2. Observation Site and Measurements

Transcription

1 1 Abstract Thermally induced fractures or thermal cracks, and pronounced seismic events as snoquakes ere studied at Mizuho Station, East Antarctica from June 1976 to January Fractures due to thermal stress ere found in the uppermost 5 cm of the sno cover as a result of sno temperature decrease at the surface, and fracture under tensile thermal stress occurs hen the stress exceeds the tensile strength of sno. Once thermal cracks are initiated, stress concentration occurs at tips of cracks, and fractures occur more easily in the smaller thermal stress than the tensile strength of sno and accompany more easily pronounced seismic events, that is, snoquake. Snoquakes occur during the decrease of temperature and then thermally induced strain rate corresponds to ductile fracture of sno. The individual snoquakes occur in the near surface and the epicenters of snoquak,es located by seismic observations are found near thermal cracks, hich indicates that snoquake is caused by the formation of cracks. The epicenters are not distributed in a ell-ordered sequence, thus the fractures of sno cover occur at random in the near surface hich is under the tensile stress during the decrease of sno temperatur,e.

2 2 1. Introduction Many thermal cracks exist on the glazed surface in the Antarctic ice sheet and pronounced seismic events as the so-called ice shocks ith loud sound have been experienced very often during the inter season. Thermal cracks are usually found on the glazed surface hich is distributed in the region here katabatic ind prevails and the glazed surface is related closely to the absence of sno accumulation or longterm hiatus in sno stratigraphy (WATANABE, 1978). SITHINBANK (1957) remarks that narro cracks in the surface sno of the Maudheim Ice Shelf are observed only during inter and suggests that they have resulted from thermal contraction. Hoever, physical processes of formation of thermal cracks are not studied ell in terms of the initiation of thermal cracks and the mechanical properties of sno. It is, therefore, very important to reveal characteristics of thermal cracks and their behavior. OMOTE et al. (1955) and HAMAGUCHI et al. (1977) studied the fracture of ice plate of the Lake Sua in central Japan. They considered that the phenomenon of ice shock might represent a model of seismic source and the plate tectonic theory, because the ice plate and the ater beneath it give a good model for lithosphere and asthenosphere of the earth. The ice faulting corresponds to the cataclysmic event due to the interaction of plate motions hich is thought to be the main cause of geophysical and geological processes of the earth's crust. NEAVE and SAVAGE (197) observed sarms of icequakes hich occurred in the Athabasca Glacier (52.2 N, W) to test a hypothesis that deep-focus earthquakes ere caused by creep-instability mechanisms. They concluded that all the events appeared to be originated from extensional faulting near the surface of the glacier and most of the icequakes occurred ithin the zone of marginal crevasses. The individual events in an icequake sarm ere distributed along a straight line of visible crevasse. Recently, KAMINUMA and TAKAHASHI (1975) observed snoquakes ith one vertical seismograph at Mizuho Station for a short period in 1973, aiming at finding the characteristics of earthquake through the phenomenon of snoquake activity. They found that the prolonged lo temperatures at night, especially hen the air temperature drops belo -35 C, caused pronounced seismic events as the results of sno contraction. Although these authors have studied ice shocks or snoquakes, there is no precise interpretation on the mechanism of ice shock or snoquake because of the lack of proper understanding of physical properties of the medium such as the ice plate or the sno cover. Giving an emphasis on the physical properties of polar sno and the physical processes of sno fracture, the present author investigated the thermally

3 Introduction 3 induced fractures and snoquake activities of polar sno cover at Mizuho Station, East Antarctica, in In this paper, the snoquakc is defined as the fracture of sno, hereas icequake is the fracture of ice. The present paper deals ith four aspects, i.e., the formation of thermal cracks and snoquakes in association ith characters of the sno temperature profiles, distribution of the: glazed surface and variation of idth of thermal crack, snoquake activities and mechanical properties of the sno cover in relation to thermally induced fractures.

4 4 2. Observation Site and Measurements From June 1976 to January 1977, the present author observed sno temperature profiles, change of idths of thermal cracks and snoquake activities by means of seismographs at Mizuho Station. The station is located at 7 42'S and 44 2'E about 28 km southeast of Syoa Station, 223 m in elevation, 21 m in ice thickness and the.annual mean air temperature of about -33 C (Fig. 1). The observational area (about 2 x 2 m) is in the lee of prevailing ind about 1 m east of Mizuho Station (Fig. 2). The observation sites for the idth of thermal cracks, a seismograph tripartite (vertical component) and the thermal crack observation area ere set in the observational area. A large glazed surface area surrounds Mizuho Station and the glazed surface sometimes lacks annual layers. The surface sno density is.35 to.45 g/cm 3 (WATANABE and YOSHIMURA, 1972). 6a s 1o s 5 YAMATO ll1's. _; t 25 6 E 35 E MIZUHO PLATEAU 4 E 45 E km Fig. I. Location of Mizuho Station (7 41'53 11 S, 44 19'54"E; 223 m above sea level; ice thickness 21 m).

