J Seismol (2008) 12:21–33DOI 10.1007/s10950-007-9068-9

ORIGINAL ARTICLE

Estimation of an upper limit on prehistoric peak groundacceleration using the parameters of intact speleothemsin Hungarian caves

Gyozo Szeidovitz · Gergely Surányi ·Katalin Gribovszki · Zoltán Bus ·Szabolcs Leél-Ossy · Zsolt Varga

Received: 21 December 2006 / Accepted: 9 October 2007 / Published online: 23 November 2007© Springer Science + Business Media B.V. 2007

Abstract The examination of speleothems inthe Hajnóczy and Baradla caves (northeasternHungary) allows estimating an upper limit forhorizontal peak ground acceleration generated bypaleoearthquakes. The density, the Young’s mod-ulus and the tensile failure stress of the samplesoriginating from a broken speleothem have beenmeasured in a laboratory, whereas the naturalfrequency of intact speleothems was determinedby in situ observations. The value of horizontalground acceleration resulting in failure, the nat-ural frequency and the inner friction coefficient

G. Szeidovitz · K. Gribovszki · Z. Bus (B)Hungarian Academy of Sciences, Geodeticand Geophysical Research Institute, SeismologicalObservatory, Meredek u. 18., 1112 Budapest, Hungarye-mail: bus@seismology.hu

G. SurányiMTA-ELTE Geological, Geophysical and SpaceScience Research Group, Pázmány Péter sétány 1/C,1117 Budapest, Hungary

S. Leél-OssyDepartment of Physical and Historical Geology,ELTE University Budapest,Pázmány Péter sétány 1/C,1117 Budapest, Hungary

Z. VargaInstitute of Isotopes, Department of Radiation Safety,Hungarian Academy of Sciences, Konkoly-ThegeMiklós tér 29-33., 1121 Budapest, Hungary

of speleothems were assessed by theoretical cal-culations. The ages of the samples taken from astalagmite 5.1 m in height (Baradla cave) havebeen determined by inductively coupled plasmamass spectrometry analysis and alpha spectrom-etry. The measured ages fall between 140,000 and70,000 years; therefore, we assume the speleothemhas not been changed since the end of this timeinterval. According to our modeling results, thisspeleothem has not been excited by a horizontalacceleration higher than 0.05 g during the last70,000 years.

Keywords Speleothems · Paleoearthquakes ·Earthquake hazard

1 Introduction

In territories with low or moderate seismic ac-tivity, the recurrence time of large earthquakesbelonging to the same source zone can be aslong as 10,000 years (Scholz 1990). Therefore, wecannot draw well-grounded inferences in the fieldof seismic hazard assessment using exclusively thedata of earthquake catalogues, as they are basedcharacteristically on 1,000- to 2,000-year observa-tional period.

To obtain more reliable and realistic data re-garding the frequency and magnitude of earth-

22 J Seismol (2008) 12:21–33

quakes, we have to investigate paleoearthquakesthat occurred before historic times.

Neotectonic and geomorphologic investiga-tions can reveal the traces of paleoearthquakesonly in some lucky circumstances, as erosion caneasily destroy the superficial formations.

The research of the relationship between earth-quakes and the growth, tilting and breaking ofspeleothems is promising, and investigations ofthis kind have been initiated in recent times.

Results of Forti and Postpischl (1984, 1988)show that examining the broken and tilted spe-leothems can be useful for revealing historic andpaleoearthquakes. Delaby (2001) recognised theoccurrence of a paleoearthquake while studyingbroken and tilted stalagmites in the Hotton cave(Belgium).

Cadorin et al. (2001) performed laboratorymeasurements and theoretical computations todetermine the horizontal acceleration that wasnecessary to break the broken speleothems inthe Hotton cave. According to their results, therewas only one sample from the 34 ones that wasbroken at an acceleration of 2 m/s2; other samples

required a horizontal acceleration amplitude of atleast 1 g. Hence, these speleothems could not beindicators of paleoearthquakes.

Lacave et al. (2000) determined by in situmeasurements the natural frequencies of varioustype of speleothems, estimated curves describingthe natural frequency as the function of the typeand length of the speleothem, and computed thespeleothems’ viscous equivalent damping. Fur-thermore, Lacave et al. (2004) constructed vul-nerability curves (probability of breaking vs. peakground acceleration [PGA] functions) for classesof differently shaped stalactites.

Kagan et al. (2005) dated broken speleothemsby U-Th and oxygen isotope method in two cavesin Israel and found a mean recurrence interval of10,000–14,000 years of large earthquakes affectingthe territory.

