Toward Understanding Subtle Instrumentation Effects Associated

with Weak Seismic Events in the Near Field

by Jiří Zahradník and Axel Plešinger

Abstract Broadband observations of small earthquakes at short epicentral distancesreveal a mixture of near-field effects and instrumental artifacts. We investigated thesephenomena at a station equipped with a STS-2 and CMG-40T sensor situated almostabove shallow M 3.0 to 3.8 events (peak ground acceleration 2 × 10�1 m=sec2).The horizontal components were systematically accompanied by tiltlike disturbances,and the tilt obtained from the STS-2 records exceeded more than 10 times the valuespredicted by the source model. We also observed a so far uncommonly recognized typeof disturbance, whose shape is the first derivative of the tiltlike disturbance. The mostlikely explanation seems to be clipping of high-frequency signal peakswithin the sensorsystem. A computational model of a broadband feedback velocimeter as a lineardynamic system with saturation proved this interpretation on a qualitative level.Generally, any asymmetry in the transfer of high frequencies in the feedback velo-cimeterwould produce a long-period disturbance of this type.Users of near-fault broad-band velocigrams may numerically simulate the disturbances, without any knowledgeof their physical nature, and subtract them from the records. The decontaminatedrecords still may have a strange, bow-shaped form, related to the near-field rampand the static displacement (of the order of 1 × 10�5 m in this article). The effectsstudied in this article seem to have a general character, for apparently any feedback-controlled broadband velocimeter.

Introduction

Earthquake seismology relies on understanding pro-cesses taking place at rupturing faults. Of particular impor-tance are observations in epicentral regions where specificnear-field phenomena provide invaluable insight into thesource physics. They include, for example, permanent dis-placements, tilts, and rotations. With recent advances indensity and configuration of broadband networks and withimprovement of the quality of the instruments, many valu-able near-fault records have been obtained also for weakearthquakes. Some of them are obscured by long-period dis-turbances whose origin has not been fully understood yet.Most likely they represent a mixture of subtle ground motionand instrumental effects, whose correct deciphering is chal-lenging. Identification and possible removal of the distur-bances has a broader impact than just into tiny details of theearthquake source. It should be a part of newer data acquisi-tion and quality control procedures. This is particularlyimportant in real-time applications, such as quick moment-tensor calculations, identification of fault planes, and releaseof the shake maps, where disturbed records might bias evengross estimates of the earthquake parameters.

Near-field effects (such as a permanent displacement,tilt, and rotation) have been well-known in theory and also

observed during strong earthquakes for quite a long time(Bouchon and Aki, 1982), but their observational analysisfor small earthquakes is still quite rare. This article is focusedjust on small events at short epicentral distances.

Long-period disturbances have already received atten-tion in relation to tilts (Wielandt and Forbriger, 1999; Kalkanand Graizer, 2007), baseline corrections (Boore et al., 2002),strong-motion data processing (Graizer 2005), coseismicdeformation and permanent displacement (Boroschek andLegrand, 2006; Wu and Wu, 2007), sensor nonlinearity(Delorey et al., 2008), nonvertical installation of sensors (Pil-let and Virieux, 2007). The present article is a follow-up ofour previous investigation of weak events at near stations inGreece, often accompanied by tiltlike disturbances on CMG-3T and LE-3D/20s records (Zahradník and Plešinger, 2005).

A strong motivation for this article came from the recentearthquake swarm in West Bohemia, on the border betweenthe Czech Republic and Germany. Long-period disturbancesoccurred quite systematically on the Streckeisen STS-2 re-cords ofM ∼ 3 events. Fortunately, a station in the epicentralregionwas equipped alsowith aGuralp CMG-40T instrument.The two collocated sensors opened a way to better under-standing the tiltlike disturbances, similar to thosewe observed

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Bulletin of the Seismological Society of America, Vol. 100, No. 1, pp. –, February 2010, doi: 10.1785/0120090087

in Greece. In particular, we tried to answer the fundamentalquestion whether we actually record a ground-motion tilt, oran instrumental artifact. Even more importantly, during thestudy a new kind of disturbance also emerged. Its shape isthe first derivative of the tiltlike disturbance. Considering thatthe tiltlike disturbance is formally equivalent to a step in inputacceleration, the new kind is equivalent to a step in inputvelocity. Because the velocity step has no plausible physicalexplanation in terms of the near-field effects, it had to be in-vestigated as a purely instrumental artifact.

Therefore, the general objective of this article is to betterunderstand how subtle ground-motion effects (small perma-nent displacements and tilts) are mixedwith subtle instrumen-tation effects. More specifically, we try to use two collocatedbroadband feedback velocimeters, STS-2 and CMG-40T, tostudy disturbances duringMw 3 to 3.8 earthquakes, recordedat epicentral distance of 3 km. We are mainly interested in anew kind of a long-period disturbance, called U-shapeddisturbance, whose shape is the first derivative of the tiltlikedisturbance.

As a tool, we use simple source models and syntheticseismograms, together with modeling a broadband feedbackvelocimeter as a linear dynamic system. We show in thisarticle that very large tiltlike disturbances on STS-2 recordsare definitely due to an (unknown) instrumental effect. Thenew U-shaped disturbance is interpreted as caused by instan-taneous clipping of high-frequency signals within the instru-ment, excited by high-frequency ground motions. We alsodemonstrate how to remove these disturbances from the re-cords through their numerical modeling, even without exactknowledge of their physical origin. As a result of subtractingthe modeled disturbance, we show that a permanent ground-motion displacement can be resolved from the near sourcerecordings of small earthquakes, for example, of the orderof 1 × 10�5 m for the Mw 3.6 earthquake studied in thisarticle.