5 Observation Site and Measurements 5 I :... stake farm 2 4 6m N.1 1: 5 I T. N. \j l1il NO Prevailing ind._. Mizuho Station 11 NO CD 3 Strain grid of 1-4 therma 1 crack '1' - fj" a Seismograph 'Y'-:V (Vertical component) 1_13 Artificial shot point - A-C Strain-meter Strain-meter Therma 1 crack observations area Fig. 2. Sketch map of observation site for the idth of thermal cracks (Nos. 1-4), a seismograph tripartite and the thermal crack observation area Sno temperature profiles Ten thermistors ere buried in the sno near No. 3 seismograph shon in Fig. 2 and continuous records ere obtained from May 26, 1976 to January 25,1977. Thermistors ere set at the surface (about 1 cm deep), and at depths of. 1,.2,.3,.5, 1, 2, 3, 5 and 1 m; sensors in the upper levels ere covered ith hite stainless steel tube to reduce radiation errors. The output of thermistors as continuously recorded by a 12-channel recorder and the overall accuracy of the measurements as ±.3 C. In the present paper, the sno surface temperature is defined as the sno temperature measured at a depth of about 1 cm Width of thermal cracks Many glazed surface areas ere found on the sno surface around Mizuho Station, and most of the thermal cracks ere developed on the glazed surface. The observation area of thermal cracks, hich is shon ith a hatched area in Fig. 2, as kept intact and the observation of patterns of thermal cracks has been carried out since July 197 (WATANABE and YOSHIMURA, 1972). To investigate the formation of thermal cracks and the opening and closing of thermal cracks, idths of thermal cracks ere measured once a day at four sites, here three of them (Nos. 2, 3 and 4) ere located near the seismographs and No. 1 as installed in the stake farm as shon in Fig. 2. The distance of to reference points across a crack as measured ith a vernier calliper ith the accuracy of measurements to the nearest 1/2 mm (Fig. 3a). The reference points ere made of stainless steel

6 6 Thermally Induced Fractures and Snoquakes of Polar Sno Cover -- a V, --.- LEAD CRACK N TUBE b r CRAC: CRACK (2) A B C CRACK (3) A llj C ol-\-1c CRAC 'ri - 7 D BA O 5cm Fig. 3. Method of measurement of distance beteen to reference points across a thermal crack (a); and configuration of four grids composed of four reference points (b). tube hich as tightly inserted into the holes in the surface sno layer. As illustrated in Fig. 3b four reference points of A, B, C and D ere prepared to form a square ith sides of about 4-5 cm across thermal crack at four sites (Nos. 1, 2, 3 and 4) as shon in Fig. 2. The distances beteen four reference points such as the sides of AB, BC, CD, DA, AC and BD ere measured by the vernier calliper and the reading of vernier calliper as corrected for the air temperature, that is, the corrected value of distance beteen to reference points as obtained, subtracting an appropriate temperature correction at C from the readings of the distance Snoquake activities Three electromagnetic seismographs (vertical component) of moving-coil type ere used to detect elastic aves of snoquakes. As illustrated in Fig. 4, the frequency response of seismograph ith the natural frequency of 1 Hz as measured on the shaking table, giving flat characteristics in the frequency range of 1-5 Hz. The seismographs ere installed in a sno pit at a depth of about 5 cm to reduce indgenerated noise; they ere in the distance of about 2 m to the east from the facilities of Mizuho Station here artificial ground noises, such as the noise of poer supply generator, originate. Hence, all the recording of seismographs installed in the sno pit as done to take advantage of the loer noise level. To determine the epicenters of snoquakes near the sno surface, the seismographs ere arrayed in a triangle (tripartite) ith the sides of 115, 175 and 133 m. Seismograph signals ere transmitted ith cables and recorded at Mizuho Station. The signals ere fed to an amplifier MTKV-1C => 1- ::J a.. <( FREQUENCY (Hz) 5 Fig. 4. Frequency response of seismograph (natural frequency 1 Hz) measured on the shaking table, in hich the response is uniform in the frequency range of l-5hz.

7 Observation Site and Measurements 7 and recorded on a portable data-recorder (TEAC, R 7A) ith a cassette tape at a speed of 4.76 cm/s. Playback of the cassette tape as carried out ith a four-channel precision tape recorder (Model SDR-83, Hikari Tsushinki Co., Ltd.). The playback speed as I/2th of the recording speed, using a four-penrecorder ith a.9 Hz high pass filter. The normalized overall frequency response of the recording and playback system is shon in Fig. 5, hich indicates the flat frequency response in the range of more than 5 Hz. Figure 6 shos an example of snoquake signals recorded ith the tripartite. Since three seismograph outputs and I-second time mark from a chronometer ere recorded simultaneously on the same tape, arrival time differences beteen seismographs ere measured precisely. The chronometer calibration as made ith the time signal of JJY at 12-hour to 6-day intervals. The I-second time marks ere used for correcting the very minor fluctuation in the paper speed of the penrecorder, hich gave a negligible correction. The observation of snoquake activities ith the seismographs and the recording system as carried out beteen June 1976 and January No natural earthquakes ere detected during this period, but very many sarm type snoquakes ere recorded. To determine the propagation velocity of longitudinal aves (V P ) in sno around Mizuho Station, the refraction shooting method as used to calculate V P from the travel-time curve as shon in Fig. 7. Three seismographs ere spaced at 2 m intervals FREQUENCY (Hz) 1 1 Fig. 5. Normalized overall frequency response of the recording and playback system. I Cl 5 S 3 I Ir Fig. 6. A record of snoquake signals from the three seismograph array. Numerals correspond to the signals from seismograph Nos. I, 2 and 3.

