Magnetic and seismic reflection study of Lake Cheko, a possible impact crater for the 1908 Tunguska Event



[1] A major explosion occurred on 30 June 1908 in the Tunguska region of Siberia, causing the destruction of over 2,000 km2 of taiga; pressure and seismic waves detected as far as 1,000 km away; bright luminescence in the night skies of Northern Europe and Central Asia; and other unusual phenomena. This “Tunguska Event” is probably related to the impact with the Earth of a cosmic body that exploded about 5–10 km above ground, releasing in the atmosphere 10–15 Mton of energy. Fragments of the impacting body have never been found, and its nature (comet or asteroid) is still a matter of debate. We report here results from a magnetic and seismic reflection study of a small (∼500 m diameter) lake, Lake Cheko, located about 8 km NW of the inferred explosion epicenter, that was proposed to be an impact crater left by a fragment of the Tunguska Cosmic Body. Seismic reflection and magnetic data revealed a P wave velocity/magnetic anomaly close to the lake center, about 10 m below the lake floor; this anomaly is compatible with the presence of a buried stony object and supports the impact crater origin for Lake Cheko.

1. Introduction

[2] Unusual phenomena were detected on 30 June 1908 over Northern Europe and Central Asia. They included seismic and pressure waves, recorded at several observatories; bright luminescence in the night skies (in London, it was possible to read the newspaper at midnight of the same day without artificial lights); anomalous optical phenomena in the atmosphere, such as massive glowing silvery clouds, brilliant colorful sunsets, etc. [Busch, 1908; Zotkin, 1961; Vasilyev et al., 1965].

[3] These phenomena were later interpreted as being caused by the explosion of a cosmic body in a remote region of the Central Siberia, close to the river Podkamennaya Tunguska, where a number of eyewitness observed a huge fireball crossing the sky from the SE. This is the so-called “Tunguska Event” (TE), an explosion that released from 10 to 15 Megatons of energy in the atmosphere, and is considered to be the major event of this kind in historical times.

[4] Several expeditions followed the first, the earliest led by Kulik in the late twenties and thirties. Kulik identified the epicenter of the explosion in a heavily forested area from the radial distribution of flattened trees. He also found that directly below the explosion, many trees were left standing, although deprived of their branches, and partially burned (the so-called “telegraph poles”). Kulik concluded that he had discovered the remains of a large impact crater now hidden by a swamp (Figure 1), and a number of secondary bowl-shaped holes of different sizes (from a few meters to tens of meters in size, less than a few meters deep) covered by peat bogs. This pattern could have been caused by a meteorite that fell in a swarm of separate fragments [Kulik, 1933, 1940]. Other authors questioned this interpretation, suggesting that the circular features observed in the epicenter area were not necessarily related to any extraterrestrial impacts, but probably to seasonal thawing and freezing of the ground [Krinov, 1949]. All attempts at finding macro-remnants of the cosmic body, the “Tunguska Cosmic Body,” as it was called subsequently, by digging into these circular depressions were unsuccessful; therefore, the hypothesis of an impact with the ground was abandoned. Subsequent expeditions have been thus devoted mainly to the study of the tree patterns in the devastated taiga and to the search for micro-particles of the cosmic body, under the assumption that it exploded from 5 to 10 km above the ground.

Figure 1.

(left) Landsat image of the Tunguska area with indicated the pattern of trees flattened after the 1908 explosion and the inferred epicenter [Longo et al., 2005]. Yellow box indicates location of topographic map. (right) Topographic map of the epicenter region. Lake Cheko and the southern and northern swamps are indicated, as well as the most probable trajectory of the cosmic body.

[5] Geochemical markers of a cosmic impact were searched for within different potential “reservoirs” in the Tunguska region. Small iridium anomalies and hydrogen, carbon and nitrogen isotopic compositions similar to those of C-1 and CM carbonaceous chondrites, were found in Tunguska peat layers dating from the TE [Kolesnikov et al., 1999; Hou et al., 2004]. Moreover, a concentration of microparticles of inferred cosmic origin was found in tree resins dating from the TE [Serra et al., 1994; Longo et al., 1994]. Although these data are compatible with the hypothesis of a cosmic body impact, they are by no means conclusive.

