https://doi.org/10.1007/s10950-020-09944-1

ORIGINAL ARTICLE

Single-station seismic microzonation using 6Cmeasurements

Sabrina Keil · Joachim Wassermann ·Heiner Igel

Received: 28 February 2020 / Accepted: 15 July 2020© The Author(s) 2020

Abstract Microzonation is one of the essential toolsin seismology to mitigate earthquake damage by esti-mating the near-surface velocity structure and devel-oping land usage plans and intelligent building design.The number of microzonation studies increased in thelast few years as induced seismicity becomes morerelevant, even in low-risk areas. While of vital impor-tance, especially in densely populated cities, mostof the traditional techniques suffer from differentshortcomings. The microzonation technique presentedhere tries to reduce the existing ambiguity of theinversion results by the combination of single-stationsix-component (6C) measurements, including threetranslational and three rotational motions, and moretraditional H/V techniques. By applying this new tech-nique to a microzonation study in the downtown areaof Munich (Germany) using an iXblue blueSeis-3Arotational motion sensor together with a Nanomet-rics Trillium Compact seismometer, we were able toestimate Love and Rayleigh wave dispersion curves.These curves together with H/V spectral ratios arethen inverted to obtain P- and S-wave velocity pro-files of the upper 100 m. In addition, there is a goodcorrelation between the estimated velocity models andborehole-derived lithology, indicating the potential ofthis single-station microzonation approach.

S. Keil (�) · J. Wassermann · H. IgelDepartment of Earth and Environmental Sciences, LMUMunich, Theresienstraße 41, 80333, Munich, Germanye-mail: skeil@geophysik.uni-muenchen.de

Keywords Microzonation · Rotational seismology ·Ambient noise

Highlights

• Testing a novel method for microzonation com-bining single-station six-component measure-ments and H/V ratios

• Estimation of Love and Rayleigh wave dispersioncurves from single-station six-component data

• Positive correlation between inverted velocityprofiles and borehole-derived lithology

1 Introduction

In seismic microzonation, the velocity structure of theupper few 100 m is estimated in order to character-ize the local earthquake shaking characteristics. Thereare two common methods that allow the determina-tion of 1D subsurface wave velocity structures: (1)array-based methods, such as spatial autocorrelation(SPAC) (Aki 1957) and frequency-wavenumber (FK)analysis (Capon 1973); (2) single-station approaches,including horizontal-to-vertical (H/V) spectral ratios(Nogoshi and Igarashi 1971). In general, array-basedmethods are well understood and give reliable results(e.g., Marano and Fah (2014)). However, as a severelimitation, the installation and maintenance in anurban area are very complex. Due to its simplicity,

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/ Published online: 5 August 2020

the single-station H/V method is commonly applied inmicrozonation studies, but its theoretical foundation isstill not completely understood and the results highlydepend on the quality of the noise (e.g., Malischewskyand Scherbaum (2004)).

Wassermann et al. (2016) demonstrated that asingle-station six-component approach, combiningrotational motion measurements (which are relatedto the gradient of a seismic wave field) with tra-ditional translational recordings (i.e., recordings ofground velocity), may give comparable results to arraytechniques for the estimation of the 1D local veloc-ity structure and the dominant direction of the incidentwave field.

In addition, Bernauer et al. (2018) showed thata portable and reliable broadband rotational sensor,the blueSeis-3A (iXblue 2017), is now available. Inorder to test the performance of this six-componentapproach in a real-world application, we conduct anexperiment using a Trillium Compact seismometerand the blueSeis-3A rotational sensor within Munich,where the largest inner city geothermal power plantgives rise to concerns about induced seismicity in adensely inhabited area. Using noise measurements, therelation between rotational and translational motion isexploited to estimate Love and Rayleigh wave disper-sion curves, which can then be inverted for the local1D velocity structure (Wassermann et al. 2016). Toget as much information on the subsurface as possi-ble, the H/V method is used to complement the data

in the lower frequency range (< 5 Hz). Finally, theinverted velocity models are compared with lithologicprofiles, derived during the GeoPot (Geo-potentials ofthe tertiary subsurface) project (TUM 2018) of theTechnical University of Munich (TUM), to identifyany correlations between wave velocity and geology.