Understanding of the disturbances gained in this articleimplies that similar effects are likely to be present at nearrecordings of weak events anywhere in the world, on differ-ent types of broadband feedback velocimeters. Therefore, atthe end of the article we give also two examples from Japanfor shallow crustal earthquakesM ∼ 4, recorded at epicentraldistances 1 to 13 km with a disturbance on STS-1 and STS-2.

If these effects represent an important general phenom-enon, then why have they not been broadly recognized yet?The reason obviously is that for interpreters they usuallyrepresent merely noise, so such records are excluded fromanalyses. Much worse are situations when the disturbancesare simply overlooked in routine data processing, becausethen they may potentially bias any long-period sourcestudies. That is why newer automated data quality proce-dures should include identification of the disturbed recordsand, possibly, also their correction. As a by-product, thearticle might be a challenge also for the producers ofnew instruments: intrinsic clipping due to high-frequencymotions near the source is to be better treated even if the

instrument is primarily developed for precise recording ofweak low-frequency ground motions.

Station and Events

The West Bohemia region has been well-known for itsearthquake swarms (Neunhöfer and Meier, 2004). About20,000 events were instrumentally recorded there duringthe last crisis in October 2008. The activity is tightlycompacted in a spatially concentrated fault segment of a 3 ×3 km size, thus providing similar, systematically repeatingrecordings. A 13-station short-period permanent network,theWEBNET,monitors the region and provides data for highlyaccurate locations and focal mechanism studies (Horáleket al., 2000, 2008; Fischer and Horálek, 2003; Fischer andMichálek, 2008). The cited articles provide all necessarydetails about regional tectonics, local site conditions, instru-ment installations, etc. One of the stations, NKC (50.2331° N,12.4479° E), is situated almost above the October 2008swarm. This station, belonging to the CzechRegional SeismicNetwork, is also equipped with two broadband instruments,a Streckeisen STS-2 and a Guralp CMG-40T. Some otherbroadband stations have been in operation near the sourceregion at epicentral distances up to 25 km, but none of themprovided disturbances as large and clear as those observedat NKC.

The 2008 data set can be briefly characterized as follows(T. Fischer, personal comm.): nine of the 9–28 October eventshad localmagnitudes between 3.0 and 3.8.Within an accuracyof 1 km, sufficient for this article, the epicenter position of allevents was the same (50.21° N, 12.45° E). Their depths variedbetween 8 and 10 km; the epicentral distance of the NKCstation was 2 km. Focal mechanisms were retrieved fromamplitudes and polarities at the local stations by severalapproaches, providing strike 166° to 177°, dip 55° to 72°,and rake�19° to�47° (A. Boušková, personal comm.). Theseranges include both the intraevent and the intra-approachvariations. Independently, our solution for two events ob-tained by waveform inversion of near-regional records pro-vided similar strike/dip/rake values; for example, the valuesof 169°=59°= � 41° were obtained for the Mw 3.6 event of28 October. From the practical point of view, we have a setof events with almost identical hypocenters and mechanisms,resembling a repeatable laboratory experiment.

Records

We inspected visually the records of all nine ML > 3

events and of many smaller ones (see the Data and Resourcessection). We found great similarity not only among theirwaveforms, but also among the disturbances. We demon-strate these effects by a representative example with a verygood signal-to-noise ratio: records of theMw 3.6 event of 28October 2008 at 08:30:11 UTC.

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Data Processing

We used continuous and triggered STS-2 records sampledat 20 Hz and 100 Hz, respectively (corresponding antialiascorner frequencies fc � 8 and 40 Hz), and continuousCMG-40T records sampled at 250 Hz (fc � 100 Hz). Thethree-component raw files were transformed from counts tometers per second, but neither filtering nor instrumentalcorrection was performed in order to keep the whole broad-band spectra untouched. On the contrary, the instrumentalresponse was convolved with the calculated ground motionsto be compared with the records (see later discussion in theSynthetic Seismograms section). Such a forward approachhas been strongly preferred against deconvolving the instru-ment response from the records. As a next step, the velocityrecordswere integrated in the time domain. This so-called rawdisplacement is proportional to ground acceleration forfrequencies f < f0 and to ground displacement for frequen-cies f > f0, where f0 is the instrumental low-frequencycorner (1=120 Hz for STS-2, 1=30 Hz for CMG-40T).

Long-Period Disturbances

Even a brief look at a typical integrated STS-2 veloci-gram (raw displacement record) shows an impressive pattern(Fig. 1): Both horizontal components are dominated by avery large long-period disturbance. It can be characterizedas a smooth baseline change, or step, lasting about 120 sec.The amplitude of the step is much larger than the P- andS-wave signals on both the EW- and NS-components. Thevertical component (Z) has a smaller disturbance whoseamplitude is comparable to the seismic signal. Its shape(hereafter called U-shape) strongly differs from the horizon-tal components: it looks like the first derivative of the EWand NS disturbances. The collocated CMG-40T records havesmall disturbances, too (e.g., on the Z-component in Fig. 1b);however, none of them is as large as the huge steps on thehorizontal components of the STS-2.

Ramps

The other important feature of the raw displacementrecords is the steady amplitude increase between the P- andS-wave onsets; see Figure 2. This is a typical ramp due to thenear-field source effect (e.g., equation 4.29 of Aki and Ri-chards, 1980). Lasting roughly 1 sec, it has nothing to dowiththe considerably shorter source duration (of about 0.2 sec). AtNKC station the ramp can be easily identified on all threecomponents (on both STS-2 and CMG-40T records). Whybe concerned about the ramp? First, note that the ramp ampli-tude is by far not negligible with respect to the P- andS-amplitudes. It represents a first-order effect of a broad spec-tral content. As such, the ramp brings an important piece ofinformation about the focal mechanism, independent of theP- and S-wave amplitudes, because the correspondingnear-field term has its own directional dependence. It canbe used to check an assumed focal mechanism, or facilitate

its retrieval from waveforms if only few near-source stationsare available for weak events. Second, a clear ramp in the in-tegrated record indicates that the ground motion has a static(permanent) displacement of comparable size, theoretically ofinfinite duration after the S-wave transient signal. Usually thestatic displacement cannot be readily seen. This is because it isa low-frequency effect; at f < f0 the raw displacement recordis proportional to ground acceleration, not to ground displa-cement. Later we explain where the static displacement isencoded in the original records.

