longitudinal downsizing of hummocks by the freely

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Faculty of Science and Engineering, Chuo University. Kasuga, Bunkyo-ku, Tokyo, , Japan (Present

address : College of Economics, Kanto Gakuin University. Mutsuura-higashi, Kanazawa-ku, Yokohama,

, Japan).

Received June , . Accepted January , .

*

* Graduate School of Frontier Sciences, The University of Tokyo. Kashiwanoha, Kashiwa, Chiba, ,

Japan.

* a Corresponding author : hyoshida@kanto-gakuin. ac. jp

Hummocks of debris avalanches distributed at the skirt of volcanoes have beeninvestigated mainly to prove the occurrence of catastrophic sector collapse and todiscuss the flow mechanism. The hummocky topography, however, is expected toshow some other geomorphological aspects about the collapse and debris avalanche.This study tries to find some new geomorphological meanings of debris avalanchehummocks on the basis of their longitudinal distribution pattern. Four debris ava-lanches, which are typical cases of freely spreading debris avalanches, were selectedfrom four di erent volcanoes in Japan. Numbers of the debris avalanche hummocksinvestigated in this study are at Shiribetsu volcano, at Usu volcano, atIwaki volcano, and at Nasu volcano. Morphological data of hummocks weremeasured using aerial photographs and GIS techniques.

Deposition of hummocks starts at the lower part of volcanic piedmont, forming agently sloping depositional surface, and terminated in the plain with rolling hillylandforms. The longitudinal distribution patterns of hummocks along the course ofdebris avalanche vary with avalanches, showing that hummocks are in clusters. Sizesof hummocks, however, generally decrease downstream for each of the four ava-lanches, and regression analysis of size-distance relationship shows that the relation-ship can be described by exponential functions with high correlation. The regressionfunction indicates that the size of hummocks at source area should be determined bythe volume of collapsed volcanic body. Namely, the cracks created in the collapsedvolcanic body are potentially controlled by the magnitude of collapse. On the otherhand, the downsizing rate of hummock is indicated to be controlled by the fluidity ofdebris avalanche which is expressed by the reversed values of equivalent coe cientof friction of debris avalanche. When avalanche is terminated in short distance, sizeof hummocks rapidly decreases downstream, while when avalanche flows down for along distance, size slowly decreases. Namely, the higher in fluidity the avalanche is,the lower in downsizing the hummock is. As mentioned above, the size-distancerelationship for the hummocks of volcanic debris avalanches in Japan shows thephysical properties of volcanic body and of flow of avalanche.

fice is one of the large-scale topographic changesoccurring at mountain regions (Ui, ; Siebert,

A large-scale slope failure of a volcanic edi- ). The sector collapses have potential to

Hidetsugu Yoshida* , Toshihiko Sugai* and Hiroo Ohmori*

volcanic debris avalanche, hummocks, size-distribution, regression analy-sis, Japan

Keywords :

I. Introduction

Longitudinal downsizing of hummocks by the freely-spreading

volcanic debris avalanches in Japan

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Yoshida, H., Sugai, T. and Ohmori, H.

lanches (Kienle ; Siebert, ; Carrasco

mechanism (Nakamura, ; Mimura ;Watanabe, ; Ui ; Glicken, ;

although above-cited achievements are all valu-

the freely-spreading volcanic debris avalanches,

and Scott, ; Beget, ; Capra and Macias,

). Hummocks over the debris avalanche de-

cause severe damage to human society directly cal significances of hummocky topographyor through secondary catastrophic events like should be examined more satisfactorily thantsunamis and lahars, producing debris ava- proving “the evidence of the sector collapse”,

Nunez , ; Orton, ; Vallance able from a viewpoint of data accumulation ofgood quality. Another problem for the previ-

; Ward, ; Francis and Oppenheimer, ous studies is that they mostly provided anddiscussed the data for individual cases. The

positional surfaces are the most characteristic authors consider that it needs to do compara-landforms of debris avalanche deposits, to- tive investigation using various parameters forgether with their associated collapse scars many cases, such as Siebert ( ) preliminary(Crandell ; Glicken, ; Ui showed ; the transition of hummock height

). Hummocks have been subjected to study with run out distance from the source for somefor years, especially since the shocking experi- typical cases around the world. With a back-ence of the Mount St. Helens in USA ground as the above-mentioned, the present(Voight ; Glicken, ). From the study tries to find some new geomorphologicalperspective of volcanic geology, there are a implications of hummocks through quantita-number of researches in the world, showing the tive description and comparative discussioninternal sedimentological features of deposits, for some typical debris avalanches in Japan,in the context of debris avalanche transport providing their geomorphological clues regard-

ing the nature of debris avalanches.