8 8 Thermally Induced Fractures and Snoquakes of Polar Sno Cover 1 MIZUHO STATION llj llj Fig. 7. DISTANCE IN METERS Travel-time curve for refraction at Mizuho Station. and elastic aves at the sno surface ere generated by the artificial shot ith a steel hammer at distances up to 2 m to the east from the end of the seismograph line near the seismograph site No. 3 in Fig. 2. Therefore, the velocity profile of longitudinal aves in the sno cover as determined from the travel-time curve. On the other hand, sno density of core samples at Mizuho Station as measured in detail by NARITA et al. (1978). The overall density-depth curve shos that near the sno surface the mean density is around.4 g/cm 3 and increases ith the depth, and it reaches.84 g/cm 3 at about 55 m. Taking this density profile into consideration, ISHIZAWA (1981) discussed the velocity profile of longitudinal ave don to 8 m at Mizuho Station here he carried out ave velocity observations in The travel-time curve obtained by the refraction shooting method as used to determine the location of each snoquake epicenter by an iterative least-square procedure from the arrival times of longitudinal aves. At first, an appropriate position of snoquake epicenter as assumed as the initial location; then the travel-time curve 111 SEISMOGRAPH o ARTIFICIAL SHOT POINT G) Fig. 8. 5m UNDETERMINED Calculated positions (hite circles) of artificial shots by means of an iterative least-square procedure from arrival times of P aves at each seismograph and positions of the artificial shots (black dots). Coordinates (X, Y ) indicate the initial location to start the iterative least-square procedure to determine the calculated positions; arros ith dotted line indicate the features of converging to the calculated positions. :3.

9 Observation Site and Measurements 9 beteen the assumed location and each seismograph site is calculated from the traveltime curve measured by the refraction shooting method, and the least-square procedure as iterated to determine the accurate snoquake epicenter. The accuracy of this procedure as estimated by comparing the calculated position of artificial shots from the arrival times of longitudinal aves detected at each seismograph ith the actual position of artificial shots. In Fig. 8, six artificial shots (1, 2, 3, 8, 9 and 1) on the sno surface are shon and these positions are directly measured ith reference to the seismograph sites. The artificial shots ere also used to check for polarity reversals both in recording and playback system. In general, the accuracy of position determined by means of the tripartite method is usually good ithin the array, but the accuracy deteriorates outside the array. As illustrated in Fig. 8, the calculated positions of artificial shots ithin the array are ithin about ± 1 m, including shot site 9 outside the array, though at shot site 1 the error is in the order of ±2 m. At shot site 3 outside the array, the calculated position as not obtained by means of an iterative least-square procedure, because the signals recorded at seismograph No. 3 ere very eak. Thus, it is considered that the position of snoquake epicenter ithin the array is determined ith an accuracy of the order of ± 1 m.

10 1 3. Temperature Variations in the Surface Sno Cover The snoquakes around Mizuho Station occurred hen the air temperature decreased (KAMINUMA and TAKAHASHI, 1975), consequently crackes in the surface sno layer ere formed, namely thermal cracks. Since the snoquake activities are closely associated ith the variations of sno temperature near the surface sno layer, temperature regime ill be examined. Figure 9 shos the mean daily sno temperature at the surface, and at depths of.1,.2,.3,.5, 1, 2, 3, 5 and 1 m for the period from June 1976 to January c =-::=::::======= =- -_-_-_ -_ -_-_- ::_--"' " -so -,ot _ ot Cr-- --================================================io = m=== m :, Fig. 9. Mean daily sno temperature at the surface,.1,.2,.3,.5, I, 2, 3;5 and 1 m. 2

11 Temperature Variations in the Surface Sno Cover 11 At the sno surface the annual temperature variation has the amplitude of about 4 degrees. During inter there are temperature fluctuations of several days ith the amplitude of about 2 degrees, hich as due to the influence of climatic disturbances such as cyclones penetrating into the inland. As illustrated in Fig. 9 the mean daily surface temperature indicates gradual arming at the end of inter around October and fluctuations become small during summer. To find the periodicity of the sno surface temperature fluctuations, a spectral analysis technique (I ABUCHI et al., 1978) based on the maximum entropy theory as applied to the hourly readings of surface sno temperatures. The poer spectrum shon in Fig. 1 indicates significant peaks at periods of 7.3, 3., 1. and.5 days. In this analysis, the annual cycle as not resolved from a ingle year's data, but the presence of annual cycle is recognizable from Fig. 9. To examine the propagation of temperature aves into the sno from the surface, a heat conduction equation ill be solved under a simple sinusoidal variation of surface temperature as a boundary condition (CARSLAW and JAEGER, 1959; PATERSON, 1969). The surface temperature is given by, T(O, t)= T + T s cos t, ( 1 ) here Tis temperature, t the time, T the mean annual temperature, T s the amplitude and /2-rr the frequency of the surface temperature change as already shon at periods of.5, 1., 3., 7.3 days and 1 year in Fig. 1. DEPTH = O cm I 3. I 1. I : -4 3: Fi'g. 1. PERIOD (days) Poer spectrum of hourly sno surface temperature at Mizuho Station. The temperature regime ithin a semi-infinite sno cover can be obtained by solving the folloing heat conduction equation: k at2 = at az 2 at ' ( 2 ) here k is the thermal diffusivity of sno and z the depth. The solution of eq. (2) for the boundary condition given by eq. (1) is:

12 12 Thermally Induced Fractures and Snoquakes of Polar Sno Cover This solution shos, at first, that any variations of surface temperature attenuate ith depth according to the factor of ( 3 ) Thus, the presence of the term -() in the exponent means that rapid temperature fluctuations at the surface are more quickly attenuated than sloer ones. In reality e find that diurnal temperature variations are attenuated to about 5% of their surface temperature at the depth of 5 cm, hile the annual cycle is attenuated to about 2.5% of its surface amplitude, the annual temperature ave ith the amplitude of.9 C, hen it reaches 1 m depth. Therefore, it is seen that at most depths the annual temperature ave dominates over other shorter period variations. Secondly, the speed of propagation of the temperature minimum or maximum is expressed as the phase term z(/2k) 1 12, hich has the effect that more rapid fluctuations are more rapidly transmitted. Thus, e find that, for example, at a depth of 1 m, the minimum of diurnal temperature variations occurs about one day after the minimum at the sno surface, hile the minimum of the annual cycle propagates to 1 m depth in a time of about 18 days. These effects of selective attenuation and phase delay can be seen clearly from Fig. 9. a' > < ::. z u ] :i:: 5 l- 5 1 '-- - s -'- o -----L---._ 4ō L ,o 1 SNOW TEMPERATURE ('C) Fig. 11. Monthly sno temperature profiles at Mizuho Station in Sno temperature profiles as a function of depth at the beginning of each month throughout the hole year are plotted in Fig The tautochrone of sno temperature profiles indicates rapid arming. at the beginning of summer and rapid cooling at the end of summer; this situation is also to be seen in Fig. 9. This is typical 'coreless inter' temperature pattern, hich is.cl characteristic feature in eather patterns in the interior of the Antarctic (LOEWE, 1969).