Peak Values

With 20 Hz sampling we get underestimated peakvalues. On the other hand, differentiating the triggeredSTS-2 (100 Hz sampling) and the continuous CMG-40Tvelocigrams (250 Hz sampling), we arrive at almost identicalpeak accelerations of about 2 × 10�1 m=sec2 in the S-wavegroup of the largest observed events, without any visible clip.The peak velocities reached 3 × 10�3 to 5 × 10�3 m=sec.Such velocities are often recorded during stronger distantevents, without any long-period disturbance; their accelera-tion is, however, much smaller. As an interesting example letus mention the 26 December 2004, Mw 9 Sumatra earth-quake, recorded at NKC with the same peak velocity asthe studied M 3 to 3.8 events, while the acceleration wastwo orders of magnitude smaller than in the local events.This is a typical feature of the disturbances, already dis-cussed in relation with similar events in Greece (Zahradníkand Plešinger, 2005): the high-frequency content of theground motion is a prerequisite for this phenomenon.

Methods of Analysis of the Records

Two tools have been used to analyze the records: (1) for-ward simulation of a step response, and (2) synthetic seis-mograms.

Step Response

By step response we understand the integrated output ofthe broadband velocigraph with a simple steplike input. Wemay consider a step in input acceleration, velocity, or displa-cement (Fig. 3a). Note equivalent cases: for example, thevelocity step is equivalent to the pulselike acceleration andalso equivalent to an infinitely linearly growing displace-ment. The method is straightforward: knowing the poles andzeros of the transfer function of an instrument, we calculateits response to the unit-amplitude input step (Fig. 3b). Then,by trial and error, or by the least-squares method, the long-period trend of the record is fitted by manipulating just twoparameters: the onset time and the amplitude of the step.

Synthetic Seismograms

This is a tool enabling forward simulation of the records,including ground motion and instrumental response. We use

Toward Understanding Subtle Instrumentation Effects Associated with Weak Seismic Events 3

Figure 1. Long-period disturbances at NKC station for a Mw 3.6 event (28 October 2008 at 08:30:11 UTC). Shown is the integratedvelocity output (raw displacement). (a) STS-2 record. Note the U-shaped disturbance on the vertical component, contrasting with thepredominating steplike disturbance on the horizontal components. Seismic signals need a zoomed view (Fig. 2). (b) CMG-40T record fromthe same pier; the only clear disturbance is on the vertical component. This is a typical pattern of all inspected events.

4 J. Zahradník and A. Plešinger

the discrete wavenumber method (code AXITRA of Bouchon,1981 and Coutant, 1989; and code ISOLA of Sokos and Zah-radnik, 2008), providing complete wavefield, including allnear-field terms of the Green function. A local 1D layered

crustal model is adopted (Novotný, 1996). A point-sourcemodel is used because with a single near station a finite-extent model is not available and the directivity effect is notinvestigated. The source is described by its hypocenter posi-tion (50.21° N, 12.45° E , depth 8 km) and focal mechanism(strike=dip=rake � 169°=59°= � 41°). The slip rate is mod-eled by a triangle of a duration of 0.2 sec. The ground motionis calculated up to 5 Hz. This frequency range is narrowerthan in real data, but it is sufficiently broad for qualitativemodeling of the near-field ramp between the P and S phasesand for the static displacement (Fig. 4). The instruments aredescribed by the poles and zeros of their transfer function,and the synthetic ground motion is convolved with it. Ifthe interest is only in the static ground-motion displacementand its spatial variability, it is not necessary to calculateseismograms. Then we use the static solution for a crack inhalfspace (Okada, 1992), code Coulomb 3.1 (Toda et al.,2005). Horizontal gradient of the static displacement on ver-tical components provides a model estimate of the ground-motion tilt.

Results of Analysis of the Records

Tiltlike Disturbances on Horizontal Components

It was demonstrated in Figure 1 that the main distur-bances on the integrated horizontal components of STS-2have the form of a smooth steplike baseline change. Thus,the first approximation can be made in terms of the instru-ment response to a step in input acceleration. As seenfrom Figure 5a, the EW and NS components can be well

Figure 2. Detail of the same records as shown in Figure 1,STS-2 and CMG-40T superimposed. The near-field ramp betweenthe P- and S-wave onsets is well developed on all three components(time 2 to 3 sec). Note the almost identical records from both in-struments until the onset of the disturbances in the S- wave group.

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Toward Understanding Subtle Instrumentation Effects Associated with Weak Seismic Events 5

matched by the acceleration steps of 2:5 × 10�6 and �1:6×10�6 m=sec2, respectively.

In principle, an acceleration step of amplitude A on ahorizontal component may be related with a step in tilt,Θ � A=g, where g is the acceleration of gravity (Wielandtand Forbriger, 1999). Thus, the observed steps of the orderof A ∼ 1 × 10�6 m=sec2 would correspond to a tilt of theorder of Θ ∼ 1 × 10�7 radians. The ground-motion tilt canbe estimated from the calculated synthetic motions near theNKC station. They provided the vertical static displacementof about �2:0 × 10�5 m, with a horizontal gradient around0:6 × 10�8 radians. This is an order of magnitude smallerthan the Θ value derived from the recorded disturbances. Itindicates that, partially or completely, the tiltlike disturbanceson STS-2 records are an instrumental artifact.