Takarada ; Clavero ; Ber-nard ; Shea ). Research fields are the hummocky terrains

Meanwhile, from geomorphological aspects, distributed around four Quaternary volcanoeshummocky topography has been attracted at- in Japan. The source volcanoes are Shiribetsu,tention for a long time before the s in Usu, Iwaki, and Nasu from the north in orderJapan, because of its high visibility as con- (Fig. ). With special attention to the di e-spicuous landforms ( Mizuno, , ; rences in volcano size or location, in order toHashimoto , ). Early scientists examine whether or not such di erences a ectalready discussed the morphological properties the distribution pattern of hummocks, the prin-of hummocks such as size and orientation, and cipal reasons for selection of these examplestheir relationships with the distance from the are as follows : ) hummocks are derived bysource and the flowage direction. However,these pioneering findings were basically quali- ) it is highly possible that any topographicaltative or semi-quantitative due to technical barriers did not disturb the flows of debrisand data limitations at that time. Recently, it avalanches, and ) there remain a number ofhas become easier to handle digital data with hummocks enough to analyze. These are ad-progress of GIS technique, together with accu- vantageous to find out common characteristicsmulation of advanced volcanological knowl- of hummocky landforms.edge concerning volcanic debris avalanches. Additionally, as stated next chapter, thereThen, recent some researches tried to describe exists variation in occurrence age of sectorquantitatively the morphology of debris ava- collapses. This suggests the necessity to con-lanche hummocks in Japan and overseas (Siebe sider the possibility of the time-series morpho-

; Hoshino ; Glicken, ; logical changes of hummocky terrain. But theSango ; Clavero ; Koarai present study gives no thought for this issue,

; Shea ). They focused because we know little about topographicalmainly on proving the occurrence of huge sec- changes of hummocky landforms quantita-tor collapse of volcanic body. Thus, the pre- tively after their formation and also becausesent authors consider that the geomorphologi- we selectively picked up the representative

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II. Study area

The Quaternary Research, ( )56

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Fig. Location of studied volcanoes (a) and topography around Shiribetsu and

Usu volcanoes (b), Iwaki volcano (c), and Nasu volcano (d)

Hummocky terrains in Figure are outlined by squares. Shaded relief maps are

compiled from Digital Map m Grid (Elevation) published by GSI.

Longitudinal downsizing of hummocks by the debris avalanches

m. It is a small, andesitic composite strato- western Hokkaido bordering Funka Bay (Fig.

width of km in diameter breaching widely

well-preserved hummocky terrain. Pre-collapse

cases distributing debris avalanche hummockssequentially within their depositional surfaces. to the west. The caldera was created by a mas-

This research focuses on “the longitudinal sive debris avalanche named the “Rusutsu de-distribution of hummock size”. Among some bris avalanche” during late Pleistocene (parameters expressing the hummock size, the ka) (Moriya, ; Inokuchi, ), forming a“hummock plane area” is examined. This pa-rameter is the most fundamental, and is less height of the volcano is supposed to have beena ected by topographical change after ava- m a.s.l., from the remnant of vol-lanche event compared with the hummock canic edifice. Judging from the size of horse-height as shown by Siebert ( ). shoe caldera in Shiribetsu volcano slightly

larger than that of Usu volcano as describedlater, volume of the Rusutsu debris avalancheis estimated as large as km .

Shiribetsu volcano is located immediatelysoutheast of Yotei volcano, southwestern Hok- Usu volcano is one of presently the mostkaido (Fig. a, b), with a present altitude of active volcanoes in Japan, located in the south-

volcano with a few lava domes. It has a horse- a, b, Soya ). The main body of Usushoe (U shape) caldera (amphitheater) with a volcano, which is situated on the southern rim

ca.

et al.,

The Rusutsu debris avalanche from Shiri-betsu volcano

.. The Zenkoji debris avalanche from Usu

volcano

III. Outline of the debris avalanches

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Table Brief information of studied volcanoes


surveyed, although there is a discrepancy among

fumaroles (Yamamoto and Ban, ). Restricted

(Ofujiyama) debris avalanche” is focused. It run

composed of alternative layers of andesitic lava

of volcano (Hashimoto ; Sasaki, ).