[6] A geological/geophysical study of a small lake (Lake Cheko) was carried out during an Italian expedition to Tunguska in July 1999 (Tunguska99). The lake was considered a promising target because it is located very close (about 8 km NW) to the inferred TE epicenter (Figure 1). The objective of the study was to search the lake deposits for possible geochemical/sedimentological markers of the TE. During this work, a second objective arose: to test the idea that the lake might fill an impact crater. Analysis of sediment samples collected from the lake floor indicate that the formation of Lake Cheko is as old as the TE, and its morphology (Figure 2) and sediment infill suggest that it could have formed as a consequence of an extraterrestrial impact [Gasperini et al., 2007, 2008, 2009]. However, this hypothesis was questioned on the basis of theoretical arguments [Collins et al., 2008].

Figure 2.

Morphobathymetric map of the Lake Cheko obtained by Tunguska99 survey data over an aerial photograph collected during TUNGUSKA99 expedition. Note the funnel-like shape morphology, not typical of Siberian thermokarst lakes. The small prograding delta generated by the inflowing River Kimchu is also visible in the SW shore.

[7] Results obtained from the study of Lake Cheko [Gasperini et al., 2007, 2009] can be summarized as follows:

[8] 1) geophysical data show that morphology and seismostratigraphy of Lake Cheko are peculiar, and indicate a recent formation; two seismic units were identified and correlated to a sediment core collected close to the lake center;

[9] 2) based on 137Cs and 210Pb, the time of the TE corresponds to the transition from a finely laminated (upper) sequence, down to about 80 cm of depth in the core, to a chaotic unit observed below about 100 cm from the lake floor;

[10] 3) the post-TE sequence, from ∼80 cm to the top, consists of laminated fine-grained, clay-rich sediment containing abundant aquatic plants remains. This upper sequence accumulated at a rate of about 1 cm/year by quiet deposition in a body of water similar to the present-day Lake Cheko;

[11] 4) the lower, pre-TE (deeper than ∼100 cm) portion of core TG-22 consists of non-laminated sandy mud, coarser and poorer in organic matter than the post-TE upper deposits. In contrast to the upper section, it contains no aquatic plant remains.

[12] 5) These observations suggest that Lake Cheko did not exist when the lower pre-TE sequence was deposited. An interval of transition between the upper post-TE and the lower pre-TE sections, consisting of compact sandy mud deposits, lies in the 80–100 cm depth interval.

[13] These observations indicate that Lake Cheko formed at about the time of the TE. This could either be considered a coincidence or it implies a cause-and-effect relationship between the two phenomena.

[14] If Lake Cheko is an impact crater, its shape and size might have been strongly affected by the unusual nature of the target (swampy and with permafrost), and modified immediately after the impact; for this reason, standard reconstructions of the nature/size of the impacting body based on crater dimensions are highly uncertain.

[15] Most of the theoretical analogue and numerical modeling devoted to explaining the TE, including that of Artemieva and Shuvalov [2007], suggest that the Tunguska body disintegrated and vaporized 5–10 km above ground, with broad dispersion of the resulting debris/gaseous jet. However, these models do not exclude the possibility that one or more fragments survived the entry process and hit the ground in the vicinity of the explosion.

[16] A prominent seismic reflector (Reflector-T), identified ∼10 m below the deepest part of Lake Cheko, was described as a possible indicator of the presence of the impactor, or of a consolidated layer caused by impact-related overpressure within the substratum. In order to verify the nature of this anomaly, we collected a new set of magnetic profiles (Figure 3, right) and re-processed over 30 single-channel seismic reflection lines collected during Tunguska99 (Figure 3, left). The results are presented here.

Figure 3.

(left) Grid of seismic reflection lines collected during the 1999 from Lake Cheko. (right) Magnetic profiles acquired in the 2008 expedition. Black thick line indicates position of magnetic profile shown in Figure 8.

2. Methods

[17] A close-spaced grid of seismic profiles was collected during the 1999 expedition, using a DataSonics Bubble-Pulser system. The seismic source consisted of an electromagnetic transducer generating narrow band, 400 Hz pulses, at 200 J of energy. The data were recorded employing a 7 m long, single-channel, 16 elements streamer, connected to an analog amplifier/filtering unit. Data were digitally sampled using the ISMAR seismic acquisition software SeisAcqon a laptop PC with 16-bit of resolution and 1 msec of sampling rate. Positioning during data acquisition was controlled with a DGPS receiver, with an accuracy of ± l m. Seismic reflection data were constant-velocity time-migrated using Seismic Unix [Stockwell, 1997]. Final processing and interpretation of seismic section were carried out using SeisPrho [Gasperini and Stanghellini, 2009].