2 Data acquisition

The six-component measurements require the simulta-neous recording of translational and rotational motion.In this study, two instruments are used; a Nano-metrics Trillium Compact 120s seismometer and aniXblue blueSeis-3A rotational motion sensor (iXblue2017). In order to record the same movement, the seis-mometer and the rotational motion instrument haveto be installed on a single rigid base. Nevertheless,there also exist six-component instruments, so-calledRotaphones, which measure three rotational and threetranslational components in a fixed frame (Brokesovaet al. 2012). The rotational seismometer blueSeis-3A(iXblue 2017) is based on an interferometric fiber-optic gyroscope (FOG), which is strictly insensitive totranslational motions (Bernauer et al. 2018). A moredetailed description of the working principle of FOGsis given in Lefevre (2014).

Bernauer et al. (2018) conducted several labora-tory tests in order to determine the performance ofthe blueSeis-3A. They found that the sensor has a

Fig. 1 Self-noise powerspectra of the threecomponents of the blueSeis-3A (dots, triangles, andstars) determined during alaboratory experiment at theGeophysical Observatory inFurstenfeldbruck, Germany.The sensor was placed onan auxiliary monument in aquiet location. All threecomponents show flatself-noise levels over afrequency range of 0.001 to50 Hz. The X-componentexhibits significant peaks at58 and 83 Hz, and theZ-component at 74 Hz,probably due to seismicambient signals (cf.Bernauer et al. (2018))

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flat self-noise level lower than 30 nrads−1Hz−1/2 overa wide frequency range of 0.001–50 Hz, as can beseen in Fig. 1. In addition, the sensor is very stablein changing ambient conditions, such as temperatureand magnetic field, which makes it suitable for fieldinstallations (Bernauer et al. 2018).

The instrument setup used in this study is shownin Fig. 2. For the installation of the Trillium Compactseismometer and the blueSeis-3A rotational sensor, athin layer of the top soil has to be removed in orderto establish better coupling to the ground. The twoinstruments are then placed next to each other on aconcrete slab to guarantee a stable position and areconnected to power and GPS. The seismometer isadditionally connected to a REFTEK digitizer. Thedistance between the two instruments is about 10 cm,which is negligible compared with the smallest wave-length of a few meters. Therefore, the setup can beconsidered a single-station measurement, where bothinstruments record the same movement. To shield the

Fig. 2 Setup for the single station six-component noise mea-surements. The two instruments, the blueSeis-3A rotationalsensor on the left and the Trillium Compact 120s seismometeron the right, are placed about 10 cm apart on a concrete slab. Theinstruments are connected to GPS, power, and the seismometerto a REFTEK digitizer (inside of metal box). Before starting therecording of the data, a styrofoam insulation box is placed overthe instruments

devices against wind and direct sun radiation, a sty-rofoam insulation box is placed over them. Ambientnoise is recorded during daytime with sampling ratesof 200 Hz for approximately 2 h, which is enoughto get a good representation of the wavefield in therecorded frequency range. In addition, increasing themeasurement time to several days would make instal-lation and maintenance more complicated and thusreduce the impact of the method. The desired fre-quency band for the estimation of the velocity profileslies between 1 and 20 Hz, which corresponds to urbannoise, as was shown by numerous authors (e.g., Asten(1984) and Gutenberg (1958)). Measurements are per-formed at several locations in the city of Munich inthe vicinity of the landing points of the geothermalwells, since these are the most likely regions for thenucleation of induced earthquakes. The study area ismarked in Fig. 3.

3 Methods

3.1 Love and Rayleigh wave dispersion estimation

Six-component measurements provide a new way ofcomputing Love and Rayleigh wave dispersion curves.Under the premise that we only have to deal withplane, fundamental mode surface waves, it was shownby several authors (e.g., Ferreira and Igel (2009) andKurrle et al. (2010)) that simple relations between therotational motion and the translational acceleration ofa seismic signal exist. In case of a fundamental modeLove wave, the relation is:

cL(f ) = − aT (f )

2ωZ(f )(1)

where cL(f ) represents the frequency-dependentphase velocity, aT the transversal component of accel-eration, and ωZ the vertical rotation rate.