Recently, Becker et al. (2006) gave a compre-hensive critical review of speleoseismology. Theydescribe processes other than earthquakes thatcan have the same or very similar effects on spele-othems, and they conclude that, before a decisionis made on the seismic origin of deformations and

Fig. 1 Location of the Baradla and Hajnóczy caves (BCand HC, respectively) and the historical and instrumentalseismicity of the Pannonian region. The epicenter distribu-tion of historical (456–1994) earthquakes are displayed bygray circles, whereas black circles represent recent (1995–2004) well-located events (after Tóth et al. 2007). The

size of the circles is proportional to the magnitude. Theblack lines illustrate the neotectonic active structures afterHorváth et al. (2006). The rectangles, triangles and arrowson the lines indicate normal, reverse and strike-slip faults,respectively, whereas the diamonds show the anticlines

J Seismol (2008) 12:21–33 23

damages found in caves, alternative explanationsmust be taken into consideration as well.

The connection between earthquakes and thebreaking and tilting of speleothems has not yetbeen investigated in Hungary, but research aboutthe age and formation of dripstones proved to besuccessful (Lauritzen and Leél-Ossy 1999).

The territory of Hungary is rather rich indripstone caves, they can be found in severalregions of the country (e.g. Transdanubian Cen-tral Range, Mecsek and Villány Mountains, BükkMountains, the Aggtelek Karst). Based on thereview of the Hungarian speleological literature(e.g. Kordos 1984), discussions with experts andour visits to caves, it seems that, in Hungary, onlyin the Hajnóczy and Baradla caves (Fig. 1) can befound speleothems that are well suited to the pale-oseismic investigations; that is, they have the nec-essary large height/diameter ratio (Cadorin et al.2001). Our preliminary investigations suggestedthat the stalagmites of these caves can break evenat low horizontal acceleration. These speleothemstherefore could be used as indicators whether ornot large paleoearthquakes occurred within thegiven region.

During our research, the density, the Young’smodulus and the tensile failure stress of speleo-them samples have been measured in laboratoryfor subsequent theoretical modeling, whereas thenatural frequency of intact speleothems was de-termined by in situ observations. The value ofhorizontal ground acceleration resulting in failure,the natural frequency and the inner friction coeffi-cient of speleothems were assessed by theoreticalcalculations. The ages of the samples originatingfrom a specific stalagmite have been determinedby inductively coupled plasma mass spectrometry(ICP-MS) analysis and alpha spectrometry.

2 Seismicity of Hungary

The seismic activity inside the Pannonian basin(Fig. 1) can be considered moderate compared tothat of the peripheral areas (Tóth et al. 2002).Construction of a reliable seismotectonic modelfor this territory proved to be a challenging task,due to the relatively small number of earthquakesand the diffuse distribution of epicenters.

Nevertheless, nowadays, it is clear that theearthquake activity and present-day deformationare mainly driven by the counterclockwise rota-tion and northwards indentation of the Adriaticmicroplate (e.g. Bada et al. 1999). The rheologicalweakness of the Pannonian lithosphere (Gerneret al. 1999; Lenkey et al. 2002) poses a constrainton the maximum magnitude of earthquakes, andas a consequence, the largest part of the eventsoccurs at shallow depths (Tóth et al. 2002).

According to the Hungarian Earthquake Cat-alogue (Zsíros 2000), which contains earthquakesas from the year 456 a.d., the maximum observedmagnitude was 6.3 in the Hungarian part of thePannonian basin.

In spite of the diffuse characteristics of theearthquake activity, some zones with above aver-age seismic activity can be identified in Hungary.They are mainly located in the western and centralpart of the country, whereas the level of seismicityin the northeastern part of Hungary is rather low.

The map of the expected PGA with a 90%probability of non-exceedance in 50 years (475-year return period) for the Pannonian region com-piled by Tóth et al. (2006) shows that the expectedPGA is 0.068 g in the vicinity of the Baradla caveand 0.086 g near the Hajnóczy cave.

3 The caves

The Baradla cave (Fig. 2) is the longest cave ofHungary (with a length of around 26 km, fromwhich approximately 5 km belongs to Slovakia)and is one of the UNESCO’s World HeritageSites. The cave is located in Northern Hungary, inthe Gömör–Torna karst region. It has been knownsince prehistoric times and was used as a shelterand a dwelling in the Paleolithic and Neolithicperiods. The cave’s passages have been formed inthe Middle and Upper Triassic limestone (partlyin dolomitic limestone). The horizontal and verti-cal dimensions of the passages can reach a valueof a few 10 m. The Baradla cave is decoratedwith a large amount of stalagmites, stalactites anddripstone pillars of a maximum height of 18 m.

