Title Time Trend Analysis of the Plio-Pleistocene Sequence in the ...

Title Time Trend Analysis of the Plio-Pleistocene Sequence in theCentral Part of Kinki District, Japan

Author(s) Yamamoto, Kaichiro; Nakagawa, Yonosuke

Citation Memoirs of the Faculty of Science, Kyoto University. Series ofgeology and mineralogy (1974), 40(2): 45-65

Issue Date 1974-03-20

URL http://hdl.handle.net/2433/186597

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

MEMoms oF THE FAcuLTy oF SciENcE, KyoTo VNrvERsrTy, SERiEs oF GEoL. & MtNERAL., Vol. XL, No. 2, pp. 45-65, March 20, 1974

Time Trend Analysis of the Plio-Pleistocene Sequence

in the Central Part of Kinki District, Japan

By

Kaichiro YAMAMoTo and Yonosuke NAKAGAwA*

(Received October 8, 1973)

Abstract

A computer program has been designed to systernatically process stratigraphical, time sequencialdata for establishing the analytical methods of sedimentary environments. Using the program, aseries of time trend analyses were performed on the fourteen sets of coiumn data pbtained from deepwells and outcrops of the Plio-Pleistocene sequence which is distributed in the Osaka Plain, the central

part of Kinki district in Japan, and mainly consists of the Osaka Group. As the result, the time trends extracted from the columns show a definite pattern in common witheach other. The pattern indicates that the Plio-Pleistocene sedimentary sequence in this region canbe divided into four parts in terrns ofthe history ofsedimentary environments. Each boundary appears

to be consistent with the stratigraphical boundary of the Osaka Group generally accepted by rnanyauthors (IKEBE, N., 1970; and others). It has been clarified that such a systematic time trend analysis as performod in the present studyis very eMcient for the understanding of the history of sedimentary environments. Furthermore, ithas been also proved that the analysis can provide for processed data which are quite usefu1 in the further

comprehension of the history of sedimentary environments.

I. latroduction

Sedimentation generally takes place according to a certain trend called a trend

of sedimentation. Such a trend, however, tends to be overlooked or misunderstoodbecause of the existence ofaccidental factors in the records ofsedimentation, i,e., in

asedimentary sequnece forexample. Therefore, those accidental factors are required

to be fully removed in order to well appreciate the trend of sedimentation. Forthis purpose, the time trend analysis is considered to be one of the most usefu1 ways.

VisTEuus (1967) has given the rock-ranging, which expresses the strength oferosion by means of a graded number, to the bed as one of parameters which quan-titatively indicates the sedimentary environments. Then he extracted the trend of

sedimentation by smoothing the oscillating curve formed by a sequence of the para-

meters, and succeeded to obtain the several trends ofsedimentation concerning some

sedimentary sequences of the Permian, the Pliocene and oth'er ages. Thereby, he

* Engineering of Soil and Foundation Co., Osaka.

46 Kaichiro YAMAMoTo and Yonosuke NAKAGAwA

has been successfu1 in the correlation of columns observed from such sedimentary

sequences that scarcely bear either characteristic mineral associations or significant

fossils. As for the correlation, however, he emphasized in his works the necessity

of existence of a conmion trend among the columns to be correlated. A series of time trend analyses have been made on the several sets of the column

data derived from wells and outcrops relating mainly with the Osaka Group*.The purposes of the present investigation are as follows:

(1) Designation ofa systematic procedure and a computer program for the time trend analysis ofsedimentary processes.

(3)

(4)

Confirmation of the presence of any trend in common with all the columns

concerned with such a group as the Osaka Group, in which some sedimentary

facies abruptly changed their thickness and/or compositions.

Examination of the applicability of a trend of sedimentation, if any, to the

correlation among sedimentary sequences.

To investigate that what sorts of suggestions for the study of sedimentary

processes are obtained as the result of time trend analysis.