The transversal acceleration can be further definedas:

aT (f ) = sin(φL)aN(f ) − cos(φL)aE(f ) (2)

Where φL is the back azimuth of the wavefield, aN

the N–S component of acceleration, and aE the E–W component, respectively. This allows Eq. 1 to berewritten as:

−2cL(f )ωZ(f )=sin(φL)aN(f )−cos(φL)aE(f ) (3)

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Fig. 3 Map of Munich. The location of the geothermal powerplant is marked by the dot. The study area is indicated by therectangle. The magnified map in the upper right corner showsa part of the study area. The dots represent the measurement

locations, including stations SWMHK and BRUD, which arediscussed in more detail. Station SWMHK is located at thegeothermal power plant

The phase velocity cL(f ) and the back azimuthφL are both unknown properties, which have to beestimated in the following steps.

Accordingly, the relation for the phase velocity offundamental mode Rayleigh waves can be derived bytaking the ratio of the vertical component of acceler-ation aZ and the transverse rotation rate ωT (e.g., Linet al. (2011)).

cR(f ) = aZ(f )

ωT (f )(4)

By substituting ωT with its N–S and E–W rotationrate components (ωN and ωE), Eq. 4 can be rewrittenas:

aZ(f )

cR(f )= sin(φR)ωN(f ) − cos(φR)ωE(f ) (5)

To solve these equations and estimate the Love andRayleigh wave dispersion curves, an updated versionof the python package ROLODE (ROtational LOve

Dispersion Estimation; Wassermann et al. (2016))is used. This program simultaneously estimates thedirection and the velocity employing the principle oforthogonal distance regression (ODR). To fulfill theadditional assumption of a single source active at atime, the data are analyzed at each frequency band inshort sliding time windows. Each time window givesan estimate of phase velocity and back azimuth. Akernel density estimation (kde) is used to bin the esti-mates in error weighted histograms and model thesehistograms with Gaussian functions. The quality ofthe fit can be improved by introducing a weightingscheme to the computation of the histograms, whichaccounts for the goodness of the straight line fit bythe ODR (i.e., the correlation between the two quan-tities). The estimated phase velocities from the ODRare weighted according to:

wxnorm = (1 − 1

w)x (6)

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where

w =∑I

i (ωZ(f )[i])2

∑ii (ε

2i + δ2

i )(7)

with I the number of processed time windows, x > 0,and δ and ε the errors of the dependent and observedvalues in the ODR.

The mode of the kde function and its variance arethen used to determine the phase velocity and theerror. From the velocity estimates at each frequencyband the dispersion curve is derived. The procedure isdescribed in more detail in Wassermann et al. (2016).

3.2 Horizontal-to-vertical spectral ratios

The method of horizontal-to-vertical spectral ratios(H/V) was first introduced by Nogoshi and Igarashi(1971), who described it as the ratio between theFourier amplitude spectra of the horizontal and thevertical components of microtremors. Several morerecent studies interpret the H/V ratio as the elliptic-ity χ of Rayleigh waves, which can be computed bydividing the horizontal over the vertical component of

particle motion (e.g., Malischewsky and Scherbaum(2004)).

χ =| H

V| (8)

Numerous authors (e.g., Sylvette et al. (2006) andMalischewsky and Scherbaum (2004)) have shownthat the H/V ratio exhibits a pronounced peak closeto the fundamental S-wave resonance frequency of thesite, when the surface layer exhibits a sharp impedancecontrast with the underlying stiffer formations. Thismakes the ellipticity an important parameter to reflectproperties of the underground structure (Sylvette et al.2006) and gives additional data, especially in the lowerfrequency band.

The H/V curves, computed with the Geophys-ical Signal Database for Noise Array Processing(GEOPSY) software package (Wathelet et al. 2004;Wathelet 2008), are used to complement the dis-persion curves for the surface wave inversion. The1D velocity profiles are then derived with theDINVER module in the GEOPSY software pack-age, which implements a neighborhood algorithm(Wathelet 2008).

Fig. 4 Power spectral density of the three components of the a blueSeis-3A rotational sensor and b Trillium Compact seismometerfor station SWMHK. The dashed line in a marks the self-noise level of the rotational sensor, which lies at about 30nrads−1Hz−1/2

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4 Results and discussion

The power spectral densities (PSD) of the recordedrotational and translational data for station SWMHK,which is located right next to the geothermal powerplant (Fig. 3) are presented in Fig. 4. It is easy to noticethat the PSD for the translational components is abouttwo orders of magnitude larger than for the rotationalcomponents. Additionally, an energy decrease towardlower frequencies can be observed in both cases. Atabout 5 Hz, the self-noise level of the rotational sensoris reached, which lies at 30nrads−1Hz−1/2 (Bernaueret al. 2018), explaining the flat trend of the curve inFig. 4a.