In the Baradla cave, the broken speleothemsare abundant. Most of them can be found nearthe entrance and all along the tourist paths. These

24 J Seismol (2008) 12:21–33

Fig. 2 Map of theBaradla cave

damages are probably attributable to human in-fluence. According to Jakucs (1952), in the nine-teenth century, the cave tour guides broke thespeleothems with their sticks for the tourists.The deep impact marks and fractures oblique tothe growth axis of speleothems also indicate an an-thropic origin (see e.g. Crispim 1999). The growthof speleothems has continued from the time ofbreaking, but only a very thin coating formedsuggesting that the damages occurred recently. Inthe Baradla cave, stalagmites several meters inheight and up to almost 1 m in width can be found,which are tilted or broken. These ones are situatedon clay or debris slopes or near the watercourse.

The collapse, breaking and tilting of these spele-othems might have been caused by sliding or soilcreeping, or they might have been washed awayby running water. Conclusively, our investigationseem to suggest that the damaged speleothems arenot of seismic origin.

The Hajnóczy cave (Fig. 3) can also be foundin Northern Hungary, in the southern part of theBükk Mountains. The cave, which was discoveredin 1971, has been formed in the Middle and UpperTriassic flinty, gray limestone. It has a complicatedlayout and possesses multiple levels. Its structureextends vertically for 135 m, and the total lengthof the known passages is around 3,000 m. In the

Fig. 3 Map of theHajnóczy cave

J Seismol (2008) 12:21–33 25

Fig. 4 A stalagmite (Speleothem N◦ 3) in the Sárkány hallof the Baradla cave

passages, the traces of hydrothermal activity canbe found, which indicates that hot aqueous solu-tions probably played an important role duringtheir formation. The Hajnóczy cave is exception-ally rich in speleothems. In its large halls, the slimand tall stalagmites and columns are typical (theyoften have a diameter of a few centimetres and aheight of several metres).

The Hajnóczy cave is practically free of brokenspeleothems. This observation can be explainedby the lack of human influence, as it has only beendiscovered recently.

It is known that, with the deepening of thecaves, the attenuation of the seismic waves rises(Becker et al. 2006). Therefore, it is importantto mention that the caves where the investigatedspeleothems stand are situated at shallow depth.The Olimposz hall in the Baradla cave is locatedat 35–40 m below surface, the Sárkány hall in

Baradla cave is situated at 45–50 m depth, andthe surface above both halls makes up a platformridge. The Hajnóczy cave can be found in 60 mdepth beneath the surface, topographically undera hillside.

4 Non-intrusive examination of speleothems

Considering that the in situ measurements hadto be done non-intrusively, we confined ourselvesonly to determine the dimensions and natural fre-quency of speleothems.

To measure the natural frequency, small am-plitude forced vibration was obtained by a gentlehit using one’s hand or a rubber hammer. Thehorizontal acceleration of the speleothem was reg-istered by an SM6 geophone (its natural frequencyis 4.5 Hz) and a SIG SMACH SM-2 digitiser. Thegeophones were mounted by means of adhesivetape onto the speleothems (Figs. 4 and 5). Thesampling rate of the analog–digital converter was

Fig. 5 Sampling a stalagmite of 5.1 m high (SpeleothemN◦ 6) in the Olimposz hall of the Baradla cave

26 J Seismol (2008) 12:21–33

set to 256 Hz, whereas the cut-off frequency of theanti-aliasing filter was 50 Hz.

The power spectral density of the vibrationhas been determined by fast Fourier transform.The measured traces and their spectra for certainspeleothems are displayed in Figs. 6, 7 and 8.

Table 1 shows, among other parameters, thehorizontal and vertical dimensions of the seven

studied speleothems and the in situ measured nat-ural frequencies ( f0).

The diameter of the dripstones ranges between4 and 30 cm, but the characteristic diameter(which parameter describes the typical horizon-tal dimension) of the more or less cylindricallyshaped speleothems falls in the range of 5 and11.5 cm. Their height varied from 2.1 to 5.1 m.