13 13 4. Characteristics of Thermal Cracks Most of the thermal cracks observed on the sno surface are located on the glazed surface hich is classified as the long-term hiatus form in surface features and is related closely to the absence of annual layers (WA TANABE, 1978). The glazed surface ith multi-yeared ice crust is distributed idely around Mizuho Station and developed on the upper part of sno mounds on the ice sheet surface here accumulated sno is scarcely found. Thermal cracks are usually visible on the glazed surface and exhibit polygonal patterns as shon in Fig. 12 and the cracks often exhibit parallel strips. Thermal cracks are also observed on the smooth surface ithout sastrugi ; in this case, thermal cracks are almost in the pattern of parallel strips. Most of the thermal cracks are narro in idth, less than several centimeters, but thermal cracks ider than about IO cm are frequently found. Figure 13 shos the vertical section of thermal crack in a trench all at Mizuho Station ; the maximum idth of the thermal crack is about IO cm and its depth belo the surface is about 2.5 m. In general, most of thermal cracks observed are narro, less than several centimeters in idth, and are as shallo as I min depth. It is likely that occurrence of narro thermal cracks in the surface sno layer Fig. 12. Glazed surface and polygonal pattern of thermal cracks near Mizuho Station.

14 14 Thermally Induced Fractures and Snoquakes of Polar Sno Cover Fig. 13. Vertical section of thermal crack in a trench all at Mizuho Station. The maximum idth is about IO cm and its depth is about 2.5 m belo the surface. as due to the result of thermal contraction hen the surface temperature decreased and these narro thermal cracks ill open and close according to sno temperature fluctuations. We ill describe in detail the characteristics of cracks of thermal origin in the folloing subsections Distribution of thermal cracks on the sno surface It as mentioned that thermal cracks observed are located on the glazed surfaces. Then, the areal distribution of glazed surfaces should be shon in order to kno the distribution of thermal cracks on sno surface. FUJIWARA and ENDO (1971) reported that along the traverse route of about 43 beteen Syoa Station and the South Pole in the glazed surfaces ere remarkably developed on the upper part of the mound formed on the katabatic slope beteen 7 and 72.5 S, hereas on the interior slope beteen 82 and 89 S the glazed surfaces ere also found on the top of undulations. On the other hand, WATANABE (1978) pointed out that the glazed surface as developed in a region here the surface elevation as beteen 18 and 32 m. It can be considered that the glazed surface is formed in a belt-shaped zone ith an interval of I -2 km along the direction of prevailing ind. The average idth of glazed surface in the direction normal to the prevailing ind seems to be a fe km, hile some of the most developed belts of glazed surface are a fe J O's km in idth. The occurrence of glazed surface becomes more often in the range of elevation from 25 to 31 m, and in the vicinity of the glazed surface in this area the surface is smooth and the patch-like glazed surfaces are seen. The glazed surface is defined as the surface feature in long-term hiatus form hich is related closely to the absence of sno accumulation in annual layers. Therefore, it should be expected that the glazed surface ith thermal cracks as shon in Fig. 12 ill be observed on the surface condition hich shos no sno accumulation. Figure

15 Characteristics of Thermal Cracks 15 (cm) 6 5 SNOW ACCUMULATION I I I I' I ' I) 11 L ATI O N _: : A B C A B C H ZS Z-ROUTE MI ZUHO STATION 1 Fig. 14. Relation beteen sno accumulation and frequency of occurrence of thermal cracks observed along the Z-route beteen Mizuho Station and Station H29 miday beteen Syoa and Mizuho. Sno accumulation at every 2 km as measured from January 1976 to January shos the relation beteen the sno accumulation measured by sno stakes at every 2 km and the frequency of occurrence of thermal cracks observed on the glazed surfaces along the route from Mizuho Station to Station H29 situated miday beteen Syoa and Mizuho. The frequency of occurrence of thermal cracks is defined by number density of crossed thermal cracks ithin 1 km long survey line, and classified into three cases; the number density is more than 5 (A), IO to 5 (B) and less than IO (C). It is clear from Fig. 14 that the thermal cracks could be observed on the glazed surfaces here there is no sno accumulation or ablation at the surface, and that the higher number density of thermal cracks is remarkably observed in high sno ablation area, hile no thermal crack as observed here there is much sno accumulation, namely depositional form in surface features. Around Mizuho Station a large area of glazed surface ith thermal cracks occupies the surface sno cover and the thermal cracks indicate a particular pattern in the form of polygons or parallel strips as illustrated in Fig. 15. The observation of the pattern of thermal cracks on the surface sno cover ithin the seismograph array as carried out in November 1976 hen snoquakes ere highly active due to fracturing of the surface sno cover. As seen in Fig. 15 the spacing of individual crack shos various length. In the form of parallel strips, most of crack spacing as about 5 to 2 m, hile the crack spacing in the pattern of polygons as mostly a fe meters. Since July 197 the observation of pattern of thermal cracks has been carried out in the same area of glazed surface hich as kept intact near seismograph No. 2 as shon by a square area in Fig. 15. Figure 16 shos the patterns of thermal cracks hich ere observed on four occasions, July 197, January 1971 (WATANABE and YOSHIMURA, 1972), December 1971 (YAMADA, 1975) and January 1977 (NISHIO, 1978). It can be seen that beteen July 197 and December 1971 nearly the same polygonal thermal cracks appeared and in places several cracks gre and crossed other cracks, and during 2 3 km