of Toya Caldera, was formed by repeated erup- researchers especially in age of the collapse ;tions of lava and scoria of basalt and mafic ka (Mimura and Kanaya, ) or afterandesite since the end of late Pleistocene. After ka (Sasaki, ). There is presently no topo-the completion of Usu stratovolcano, about or graphic trace of sector collapses on Iwaki vol-

thousand years ago, its summit was catas- cano. Isshiki and Ozawa ( ) approximatedtrophically collapsed accompanying the “Zen- the volume of the debris avalanche deposits askoji debris avalanche” (Moriya, ; Soya km .

). The collapse resulted in formation ofthe amphitheater with a diameter of km,open to southwest. Although present summit The Nasu volcanic group is located at thealtitude of Usu volcano is less than m a.s.l., southern part of northeastern Honshu (Fig.the altitude should have reached m as a, d). It consists of five composite volcanoes.maximum before the sector collapse. There are According to Yamamoto and Ban ( ), thea number of lava domes and cryptodomes on history of the Nasu volcanic group started atthe northern flank created by historical activi- ka. Since then up today, at least fourties during last three centuries. The deposi- huge sector collapses have occurred, producingtional landforms of the Zenkoji debris ava- debris avalanches. Among them, the “Ofujisanlanche, with a volume of about km or nomore than km (then, average is km ), is down over the southeastern flank in aboutwell preserved at the southwestern foot of Usu ka (Fujita, ). The amphitheater remainsvolcano (Takarada and Melendez, ). The partially still now, surrounding the Chausu-most distal materials were deposited in Funka dake edifice ( m a.s.l.) which is the onlyBay. post-avalanche active volcanic body with his-

torical eruption records and presently active

Iwaki volcano, with a present altitude of by the southern hills adjacent to the course ofm, is typical one among conical-shape the Ofujisan debris avalanche, far from km

volcanoes in Japan (Fig. a, c). It is mainly from the source, the debris avalanche con-verged into the Yosasa River valley, changing

flows and pyroclastic deposits. Some hum- the avalanche from fan-shape to tongue-shape.mocky terrains can be recognized at the skirt The volume of the collapse having caused the

Ofujisan debris avalanche is estimated as kmAmong them, this paper handles the northeast- at most by Fujita ( ).ern hummocky topography produced by the“Tokoshinai (Tozurasawa) debris avalanche”(Mimura and Kanaya, ), which was oncecalled as the “Akakurazawa mudflow” (Hashi- The outline of hummocks was traced on aer-moto ; Sasaki, ). The debris ava- ial photographs using stereoscopes, referringlanche examined has been comparatively well to the existing geomorphological and geologi-

cal maps. The aerial photographs were taken

et al.,

etal.,

ca.

ca.

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et al.,

The Tokoshinai (Tozurasawa) debris ava-lanche from Iwaki volcano

. The Ofujisan (Ofujiyama) debris ava-lanche from Nasu volcanic group

.

. Interpretation of aerial photographs

IV. Methodology


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by the Geographical Survey Institute. Although

nant volcanic edifices. For Iwaki volcano, there

by the Geographical Survey Institute, Japan necting the centroid of a corresponding hum-(GSI), in the s and the s, with scales mock polygon and pre-failure summits of vol-between / and / (Table ). Hum- canoes were measured (Fig. ). The pre-failuremocky islands in the sea for the Zenkoji debris summits of Shiribetsu and Usu volcanoes wereavalanche, Usu volcano, were out of examina- estimated based on the amphitheater and rem-tion because correct shapes of the hummocksin the sea might be misjudged, and the hum- is no topographic remnant possible to recon-mocks distributed on the eastern side of the struct the pre-failure landforms of volcano.Yosasa River for the Ofujisan debris avalanche, Thus, the present summit was used as the topNasu volcano were also out of examination, of collapse. And for Nasu volcano with littlefor excluding to confuse with older hummocks information of pre-failure landforms of vol-than the hummocks of the Ofujisan debris ava- cano, the present summit of Chausudake peaklanche. inside the amphitheater was preliminarily used

as the top of collapse, and distance was meas-The interpreted photographs were scanned ured using lines with two segments connecting