* The Osaka Group, the Plio-Pleistocene strata, distributed in the central part of Kinki district, consists of unconsolidated gravels, sands and muds, and partly contains marine clay beds and vol- canic ash layers (Fig, 1). The age of this group ranges from early Matsuyama reverse epoch to middle Brunhes normal epoch. The total thickness is 300-troO metres at the hillside, but generally much thicker under the alluvial plain. The lower part of the group consists mainly of sand and gravel beds; the middle to upper part is composed of the alternation of sand-gravel beds and 11 layers of marine clay bed, which are named Ma O, Ma 1, Ma 2, and so on upward. Ma 3 contains "Azuki tuff" consisting of two pyroxene andesitic tuff. "Azuki tuff" is datod within Jara- mi11o event, and is one of the most useful key beds in the group as weU as Ma 3 (Fig. 3).

The group yields a large amount of both animal and plant fossils. Stegoden akashiensis occurs in the horizons below Ma O; ElePhas shigensis from Ma O to Ma 5, and Stegodon on'entalis above Ma 5. The temperate Tertiary flora is found in the horizons below Ma 3, while the cold flora becomes dominant from Ma 3. The assernblage of microfossils suggests that the alternation of sand-gravel beds and marine clay bods in the middle to upper part of the group indicates the fluctuation of $ea level which occurred during the glacial and interglacial times.

U. Precedure

An intimate relatiomship is very likely to exist between particle sizes and their

sedimentary environments, in other words, particle sizes can be considered tonumerically indicate sorne aspect of their sedimentary environments. Therefore,it can be expected that the vertical tramsition of particle sizes we!1 reflecs the history

of sedimentary environments. The data obtained by the observations of theminvolves three kinds of factors, that is, a general trend (or functional trend), seasonal

effects and random errors named 7(t), (t') and t respectively. The observation ofa given series, z,, is defined as

Time Trend Analysis of the Plio-Pleistocene Sequence 47

zt= y(t)+6(t')+et

where t' is a relative time ina season. Therefore, if e(t') and ecould be suMciently

eliminated from the data of the observatiops, a certain general time trend of sedi-

mentary environments would be extracted. Although there are many techniques for this type of trend analysis, a moving

smoothing method (5 and 21 terms) was applied for finding local and general trends

and a Fourier analysis was supplemented for examining cyclic trends.

For the moving smoothings, two well known formulae as below were applied(VIsTEuus, 1967) :

1 {17.Zi+12•(Z-,+Zi.,)-3•(Zi--2+Zi+2)} Zcat,i= 35

' (for 5 terms one; i=3, 4,..., n-2)

1 Zcai,i=3so {60'Zi+57'(Zi-i+Zi+i)+47'(Zi--2+Zi+2)

+ 33. (Zi-, + Zi.,) +18.(Zi-4+ Zi.4)

+6•(Zi.-,+ Zi.,) -2• (Zi-6+ Zi+6)

-5.(Z,-,+Zi.,)-5.(Zi-s+Zi.s)

-3.(Zi.,+Z,.,)-1.(Z-io+Zi.io)}

(for 21 terms one; i--l1, 12, ...,n-10)

where n is the number of time points in a series of the observations, and they are equal-

ly spaced.

The Fourier analysis was performed as follows :

The Fourier coeMcients of the Fourier sine and cosine series were obtained by

the numerical integration. And the series was defined as

z,.t,k(t) :a,+ize]laicos ti t+izilbisin ti t;

m=(n-1)12 (when n is an odd number)

pa=(n-2)/2 (when n is an even number)

where k i$ the degree of the FQurier series, and

os Kaichiro YAMAMoTo and Yonosuke NAKAGAwA

1gksm--1

Then, from the Fourier coeMcients obtained by the formula above, the power-spectrums (SP2) were calculated as follows (HARBouGH, 1967) :

SP?• =a?• +b?•

where i is the degree of the Fourier series. The power-spectrums indicate how each

set ofthe coeMcients influences the oscillation of the series. Hence, the major periods

of the series, if any periodicity exists, could be observed in the power-spectrums.