16 16 Thermally Induced Fractures and Snoquakes of Polar Sno Cover No.1 EB N 2 4 m No.4 EB o Stake D Seismograph Thermal Crack = MIZUHO STATION //( ,'B I no observation I Prevail ing ind direction E-W Ii ne... C I =1 Ill I ' I z, I I --- \,',,t N: Fig. 15. Pattern of thermal cracks on the glazed surface ithin the array of seismograph. Details of thermal crack in the square near seismograph No. 2 have been observed since July m l...lu:::j..j PREVAILING WIND DIRECTION :::::::: JULY JANUARY DECEMBER JANUARY 1977 Fig. 16. Pattern of thermal cracks in the square observation area (Fig. 15). No sno as deposited beteen July 197 and December 1971, but about 5 cm of sno as deposited from December 1971 to January that period no accumulation of sno as observed by stakes installed at four corners of the square observation area. Hoever, the pattern of thermal cracks changed beteen December 1971 and January 1977 and about 5 cm of sno accumulated during this period; the change in the pattern of thermal cracks ithin about 5 years may have resulted from the sno accumulation on the glazed surface.

17 Characteristics of Thermal Cracks 17 Figure 17 shos the vertical section of the uppermost 1.5 m of the sno cover at a distance of about 2 m in the lee-ind side of the thermal cracks observation area in Fig. 16. Although no thermal crack as found on the sno surface, there existed many thermal cracks at a depth of about 5 to 6 cm. The fine-grained surface sno layer of 5 to 6 cm in thickness ith a density of.4 g/cm 3 is equivalent to the amount of sno accumulated on the glazed surface in the square observation area of pattern of thermal cracks. Thus, it is found that the pattern of thermal cracks E :x: 1 cm... SNOW SURFACE no thermal crack observed DENSITY.3.4.s ',, I I I I :' C 1 15 Thermal crack strike \ z s 1 5 S\ I TRENCH 5!Om Fig. 17. Vertical section of thermal cracks in the trench all hich is located about 2 m in the leeard of the thermal crack observation square in Fig. 15. on glazed surfaces is maintained and cracking is ell propagating in response to thermal strain due to sno temperature fluctuations. Once thermal cracks on glazed surface are covered ith a thick sno layer such as barchan or dune, the formation of thermal cracks ithin the sno cover is unlikely unless the thermal stresses attain large enough to initiate cracks (see Fig. 17). Once a thermal crack is initiated in the sno cover, e ould expect stress concentration at the tip of the crack and cracking ill ell propagate even under loer thermal stresses. There as a surface sno cover of about 5 cm thick in January 1977 as shon in Fig. 16, and the formation of thermal cracks in this sno cover ill take place hen the thermal stress is considerably large Variation of idth of thermal cracks Temperature aves ith various amplitudes and periods propagate into the sno cover. This ill cause the expansion and contraction of the surface sno cover. In considering the fracture of sno cover ithout cracks, e shall be concerned not only ith the average thermal stresses in the sno cover, but ith the maximum thermal stresses for the initiation of fracture. Cracking ill occur hen the maximum thermal stress exceeds the fracture strength of the sno cover. Once cracking is initiated in the sno cover, e should expect the progress of stress concentration at the tip of crack to allo it to propagate ell beyond the region in hich the thermal stress attains less than the maximum thermal stress to initiate crack. Thus, in the sno cover ith many thermal cracks, fracture ill occur not only in excess of the maximum thermal

18 : :: : : 18 Thermally Induced Fractures and Snoquakes of Polar Sno Cover stress, namely the tensile strength of sno, but also in the minimum stress required to propagate a crack. On the other hand, once thermal cracks in the sno cover ere formed, it may be possible that thermal cracks close hen the temperature increases during the summer, and again thermal crack is formed hen the temperature decreases and the stress again exceeds the fracture strength of sno. As as mentioned earlier, the length of to reference points across thermal crack as measured by using a vernier calliper. Here e treat the variation of the length as the variation of idth of thermal crack. As shon in Figs. 18a and 18b, the length of sides of AB, CD, BC and AD, and of diagonals of AC and BD in the square illustrated in the Fig. 3b ere measured once a day. The variation of length of side across thermal crack such as AB, CD, AC and BD is remarkably depending on the variation of the surface sno temperature. During the inter from June to September the length across thermal crack became longer ith decreasing temperature and the fluctuations of distances ithin several days ere a fe mm. From the beginning of October the length across thermal crack quickly decreased and shortened by 5-8 mm ith the temperature increasing during the summer. On the contrary, the length of BC and AD on both sides of the thermal crack did not follo the variation of the sno surface temperature. Thus, it is considered that the variations of length across thermal crack indicate the variation of idth of thermal crack due to temperature variations. CC) (cm) 52.3 CRACK (1) 52.2 _52. 1 AB! CD _58.7 BD } _ 3.3 [ BC AD [,..f't, _.--i,...,..._-----l,--...j_ ,----j r AD_-- Fig. 18a. JUNE JULY AUG. SEPT. OCT. NOV. DEC. JAN. Variations of length of sides and diagonals of the square across the thermal crack No. I in Fig. 3b.