by the scanner connected with computer. The each hummock with the Chausudake peak.scanned image resolution is dpi. Then, us- For regression analysis, the equivalent co-ing GIS, these digital images were converted e cient of friction of each debris avalanche,into digital orthophotographs rectified with is used. In this paper, is defined as thethe digital elevation models (DEMs) published altitudinal di erence between the top of col-

lapse (pre-collapse summit altitude) and themaking orthophotographs was previously ex- farthermost hummock, and the error of estima-pensive and required professional skills, ad- tion should be less than some hundreds meters.vanced GIS software, such as TNTmips (Micro- is the horizontally straight length betweenImages, Inc.) with existing DEMs, runs on a summit and the farthermost hummock and ispersonal computer and can produce digital or- longer than some kilometers. In general, isthophotographs suitable for geospatial analy- more than five or six times as large as Thus,sis (MicroImages, ). After that, hummocks the equivalent coe cients of friction of debriswere digitized into polygons with coordinates avalanches do not have serious errors, even ifon the GIS. the above geomorphological estimation might

be rough in some cases.The data of plane area with distance from

the source were calculated for each hummock,and analyzed in terms of regression analysisusing Microsoft Excel. The linear distance con- Debris avalanche hummocks interpreted on

H/L, H

L

LH.

. Digital data acquisition using GIS

. Data analysis

. Longitudinal distribution of hummocks

V. Results and discussion

April 59

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Fig. Distribution of hummocks of the studied debris avalanche deposits, interpreted

from aerial photographs

The associated amphitheaters partially remain for Shiribetsu, Usu and Nasu volcanoes,

shown by heavy dashed lines. Shaded relief maps are compiled from Digital Map m

Grid (Elevation) published by GSI. Contour interval is m, generated by GIS.


aerial photographs are for the Rusutsu de- for the hummocks of the Tokoshinai debrisbris avalanche, Shiribetsu volcano, for the avalanche, Iwaki volcano by HashimotoZenkoji debris avalanche, Usu volcano, for ( ).the Tokoshinai debris avalanche, Iwaki vol- Also in any of the four cases, it is obviouscano, and for the Ofujisan debris avalanche, that sizes of hummocks decrease toward theNasu volcano (Fig. , Table ). It is clear that distal end of the deposits as shown in Figure .hummocks are distributed in clusters at the On the basis of the semi-log graph of Figure ,skirt of volcano for all cases (Fig. ), as notified exponential function is acceptable for statisti-

et al.


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and hummock area with regression lines using

Fig. Relationship between distance from the source and area of all hummocks

Fig. Relationship between distance from the source

moving average values


four cases examined. The function is expressed

size-distance relations are significantly approxi-

cal analysis of the longitudinal distribution ofhummock size. For non-biased relation of size-to-distance, moving average values of hum-mock size in every m (partly m) zoneof distance along the course of debris ava-lanche, with those which moves at step with aninterval of m (partly m), were calcu-lated. In functional approximation using suchcomposite data, the uppermost (nearest) zoneand lowermost (farthermost) two zones areconsidered to be inappropriate because of thelower density of hummock than the others. Asdescribed in section , since the lower part ofthe Ofujisan debris avalanche converged intothe Yosasa River valley at km from thesource and the topographic condition mightmarkedly a ect the flow dynamics, only the Table ). Correlation coe cients are largerupper part of the Ofujisan debris avalanche than (Table ), and the t-test shows thatwas analyzed. Regression analysis shows that the goodness of fitness is significant.

mated by exponential functions for all of the First, the variations of coe cient , an inter-cept value in the diagram, are discussed. This

by ; coe cient indicates geomorphologically thehummock size at the distance of zero, which

* exp * ( )means the potential block size of the earliest

where is area and is distance from the stage of the sector collapse at the source area.source, and and are coe cients (Fig. , Values of have a good relation with the vol-

A D

A D

Potential hummock size at the source area.