Applying the ROLODE method to the recordeddata, the phase velocities for each frequency band can

be estimated and are arranged in error weighted his-tograms. Figure 5 displays the distribution for four dif-ferent frequencies. The data are modelled with Gaus-sian basis functions, where the mode is marked by avertical dotted line. For each frequency band underconsideration, using the mode as phase velocity esti-mate and the corresponding standard deviation of thekde function as the associated error, a complete disper-sion curve can be derived. Figure 6 shows the resultingLove and Rayleigh wave dispersion curves for sta-tion SWMHK. Between 5 and 20 Hz, the data show anormally dispersive trend in which the phase velocityincreases with decreasing frequency. However, below5 Hz, the curves drop, indicating a limitation of thismethod in the lower frequency range. This is observedin the dispersion curves of all the measurements.

Fig. 5 Histograms of estimated Love wave phase velocitiesusing the SciPy ODR package for selected frequency bands:a 1.79 Hz, b 5.08 Hz, c 7.18 Hz, and d 14.35 Hz at sta-tion SWMHK. The bright bars represent the histogram of the

non-weighted velocity estimates and the darker bars indicatethe weighted estimates according to Eqs. 6 and 7. The dashedand solid curves give the best fitting Gaussian. The mode of theweighted distribution is shown as a vertical dotted line

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Fig. 6 Estimated a Love and b Rayleigh wave dispersion curves using the ROLODE method. The error bars represent the standarddeviations of each frequency band. The rectangular boxes give the frequency region where the inversion is applied

This limitation in the lower frequency range can beexplained by re-visiting the PSD of the rotational sen-sor in Fig. 4a. At about 5 Hz, the self-noise level ofthe blueSeis-3A is reached and therefore no rotationscan be recorded below that. This causes the drop in theestimated dispersion curves. Reasons could includeeither the lack of these lower frequencies in the noisespectrum of the city and/or the rotations are too smallto be recorded by the rotational sensor. In this con-text, one has to keep in mind that the rotational motionamplitudes are equal to the ground acceleration valuesscaled by the ground velocity (cf. Eq. 1). Exploiting

Fig. 7 Expected rotation rates at station SWMHK calculatedfrom a forward modelled Love wave dispersion curve and themeasured translational data using (1). The dashed line marks thesmallest rotation rates that can be recorded by the sensor. Thesevalues were extracted from an operating range diagram (ORD)

this relation, a rough estimate of the expected rotationrates can be calculated (Fig. 7). Therefore, a for-ward computation for the Love wave dispersion curveusing the derived velocity profile at station SWMHK

Fig. 8 Ellipticity curve for station SWMHK computed withGEOPSY (Wathelet et al. 2004; Wathelet 2008). Each individ-ual thin curve represents the computed H/V ratio for a singleselected time window. The solid black curve indicates the geo-metrically averaged ellipticity curve over all individual H/Vratios. The two dashed lines represent the H/V standard devia-tion. The gray vertical bars mark the estimated ellipticity peakand its error. The rectangular box gives the frequency regionwhere the inversion is applied

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Fig. 9 P- and S-wave velocity profiles for a three-layer inversion at station SWMHK using DINVER of GEOPSY (Wathelet 2008).Only Love and Rayleigh wave dispersion curves were used as an input. The shading gives the misfit of the computed models

(Fig. 10) was performed. The phase velocity valuestogether with the actual recorded translational data atthis station were inserted into (1) to obtain the theo-retical rotation rates. It can be seen that the rotationrates below 5 Hz are in the order of 10−8 to 10−9 andare therefore too small given the self-noise level of thesensor.

To complement the data in the lower frequencyrange and to enable an inversion to greater depth,the H/V curves are computed from the three transla-tional components using the GEOPSY (Wathelet et al.2004; Wathelet 2008) software package. The programdivides the data into small time windows, for whichthe H/V ratio is computed separately. For the windowselection, an anti-trigger algorithm is implementedwith the objective to keep the most stationary partsof ambient vibrations and to avoid the transients, asexplained in more detail by Bard et al. (2008). As afinal step, an average over all single H/V ratios is com-puted. Figure 8 shows the ellipticity curve for station

SWMHK, which exhibits a pronounced peak at about2.5 Hz.