Furthermore, the nonbiased variance S2 for each series (its degree, k, is 1 to m-1)

was calculated in order to observe the degree of fitness.

S2 ='E'(Zt ' Zcat(t))2

n'-2K-1

where n' reprensents either n, when n is an odd number, or n- 1, when n an even one,

There exist some differences between the observational value Z, and the calcula-

ted one Z,.t(t). As a result, it may be seen that the values based on the observations

are scattered around the curve ofthe calculated ones. In order to determine whether

such a phenomenon described above satisfies randomness or has any trend, one ofrun tests was adopted. The test was performed to examine to what degree the sea-

sonal effects and the randorn errors could be eliminated. The run test applied here

was carried out according to the following principles:

In the first place, one can fix a sequence of both positive (+) and negative (-)

elements depending on whether the individual observational value falls above or below

the calculated value (or curve). Such a sequence may be illustrated as ++-++

---- ++ for example. Hence, a run is defined as a sequence ofone or more simi-

lar elements, preceded and followed by different elements (MiLLER, 1962). In the

example mentioned above, there are 12 elements, and 7 of them are positive (+)and the remained 5 negative (-), and there are 5 runs. Then if it is assumed that

the sequence ofthe elements is ordered at random, one could estimate the expectation

and the standard deviation of the runs from the numbers of both the positive (+)

and the negative (---) elements. Therefore, it can be examined whether the number

of the observed runs is exceptionally low or high as compared with the estimated

expectation, and consequently the assumption could be evaluated.

In time trend analysis, it is often required to examine ifa time series has any

periodicity, and ifany, the period should be inferred. In order to satisfy the require-

rnent, one of the autocorrelation analyses was performed. In the analysis, a time

series partly overlapped itself, and the correlation coeMcient was computed in the

Qverlapped part. The Qverlapped part was gradually moved, and a serics Qf the

Time Trend Analysis ofthe Plio-Pleistocene Sequence 49

correlation coethcients was obtained as a function K(T), as

mmm Zxi.xi+.-Zxi.Zxi+./m - i--1 i;l i=1

follows (VIsTER:us, 1967):

K(r) m m m m ; (Z] x?• -(Zxi)2/rn)(E x7•,. -- (Zxi+.)2/nz) i--1 F-1 i--1 i---1 m=n-r (n is the number of the observation points)

where T is the lag value for overlapping, and x, is either the observational or the

calculated value. The better the fittness of overlapped part is, the nearer the value

of K(T) is to +1. Therefore, it is possible to infer the period of the periodicity,if any.

Before starting a series of the analysis mentioned above, it is required to collect

such data that the values are both quantitative and continuous, and the observedtime points are equally spaced. Actually, however, lithological characters are usually

described in a qualitative manner in the most of data from wells and outcrops.Therefore, in the present investigation, all the data were converted to quantitative

ones which have been named "assumed'mean size", as the following manner: Firstly, the sediments were divided into four components, that is, into gravel,

sand, silt and clay, and the numerical grades, 24, 12, 4 and O.5, were given to them

respectively. Then, the proportion of the components at every one metre wascalculated from the lithological description of a given series. And the ratios multip-

lied by the grade were totalled. Finally, the average of the totals of every 10 met-

res in the column of the series provided the assumed mean size.

Ill. Results

In the present investigation were processed 14 sets of column data, 12 of which

were obtained from wells and the rests from outcrops, The locality of the samples

is shown in Fig. 1, and some comments on the data are given in Tab. 1. All the data

were offered by Dr. S. IsHiDA of Kyoto University.

The data were processed by the four kinds of analyses described in Chapter II:

the moving smoothing method, the Fourier analysis, the run test and the autocorrela-

tion analysis. The results were output from a computer in certain printed forms,graphs or tables.

Several examples, the results on the data No.2 SHIGINO, are displayed in Fig.

2 and Tab. 2. The results of the moving smoothings are graphically shown in Fig.