April 61

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Table Parameters in functional analysis

Fig. Relationship between collapse volume and

Fig. Relationship between major axis diameter

(longest diagonal line of polygon) and area


canic body are determined by the collapse mag-

ume of collapsed volcanic body (Fig. ), whichis an index of magnitude of the collapse. Then,specifically expressing, the larger the collapsemagnitude is, the larger the original block sizeof hummock is. This indicates that the cracksinitially created in the block of collapsed vol-

nitude.On the other hand, length of major axis of ; Voight ).

hummock has a good correlation with area of The authors have once investigated the sec-hummock for each of the four cases, expressed tor collapse of Asama volcano (Yoshida andby : Sugai, ). For the avalanche of Asama vol-

cano, it was also found out in distribution of* R ( )

hummocks within the depositional extent thatwhere, is hummock area and is long axis of hummock size exponentially decreases withhummock (Fig. ). Based on this relationship distance from the source. Based on this expo-and the above-mentioned relationship between nential relationship, the initial diameter of the

and volume of collapse, the major axis diame- maximum debris avalanche blocks was esti-ter of an initial block is estimated to be mated to be several hundreds to m. Them, if the collapse is km in volume. This volumetric magnitude of Asama collapse, how-estimation is quite appropriate in order of size, ever, is calculated as km (Yoshida andindicating that hummocks are produced by a Sugai, ). It is at least twice larger than theprocess of the multi-sequential collapse as ob- four cases in this study. From the distributionserved at Mount St. Helens (Ui and Aramaki, of the Asama deposits, a collapsed sector was

et al.,

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Zenkoji debris avalanche, Usu volcano (Takarada

downsizing rate decreases with fluidity. Namely,

fore, the high correlation between and equiva-

the volcanic or tectonic seismicity (Unzen-type),

and Melendez, ). According to this model,the lower boundary layer of debris avalancheis strained by the extensively large shearstress, and the collapsed mass is repeatedlyfractured into blocks, producing many hum-mocks (Takarada ; Ui ). Asa result, the size of hummock becomes smalleras far from the source. When the avalanchefreely spreads over the slope of volcano, thethickness of debris avalanche should becomethinner downstream, and the downsizing rateof hummock might be accordant with the thin-ning rate of debris avalanche. As a result, sizeof hummock should decrease downstream, and

divided into two lobes immediately after the when debris avalanche terminates at a shortcollapse, having run separately both to north distance due to the low fluidity, size of hum-and to south. The volumetric magnitude of mock should rapidly decrease downstream.each divided debris avalanche is estimated to Geological conditions of collapsed volcanoesbe km . Thus, the magnitude of each di- may a ect the collapse magnitude and fluidityvided avalanche of Asama volcano is conse- of avalanche. However, there is no critical dif-quently almost the same as those of the four, ference in geology among the studied fourand the order of initial size of hummocks esti- cases (Table ). It is well known that the hy-mated at the source also coincides approxi- drothermal system of volcano makes a part ofmately with those of the four. volcanic edifice weak, leading an occasional oc-

currence of huge flank collapse (Siebert, ;Coe cient of regression function, which is Lopez and Williams, ; Reid ).

an indicator of the downsizing rate of hum- There has been, however, no report pointingmocks, also has di erent values among the out the significant influence of hydrothermalfour cases. Absolute value of decreases with system on the occurrence of sector collapsesthe size of volcano and they show a high corre- for the four cases examined. Thus, there islation with the equivalent coe cient of fric- little necessity to allow for the influence of dif-tion of debris avalanche, that is, the height-to- ference in geological conditions at the moment.length ratio (H/L) (Fig. ). The equivalent co- There are some commonly invoked mecha-e cient of friction is an index of fluidity of nisms for triggering edifice collapse such as thedebris avalanche. Precisely expressing, the flu- magmatic body intrusions (Bezymianny-type),idity is expressed by the reversed value ofequivalent coe cient of friction ; L/H. There- and the tectonic gravity-driven processes like

spreading and slumping (Siebert ;lent coe cient of friction indicates that the van Wyk de Vries and Francis, ; Inoue,

). Such triggering also may be an e ect onthe higher the fluidity of debris avalanche be- the physical process of debris avalanches. Thecomes, the lower the downsizing rate of hum- amount of data is insu cient at present to ad-mocks becomes. dress such issues. We need more examples also

The above phenomenon is explainable by from the viewpoint of the more intensive func-introducing the debris avalanche flow mecha- tional examinations, such that whether or notnism as follows : Among several dynamic em- the empirical relationships limited for Shiri-placement models (Ui ), an initial betsu and Usu volcanoes should be di erent-sliding and later plug flow of debris avalanche iated with those limited for Iwaki and Nasuhas been proposed for the mechanism of the volcanoes, as implied by Figures and . Fur-

et al., et al.,

ca.

et al.,

et al.,

et al.,

. Downsizing rate of hummocks

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Carrasco Nunez, G., Vallance, J.W. and Rose, W.I. ( )

placement mechanisms. Journal of Volcanology and

Crandell, D.R., Miller, C.D., Glicken, H.X., Christiansen,


Beget, J.E. ( ) Volcanic tsunamis. Sigurdsson, H.,Houghton, B.F., McNutt, S.R., Rymer, H. and Stix, J.(eds.) Encyclopedia of volcanoes : , Aca-demic Press.