A confirmation comes from the collocated CMG-40Tinstrument. The comparison of STS with CMG is legitimate,thanks to an experiment in which a technician stood on the

pier and generated a tiltlike response on both STS andCMG sensors, roughly proportional to their accelerationsensitivities. Nevertheless, as proved in Figure 5b, the tiltmeasured by CMG-40T was three to five times smaller thanon the STS-2, if any. It corresponds to the acceleration stepsof �0:5 × 10�6, �0:5 × 10�6 m=sec2 for the EW and NScomponents, respectively, still larger than the theoreticalestimate, but these disturbances are already close to thelong-period noise level.

U-Shaped Disturbances on Vertical Components

On the Z component of the STS-2 we observe a distur-bance whose shape is the first derivative of the tiltlike distur-bance (Fig. 1). It can be matched with the STS-2 response to astep in velocity of �0:45 × 10�5 m=sec, if combined with adisplacement step of �2:0 × 10�5 m (Fig. 5a). Such a staticdisplacement is in good agreement with the computationalestimate previously discussed. On the other hand, the velocitystep must be an instrumental artifact. The vertical componentof the CMG-40T record yields similar estimates: �0:6×10�5 m=sec and �2:0 × 10�5 m.

U-Shaped Disturbances on Horizontal Components

A visual inspection of the EW component of the STS-2record in a 20 -sec window after the seismic signal (Fig. 5a)suggests a mixture of the effects dominating on NS and Z.Indeed, a good approximation is obtained with superpositionof the acceleration step of 2:5 × 10�6 m=sec2 and the veloc-ity step of �3:0 × 10�5 m=sec. The latter velocity step is sixtimes larger than on the Z component; it is perhaps surpris-ing, not obvious from visual inspection, because the accel-eration step is dominant. Other events show velocity stepresponses on all three components. No disturbances of thiskind were identified above the noise level on horizontal com-ponents of the CMG-40T records.

Because the STS-2 is a symmetrical triaxial system con-sisting of three identical inclined pendulums yielding outputsin the U, V, W coordinate system (Melton and Kirkpatrick,1970), we also applied the inverse rotation to get from therecorded (recombined) conventional E, N, and Z compo-nents back to the actual U, V, and W channels. All of themrevealed a mixture of tilt-type (acceleration step) as well asU-type (velocity step) responses; no singular behavior of anyof the three pendulums has been found.

A partial conclusion is that the disturbances on the hor-izontal components of the CMG-40Tmay relate to true tilt, buta poor signal-to-noise ratio makes this conclusion uncertain.Unfortunately, no events were found in the analyzed data setto make a more specific conclusion of this kind. On the otherhand, quite certainly the STS-2 experienced a much largertilting, definitely not due to the earthquake ground motion.We can only speculate about possible reasons; for example,an additional local tilt might have been provoked by thehigh-frequency ground vibrations in the instrument feet, orperhaps even inside the case; all this remains hitherto unclear.

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6 J. Zahradník and A. Plešinger

The big advantage is the collocation of the two instruments;the absent evidence of a large tilting in the CMG-40T recordsexcludes possible explanations of the large disturbances in thehorizontal components of the STS-2 as tilt due to local effectsprovoked by the high-frequency vibrations in a small under-lying block of rock, such as we made in our study in Greece(Zahradník andPlešinger, 2005), as tilting due to undergroundfluid motion (such as magma motion studied by Gambinoet al., 2007), or as liquefaction of the sand around the seis-mometer base (Kinoshita, 2008). The U-shaped disturbancesare new. They are most clear on the vertical components of theSTS-2 and CMG-40T, where they are not masked by tilt, butgenerally they may exist on all three components. Being

equivalent to the instrument response to a step in velocity(pulse in acceleration), for which we have no theoreticalexplanation in terms of the source effect, the U-shaped dis-turbances are understood as a pure artifact, calling for anexplanation.

Physical Model of the U-Shaped Disturbance

Seismograph: Dynamic System with Nonlinearity

A physical model potentially producing long-period dis-turbances is the seismograph understood as a time-invariantdynamic system with internal nonlinearities. We used Matlab

Figure 5. Same records as in Figure 1 (solid line), with disturbances formally matched by various step responses detailed in the text (grayline). (a) Forward modeling, STS-2: This step in the input velocity is obtained by deconvolving the Z-component of the raw-displacementrecord shown in Figure 1b; this is an independent validation of the forward modeling represented by the gray line in the Z-component of panel(b); in order to make the step visually perceptible, the deconvolved signal has been filtered by a 4-pole 1 Hz low-pass filter. (b) Forwardmodeling, CMG-40T: The same raw displacement record is deconvolved to input displacement; no static displacement is visually detectablein the ramp corresponding to the spurious step in the deconvolved (input) velocity. (c) Deconvolution, CMG-40T: The same input displace-ment is shown after removal of the ramp with onset time (1.22 sec after the P onset), exactly coinciding with the maximum amplitude in theoriginal broadband velocigram; a permanent displacement of the same order as obtained by forward modeling clearly emerges.

Toward Understanding Subtle Instrumentation Effects Associated with Weak Seismic Events 7

Simulink (2002) for modeling such a system. Seeking for aplausible nonlinear behavior we assume that saturation inthe forward path is a possible mechanism. To validate thisassumption we analyze possible saturation effects in a sim-plified model of a 30 -sec force-feedback velocimeter with a1 -sec inertial sensor, proportional-integral-derivative (PID)feedback, and an upper cut-off frequency of 100 Hz. The in-strument setup is schematically shown in Figure 6. The setupcould be easily rescaled to any other analogical system, forexample, a 120 -sec to 80 Hz PID-feedback velocimeter witha 6 -sec inertial sensor, the results would qualitatively remainthe same.