2a. Where L is the sequence number of the unks, numbered from the top of thecolumn, Each unit has the thickness of 10 metres. Hence the value IOxL re-presents the depth. G(L), Y5(L), Y21(L) in Fig. 2a are the assumed mean sizeand the calculated values of 5 and 21 terms moving smoothings respectively. In


Fig. 2b are shown the given power-spectrums and the nonbiased variance of each

Fourier series. Where FA(N) and FB(N) are Fourier coeMcients; cosine and sinerespectively. The graph indicates that the values of the power-spectrums for N=2,

4, 10 and 14 are especially large (the one for N==1 should be excluded, because it

means the simple average ofobservations). It suggests the presence ofsome periodi-

cal trends whose wave lengths are 470, 157, 52 and 36 metres (corresponding to N=2,

e4z

OSAKA BAY11

ol

o 10

o3

o e14 1213

o5 e2

o6

o9

AMt. IKct4A

A Mt,S-IGI

tuo 10Km `Mt,NIJO

o

AMt.KATsuRAGI

o15

Fig. 1. LocatiQn ofwell and outcrop,


Tab. 1. Data (from well and outcrop).

NO. & NAME OFWELL/OUTCROP

TIP DEPTH ORTOTAL THICKNESS

REFERENCES

1. 0D-1

2. SHIGINO

3. KASUGADE

4. SENRIYAMA*

5. 0D-2

6. FUSE7. HOKUSETSU

9. DAITOSHI (OD-6)10. AMAGASAKI (OD-S)11. SAKAI-6-3Bl2. SAKAI--4--1l3. SAKAI-4--214. SAKAF4-315. KOKIGAWA*

907 m

500 m

430 m

374 m

667 m

700 m360 m

500 m700 m300 m250 m250 m250 m210 rn

Publishing Committee for theGround of Osaka (1966)

(1966); IKEBEet al. (1970)

(1966); (1970)ITiHARA (1961);I tmARA & TAKETsvJi (1967)Publishing Committee for theGround of Osaka (1966)

Publishing Committee for theGround of Osaka (1966);INAi & IsHiDA (1966)IKEBE et al. (l970)

(1970)MATsusHITA (l967) (1967) (1967) (1967)HARATA et al. (1963)

* outcrop

NevtNG sMOOTHING (5,21-TERHS}

VALuE OF HARt POINTS (,). Ie.eoee 2e,aooo Jo,eeoo

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11.000e 7.94e6-.eDea o.o-.oeeo e.D

Fig. 2a.

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t

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ro2 Kaichiro YAMAMoToand Yonosuke NAKAGAwA

FOURiEft ANALTStS fOuR:ER COfFHCIENTs,

COS SIN N FAcN) FS(N) 1 1,sog? O,o 7 2.f2"e O.sOTs j .o.14-6 .0,]?ST - -1.eis6 .?.2Tel 5 .1.11-e .1,?]2G 6 1.-sll O.elTs 1 e,4222 1.-sso e 1.2-61 1.)]7g g -1,2eSg o.e;J6 le .2.31?1 -O.61S2 ll -e.g]2t .o.seel 1? 1.-211 -o.oeol IS -i.463T .o.21ee 1- e,see" -?,sj2b 1) e.1?e- -e,1?ee le o.s2go -2.o12e ll .o.g)" -o,S221 le o.31se .e.4esg lg o.lee- .e,e6og 20 o,s?1- O.Ts16 ?1 1.0-IS .1,444g 1? e.e]v6 -o,ol-e 2] o,seLl o.?e"e Fig. 2b.