[18] The high resolution magnetic data from Lake Cheko were collected in 2009, using a GEM Overhauser magnetometer installed on a completely amagnetic rubber rowboat. The magnetometer was interfaced with a DGPS receiver for positioning. Magnetic data were sampled along the acquisition lines at the rate of 1 Hz, corresponding approximately to 1 m. During the survey 37,841 readings were collected, over a total distance of 32,495 m.

[19] The entire lake surface was covered by a grid of 95 N-S oriented parallel acquisition lines spaced ≈10 m apart (Figure 3). Three orthogonal and oblique tie lines were collected to evaluate possible cross over errors. After standard processing, magnetic data collected over the lake show an anomaly pattern ranging from −310 to 203 nT. The geometry of the planned survey and the high density distribution of the acquired track lines provided the resolution needed to resolve the high frequency components of the magnetic anomaly field, which could be correlated with the lake structure and the supposed buried bodies.

[20] The contributions of the diurnal variation and transient events were subtracted from the raw data using records from two Russian geomagnetic observatories, Irkutsk and Novosibirsk (data from INTERMAGNET). Both observatories showed maximum variations of about 40 nT (i.e., −14/26 nT from Irkutsk observatory), indicating that magnetic storms or other strong perturbations of the field did not occur during the survey. The magnetic anomaly field was computed using the coherent magnetic reference field model (IGRF-09, IAGA 2009). A de-spiking procedure and statistical leveling were applied to the data set to remove crossover errors between survey lines (we estimated an overall cross- over error of about 40 nT). Inaccurate positioning effects, such as lag and heading errors, were estimated and removed from the raw data. Finally, a micro-leveling technique (de-corrugation filter in the Fourier domain) was applied to remove residual high frequency noise. The processed data were mapped by using a grid cell size of 10 m.

3. Results

3.1. Seismic Reflection Profiles

[21] A first analysis of the seismic reflection profiles suggested the presence of parallel sedimentary layers draping the lake-bottom morphology (Figure 4); a more careful analysis, indicated that most of the visible reflectors are not real physical discontinuities at depth, but peg-legs (short period multiples) due to the presence of a major unconformity laying from 1 to 2 m below the lake bottom (Figure 4). These artifacts disappear after application of predictive deconvolution filters (Figure 5).

Figure 4.

(top) E-W oriented, unprocessed seismic reflection profile BP-26 crossing the lake S slope, the delta, and continuing upstream the Kimchu River. (bottom) Interpretation line drawing of the profile, with the main morphologic/stratigraphic features indicated (see text for details).

Figure 5.

N-S oriented, time-migrated seismic reflection profile BP-22 across the lake center. Note the absence of coherent reflectors 10 msec. below the lake's floor, and the chaotic pattern of the lower unit. A prominent reflector (T) a series of causing peg legs is visible at the lake center about 13 msec. TWT below the lake's floor, corresponding to ≈10 m of depth assuming a P wave velocity of 1600–1700 m/sec.

[22] Deconvolved seismic section were subsequently time-migrated using a constant velocity function, because estimating velocities is not possible with this type of data. This implies that geometries we observe in the section are not necessary real, depending on the choice of the velocity function, which is unknown. However, all the seismic lines crossing the lake center displayed a single flat strong reflector, that appears to be caused by a localized discontinuity (Reflector-T,Figure 5). Using all available profiles we compiled the map shown in Figure 6, that enabled us to determine the lateral extent of the density/velocity anomaly at the lake center. In Figure 6(left) we observe the top of Reflector-T obtained by manual picking of migrated seismic sections. Reflector-T is visible in a 70–80 m wide area around the lake center, at a depth ranging from 10 to 15 msec (≈10 m) below the lake bottom. However, differences in depth are not well constrained, since the P wave velocity function is unknown. The map shown inFigure 6(right) was obtained by sampling the entire seismic profile data set at the constant depth of −80 msec, averaging the absolute value of the reflection amplitude in a 10 msec window. Data were subsequently gridded using a nearest-neighbor algorithm. This semiautomatic procedure allowed us to evaluate the reflected energy, which, according to theFigure 6 map, appears concentrated at the lake center.