19 Characteristics of Thermal Cracks 19 rel -4 -'-3 CRACK (4), i--- SNOW SURFACE TEMPERATURE ! (cm _ 37.3 AB t CD 39.2 t "' AC 45.3 o 45.2 ± AB _45.4 BD AC BD _ 26.4 [ BC 26.3 _ [ DA DA SEPT. OCT. NOV. DEC. JAN. Fig. 18b. Variation of length of sides and diagonals of the square across the thermal crack No. 4 in Fig. 3b. We shall discuss the variations of idth of thermal crack and the character of the strain rate field surrounding the crack. Figure 19 shos a field of thermal cracks at spacing of /. Thermal cracks ill open and close according to sno temperature fluctuations, but the idth of opening depends on the degree of expansion and contraction of sno beteen thermal cracks. Near the surface, immediately on the boundary of a thermal crack, the sno is free to expand and contract in response to fluctuations of sno temperature, but any thermal straining of expansion and contraction is attenuated ith depth ith regard to the heat conduction properties already mentioned and is also attenuated ith distance inards from a thermal crack according to the Saint Venant's principle concerning edge effects. Attenuation of temperature ave ith depth depends on frequency and occurs according to exp [-z(/2k)] Here, skin depth of z is defined as z =(2k/) 1 l 2 represf:nting the depth at hich temperature effects are attenuated by a factor of 1/e. We shall use this skin depth as a characteristic distance for the attenuation of thermal effects in the z direction, and shall make the further assumption that it also characterizes the attenuation ith distance inards from a thermal crack in the x direction as suggested by SANDERSON {1978). This is a ay of expressing the principle that edge effects generally die aay from a free boundary. This means that e can approximately express the strain rate field as a function of x and z: s xx (x, y)=(s xx )o exp (-z/z o ) exp (--r/z o ) (4)

20 2 Thermally Induced Fractures and Snoquakes of Polar Sno Cover z - (2 k/w)2 : SKIN DEPTH r - l/ 2 - IXI i---r Fig. 19. A schema illustrating strain rate field surrounding thermal cracks undergoing thermal strain in the sno cover near the surface. Appreciable strain occurs ithin a region of order z surrounding a thermal crack. And r=l/2-x, is the distance aay from a crack. (s xx ) o is the strain rate hich a free sno mass ould undergo if subjected throughout to the sno surface temperature fluctuation, that is, (s xx )=aar;at, here a is the linear expansion coefficient of sno given by YAMAJI (1957), a.=5.4 X X I- 7 T, ( 5 ) here Tis the sno surface temperature. We can no calculate the rates of opening of thermal cracks. Taking the origin of coordinates in the middle of spacing / as a stationary point, and then integrate the strain rate ith respect to x to find the rate of movement V of idth of thermal crack. This gives, for the sno surface, z=o, \ 1/2 Ve = 2 Sxx (x, O)dx Jo =2(sxx)ozo[l-exp (-1/2zo)], (6) and provided that / z, that is, the thermal crack spacing is by far greater than the skin depth because most of thermal crack have the spacing of more than several meters as mentioned in the previous subsection, then e can rite the velocity of opening and closure of thermal crack, as For the maximum idth W of thermal crack e can rite the folloing equation in the same ay, ( 7 ) ( 8 )

21 Characteristics of Thermal Cracks 21 here (e xx ) ma x is the maximum strain hich a free sno mass should undergo if subjected throughout to the sno surface temperature cha.nge, that is (e x x) max =a LIT,.. here LIT is the sno surface temperature change. As derived from eqs. (7) and (8), the rate of movement of idth of thermal crack V and the maximum idth of thermal crack W have a. function of only skin depth z Table 1 shos a comparison of calculated and measured values of skin depth, rate of movement of crack edge and the maximum idth of to thermal cracks, crack (1) and crack (4). There are many cases in thermal fluctuation ith different skin depths, but for the purpose of accounting for the variation of idth of thermal crack e dealt ith to cases of sno surface temperature, daily oscillation ith an amplitude of 13.5 C, and annual oscillation ith an amplitude of 4 C, for hich the associated skin depth is about 2 and 3 cm respective:ly. Table 1 clearly indicates that the variation of idth of thermal crack is strongly depending on the air temperature aves, and shorter-period ave gives the more rapid but smaller opening and closing, and longer period ave gives the sloer but larger opening and closing. Table 1. Skin depth, rate of movement of thermal crack edge and the maximum idth of thermal crack. Diurnal cycle Annual cycle I November 29-3, 1976 August 1976-January 1977 (1 day) (18 days) I Crack I Crack I Crack Crack No. 1 No. 4 No. 1 I No. 4 Calculated \ Measured Calculated Measured I Skin depth z (cm) Rate of movement of thermal crack edge V (x1-8 cm hour- 1 ) Maximum idth of thermal crack W (cm) Amplitude of sno surface temperature L1T ( C) During repetition of opening and closing of thermal cracks, narro cracks may gro ider oing to the progress of sno metamorphism of the all of thermal crack in the vertical direction because hoarfrost formed by sublimation as observed on the all Thermal cracks and snoquake activities The variation of idth of thermal cracks is dependent on the thermal expansion and contraction induced by temperature change, also the formation and groth of thermal cracks are strongly associated ith snoquake activity. Thermal cracks already existed are found to be remarkably influenced by the temperature aves, that is, the opening and closing of thermal crack, and the formation of thermal crack and the propagation of a tip of thermal crack may cause snoquakes hen the thermal stress induced by sno temperature variations exceeds the fracture strength of the sno cover.