Fig. 6 The oscillation ofthe stalagmite of 3.35 mhigh (Speleothem N◦ 1)in the Sárkány hall of theBaradla cave and itspower spectral density

–1.2

–0.8

–0.4

0.0

0.4

0.8

1.2

Acc

eler

atio

n [m

/s2 ]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time (s)

–90

–80

–70

–60

–50

–40

–30

–20

–10

0

PS

D (

10. lo

g(m

/s2 )

2 /H

z))

[dB

]

0 5 10 15 20 25 30 35 40 45 50

Frequency (Hz)

J Seismol (2008) 12:21–33 27

Fig. 7 The oscillation ofthe Speleothem N◦ 3 inthe Sárkány hall of theBaradla cave and itspower spectral density

–1.2

–0.8

–0.4

0.0

0.4

0.8

1.2

Acc

eler

atio

n [m

/s2 ]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Time (s)

–90

–80

–70

–60

–50

–40

–30

–20

–10

0

PS

D (

10. lo

g(m

/s2 )

2 /H

z))

[dB

]

0 5 10 15 20 25 30 35 40 45 50

Frequency (Hz)

Consequently, the height/diameter ratios were ex-ceptionally large (24.7 ≤ H/D ≤ 72). It is inter-esting to note that the maximum H/D ratio foundby Cadorin et al. (2001) for the speleothems of theHotton cave was only 20.

The measured natural frequencies are in therange of 1.4 and 27.9 Hz, but only in two casesfrom the seven was f0 above 25 Hz, in the othercases it fell below 13 Hz.

5 Oscillation of stalagmites – theoreticalconsiderations

In our modeling, the stalagmites were consideredas vertical cylinders of height H and diameter Dwith a circular cross-section. We supposed thatthe bottom of the cylinders is firmly fixed to theground and the top can move freely. The materialof the stalagmites was considered homogeneous.

28 J Seismol (2008) 12:21–33

Fig. 8 The oscillation ofthe stalagmite of 5.1 mhigh (Speleothem N◦ 6)in the Olimposz hall ofthe Baradla cave and itspower spectral density.The dripstone is crackedat 4.76 m high, whichcan justify the presenceof the relatively strongsecondary peaks at higherfrequencies

–1.00

–0.75

–0.50

–0.25

0.00

0.25

0.50

0.75

1.00

Acc

eler

atio

n [m

/s2 ]

0 1 2 3 4 5 6 7 8 9 10 11 12

Time (s)

–100

–90

–80

–70

–60

–50

–40

–30

–20

PS

D (

10. lo

g(m

/s2 )

2 /H

z))

[dB

]

0 5 10 15 20 25 30 35 40 45 50

Frequency (Hz)

Following the study of Ferencz and Péterfalvi(2002), the coordinate axes x and z correspondto the vertical and horizontal directions, respec-tively, and moreover, the z axis is directed towardsthe hypothetic earthquake epicenter.

The driving acceleration ( f ), originating fromthe elastic waves of the earthquake, depends onthe time (t), but not on the x coordinate. How-ever, to obtain the equation of motion, it is use-ful to write f as f (x, t) = f (t)

∑∞i=0 si(x)ci, where

∑∞i=0 si(x)ci = 1, as the si(x) eigenmodes of the

speleothem form a complete orthonormal systemof eigenfunctions.

The restoring force per unit length arising inbended rods is proportional to the fourth deriv-ative of the displacement:

Fe(x, t) = −EI∂4z(x, t)

∂x4, (1)

J Seismol (2008) 12:21–33 29

Table 1 Geometrical parameters of the investigated speleothems, the horizontal acceleration needed to break them andtheir theoretical and measured natural frequencies

N◦ Description H [m] D [m] H/D ag [m/s2] f0 [Hz] f0 [Hz]theoretical measured

1 Stalagmite 3.35 0.075 44.7 1.13 2.8 5.1Baradla cave (3.35–3.45) (0.045–0.12)Sárkány hall

2 Pillar 3.9 0.07 55.7 25.8Baradla cave, (3.79–3.9) (0.045–0.08)Sárkány hall

3 Stalagmite 2.85 0.12–0.29 11.3, 12.5Baradla cave, complicatedSárkány hall form(Fig. 4)

4 Stalagmite 2.84 0.115 24.7 2.41 5.9 9.8Baradla cave, (0.08–0.15)Sárkány hall

5 Stalagmite 2.1 0.085–0.28 27.9Baradla cave, upwardsSárkány hall thickening

6 Stalagmite 5.1 0.085 60.0 0.55 1.3 1.4Baradla cave, (cracked at (0.075–0.1)Olimposz hall 4.76)(Fig. 5)

7 Stalagmite 3.6 0.05 72.0 0.65 1.6 4.0Hajnóczy cave,Óriás hall

where E is the Young’s modulus and I is thebending moment.