For the following joint inversion of a 1D groundvelocity profile, the appropriate frequency range ofthe input data has to be selected, marked by the blackboxes in Figs. 6 and 8. For the inversion at stationSWMHK, the input consists of the H/V ellipticity esti-mates between 1 and 10 Hz, as well as the derivedLove and Rayleigh wave dispersion curves. In case ofthe dispersion curves, normal dispersion is assumed,restricting us to use the data in the frequency range of5–20 Hz. In the next step, the number of subsurfacelayers to be inverted for has to be defined. The neigh-borhood algorithm of the program then generates dif-ferent ground models and computes the correspondingdispersion and H/V curves for each of those models.The comparison of the computation results with themeasured dispersion and ellipticity curves provides amisfit value that indicates how far the generated modelis from the data fit (Wathelet et al. 2004). In general,

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a velocity model with a low misfit value is desired;however, overfitting of the data has to be avoided.Increasing the number of parameters for the inversionmost likely decreases the misfit because of the higherdegree of freedom (DOF). Several tests with a differ-ent number of layers showed that the most significantreduction in the misfit can be achieved when increas-ing the number of model layers from 2 to 3. Becauseof that and in order to avoid overfitting of the data, athree-layer model for the inversion was chosen.

As part of the inversion, the linkage between thedifferent free parameters (vp, vs , density, and Poisson’sratio) has to be chosen. While Love waves consistof multiple reflected SH waves only, Rayleigh wavesare a combination of P and SV waves. Because ofthat, the analysis of these surface waves providesmore information about the S- rather than the P-wave.Therefore, the P-wave velocity model was linked tothe S-wave model during the inversion by Poisson’sratios between 0.2 and 0.5, which includes the typicalvalues for soil and sedimentary rocks (Gercek 2007).

The results for a three-layer inversion at stationSWMHK, using only Love and Rayleigh wave disper-sion curves as an input, are shown in Fig. 9. Due to thelimitation of rotational motion in the lower frequencyrange, the inversion results are only sensitive to about30 m depth. The velocity steps in the S-wave profileare well constrained, with the upper one at about 4 mdepth and the second one at 14–16 m. Compared withthis, the P-wave velocities are widely spread, eventhough the P-wave model was linked to the S-wavemodel. The reason for this is the large variance of theother free parameters due to the fact that there are lessinformation on the P-wave.

In order to get more information about deeper struc-tures, the dispersion curves are complemented withthe H/V ratios, which provide data to a lower fre-quency range. All input data are inverted with a weightof 1. Figure 10a gives the preferred P- and S-wavevelocity model at station SWMHK for a three-layerinversion. There are two apparent velocity steps vis-ible. Both velocity steps are shifted to greater depth,

Fig. 10 a Resulting three-layer P- and S-wave velocity pro-files at station SWMHK using DINVER of GEOPSY (Wathelet2008). For the inversion, Love and Rayleigh wave dispersioncurves, together with H/V ratios, were used with a weight of 1.

The shading gives the misfit of the computed models. b Litho-logic profile estimated from borehole data during the GeoPotproject of TUM (TUM 2018). The groundwater table is markedby the triangle

J Seismol (2021) 25:103–114 111

compared with the model in Fig. 9. Furthermore,the resolution of the P-wave profile increased due tothe additional information from the Rayleigh waveellipticity curve. Adding more layers to the inversionresults in thin upper layers; however, the main velocitycontrasts remain at the same depth range.

In the next step, the velocity profiles are comparedwith lithologic profiles to identify any correlationbetween the wave velocity and the geology. The litho-logic profiles presented in Figs. 10b and 11b wereextracted at the exact measurement locations fromthe geologic 3D model of Munich, derived duringthe GeoPot project (TUM 2018). The 3D model wasconstructed through interpolation of borehole data.Therefore, the lithologic profiles presented here areinterpolated and could slightly deviate from the realstructure. However, we assume that the deviation issmall, since the borehole data are very dense withinMunich. The distance between the closest boreholesand the stations SWMHK and BRUD is less than

100 m. Comparing the velocity profile of stationSWMHK with the geology (Fig. 10), it is apparentthat the upper velocity step at 8–10 m depth coin-cides with the change in lithology from sand to clay.In addition, the groundwater table also occurs at thisdepth range, which could influence the wave velocity.The second velocity contrast at 35–45 m depth coin-cides with a 10-m-thick sandstone layer. This indicatesa correlation between the change in lithology and theincrease in wave speed, while the very thin sandstonelayers cannot be detected because of the decreasingresolution with depth.