Figure 6.

(left) Isochronopach map of Reflector-T. Color scale indicates the depth in msec (two way travel-time) below the surface. (right) Time-slice map obtained by the entire seismic reflection data set for the 85 msec. TWT level; color scale indicates the amplitude of seismic signal normalized between +1.5 and −1.5. In both figures bathymetric contours (5 m spaced) are superimposed.

[23] Seismic reflection profile BP-26 (Figure 4) extends ≈350 m upstream of the inflowing river and imaged the upper part of the alluvial sedimentary sequence. Assuming a minimum P wave velocity of 1600 m/sec within the sediments, we estimated a minimum thickness of about 25 m for the fluvial deposits, and of about 15 m for the lacustrine wedge across its maximum vertical section. Seismic section BP-26 (Figure 4) shows clear differences between seismic facies in the river and lake domains: the sedimentary wedge that enters the lake at the mouth of the inflowing river appears acoustically transparent, i.e., relatively homogeneous, and shows offlapping reflectors terminating sharply over the continuous, high-amplitude horizon that marks the lake bottom. Moving upstream along the inflowing river axis (Figure 4), the fluvial deposits are well layered and less homogeneous, showing the typical pattern of fluvial valley infilling, caused by lateral migration of meanders; a sharp unconformity separates these two domains (R1, Figure 4). We interpreted this unconformity as marking the onset of a lacustrine delta over older, alluvial/fluvial deposits. Interestingly, the lacustrine part of BP-26 does not show any reflector across the lake axis. This confirms that the presence of Reflector-T is limited to the lake center.

3.2. Magnetic Data

[24] After processing, the magnetic data were used to construct maps of the Reduction To the Pole (RTP) magnetic anomaly, apparent magnetization, and 3D analytic signal (Figures 7a–7c, respectively).

Figure 7.

(a) Reduced to the Pole (RTP) anomaly field map of Lake Cheko. Reduction was applied using local declination and inclination of magnetic field. A clear NW-SE decreasing trend of anomaly is observable. RTP elaboration highlights local high frequency anomalies in particular close to the area of maximum depth. (b) Map of apparent magnetization. Recovered model was derived by an inversion of magnetic anomaly data set. Very short lateral variations of magnetization patter are observed in the central of the lake close to Reflector-T ofFigures 5 and 6. (c) Map of 3D analytic signal. Horizontal and vertical derivatives of the magnetic data were computed in the Fourier domain applying the Hilbert transform. Circular pattern of the analytic signal (yellow dashed circle) suggests the existence of local abrupt variation of the magnetization below the lake. This feature is also confirmed by the data coming from the inverse approach.

[25] Figure 7ashows that the SE portion of the lake is dominated by a high positive magnetic anomaly peak, about 100 m wide; it is probably associated with a small positive magnetic source located below the lake. Several high-frequency anomalies correlated with bathymetric features and other targets located near the shoreline are also visible. The high frequency magnetic components are superimposed on a clear SE-NW long-wavelength trend, that persists after the IGRF-model correction, and is probably due to a regional effect. The dipolar shape of the magnetic anomaly field has been removed applying the RTP procedure, knowing the direction of the Magnetic Field vector for the study area (Inclination 78.6° and Declination −1.36). This FFT-based procedure generated a northward shift of the anomaly with a recalculation of the field amplitude.

[26] The reduced anomaly ranges from −358 to 127 nT (Figure 7a), and the negative pattern can be interpreted as correlated to a strong remnant magnetization contribution. The Koenigsberger ratio computed for a rock sample collected from NE portion of the lake is about 39, confirming the strong remnant contribution of the magnetization beneath Lake Cheko.