The energy of the oscillating stalagmite dissi-pates due to the inner friction. The correspondingforce per unit length is equal to

Ff = −κq2 ∂4z(x, t)∂x4

, (2)

where κ is the inner friction coefficient and qis the cross-section of the speleothem. The dotabove the variable denotes its time derivative. Ourequation of motion:

ρqf (x, t) + Fe(x, t) + Ff (x, t) = ρqz(x, t), (3)

If only the fundamental mode of the vibration(s0(x)) is considered, we get

c0s0(x) f (t) − α∂4z(x, t)

∂x4− β

∂4z(x, t)∂x4

= z(x, t)

(4)

with α = EI/ρq and β = κq/ρ, ρ is the density ofthe speleothem. The solution of the equation ofmotion is

z(x, t)= c0

a

[sinh(λ0x)−sin(λ0x)+B(cosh(λ0x)

−cos(λ0x))]∫ ∞

0f (t−τ)e−bτ sin(aτ)dτ

(5)

where c0 ≈ −0.57481, a =√

αλ40 − β2λ8

0/4, b =βλ4

0/2, B = −(sin(λ0 H)+ sinh(λ0 H))/(cos(λ0 H)+cosh(λ0 H)) and λ0 ≈ 1.8751/H.

If the effect of the inner friction can be ne-glected (β2λ4

0 � α), it is possible to show that thenatural frequency of a stalagmite:

f0 ≈ 1

π

√3.1ED2

16ρH4(6)

30 J Seismol (2008) 12:21–33

The static, horizontal ground acceleration re-sulting in failure (Cadorin et al. 2001):

ag = Dσu

4ρH2(7)

where σu is the tensile failure stress of the spe-leothem. It can be seen that both the naturalfrequency and horizontal ground acceleration re-sulting in failure depend on the geometrical prop-erties of the stalagmite in the same way, i.e. theyare proportional to D/H2.

6 Mechanical properties of speleothems

Laboratory measurements were performed onsamples originating from a speleothem that wasfound lying broken on the ground in the Olimposzhall of Baradla cave.

According to our results, the average density is2,394 kg/m3, the standard deviation of the mea-sured 16 values is 155 kg/m3.

The Young’s modulus has been calculated us-ing the data of a uniaxial compressive strengthtest. The mean value is 20,813 MPa, the standarddeviation 5,921 MPa (the number of the sampleswas four). The mean tensile failure stress of the13 samples was 1.62 MPa (with standard deviationof 0.48 MPa), which has been measured by theBrazilian test.

Using the free vibration decay of a stalag-mite, we can determine the inner friction para-meter. The horizontal acceleration along a freelyoscillating stalagmite is z(x, t) = d(x) e−bt sin(at)where d is simply the product of constants andx-dependent parameters.

The “smoothly” decaying oscillation of Spele-othem N◦ 1 (Fig. 6) allows the estimation of itsκ coefficient. The parameters (d,b ,a) have beencomputed by least squares fitting. From the result-ing b = 0.236 1/s value, the inner friction is κ =2.61 · 106 kg/(ms). This value justifies the neglectof the effect of inner friction in computing thenatural frequency (e.g. in the case of SpeleothemN◦ 1 α/(β2λ4

0) ≈ 1,300).

The measured natural frequency of the inves-tigated speleothems changed in the range of 1.4–27.9 Hz.

It is interesting to note that our results are veryclose to the ones gained by Lacave et al. (2000).In Fig. 1 of their paper, they show the estimatednatural frequency values for speleothems of dif-ferent type, based on in situ measurements inFrench caves. The measured frequencies for ourspeleothems N◦ 1, N◦ 6, and N◦ 7 fall betweentheir two curves describing the natural frequencyof stalagmites with diameters of 5 and 10 cm (thefrequency value belonging to stalagmite N◦ 4 witha characteristic diameter of 11.5 cm is close tothis stripe from above). As the diameter of theabovementioned speleothems lies in this 5- to 10-cm range, we can conclude that the frequencyvalues determined in the two studies are in verygood agreement in spite of the different measur-ing techniques.

If the natural frequency is below 20 Hz (whichis the approximate upper limit of the frequencyrange of nearby earthquakes), then resonance canoccur (this is the situation in five cases from theseven). Our analysis did not take into considera-tion the phenomenon of resonance, which meansthat, in reality, the dripstones would break at alower value of horizontal acceleration than thecomputed one.

The observed and theoretical natural frequen-cies (Table 1) differ at most by a factor of2.5 (the theoretical values were in every casesmaller than the measured ones). The differenceprobably comes from the used approximations, asthe shape of the speleothems more or less differfrom the shape of a cylinder, their material is nothomogeneous, and the material parameters arebased on measurements performed on a specificspeleothem.