To demonstrate how a PID-feedback velocimeter reactsto impulsive near-field ground motions comprising static dis-placement and a tilt in situations without and with saturation,we show in Figure 7 the respective responses to the syntheticseismogram for the N-component of the 28 October 2008,Mw 3.6 event. The synthetic ground displacement signal(a) produces at the output of the amplifier of the mass-to-ground transducer output a high-frequency signal with peakamplitudes �2:1 and 1.7 (dimensionless) (b). No saturationoccurs, and the long-period component in the integratedvelocigram (raw displacement record, output of the massposition channel) (d) represents the natural, linear responseof the system to the static displacement in the synthetic seis-mogram. Panel (c) shows the output of the amplifier in caseof symmetric saturation on a level of �1:5. The asymmetricsignal peaks exceeding this level are cut off, and the systemreacts to this subtle internal asymmetry very sensitively byproducing a spurious long-period, U-shaped disturbance (e).The natural system response to the static ground displace-ment is masked by this disturbance. In most situations typical

for observations near the seismic source it is impossible toreveal the clipped peaks responsible for this disturbance inthe original broadband velocigram. If a tilt is added to theinput, regardless whether of natural or instrumental origin,its effect is also invisible in the velocity output but becomesapparent in the raw displacement record (f), as a long-perioddisturbance with permanent offset gradually predominatingthe saturation disturbance.

In very special situations, saturation does not necessarilyyield the effect demonstrated in Figure 7e. This is the case ofperfectly symmetric saturation of perfectly symmetric inputsignals, when spurious pulses of equal amplitude in bothpolarities appear and their effects mutually cancel each other.Therefore, when speaking about disturbances due to satura-tion, we implicitly mean asymmetric saturation. Asymmetrycaused by the signal, of course, not asymmetrical saturationof some active element in the system, because this is veryunlikely if not entirely impossible.

Simulation of saturation in the feedback loop has shownthat its consequence is qualitatively quite the same as that ofsaturation in the forward path, but its effect is much stronger.The explanation is simple. Denote the frequency response ofthe feedback and forward path by β�f� and K�f�), respec-tively. The overall frequency response of the closed-loop sys-tem is S�f� � K�f�=�1� β�f�K�f��. In the frequency bandin which jβ�f�K�f�j ≫ 1, we have jS�f�j ∼ 1=jβ�f�j;hence, the transfer properties are governed by the feedback.Up to seismic frequencies for which jβ�f�K�f� ≫ 1, anynonlinearities in the forward path (for instance, those of themechanical inertial sensor) are efficiently suppressed, butany nonlinearities in the feedback manifest themselves undi-minished. In reality, nonlinearity in the feedback is unlikely

Figure 6. Schematic diagram of a 0.033–100 Hz force-feedback velocimeter with PID feedback. The feedback path is considered to belinear. In the forward path, the largest high-frequency signals appear on the output of d.c. amplifier A; saturation is therefore modeled in thispoint. The setup allows recording of the individual outputs for any sort of theoretical, synthetic, and actual input ground motions. Tilt issimulated by a parabolic ramp of input displacement.

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since PID feedback is implemented, except the integratingoperational amplifier, exclusively by passive, linear elements(capacitors, resistors). We perhaps could consider possiblesubtle nonlinearities in the magnet-coil assembly of the

force-feedback transducer at high frequencies, but that wouldbe pure speculations. Even if there were any, we have noknowledge about their nature nor do we know how to quan-tify them.

Figure 7. Responses (integrated velocigrams) of the system simulated in Figure 6 to a near-field ground motion. (a) Input ground dis-placement (N-component of the synthetics shown in Fig. 4); (b) amplifier output, no clipping; (c) same as (b), amplifier output symmetricallyclipped; (d) natural (linear) system response to ground motion comprising a static displacement, no clipping; (e) same as (d), slight instan-taneous symmetric clipping according to (c); a U-shaped disturbance, such as that in Figure 1a, is produced; (f) combined effect of symmetricsaturation and a tilt.

Toward Understanding Subtle Instrumentation Effects Associated with Weak Seismic Events 9

Although producing huge long-period disturbances, theinstantaneous saturation itself is a tiny effect that cannot berecognized in the output as a series of cut peaks, a patterncommonly known in the observatory practice as clipping.Note also that the saturation we propose for explanationof the observed records is not simply related to the standardclip level (such as routinely estimated from the frequencydependence of the instrumental sensitivity to displacement,velocity and acceleration), because the peak motions of thedisturbed records are well below such a level. In fact thevelocity clip level, VCL, of a feedback velocimeter is not afrequency independent parameter but decreases with the firstpower of frequency beginning at some threshold frequency,fCL. E.g., for the 40 Vpp version of a KS-2000, the standardVCL � 10 mm=sec, fCL ∼ 4 Hz, and for f � 40 Hz the cliplevel is 10 times lower, that is, 1 mm=sec. According to thetechnical specifications of a standard STS-2 and CMG-40T,fCL ∼ 20 Hz and VCL ∼ 13 mm=sec for both instruments,and the clip level drops to about 5 mm=sec at 50 Hz. Thesevalues are not much higher than our observed peak veloci-ties. It is also quite possible that parasitic resonances in theinertial sensor at very high frequencies, at which jβ�f�K�f�japproaches 1 and the transfer properties of the system are nomore governed by the feedback, are the cause of saturation ateven lower levels than the presumed high-frequency(f > fCL) clip level. The complex nature of intrinsic satura-tion cannot be better investigated on this phenomenologi-cal level.

To summarize the section on simulation, the physicalmodel has one main advantage: compared with the formalmodeling in the preceding sections, where an additional spu-rious pulse (of unknown nature) had to be added to the groundmotion, here the input motion remains completely realistic.We just allow for an internal nonlinearity (momentaneoussaturation) at high frequencies (f > ∼10 Hz); the resultingsignal asymmetry introduces a small spurious d.c. componentinto the system. The response of the system to this d.c. com-ponent appears in the integrated velocigram (raw displace-ment record) as a U-shaped disturbance which heavilydestroys the very low (f < 0:01 Hz) seismic frequencies.