[27] The apparent magnetization map (Figure 7b) shows again the NW-SE regional trend and the high frequency contributions to the magnetic field. A 2D distribution of apparent magnetization was achieved by inverting the total intensity magnetic anomaly field. This interpretative tool maps the lateral magnetization of the crust and aids the determination of the geographic position of buried magnetic sources. A synthetic prismatic model was carried out knowing the bathymetry of the lake (0.5 m grid spacing). Inversion was constrained using a prismatic mesh having the bathymetry surface as a top and an average thickness of 100 m. Synthetic magnetic anomaly values were computed employing a prismatic mesh as magnetic sources with uniform magnetization. The sensitivity matrix was evaluated followingBhattacharyya [1964], who derived the analytic relationship for the magnetic field generated by a rectangular prism. The inverse algorithm computes and optimizes the misfit between the synthetic and observed magnetic anomaly obtaining a vector of magnetization for the region of interest [Caratori Tontini et al., 2006]. In this case, the mesh was created using a matrix of 50 × 50 cells, inverting a set of 16,500 real magnetic anomaly values. The recovered model has a grid-cell resolution of 10 m, and represents the apparent magnetization distribution confined in the upper 100 m of substratum. The computed magnetization pattern shows a relatively low amplitude, ranging between −8 to 6 A/m. Concerning the spatial distribution of the magnetization, the southern sector of the lake is characterized by a positive magnetized body, while the central portion by a local negative peak (−4 A/m) close to the point of maximum depth (Figure 7b). This pattern indicates a complex distribution of the magnetization within the lake, correlated mostly to bodies with low magnetization. We also note that the distribution of magnetic anomalies in the lake is not correlated to its morphology, as shown, for example, in the Figure 8 (top) profile. In fact, we estimated the magnetic topographic effect performing a direct synthetic computation using the prismatic framework also employed for the inversion. A magnetic anomaly model was thus obtained considering a constant magnetization of 1 A/m. Note that the topographic correction is independent from the value of magnetization used for its computation.

Figure 8.

(top) Magnetic profile crossing the lake center (see Figure 3 for location). Red line: observed magnetic anomaly; black line: magnetic profile after topographic effect correction (see text for details). (bottom) Apparent magnetization (red line) versus lake bottom topographic profile (black line).

[28] From the apparent magnetization profile of Figure 8 (bottom), we see that the central portion of the lake is characterized by a small and spatially limited (about 50–80 m) variation of the magnetization properties. This pattern, not dependent on the lake's morphology, is not visible in other sectors of the study area.

[29] We interpret this anomaly as caused by a body with different magnetic properties relative to the surroundings. This pattern is also confirmed in the map of the 3D analytic signal (Figure 7c), calculated as a combination of the horizontal and vertical gradients of the magnetic anomaly [Nabighian, 1972]. As well known, the distribution of the analytic signal amplitude forms a bell-shaped function with its maximum on the lateral boundaries of the magnetic structure, and it is used to detect the lateral extent of magnetic sources. In case of an area with high contribution from remnant magnetization, as in the Lake Cheko, the edge estimate calculated using the 3D analytic signal is preferable to the classic Horizontal Gradient Magnitude application [Li, 2006].

[30] The high frequency noise intrinsically generated by the analytic signal computation has been attenuated through an upward continuation of the analytical signal data to 10 m. The distribution of the analytic signal (Figure 7c) correlated to the magnetic anomaly of Lake Cheko (Figure 7a) shows a peculiar pattern with a well constrained semicircular area located close to the center of the lake (Figure 7c) reflecting a strong lateral variation of magnetic properties and the position of an anomalous body (or a cluster of bodies).

4. Discussion

[31] The inverted cone morphology of the lake is very different from that of typical Siberian lakes, and difficult to explain by “normal” erosion/deposition processes from the small River Kimchu in a region with low-topographic gradients [Gasperini et al., 2007]. Considering secondary processes, such as post-impact dewatering and degassing in a “wet” swampy target with permafrost, Lake Cheko's morphology is compatible with an impact origin. If Lake Cheko's formation was caused by an extraterrestrial impact, its effects should have been enhanced by the peculiar nature of the target, a swampy taiga with permafrost [Gasperini et al., 2007, 2008]. In this scenario, a “soft” impact may have occurred, where the projectile could have penetrated into the ground before causing the explosion that formed the crater. A possible consequence could have been the preservation of the projectile, although several lines of evidence (including our magnetic anomaly maps) exclude that it was an iron-rich object.

[32] The newly collected magnetic data and reprocessed seismic reflection profiles acquired during the Tunguska99 expedition indicate that a magnetic/seismic anomaly, located about 10 m below the lake bottom and at its center, does exist.