It can be observed that the maximum hori-zontal acceleration measured on the SpeleothemN◦ 6 (Fig. 8) significantly exceeds the computedag ground acceleration value. This phenomenon isin agreement with the solution of the equation ofmotion.

Based on Table 1, we can conclude that, forthe investigated speleothems in the Baradla and

J Seismol (2008) 12:21–33 31

Hajnóczy caves, the horizontal acceleration valuesneeded to break them are between 0.05 and 0.24 g.

7 Sampling and age determination

We took samples from the stalagmite of 5.1 m high(Fig. 5) in the Olimposz hall of Baradla cave (Spe-leothem N◦ 6) at different heights to determine itsage and rate of growth.

Due to its geometry, sampling was a very dif-ficult task. To avoid breaking the stalagmite, wetied it to a frame at several points. The 3–4 g ofsamples necessary for alpha spectrometric mea-surements was taken from four locations at differ-ent heights with the help of a core sampler (thediameter of the sample core was 12 mm).

The samples were examined and measured inthe Radiometric Laboratory of the Geophysicsand Environmental Physics Research Group ofthe Hungarian Academy of Sciences at theLoránd Eötvös University and in ICP-MS Lab-oratory of the Institute of Isotopes, HungarianAcademy of Sciences. After the dissolution ofthe sample with dilute hydrochloric acid, uraniumand thorium were pre-concentrated with iron hy-droxide followed by their extraction chromato-graphic separation using UTEVA resin. Alphasource preparation was carried out by micro-co-precipitation using NdF3. The sources werecounted by low-background alpha-spectrometers(Canberra); the duration of measurement was 8–10 days. The ICP-MS analysis was carried outusing an ELEMENT2 ICP-MS (Thermo Corp.,

Bremen, Germany) with stable sample intro-duction system (Elemental Scientific Inc.). Mea-surement and data acquisition parameters wereoptimised before the analysis. The obtained rawdata were corrected for the method blank andinstrumental mass bias.

The applied tracer was 232U in equilibrium with228Th daughter in alpha spectrometry and mixed229Th/233U/236U tracer in ICP-MS analysis, respec-tively; the chemical recovery varied between 65–95%. The measurements were processed by ourown assessment procedure based on the MonteCarlo method. The results of the measurementscarried out are presented in Table 2.

The high variation of the measurements in thecase of alpha spectrometry was due to the lowuranium content and low mass of the samplesavailable; in the case of ICP-MS, it was due to theinaccuracy of the available tracer.

Our measurements show that, below the heightof 390 cm (measured from the bottom of thespeleothem), the ages become younger with theincreasing height of the sample origin; therefore,the dating results are in good agreement with theformation mechanism of the stalagmites. How-ever, the age of the sample originating from 476cm height contradicts the previous statement, asit is older than the samples from lower posi-tions according to both the alpha spectrometricand ICP-MS measurements. This result cannot beexplained by the simple hypothesis of steadilygrowing stalagmite. It is noteworthy that simi-lar controversial age data have been observed(Siklósi, personal communication) in the Triócave in the Mecsek Mountains (Hungary).

Table 2 Ages measured at different heights for the stalagmite of 5.1 m high (Speleothem N◦ 6) in the Olimposz hall of theBaradla cave

Height of sampling Cored interval (mm) Age (year) Error (year) U-content (ppm) Methodpoint (cm) (confidence level of 95%)

476 19–39 124,000 +19,500/−17,000 0.038 ICP-MS476 19–39 140,000 +29,000/−24,000 0.034 Alpha spec.390 19–39 70,800 +7,000/−6,800 0.025 ICP-MS287 22–43 102,500 +22,500/−19,000 0.020 Alpha spec.287 3–22 102,500 +36,000/−28,000 0.020 Alpha spec.16 36–47 132,000 +14,000/−12,500 0.052 ICP-MS

32 J Seismol (2008) 12:21–33

The reason for the controversial nature of theresults for the sample at the height of 476 cm wasnot found after repeated checking of the mea-surements and assessment. Cross contaminationand 232Th-contamination have been excluded byrepeating the analysis. The uranium content of thepaint on the sampling drill was suspected, but after5 days of control measurements, the paint did notshow alpha radiation; furthermore, most of thepaint had been removed earlier.