22 22 Thermally Induced Fractures and Snoquakes of Polar Sno Cover Figures 2a and 2b sho the daily variations of length of sides and diagonals of the square across the thermal cracks (1) and (4) respectively. These variations are considered to correspond to the variation of idth of thermal crack. Sno surface temperature and number of snoquakes are also shon in the figures. Figures 2a and 2b sho considerable daily variations of the sno surface temperature during the summer. When the temperature is decreasing after the maximum in the early afternoon, the thermal crack begins to open and becomes about.5-.8 mm ide till the temperature reaches the minimum. The snoquake begins in accompany ith the rapid temperature decrease a fe hours later after the maximum sno surface temperature and during the temperature decrease the sarm-like snoquakes occur till the temperature reaches the minimum. When the sno surface temperature as increasing, snoquakes did not occur. Thus, it is evident that the opening of thermal crack and the initiation of snoquakes are closely related to the thermal contraction of the sno cover as the result of decrease of the sno surface temperature. Hoever, the initiation of sno quakes should be caused by the ne formation of thermal crack in the sno cover or the propagation of a tip of existing thermal crack. Figure 21 shos a ne thermal crack just after the occurrence of snoquakes hen the sno surface temperature as about -5 C. The ne thermal crack, about.5 mm ide, CRACK (1) (cm) [ DA _ /\AC _ A /\. (cm). --\.,. \,.....,.. "r,_ BO [ " /"'-._/ [ 58_ ,.,.-.\ j (cm) j (cm) j SNOW SURFACE TEMPERATURE1 : f4o a: 1 NUMBER OF SNOWQUAKES... 1'.; 5 LU :::, LU a: OCTOBER NOVEMBER Fig. 2a. Daily variations of length of sides and diagonals of the square across the thermal crack No. 1 in Fig. 3b, sno surface temperature and number of snoquakes.

23 Characteristics of Thermal Cracb. 23 {cm) CRACK (4) 26.3 {cm) DA 25.4 [ "' , {cm) BO '"-, [ , " ' -,,..., o /'""' 45.3 t ,.,/' ',,,.,..,,, _,/ '-,_,/ \,.,/ "' (cm) j {cm) 39 2 ] ] 39.1 {cm) j SNOW SURFACE TEMPERATURE { C) (" - 3 J i - 4 a: 1 NUMBER OF SNOWQUAKES... t 5 z LU ::J LU a: Fig. 2b OCTOBER NOVEMBER Daily variations of length of sides and diagonals of the square across the thermal crack No. 4 in Fig. 3b, sno surface temperature and number of snoquakes. about 2 cm deep and about 3 m long, as formed on the glazed surface on August 3, This observation leads to a possible explanation of the initial stage of formation of thermal crack and of the occurrence of snoquakes observed as the result of detecting elastic aves radiated by the fracture of the sno cover due to thermal contraction. Another cause of occurrence of snoquake is explained by the fracture hich as due to the process of stress concentration at a tip of already existent thermal crack. In order to kno hether the opening and closing of thermal crack are associated ith extensional faulting (tensile cracking) or ith slip faulting, calculations ere made on the deformation of triangle across a thermal crack, such as crack (I) shon in Fig. 3b. It as assumed that the strain parameters of the triangle indicate those of the thermal crack. To calculate the strain parameters in each triangle, the JAEGER's method (1969) is used as the rate of deformation of a circumscribed circle of an unstrained triangle into a strain ellipse caused by a homogeneous strain. Coordinates of each vertex of triangles in the square across thermal crack are determined ith reference to appropriate vertex of triangle in the case of each measurement of sides of the square as shon in Fig. 3b. Hence, the shape of the strain ellipse and the rotation

24 24 Thermally Induced Fractures and Snoquakes of Polar Sno Cover Fig. 2 I. A ne thermal crack about.5 mm ide, ca. 2 cm deep and ca. 3 m long, hich as formed or1 the glazed surfa ce on August 3, 1976 just after the occurrence of snoquakes at the sno surface temperature of -5 C. of the principal axis of the strain can be calculated. Taking the radius of the circumscribed circle of an initial triangle as the unity, and the length of major and minor axis of the strain ellipse being A and B respectively, the parameters of deformation of triangle such as principal strain rate, dilatation, maximum shear strain rate and rotation of principal axis of the strain, ere computed as a function of A and B. As the result of calculation of the values of A and B of each triangle, the fo lloing strain parameters ere obtained : L1: Rate of dilatation in the area of a triangle per hour, calculated from L1 = AB- I. s 1, s 2 : Principal strain per hour, calculated from s 1 = A- I and s 2 = B- 1. The positive sign indicates the tensile strain rate and the negative for compressive. The principal strain rate of s 1 and s 2 respectively the algebraically maximum and minimum values among the strains in the hole directions. a: Azimuth clockise from north of the principal axis of the strain s,. cij : Rate of counterclockise rotation of the principal axis of the strain per hour. f max : Maximum shear strain rate per hour, calculated from f nrn x =(A 2 -B 2 )/ 2A B. Its direction is ±45. Figure 22 shos the calculated strain parameters of the triangles in the square across the thermal crack (I) from October 29 to November 3. In Fig. 22, the daily variations of the dilatation Li, the maximum principal strain rate s1, the minimum principal strain rate s 2, the direction of principal axis of the strain a, the rotation of

25 Characteristics of Thermal Cracks 25 CRACK (1) X 1-4 i1 p\."-_ l l \ _j\ --\ I -\/ _j-1-" \. -- [\_ \l -t:: -1 \ ' ::, 1 NUMBER OF SNOWQUAKE.c z OCTOBER 2 3 NOVEMBER Fig. 22. Daily variations of the dilatation.j, the maximum principal strain rate 1, the minimum principal strain rate i 2, the direction of principal axis of the strain a, the rotation of the principal axis and the maximum shear strain rate t max of triangles in the square across the thermal crack No. 1. The side AB of the square and the number of snoquakes are also shon. OCTOBER 29 NOVEMBER 3 CRACK (1) A THERMAL CRACK l CRACK (2) N 1 CRACK (3) I 4 O CRACK (4) I d 5 cm Fig. 23. Direction of principal axis of the strain (tensile strain) during the occurrence of snoquakes. The direction beteen to solid-line arros indicate the tensile strain during the snoquake sarm and the daily variations of principal axis are also shon in the hatched area.