Any Other Effect ?

To explain the U-shaped disturbance in the integratedoutput, we need an acceleration pulse (velocity step) inthe input. We provided a possible explanation of such a pulseas due to intrinsic instrumental saturation at high frequencies.Is there any other physical effect which could act on the seis-mograph in the same way as an acceleration pulse? Consid-ering the horizontal components, equation (3) of Pillet andVirieux (2007) seems to suggest two possible cases: (1) atransient tilt, and (2) transient rotation (the second timederivative of the rotation angle with respect to the verticalaxis). The transient tilt may have similar time variation asground velocity, and there are two possible pulselike velocitytransients: those due to the intermediate- and near-field terms

of the Green function. By the intermediate-field pulselikevelocity transient, we mean the trapezoidal velocity ramp.Simple point-source calculations show that (similarly to thepermanent tilt) this transient tilt is too small, unable to ex-plain the observed U-shape disturbances. By the near-fieldpulselike velocity transient, we mean pulses at the P- andS-wave arrival, with the duration comparable to the sourceduration or smaller. We cannot rule out relatively largeaccelerations of such tilt transients, but modeling the high-frequency tilt (and rotation) goes already beyond the scope ofthis article. Moreover, the fundamental problem with suchan interpretation would be the systematic occurrence of theU-shaped disturbance on the vertical component. Its expla-nation through the transient tilt would imply a nonverticalinstallation (equation 6 of Pillet and Virieux, 2007), whichhad not been clearly indicated in our observations.

Removing the U-Shaped Disturbance, and Retrievingthe Permanent Displacement

Put aside for a while any possible causes of the U-shapeddisturbances, try to remove them from the record, and askwhether the decontaminated record is compatible with thesynthetic ground motion of Figure 4 as regards the near-fieldramp and the static displacement. For brevity, we concentrateon the (simpler) vertical component.

Such an experiment is demonstrated in Figure 8. Basedon the preceding analysis, we know that the vertical compo-nent of the STS-2 integrated record is disturbed by the veloc-ity step �0:45 × 10�5 m=sec. We calculate the instrumentresponse to such a step and subtract it from the record; thisis what we call the decontaminated record. At the same time,we use the synthetic ground motion of Figure 4, convolve itwith the STS-2 response, and compare it with the decon-taminated record. As a result (Fig. 8) the near-field rampis matched fairly well, thus validating the assumed focalmechanism. The following part of the synthetics (after Swave) is much simpler than the true record, due to the simplestructural model, but the long-lasting trend of the record iswell approximated, too.

This figure brings an important message to practicalusers of the broadband records: Although the disturbancehas been removed, and the decontaminated record is wellfit by the synthetics, it has a strange, bow-shaped form. Sucha form is nothing abnormal. It is simply the instrumentresponse to the near-field ramp and the static displacement,similar to the response to a displacement step (Fig. 3).A careful look at the record also shows that its bow-shapingstarts at the S-wave arrival (after the ramp), at the level of thetheoretically predicted static displacement, �2:0 × 10�5 m.This is easy to explain: Onset of the static displacementis relatively abrupt, representing a high-frequency dis-placement feature (f ≫ fo), thus it is reproduced in theoutput. On the contrary, the following constancy of thestatic displacement, representing a low-frequency displace-ment feature, is naturally distorted by the instrument quite

8

9

10 J. Zahradník and A. Plešinger

considerably. This example illustrates that some apparentlystrange records, such as the bow-shaped record previouslydescribed, might be completely free of any disturbance, anddo provide information about the static displacement.

The reason why we were so much interested in the staticdisplacement, and appreciated its agreement with the theo-retical source model, is simple. It validated usability of thesource model to estimate realistic values of the tilt in the pre-ceding sections.

Finally, we have to answer the legitimate question whythe forward simulation has been preferred against deconvo-

lution of the instrument effect. The answer should be givenseparately for the studied steps in acceleration, velocity, anddisplacement. The simplest task is to recognize presence andsize of acceleration steps; the integrated output of the broad-band instrument (raw displacement), if properly rescaled toacceleration, shows them directly. This is what we can see ata first glance in Figure 1a; the scale shown to the right of thatplot enables direct reading of the size of the step, because atvery low frequencies the raw displacement is proportional toinput acceleration. In other words, just the integration of thebroadband output and multiplication by a constant factor issufficient to get the equivalent permanent input acceleration.Regarding the permanent velocity and permanent displace-ment input, the broadband output can be deconvolved usingthe frequency response of the instrument, but success of thisinverse problem strongly depends on the signal-to-noise ratioand presence of disturbances. For instance, the vertical com-ponent of the CMG-40T record shown in Figure 1b couldsuccessfully be deconvolved to the input velocity (see theupper panel in Fig. 5c): the deconvolution revealed the samesize of the velocity step as inferred by forward modeling(�0:6 × 10�5 m=sec). However, in the record deconvolvedto input displacement (middle panel in Fig. 5c), the coseis-mic static displacement was hidden in the superimposedramp corresponding to the spurious velocity step. Aftercautious retrieval of the onset time of the ramp and itsremoval (1.22 second after the P-onset; this time exactly cor-responded to the maximum amplitude in the original broad-band velocigram), the deconvolution provided a permanentdisplacement of the same order as in our forward modeling(see the bottom panel in Fig. 5c). In this sense forwardmodeling and deconvolution have thus been equivalent ap-proaches. However, in any case we have to distinguish care-fully between superimposed effects—spurious steps and thenatural static displacement—and to interpret them correctly.In situations with lower signal-to-noise ratios, deconvolutiontends to instabilities so that forward modeling uses to be thepreferable choice.

