (Hz) 10 Figure 5. The ratio of transfer functions for an LE-3D/5s seismological system computed using equation (26), the ratio of the transfer functions of the E-W and the vertical component (blue line), the ratio of the transfer function of the N-S component and the vertical component (green line). The ratio of the transfer functions drastically changes its slope at 0.11Hz and can be explained by the influence of the instrumental noise. 18. ACTA GeOTeCHNICA SLOVENICA, 2010/2 I. TflSIČ AND F. RUNOVC: HOW TO TEST THE RELIABILITY OF INSTRUMENTS USED IN MICROTREMOR HORIZONTAL-TO-VERTICAL SPECTRAL RATIO Frequency [Hz] Figure 6. The difference between the PSD of the estimated self-noise curve (Nvv) estimated by "Three-channel Correlation Analysis Techniques" [19] and the PSD of the recorded seismic signal (Pvv) for the LE-3D/5s seismometer (s/n 59) and TROMINO (TR 19), for the vertical component. The self-noise of the TROMINO instrument is considerably higher. If- He|/1HZI Ih ^--——^ ....... ....... ...... - — — 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.510 Frequency (Hi) Figure 7. The ratio of the transfer functions of the TROMINO TR-19 seismological system computed using equation (26): the ratio of the transfer function of the E-W component and the vertical component (blue line) and the ratio of transfer function of the N-S component and the vertical component (green line). Below 3 Hz, the self-noise of the Tromino TR-19 affects the calculation and below this frequency, the ratio of the transfer functions cannot be calculated in this particular case. 18. ACTA GeOTeCHNICA SLOVENICA, 2010/2 I. TflSIČ AND F. RUNOVC: HOW TO TEST THE RELIABILITY OF INSTRUMENTS USED IN MICROTREMOR HORIZONTAL-TO-VERTICAL SPECTRAL RATIO of information and any interpretation, concerns the reliability of the HVSR curve." The basic presumption is that the HVSR curves obtained using different seismological systems at the same time and at a same place, need to be equal or at least very similar. In this study we presented two important sources in seismological systems that can cause insurrections in the HVSR curves and therefore an incorrect interpretation. The first source of error is the self-noise of an instrument that needs to be negligibly small. The second source of error is the use of non-calibrated instruments or if the transfer function is not considered in the HVSR calculations. In our paper a simple algorithm is presented that enables the reliability of the instruments used in the HVSR measurements using two broadband seismometers with better quality than tested systems as references units. In order to maintain the integrity of the recorded data, the seismograph systems need to be periodically verified. This verification is important to ensure that the instrument is performing as it was designed to, and that it measures accurately the true ground vibration [24]. Although the seismographs are designed for use in a rugged environment, they are still sophisticated electronic monitoring devices. Therefore, preventative maintenance becomes an important part of the annual verification process [25]. A simple case to confirm these findings are instruments used in our test. Using a non-calibrated instrument in measurements -without a correction for its transfer function - can cause unreliability in the estimated dynamic characteristics of a site and consequently of evaluated seismic microzonation. Because of this, we have developed a straightforward method - using two reference seismometers - to evaluate the influence of the instrument's transfer function on the validity of the HVRS procedure, without any a-priori knowledge in terms of the transfer function of any of the systems. references [1] Finn, W.D.L. (1991) Geotechnical Engineering Aspects of Microzonation, Proceedings of the Fourth International Conference on Seismic Zona-tion, 199-259., August 26-29, 1991. [2] Tuladhar, R., Yamazaki, F., Warnitchai, P., Saita, J. (2004). Seismic Microzonation of the Greater Bangkok area using Microtremor Observations, Earthquake Engineering and Structural Dynamics 33, 211-225. [3] Nogoshi, M., Igarashi, T. (1971). 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