However, a possible explanation can be given.The speleothems in the Olimposz hall contain nu-merous small diameter cavities (their size is in theorder of millimetres), which are interconnected byhairline cracks. According to our assumption, thedripping water seeped through the pore space, andcalcite filling accumulated gradually over time.As this deposit can be considerably younger thanthe primary material of the speleothem, the morerecent radiometric age of the middle part of thestalagmite (i.e. the controversial age data) can beexplained by this mechanism, namely, the datingmethod measures the “average” of the old andnew ages. Beyond that, this process of recrystalli-sation made the original laminae hard to observe.

The recrystallisation completely ruined thetraceability of the growth of the speleothem byrejuvenating the radiometric age of the sam-ples. Therefore, we cannot deduce how its shapechanged during the times. If we do not want toerroneously underestimate the level of seismichazard, or in other words, we want to give themost conservative estimation, we have no otherchoice but to use the youngest age data we mea-sured on the samples.

This is why we suppose that Speleothem N◦ 6has not been changed significantly during the past70,000 years, and we made the calculations usingthe current shape of the stalagmite.

A conceivable hypothesis for the stoppedgrowth of the stalagmite is that the clayey solutionresidue of the rock blocked the fissures throughwhich the growing speleothem got the water sup-ply or it can be the consequence of surface climatechange. By all means, at the present time, no traceof dropping can be seen in the neighbourhoodof this stalagmite. The same process of stoppedgrowth has already been observed in the Baradlacave (Lauritzen and Leél-Ossy 1999).

8 Conclusions

Speleothems with large height/diameter ratio(H/D>40) have been found in two Hungariancaves. We determined by in situ measurementsthe natural frequency of seven speleothems ofthe Baradla and Hajnóczy caves, and in labo-ratory, the material properties (the density, theYoung’s modulus and the tensile failure stress)of a speleothem specimen have been measured.The inner friction coefficient for a speleothem wascalculated, as well. Based on a simple mechanicalmodel, the theoretical natural frequency ( f0) andthe horizontal ground acceleration values result-ing in failure (ag) have been calculated for thestalagmites.

The measured natural frequencies of the in-vestigated speleothems fall in the range of 1.4–27.9 Hz. The theoretical frequencies for thestalagmites differ, of course, from the measuredones. In the worst case, the observed natural fre-quency is 2.5 times greater than the theoreticalone (Speleothem N◦ 7). We obtained the bestresult for Speleothem N◦ 6, where the differenceis smaller than 8%.

The computed ag values for the studied stalag-mites fall in the range of 0.05 and 0.24 g, whichcan arise even in the case of moderate sized earth-quakes. As in most cases, the natural frequencyof these stalagmites is in the frequency range ofnearby earthquakes; the failure acceleration canbe even smaller because of the resonance effect.

As the modelling of the 5.1 m high stalagmitein Olimposz hall of Baradla cave (SpeleothemN◦6) was remarkably successful concerning the f0

value, in our opinion, the resulting ag =0.05 gacceleration value can be considered reliable,as well.

This agreement, together with the results ofage determination, allows us to estimate anupper limit on prehistoric PGA. On the basis ofour measurements and theoretical calculations,we can assume that the geological structures closethe Baradla cave (Fig. 1) did not generate paleo-earthquakes producing a horizontal ground accel-eration larger than 0.05 g in the last 70,000 years.

This acceleration level is lower than the PGAvalue determined by Tóth et al. (2006) for a muchshorter period of time, and evidently, the expected

J Seismol (2008) 12:21–33 33

PGA would be even greater for a 70,000-yearinterval. At the present time, it is not possible toreveal the cause of this discrepancy. We must takeinto consideration, however, that the PGA wasdetermined during a regional study and a moredetailed investigation focusing on the territory ofBaradla cave (which is anyway one of the leastseismically active regions of the country) maymodify the result.

Acknowledgements The study was supported by theHungarian Scientific Research Fund projects T038099,T049713, T32433 and T061800. The authors are indebtedto Péter Gruber (Aggtelek National Park) and Dr.Miklós Gálos (Budapest University of Technology andEconomics, Department of Construction Materials andEngineering Geology). The authors thank the three anony-mous reviewers for their helpful comments. Some of thefigures were prepared using the Generic Mapping Tools(Wessel and Smith 1998).