Bernard, B., van Wyk de Vries, B., Barba, D., Leyrit,H., Robin, C., Alcaraz, S. and Samaniego, P. ( )The Chimborazo sector collapse and debris ava-lanche : Deposit characteristics as evidence of em-

Geothermal Research, , .Capra, L. and Macias, J.L. ( ) The cohesive Naranjo

debris-flow deposit ( km ) : A dam breakout flowderived from the Pleistocene debris-avalanche de-posit of Nevado de Colima volcano (Mexico). Jour-nal of Volcanology and Geothermal Research, ,

.

A voluminous avalanche-induced lahar from Cit-laltepetl volcano, Mexico : Implications for hazardassessment. Journal of Volcanology and Geother-mal Research, , .

Carrasco Nunez, G., Dıaz Castellon, R., Siebert, L.,Hubbard, B., Sheridan, M.F. and Rodrıguez, S.R.( ) Multiple edifice-collapse events in the East-ern Mexican Volcanic Belt : The role of slopingsubstrate and implications for hazard assessment.Journal of Volcanology and Geothermal Research,

, .Clavero, J.E., Sparks, R.S. J. and Huppert, H.E. ( )

Geological constraints on the emplacement mecha-nism of the Parinacota debris avalanche, northernChile. Bulletin of Volcanology, , .

R.L. and Newhall, C.G. ( ) Catastrophic debrisavalanche from ancestral Mount Shasta volcano,California. Geology, , .

Francis, P.W. and Oppenheimer, C. ( ) Volcanoes,second edition. p, Oxford University Press.

Fujita, K. ( ) Geomorphological development ofNasu volcano during the last years. Geo-graphical Reports of Kanazawa University, ,

. (J)Glicken, H. ( ) Rockslide-debris avalanche of May

, , Mount St. Helens volcano, Washington.

anonymous reviewer for constructive comments

Japan Geographic Data Center (leader : T. Sugai,

four andesitic volcanoes ; Shiribetsu, Usu, Iwaki,

distribution of hummock size on semi-log graph

ther study will provide the improved under-stand of development of hummocky landforms in improving paper. This study was supportedand their relation to debris avalanche nature. financially by a Grant in Aid in from the

the University of Tokyo), the Grant in Aid forThis paper examined quantitatively the size Scientific Research from the Ministry of Educa-

distribution of debris avalanche hummocks, tion, Science, Sport, and Culture of Japan, No.trying to find some new geomorphological sig- (leader : Y. Suzuki, Nagoya Univer-nificance of hummocky topography more than sity), and the Grant in Aid in for geosci-the evidence of sector collapse of volcanic entific research from Tokyo Geographical Soci-body. For comparative discussion, four hum- ety (leader : H. Yoshida, Chuo University).mocky terrains were selected from di erent

and Nasu volcanoes. The numbers of debrisavalanche hummocks interpreted from aerialphotographs are, for Shiribetsu volcano,

for Usu volcano, for Iwaki volcano, andfor Nasu volcano. They are typical cases

of freely spreading debris avalanches havingbeen developed over the skirts of volcanoes.The main results show that variation in hum-mock size is controlled primarily by the col-lapse magnitude and the fluidity of debris ava-lanche as follows.

. Size of hummock decreases downstreamtoward the distal end of debris avalanche. The

shows an exponential downsizing with an in-creasing distance from the source.

. Regression analysis of the size-distancerelationship indicates that size of hummockdecreases exponentially downstream for eachdebris avalanche, showing varieties both in in-tercept and slope of regression functions forindividual debris avalanches. The interceptindicates the initial size of hummock at thesource area, and the slope the downsizing rateof hummock.

. Based on the relations between the initialsize of hummock and the collapsed mass ofvolcanic body, and between the downsizingrate of hummock and the fluidity of debrisavalanche expressed by the reversed value ofequivalent coe cient of friction, these initialsize and downsizing rate of hummock are con-sidered to be controlled by the collapse magni-tude and the fluidity of debris avalanche.

We would like to extend our thanks to the

VI. Conclusion

References

Acknowledgements


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