Examples from Other Earthquakes

Disturbances such as those discussed in this article canbe found in many earthquake records from various broad-band feedback velocimeters. As a rule, to make them visibleduring routine inspection of the records, it suffices to inte-grate the original velocigrams, and/or to low-pass filter them.Here we present two examples from Japan, F-net network(see the Data and Resources section).

Japan 2002-03-11

At 06:54 UTC on 11 March 2002 (Fig. 9a), a shallowcrustal event of Mw 3.9 (34.1° N, 134.5° E) was recorded atISI station (34.06° N, 134.45° E) by an STS-1 sensor at anepicentral distance of about 1 km. This was a case where thetiltlike disturbance dominated the integrated record, making

40 50 60 70 80Time (s)

-8E-005

-6E-005

-4E-005

-2E-005

0E+000

2E-005

Raw

dis

pla

cem

ent

(m)

Z

STS-2

40 50 60 70 80Time (s)

-8E-005

-6E-005

-4E-005

-2E-005

0E+000

2E-005

Raw

dis

pla

cem

ent

(m)

ZCMG-40T

(a)

(b)

Figure 8. (a) STS-2, (b) CMG-40T. Demonstration of a bow-shaped record (solid line) obtained by removing the U-shapeddisturbance from the vertical component of the studied earthquake(cf. Fig. 1). It is well fitted by the synthetic record (gray). Theunusual, bow-shaped form of the record comes from static dis-placement, seen in the synthetic ground motion (dotted), and fromthe instrument response.

Toward Understanding Subtle Instrumentation Effects Associated with Weak Seismic Events 11

the seismic signal almost invisible. The duration of the dis-turbance was consistent with the corner period of the STS-1instrument (360 sec). A puzzling feature was the presence ofa similar disturbance on the vertical component. Similarcases elsewhere (Pillet and Virieux, 2007) were interpretedas due to a nonvertical installation.

Japan 2006-05-14

At 16:42 UTC on 14 May 2006 (Fig. 9b), a shallowcrustal event of Mw 4.3 (34.2° N, 135.2° E), was recordedat NOK station (34.16° N, 135.34° E) by an STS-2 sensorat an epicentral distance of about 13 km. The integrated re-cord looked undisturbed; however, application of the 0.01 Hzlow-pass filter revealed a clear U-shaped disturbance on thevertical component and a superposition of an U-shaped andtiltlike disturbance on both horizontal components.

We have no examples of these effects from strongerand/or more distant events (e.g., M6 events at near-regionaldistances of the order of ∼100 km); these events rather pro-duce obvious clipping at small distances, or the records atmore distant stations are free of clip, but the high-frequencywaves are attenuated, so the records are free of the distur-bances. In this sense, the range of distances (∼ < 10 km) andmagnitudes (<4) typical for these phenomena is quitenarrow. There might be exceptions from this simple rule, sothe records should be always analyzed with caution.

We have also no data to systematically investigate pos-sible effects of the local geological conditions. It seems that,ironically, rock sites might rather support the disturbancesthan to suppress them, because the high-frequency groundmotions propagate on rock sites with less attenuation thanon soft sites.

Discussion and Conclusion

Near-fault observations have to be interpreted with greatcaution. High-frequency ground motion in the proximity ofthe source may create instrumental artifacts. For example,they include permanent (static) tilts exceeding by an orderof magnitude the values estimated by the source models. Thisarticle brings new examples of this phenomenon fromM 3 to3.8 events recorded at an epicentral distance of 2 km by a120 -sec STS-2 sensor. The collocated 30 -sec CMG-40Tsensor measured a considerably smaller tilt, if any. A newtype of disturbance, so far not well recognized, has beenstudied. It is a long-period disturbance corresponding to aspurious step in input velocity, equivalent to a pulse in accel-eration. This disturbance has been found in the integratedbroadband velocigrams of more than nine ML > 3 events,with almost identical U-shape. In general it has been presenton all three components of both the STS-2 and CMG-40Trecords. Theoretically, there is no room for such an effect inthe translational earthquake ground motions. A likely expla-nation of this phenomenon in terms of an instrumental arti-fact is instantaneous saturation of high-frequency signals in

the feedback instruments. Such a saturation produces narrow,one-sided (nonzero mean value) pulses to which the feedbacksystem responds like to a spurious step in ground velocity(pulse of ground acceleration). In the integrated velocigram(raw displacement record) this response manifests itself in ashape called U-disturbance for brevity in this article. In gen-eral any asymmetry in the transfer of high-frequency signalsin the force-feedback system, possibly conjoined with intrin-sic parasitic resonances, may produce a U-type disturbance.

Once we correctly recognize the type of disturbance, wecan formally simulate it independently of the unknown de-tails of internal processes in the seismograph. This task isrelatively easy because all disturbances we faced were for-mally equivalent to a very simple perturbation of the input,just steps in acceleration or velocity. Therefore, the standardfrequency response represented by poles and zeros enablesstraightforward modeling of the onset time and step sizeof the disturbance, by trial and error, or the least-squaresmethod. In general, the step size varies among events, as wellas from one component to the other, which is why theprocedure should be applied independently to all three com-ponents of each event. The simulated disturbance can be sub-tracted from the record. Quality of the decontaminated recordobviously depends on its signal-to-noise ratio.

An important practical message for the analysts is thateven instrumentally uncorrected records free of any distur-bance may have an apparently strange, bow-shaped form.Just these records bring important information about near-field effects, including the static displacement (of the orderof 1 × 10�5 m in this article). The bow-shaped form of therecord comes from the instrument response to the ramp and(infinitely long-lasting) static displacement; as an essentiallyzero-frequency effect, it cannot be directly seen on the inte-grated broadband output, because the output is proportionalto displacement only above the instrumental low-frequencycorner.