POtER SPE[TRuM AND VAkÅ}ANCE

POvER SPfCTHU- StG?(N)e.sTsolE o2 ----t.t.------i--.--tO.sbslsE OL -----}--------t---o,1?6ggE oo .e,leoo?E ol ..-......----.--tt--to.?e"-)E ol t---.---o,?eG?o[ ol .----t-.O.2]e)4E ol ---.--.e.]g;e2E ol ---tt.-t---o.111eeE ol t--..--o.sl?etE oi ----.-t----i----o.te-s3E ol ..----O,204t9E OI ---..-O.21g-IE ol --.----O.SlllOE OI -}-..-.-f---------O.l24-IE oO .O.-1?TSE OI ---..--.-}--o,lote)E el ..--O.?669SE OO ..o,11s"6E ol "..e,e)?TsE eO ..-o,3ies?E ol ...-..---D.11bllE.02 .a.se)g6E oe tt-

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---------------------t--t-------------------------------"--------.

.------t------------------------t-"-t-t--------------

Output example of power spectrum and

variance (data: SHIGINO).

Feu-[ie

vALuE eF

DEGREE

L 1 2 s . ' 6 T e 9 10 11 i2 11 1- 11 1- IT le i" 2o 21 22 ?s ?- 2) 2S 2T 2S 1" ]e st :1 J3 14 35 36 3T ss )y 4e 41 4? 41 -- -s -s -T

ANALVSIS . LOG]CAL VALUES

HAftt PelNTs c,)le.eoee lo.oooo 3o.ooeo

,

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:

DEGREF

L.;:3:;l l•: ,gI l51 l2: 11:: l:: lg` ii:13:;;' ie12e:;;: ;i.)]: 3;• l:: 3e:::: :21: :2:::.47

10

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Tlme Trend Analy sis of the Pl io-Pleistocene Sequence 53

FOURIER

VALuE OF

DEGREE

L 1 i ; : ; lg ig l: l: l: 20 il i: 2) 26 21 ?e ?e 10 31 ]? jl ]- ]b 36 11 se 1" 40 -1 -2 -3 44 -: -6 -1

ANALYSrS . LOG[CAL

HARK POTNTS (.)10.0000 20.0000IS

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Fig . 2c.

FeORIER ANALYStS

vALuE OF HAftK io.oeeeeEST FIT vALuES

bEGREE IS

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example of calculated value of Fourier

(data: SHIGINO).

54 Kaichiro YAMAMoTOand Yonosuke NAKAGAWA

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Tab. 2. 0utput ercample of run test (data: SHIGINO).

RUU TEST 065ERVED RUNMOVS S 3-MOVS 21 15FOUR 5 25FOUR 10 2gFOUR 15 3TFOVR 20 -3

MEAN vAR22,4ee4 lo.-e2-1-,o3To 6,oJST

24,4S9- 11.4S39 2-,-eg4 11.4s3g24,-O-S 11,39902-,-S9- 11,-es9

LOGICAL LOWER

16,1421 g,221g lr,e474 17,e4T- :T,Te69 IT,e4T-

UPPER

2e,e341le,e52231.ISIS3X,131SSI,021631,iS13

PLUS

2t 11 23 23 2S 24

MINUS

22 16 24 24 22 23

4, 10, 14). It is also estimated from the graph that the 15 degree Fourier series

(N=16) is the best fit series for the observations. The calculated values ofFourier

series are illustrated in Fig. 2c, where N-1 is the actual degree ofseries. The larger

the degree of series is, the more complicated the graph becomes. The results of the

run test are systematically printed out as shown in Tab. 2. MOVS and FOURrepresent the moving smoothing and the Fourier analysis respectively. The table

shows the position ofthe number ofobserved runs with regard to the lower and upper

950/. confidential limits. When the number of observed runs is not in the givenconfidential interval, it is necessary to reject the hypothesis that the observations are

randomly scattered around the calculated curve. Therefore, if the number issmaller than the value of the lower limit, one could expect the existence of a more

cyclic trend (periodicity with a shorter period, for example). Whereas, ifthe number

is larger than that of the upper limit, he could predict the existence of a more linear

trend. In this case are not excluded the trends which are indicated by the curve

obtained by 21 terms moving smoothing and the cur'ves of Fourier series for N=5and 10, but are rejected the trends indicated by the one of5 terms moving smoothing

and the ones of Fourier series for N equal to or larger than 15.