Similar correlations can be found for the other sta-tions. As a different example, the inversion results ofstation BRUD are shown in Fig. 11. Again, the P- andS-wave velocity profiles for the three-layer inversioncompared with the 100 m deep lithologic profile esti-mated during the GeoPot project are displayed. Theupper velocity increase occurs at 4–6 m depth, whichcoincides with the groundwater level at 5 m depth and

Fig. 11 a Resulting three-layer P- and S-wave velocity pro-files at station BRUD using DINVER of GEOPSY ((Wathelet2008)). For the inversion Love and Rayleigh wave dispersioncurves, together with H/V ratios, were used with a weight of 1.

The shading gives the misfit of the computed models. b Litho-logic profile estimated from borehole data during the GeoPotproject of TUM (TUM 2018). The groundwater table is markedby the triangle

J Seismol (2021) 25:103–114112

the transition from gravel to sand. Also for locationBRUD, as it is for station SWMHK, the velocity con-trast might either reflect the presence of groundwaterand/or the change in lithology. The second increase invelocity at 25–30 m depth lies in the range of the upperedge of the sandstone layer at 30 m depth. Therefore,the material change from clay to sand influences thewave speed. The sandstone lens at 50 m depth can-not be detected even when the number of layers inthe inversion is increased because it is too thin for theresolution at this depth.

5 Conclusion

The objective of this study was to test a new single-station technique for seismic microzonation in orderto improve the resolution of the resulting 1D velocitymodels. The single-station approach using a Tril-lium Compact 120s seismometer and the blueSeis-3Arotational sensor makes measurements very simplein terms of logistics compared with an array setup,especially when working in an urban area. The six-component data allow the computation of Love andRayleigh wave dispersion curves. The limitation ofrotational motion in the lower frequency range (< 5Hz), which appears to be a combination of sensorself noise and reduced rotational noise amplitudes, canbe resolved by combining the dispersion curves withH/V ratios. The most reliable P- and S-wave velocityprofiles are obtained by constraining the inversion toa three-layer model. Increasing the number of layersresolves more velocity steps close to the surface; how-ever, the misfit value does not significantly decrease,which could be an indication for overfitting the data.As an application, the resulting 1D velocity profileswill be used in future studies to estimate the localshaking characteristics in Munich.

In general, the velocity models show a correlationto the lithologic profiles that were derived during theGeoPot project. Especially, layers close to the surfaceand the upper groundwater table could be identified.

The results have implications for any situations inwhich (1) near-surface velocity structures are soughtand (2) multi-station networks are difficult or impos-sible to implement. This may happen in urban envi-ronments, at volcanoes, at the ocean bottom, or onplanetary objects.

Acknowledgments The authors would like to thank the com-pany iXblue for the cooperation in developing a portable, broad-band rotation sensor. Thanks to SWM (Stadtwerke Munchen)for providing access to the site of the geothermal power plantin order to conduct our measurements. The authors thank thereviewer Johana Brokesova, who helped to improve this paperwith useful comments.

Funding information Open Access funding provided by Pro-jekt DEAL. The authors received the support from the researchproject SEIGER (Project. no. 03EE4003G), funded by the Ger-man Federal Ministry of Economics and Energy (BMWi) andthe research institute Julich (PTJ). HI received support from theERC-Adv Grant ROMY (Project. no. 339991).

Open Access This article is licensed under a Creative Com-mons Attribution 4.0 International License, which permitsuse, sharing, adaptation, distribution and reproduction in anymedium or format, as long as you give appropriate credit tothe original author(s) and the source, provide a link to the Cre-ative Commons licence, and indicate if changes were made. Theimages or other third party material in this article are includedin the article’s Creative Commons licence, unless indicated oth-erwise in a credit line to the material. If material is not includedin the article’s Creative Commons licence and your intended useis not permitted by statutory regulation or exceeds the permit-ted use, you will need to obtain permission directly from thecopyright holder. To view a copy of this licence, visit http://creativecommonshorg/licenses/by/4.0/.

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