[33] The general character of magnetic anomalies associated with impact craters could be complex, as a consequence of the large variation in the magnetic properties of rocks [Pilkington and Grieve, 1992]. The typical signature and dominant effect observed over craters is a magnetic low, due to a reduction in susceptibility [cf. Dabizha and Fedynsky, 1975; Clark, 1983] ranging in amplitude from tens to a few hundred nanotesla. Magnetic properties of target rocks can be modified by hypervelocity impacts as a consequence of shock waves [e.g., Gattacceca et al., 2006, and references therein]. However, if Lake Cheko is an impact crater, the speed and kinetic energy of the projectile should have been relatively low, for two main reasons: 1) the elliptical shape of the lake, that is obtained only in case of low-velocity impact; 2) the limited side-effects observed on the area surrounding the lake [seeGasperini et al., 2007]. For these reasons, the magnetic signatures observed in “typical” impact craters could be not present in the Lake Cheko case.

[34] Magnetic data reveals a peculiar pattern of the magnetic properties of Lake Cheko. Spectral behavior of the anomaly field is dominated mainly by the high-frequency contribution; this a direct consequence of the line spacing (few meters apart). The short wavelength of the prominent magnetic anomalies localized in the lake center indicates a contrast in the magnetization properties of shallowest portion of the substratum. Both analytic signal and apparent magnetization maps show a minimum around the lake center, interrupted only by two small peaks (Figure 7b). Derivative analysis has qualitatively identified an anomalous distribution of the magnetized source in the lake substratum, particularly in the area of maximum depth. The local anomaly of −4 A/m (Figure 7b) in the lake center could be due to the presence of a rocky object having a low magnetic contrast with the overburden alluvial sediments that fill the River Kimchu valley down to a level not identified by our seismic reflection profiles, but greater than several tens of meters, the maximum penetration of the seismic signal in the area. In fact, this localized minimum appears compatible with a small or almost punctiform source.

[35] Although our constraints are relatively poor, we can speculate on nature and dimension of the projectile. If we assume the impactor was an asteroid, the size of low magnetized body should have a diameter smaller than 20 m, but this value may be overestimated because of the resolution of the recovered model. The adopted inverse procedure does not allows to accurately quantify depth, position and vertical extent of the magnetic source.

[36] No data are available about P wave seismic velocities in the Lake Cheko sedimentary sequence; thus, estimating the density/velocity contrast (i.e., the acoustic impedance contrast) marked by Reflector-T is not possible from our seismic reflection data. However, analysis of the entire data set, including constant-velocity, time-migrated sections covering the entire lake surface (Figure 3) indicates that Reflector-T is visible in all the sections crossing the lake center; this suggest that it is a real feature and not an artifact caused by the peculiar lake morphology.

[37] In the light of our findings, we can re-evaluate the earliestKulik [1933, 1940]reports, that suggested a multiple impact scenario. In fact, if our hypothesis of soft deep-penetrating impact is correct, we might find other fragments of the Tunguska Cosmic Body in the epicenter area. The reason why neither Kulik's nor subsequent explorations were able to find them could be due to the nature of the target, that may have buried the cosmic body fragments after their penetration in the soft and wet substratum.

[38] Results from our survey indicate that the magnetic contrast between the buried object and the overburden is weak. Accordingly, the probability of finding further fragments of the Tunguska Cosmic Body possibly buried below the swampy soil, is very low.

5. Conclusion

[39] The extraterrestrial body that possibly formed Lake Cheko (Central Siberia) in 1908 might have been a fragment of the main Tunguska Cosmic Body that exploded in the atmosphere 5–10 km above ground. The prominent reflector (Reflector-T) observed in seismic reflection profiles ∼10 m below the bottom at the center of the lake indicates a sharp density/velocity contrast, compatible with either the presence of a fragment of the body, or of material compacted by the impact. Newly collected high-resolution magnetic profiles from the lake surface indicate that this seismic feature corresponds to a localized magnetic anomaly at the lake center. These mutually independent and consistent observations are compatible with the presence of an asteroid or a compacted and heated layer that could have been generated during the impact and is now buried below ≈10 m of alluvial/lacustrine deposits at the lake center. The observed magnetic contrast between the projectile and the overburden is weak, suggesting a rocky nature for the Tunguska Cosmic Body.


[40] We thanks all the participants to the Tunguska99 expedition, in particular G. Longo, who led the expedition, and those who helped in various forms during its preparation. We also thank Thorsten Becker, editor of G-Cubed, Randy Keller, and Enrico Bonatti for their comments and suggestions, which greatly improved the quality of the manuscript. Luigi Vigliotti performed the estimate of the Koenigsberger ratio on a rock sample collected close to the lake shore.