The results ofthe autocorrelation analysis are shown in Fig. 2d. The analysiswas performed on the series of assumed mean sizes (see Chapter II) and the ones

resulted from 5 and 21 terms moving smoothings. All the results of the analyses are rearranged in Tabs. 3 and 4, and Figs. 3 and 4.

The results ofthe Fourier analysis are shown in Tab. 3. In the right side column,

the set numbers of Fourier coeMcients, which show especially large power-spectrums,

are given with their corresponding wave length in parentheses, Except the data

ofthe four locations (OD-1, KASUGADE, OD-2, and KOKIGAWA), they indicatethat the sets corresponding to 30 to 40 metres wave-lengths possess some peculiarly

large power-spectrums. It suggests the presence of a certain periodicity with such

a wave-length as mentioned to be common. This wave-length seems to correspondapproximately to the vertical distance between two succeeding marine clay beds.

The result ofthe run test is given in Tab. 4. Those observed runs (see Chapter

II), which stay within the 950/. Iogical confidential interval, were framed. Thevalues in parenthcses show the corresponding wave-length of 50 to 80 metres, and


are about double of the wave-length, which is shown by the shorter periodicity sug-

gested before by resulting power-spectrums of the Fourier analysis. Further, itcan be concluded that the shorter one has unreasonably too high frequency to be

accepted as a general trend, because the hypothesis that the observed values, the

assumed mean sizes in this case, are randomly scattered around the cornputed curve

of the Fourier series, is rejected with respect to the shorter one of the periodicity.

As a result, it seems suitable to adopt the periodicity, ofwhich wave-length is 50 to

80 metres, as the one indicating the shortest significant wave-length. Namely,there is scarcely significance to accept any periodicity with a shorter wave-length

than the one concluded above as a general trend, because such a periodicity couldnot reject a null hypothesis that the periodicity is due to random errors on a significant

level. The wave-length of50 to 80 metres corresponds to approximately the vertical

distance between two marine clay beds inserting another marine clay bed between

them, the distance between Ma 6 and Ma 4 for example. As has been mentioned already, it is required to statistically examine the relation

between the observations and the calculated values (the expected trend). Therefore,

the periodicity and its ,wave-length must not be estimated only through the result

ofthe Fourier analysis. Most ofthe best fit Fourier series shown in Tab. 3 are suppos-

ed to possess numerous runs exceeding the upper 950/. confidential limit. Hence,it ought to be realized that all the best fit do not always show the general trend of the

time series, and, moreover, such a series is unsuitable for either exclusion of the sea-

Tab. 3. Result ofFourier analysis.

OUTCROP OUTCROP BEST- BASIC NO.OFCOEFFICIENT&CO- /WELL /WELL FIT NNrAVE RRESPONDINGWAVELENGTH NO. NAME DEGREE LENGTH (M) WHICH HAS ESPECIALLY (M) LARGE POWER-SPECTRUM

1 2+

3 4 5 6 7 9 10 11

12

13

14 15

OD-1SHIGINOKASUGADESENRIYAMA*OD-2FUSEHOKUSETSUDAITOSHIAMAGASAKISAKAI-6-3BSAKAI--4--1

SAKAI-4--2SAKAI--tF-3

KOKIGAWA*

36

16

17

3

29

22

9

1

22

9

9

2

2

4

870

470

380

340

620

690

330

480

680

290

230

230

230

200

2(870), 3(435), 11(87)

2(470), 4(157), 10(52), 14(36)

2(380), 4(127), 7(63)

10(38), 15(24)

2(620)

21(35)

7(55), 10(37)

18(28)

23(31)

4(97), 8(36)

4(77), 8(33), 9(29)

6(38), 9(29)

2(230),6(38)

3(1OO)

* outcrop data

o

100

200

300

400

sco

6oo

700

8co

900

m

OD-1

F10 MS 21 -

MalO

Ma9

Ma8

Ma7

Ma 6

Ma 5

Ma4

Ma3

mui

Ma2

Ma1

MaO

.6 ,e' e'

i>::l•

,- .-.