The long-period disturbances seem to be a general phe-nomenon accompanying almost any type of broadbandrecordings close to the source of weak events. During thisand previous work we encountered it on CMG-3T, STS-1,STS-2, and KS-2000M. Each record might have a differentappearance due to the instrument pass-band and due to acombination of various types of disturbances. It is a matterof training to properly recognize and simulate records suchas this, in particular to properly distinguish between near-field effects and instrumental artifacts. Collocated instru-ments of different type are very helpful for this task.

Removal of the disturbances is absolutely necessarybefore any use of the records in source studies using frequen-cies of the order of the instrumental corner frequency orlower. That is why future work should concentrate on iden-tification and removal of the disturbances in the frame ofautomated procedures of the data acquisition and qualitycontrol, with special importance for real-time determinationof the source parameters. It is clear that routine removal ofthe disturbances for applications not particularly interested in

12 J. Zahradník and A. Plešinger

Figure 9. Examples of long-period disturbances at other stations and instruments. (a) Integrated STS-1 velocigram of an Mw 3.9 event(Japan, ISI station). (b) Low-pass filtered integrated STS-2 velocigram of an Mw 4.3 event (Japan, NOK station).

Toward Understanding Subtle Instrumentation Effects Associated with Weak Seismic Events 13

source details may have an even simpler form than wediscussed in this article: just denoising the record by subtrac-tion of the whole time-varying long-period trend (withoutclassifying the individual disturbance types); then, however,subtle source effects, such as permanent displacement, willbe lost.

It is very well-known that the STS-2 is a highly sensitiveinstrument useful for recording small near or distant events atstation locations with very quiet background noise condi-tions (McNamara et al., 2005). Does the presence of the dis-turbances mean that this instrument is not a proper choice fornear events with magnitudes up to Mw 3.8? First of all, weemphasize that none of the analyzed records had been satu-rated in the standard sense, that is, in the form of a series ofequal-sized cut peaks directly visible in the broadbandrecord. Second, if we want to recognize and study the near-field effects of small earthquakes, we need a broadbandsensor with very low intrinsic noise at low frequencies. Allthis means that an instrument such as the STS-2 (or CMG-3T,Trillium 120, etc.) is not a bad choice; or, better speaking, itis the only possibility. The problem is, in fact, that contem-porary instruments highly sensitive at low frequenciesapparently have not been constructed in a way to avoidinstantaneous internal electronic clipping due to groundmotions including very high frequencies. And, ironically,just these instantaneous high-frequency saturations may re-sult in distortion of the low-frequency content of the records,as shown in the present article (U-shaped disturbances).Maybe a new generation of broadband sensors will be freeof these problems.

Data and Resources

The STS-2 seismograms from NKC station of the CzechRegional Seismic Network are available from the web pageof the Institute of Geophysics, Academy of Sciences of theCzech Republic, http://www.ig.cas.cz/en/seismic‑service/waveform‑request/.

The CMG-40T seismograms from the same station wereobtained from the WEBNET group belonging to the same in-stitute.

Data from Japan, stations ISI and NOK, were down-loaded from the F-net (NIED) web page www.hinet.bosai.go.jp/fnet/.

Focal mechanism of the main studied event was calcu-lated by waveform inversion with software ISOLA (http://seismo.geology.upatras.gr/isola/). Details of the solution,agency code UPSL, can be found in the Moment Tensors sec-tion of the European-Mediterranean Seismological Center(http://www.emsc-csem.org/).

All web pages referenced here were last accessedJuly 2009.

Acknowledgments

Our thanks go first of all to our colleagues A. Bouskova, T. Fischer,J. Horalek, P. Jedlicka, J. Michalek, and J. Zednik, Institute of Geophysics,

Academy of Sciences of the Czech Republic, Prague, for providing us theunique observational material for this article. We are obliged to E. Wielandt,Stuttgart, and F. Gallovic, J. Jansky, and I. Oprsal, Prague, for incentivediscussions. The examples from other stations were provided by J. Burjanekand E. Sokos. The work has been performed as part of projectsIAA300120911 and GACR 205/07/0502 (both supported by the GrantAgency of the Czech Republic) and MSM 0021620860 (supported bythe Ministry of Education, Youth and Sports, Czech Republic).

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Charles University in PragueFaculty of Mathematics and PhysicsDepartment of GeophysicsV Holesovickach 2, 180 00Prague, Czech RepublicJiri.Zahradnik@mff.cuni.cz

(J.Z.)

Institute of GeophysicsAcademy of Sciences of the Czech RepublicBocni II/1401141 31 Prague, Czech Republicpless@ig.cas.cz

(A.P.)

Manuscript received 3 April 2009

Toward Understanding Subtle Instrumentation Effects Associated with Weak Seismic Events 15

Queries

1. What is the “it” referred to in: “It should be a part of newer data acquisition and quality control”?2. Wording of “activity is tightly spatially concentrated in a fault segment”was changed to “activity is tightly compacted

in a spatially concentrated fault segment”. Is this change consistent with your intended meaning?3. Please supply the date (year) for the “T. Fischer, personal comm.”4. Please supply the date (year) for “A. Boušková, personal comm.”5. “The big advantage is the collocation of the two instruments” is a very long sentence. Please suggest a place to break

this into two shorter sentences.6. The expression “+/-1.5” was changed to �1:5. Is this consistent with your intended meaning?”7. Double parenthesis were replaced with brackets in equation S�f� � K�f�=�1� β�f�K�f��. Is this consistent with

your intended meaning?8. BSSA style does not allow contractions such as “isn’t”. Does this reworded sentence retain your intended meaning:

“Is there any other physical effect which could act on the seismograph in the same way as an acceleration pulse?”9. Is the wording change to “By the intermediate-field pulselike velocity” consistent with your intended meaning?

16 J. Zahradník and A. Plešinger