References

Bada G, Horváth F, Gerner P, Fejes I (1999) Review ofthe present-day geodynamics of the Pannonian basin:progress and problems. J Geodyn 27:501–527

Becker A, Davenport CA, Eichenberger U, Gilli E,Jeannin P-Y, Lacave C (2006) Speleoseismology: acritical perspective. J Seismol 10:371–388

Cadorin JF, Jongmans D, Plumier A, Camelbeeck T,Delaby S, Quinif Y (2001) Modelling of speleothemsfailure in the Hotton cave (Belgium). Is the fail-ure earthquake induced? Netherlands J Geosci 80(3–4):315–321

Crispim JA (1999) Seismotectonic versus man-inducedmorphological changes in a cave on the Arrabidachain (Portugal). Geodin Acta 12:135–142

Delaby S (2001) Paleoseismic investigations in Belgiancaves. Netherlands J Geosci 80(3-4):323–332

Ferencz E, Péterfalvi Cs (2002) Investigation of earth-quake related vibration and breaking of speleothems(in Hungarian). unpublished manuscript, p 17

Forti P, Postpischl D (1984) Seismotectonic and paleo-seismic analyses using karst sediments. Mar Geol 55:145–161

Forti P, Postpischl D (1988) Seismotectonics and radio-metric dating of karst sediments. Proc Hist Seismolof Central-eastern Mediterranean Region, ENEA-IAEA Roma, pp 312–322

Gerner P, Bada G, Dövényi P, Müller B, Onescu MC,Cloething SAPL, Horváth F (1999) Recent tectonicstress and crustal deformation in and around thePanonnian basin: data and models. In: Durand B,Jolivet L, Horváth F, Séranne M (eds) The

Mediterranean basins: Tertiary extension withinthe Alpine orogen, vol 156. pp 269–294

Horváth F, Bada G, Windhoffer G, Csontos L, DövényiP, Fodor L, Grenerczy Gy, Síkhegyi F, Szafián P,Székely B, Tímár G, Tóth L, Tóth T (2006) Atlas of thepresent-day geodynamics of the Pannonian basin: Eu-roconform maps with explanatory text (in Hungarianwith English summary). Magy Geofiz 47(4):133–137

Jakucs L (1952) The Cave of Aggtelek (in Hungarian).Muvelt Nép Könyvkiadó, Budapest, p 118

Kagan EJ, Agnon A, Bar-Matthews M, Ayalon A (2005)Dating large infrequent earthquakes by damaged cavedeposits. Geology 33(4):261–264

Kordos L (1984) Caves of Hungary (in Hungarian).Gondolat, Budapest, p 315

Lacave C, Koller MG, Egozcue JJ (2004) What can beconcluded about seismic history from broken and un-broken speleothems? J Earthq Eng 8(3):431–455

Lacave C, Levret A, Koller MG (2000) Measurementsof natural frequencies and damping of speleothems.Proc. of the 12th World Conference on EarthquakeEngineering, Auckland, New-Zealand, paper 2118

Lauritzen S-E, Leél-Ossy Sz (1999) Preliminary agedata of certain speleothems from Baradla Cave (inHungarian). Karszt és Barlang 1994(I-II):3–8

Lenkey L, Dövényi P, Horváth F, Cloething SAPL(2002) Geothermics of the Pannonian basin and itsbearing on the neotectonics. In: Cloetingh SAPL,Horváth F, Bada G, Lankreijer A (eds) Neotec-tonics and surface processes: the Pannonian basinand Alpine/Carpathian system, vol 3. European Geo-sciences Union, St. Mueller Special Publication Series,pp 29–40

Scholz H (1990) The mechanics of the earthquakes andfaulting. Cambridge University Press, p 467

Tóth L, Bus Z, Gyori E, Mónus P (2007) Seismicity of thePannonian basin. In: Husebye E, Christova C (eds)Earthquake monitoring and seismic hazard mitigationin Balkan countries. NATO ARW Series, Springer(in press)

Tóth L, Gyori E, Mónus P, Zsíros T (2006) Seismic haz-ard in the Pannonian region. In: Pinter N, GrenerczyGy, Weber J, Stein S, Medak D (eds) The Adria Mi-croplate: GPS geodesy, tectonics, and hazards, vol 61.NATO ARW Series, Springer, pp 369–384

Tóth L, Mónus P, Zsíros T, Kiszely M (2002) Seismic-ity in the Pannonian Region - earthquake data. In:Cloetingh SAPL, Horváth F, Bada G, LankreijerA (eds) Neotectonics and surface processes: thePannonian basin and Alpine/Carpathian system,vol 3. European Geosciences Union, St. MuellerSpecial Publication Series, pp 9–28

Wessel P, Smith WHF (1998) New, improved version ofgeneric mapping tools released. EOS Trans AGU79:579

Zsíros T (2000) The seismicity and earthquake hazard ofthe Pannonian basin: Hungarian Earthquake Catalog(456-1995, in Hungarian). MTA GGKI SzeizmológiaiObszervatórium, p 482