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ii

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FU SE

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HOKUSETSU F5

Ma6

Ma 3

Q

SAKAI -4 -1

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Ma8

Ma 7

Ma 6

@ z ttttMa5 tt tl .'-l•zMa4

SAKAI-4-2 F5

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1.1,Z..,.i-.1•i',

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SAKAI-4-3 F5

Ma9

tvlae

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QMa6

Ma5

LEGEND

1'e'6 S Ssaandndwrthgrevetsand etc

:-:-: sitt :s?\

[IIilil] granite

F5 Fourier series(N=5) FP Fburier series(N;10) tvtSM moving smoothed curve(21 terms)

aa<oj b(xsnclary based on the pattern of curve

Fig. 3. Columnar section of well and outcrop, and results of

moving smoothing and Fourier analyses.

SAKAI-6-3B F5

moMa9

Mae

Ma7

Ma6

Ma5

Ma4

Ma3

Ma2

Ma 3Azuki

Ma2

Mal

OD-2

+.+.

F10

11

,

N

:t

as

Y N 1 ,

1 , ' : ' , t t

t t 1 , t

tt '

tl

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AMAGASAKI FIO

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DAITOSHI F5

KA'SUGADE F5

MalO

Ma 9

Ma 8

Ma7

Ma6

Ma5

Ma4

Ma3

@

SENRIYAMA F5 F 10

MR7

Ma6Ma5

Ma4Ma3AzLki

Ma2

Ma1

k

'N,

-

a

r)!' a rx. (.• x, •? .-r N (. -) -'

KOKIGAWA F5

gezuki

:i a

a

Time Trend Analysis of the Plio-Pleistocene Sequence

K"}

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1 AMAGASAKrote t("IOm)

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1

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to

Fig. 4. Result of autocQrrelation anal YSIS,

57

58

Tab. 4.

Kaichiro YAMAMoTo and Yonosuke NAKAGAwA

Results of run test. Those within the logical limits are framed.

NO. & NAME OFWELLIOUTCROP

OBSERVEDKIND OF*.APPROX. RUNS MEAN

LOGICAL 950/. LIMIT LOWER UPPER

1.

0Dl

2.SHIGINO

3.

KASUGADE

4.SENRIYAMA*

5.0D-2

6,FUSE

7.

HOKUSETSU

MOVS 5 21FOUR 5

10 15 (62) 20 25MOVS 5

21FOUR 5

10 (52) l5 20MOVS 5

21FOUR 5 (95)

10 15MOVS 5

21FOUR 5 (85)

10 15 MOVS 5

FOUR 5(155) 10 l5 20 25 30MOVS 5

21FOUR 5

10 15 20 MOVS 5 21FOUR 5 (83)

10

58

30

37

43

45

55

63

34

15

25

29

37

43

26

9

21

2933

25

12

23

2733

51

29

43

47

47

4955

61

re

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36

co

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8

20

25

42.9

34.3

44.0

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14.0

24.5

24.5

24.5

24.5

19.0

10.9

20.4

20.4

20.5

16.9

8.9

17.8

18.4

18.5

30.9

23.0

32.3

32.3

32.3

32.3

32.5

32.5

33.4

25.2

35.3

34.6

35.1

35.4

15.9

8.0

17.1

17,5

34.0

26.4

35.0

35.0

34.4

35.4

35.3

16.1

9.2

17.8

17.8

17.8

17.8

13.2

6.7

14.4

14.4

14.5

11.5

5.2

12.3

12.7

12.8

23.4

16.6

24.6

24.6

24.6

24.6

24.8

24.8

25.6

18.5

27.3

26.8

27.1

27.4

10.7

4.5

11.7

11,9

51.8

42.1

53.0

53.0

52.0

53.5

53.4

28.8

18.9

31.1

31.1

31.1

31.1

24.8

15.1

26.4

26.4

26.5

22.4

12.6

23.3

24.0

24.2

38.4

29.4

co.o

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40.0

40.0

40.2

40.2

41.3

32.0

43.3

42.5

43.1

43.6

21.2

11.5

22.5

23,O


9.DAITOSHI

MOVS15

5

FOUR21

5

10

15

205

(53)

10.