26 26 Thermally Induced Fractures and Snoquakes of Polar Sno Cover the principal axis and the maximum shear strain rate t max are shon together ith the length AB and the number of snoquakes. The dilatation l becomes larger and the maximum principal strain rate s1 of the tensile strain rate is also increasing during the occurrence of snoquakes from the early evening to the early morning every day. The direction of the principal axis of the strain a in the tensile strain during the occurrence of the snoquake sarm indicates the tendency of the direction perpendicular to the strike of thermal crack. As seen in Fig. 23, the direction of the principal axis of the strain is indicative of the tensile strain and perpendicular to the strike of the thermal crack for the cases of cracks (1 ), (2), (3) and ( 4). This is evident that during snoquake sarm the tensile stress due to thermal contraction may be applied to thermal crack perpendicular to the strike and the tensile cracking may take place at the tip of thermal crack.

27 27 5. Characteristics of Snoquake Activities KAMINUMA and TAKAHASHI (1975) observed snoquakes ith one vertical component seismograph at Mizuho Station on September 1-27, They reported that many snoquakes, mostly of sarm type, ere recorded, and that these sarms occurred in the nighttime hen the air temperature as belo -35 C, and the falling rate of air temperature as -2.5 C/hour for a short period, or about -1 C/hour hen the falling of air temperature continued for a fe hours. When the largest sarm as recorded, sound generated by snoquakes as heard and many thermal cracks ere recognized on the sno surface around the source area of the sound. Therefore, the depth of the snoquake sarm as estimated to be very shallo. Some snoquakes ere interpreted to have been originated from the upper sno layers quite near the surface. From their study of snoquakes at Mizuho Station, it as expected that the snoquake activity ould be closely associated ith the fracture of sno cover such as thermal cracks due to thermally induced stress near the sno surface. But the mechanism of generation of snoquakes as still unsolved and hence the detailed investigation of the snoquakes as designed to be carried out by using three vertical-component seismographs in the array of tripartite General feature of snoquake activities From June 8, 1976 to January 11, 1977, three vertical component seismographs ere in operation at Mizuho Station. The trace amplitude larger than 2. mm in the recording chart as adopted as the snoquake, because the ground noise originated from artificial sources such as the poer supply generator as large. Solid horizontal lines in Fig. 24 indicate observation time during hich period snoquakes are detected on seismographs. The daily observation covers the period from June 1976 to January The date in the column gives from noon to noon of to successive days; for example, on June the observation duration of snoquakes as from about 14 LT June 11, through the midnight, till about 11 LT of June 12, but the solid line does not indicate the frequency of occurrence of snoquakes. From Fig. 24 three characteristic features of sno quake occurrence are clearly distinguished : (1) during the midinter from June to August, the occurrence of snoquakes is irregular, (2) from September to November, the snoquake activity indicates the daily occurrence beteen the early evening and the early morning through midnight, and (3) at the end of November, hen the summer began, snoquakes ceased

28 28 Thermally Induced Fractures and Snoquakes of Polar Sno Cover 1-2 JUNE JULY LT O 6 12 I I I I AUG. SEPT. OCT. NOV ? 9 12 I DEC I I JAN S TA RT E ND-- > Duration of snoquake occurrence Fig. 24. Daily occurrence of snoquakes detected ith seismographs. and as not observed till the early January. This pronounced seasonal variation of snoquake occurrence must be related to the variation of sno temperature and the mechanical behavior of sno, for instance, such as the fracture strength having a temperature dependence. During the midinter hen the sno temperature as mostly loer than -4 C as in the case of (1) in the previous paragraph, the snoquake started ithout exception immediately after the decrease in sno temperature. As as mentioned in Section 3, the surface temperature during inter fluctuated ith the period of several days ith an amplitude of about 2 C. This resulted from the arming and cooling hich as due to climatic disturbances such as the penetration of lo pressure into the inland around Mizuho Station. After the passing of lo pressure, the sno surface temperature decreased under the influence of high pressure system and the snoquakes began to occur. On the contrary, from the end of inter, in the case of (2), the diurnal surface temperature variations ith an amplitude of I-15 C became prominent because the sno surface as heated by the daily solar radiation change hich depends on the sun's altitude. A fe hours later after the maximum surface temperature around midday, the snoquake began to occur and during the decrease of sno surface temperature the snoquake sarm continued to occur till the temperature reaches the

29 Characteristics of Snoquake Activities 29 minimum. From September to November snoquake sarm occur almost everyday, especially in October the snoquake sarm occurred everyday except to days. a: 2 < a: " a. z :::i < :I:... u a: 2 < a: " a. z :::i <( UJ :I:... u SNOW TEMPERATURE CHANGE (d 1cm) 9 ('C) T= SNOW TEMPERATURE (ct,ocm) SNOW TEMPERATURE CHANGE - 5 ;J a: 2 <( a: UJ a.,:: 2 Fig. 25a C e 9 ;: u ::, 1 NUMBER OF SNOWOUAKE I 2 SEPTEMBER 6 SEPTEMBER 7 UJ a: 2 <( a: UJ UJ" a. z :::i <( UJ I... u c c> -2. UJ a: 2 <( ffi a. ;; z "' UJ a: 2 <( a: UJ" a. z :::i < UJ I... u J:.!-) SNOW TEMPERATURE CHANGE 1 NUMBER OF SNOWOUAKE Fig. 25b OCTOBER 19 OCTOBER 2