AMAGASAKIMOVS

FOUR21

5

10 (10)

11.

SAKAI-6-3B

12.

SAKAI-4-1

13.SAKAI-tF2

14.SAKAI-4-3

MOVS1FouR

MOVSFOUR

15

2025

5

5i (73)

10

5

5

10

MOVSFOUR

5

5 (58)

10

MOVSFOUR

5

5 (58)

10

15.

KOKIGAWA*MOVSFOUR

5

5

10

(50)

31

31

14

2931

35

43

50

2837

39

45

4957

19

17

23

15

18

21

15

17

21

13

15

21

12

13

21

17.5

23.0

14.1

25.2

25.5

25,5

25.4

33.5

25.4

35.4

35.5

35.4

35.4

35.4•

13.0

15.5

15.3

10.5

12.5

12.5

10.9

12.5

12.5

9.8

12.5

12.5

9.6

11.3

11.5

11.9

16.6

9.418.5

18.7

18.7

18.6

25.7

18.6

27.4

27.4

27.4

27.4

27.4

8.4

10.3

10.2

6.3

7.9

7.9

6.7

7.9

7.9

6.0

7.9

7.9

5.7

7.0

7.1

32.0

29.3

18.8

32.0

32.3

32.3

32.2

41.3

32.3

43.5

43.5

43.5

43.5

43.5

17.6

2e.6

20.5

14.6

17.1

17.7

15.1

17.1

17.1

13.7

17.1

17.1

13.4

15.6

15.8

*

**

outcrop data

Corresponding wave length is given in parentheses.

sonal effects or extraction of the general trend.

Therefore, it seems reasonable to adopt the Fourier series for N=5 and 10.In the present study, those for N= 5 (F5) and N== 10 (FIO) were applied for the deep

wells, and for the relatively shallow wells and the outcrops, respectively. As a result,

all the shortest wave-lengths of the Fourier series were nearly same with each other,

that is, 60 to 90 metres. Furthermore, the several results of21 terms moving smooth-

ings were adopted as such curves that indicated the more general trends. Thosecurves and the column sections are illustrated in Fig. 3. It can be suggested that

the strata including the Osaka Group and the underlying beds are divided into the

four major parts as follows:


(1) The part•above Ma 6*;with a rather smooth trend. (2) From Ma 6 to Ma 2; the fairly high oscillating part.

(3) From Ma 2 to the point of the peculiarly low value of the wave appearing just below Ma O;,with a relatively smooth trend. (4) The one below the point mentioned above; with a relatively smooth trend. It should be noted that the boundaries of the four parts, that is, the minimum

points around Ma 6, Ma 2 andjust below Ma O, are identified in most of the data.

Especially the last one is clearly identified (Fig. 3). There are, however, several

peculiar differences concerned with the lowest part (4), namely, the part below Ma O,

between OD-2 and SENRIYAMA. The curve of OD-2 suddenly rises after sinking at just below Ma O as in the case

of OD-1, while the curve of SENRIYAMA does not show such a sign so clearly. The results of the autocorrelation analysis are illustrated in Fig. 4. The curves

show the sequence of the autocorrelation coethcients concerned with the results of

5 and/or 21 terms moving smoothing. CoeMcient K(t) and iag t are represented bythe vertical and horizontal axes respectively.

Those graphs show that all the sequences of the coeMcients, except the one of

OD-2, rise up to the positive side around t==80 and/or 150 metres. The fact sug-gests that the series of assumed mean size are equipped with the periodicity of such

periods. The longer period of them nearly corresponds to the thickness of any of

the parts which are defined before in dividing the sequence into the four parts. On

the other hand, the curve of OD-2 does not possess such a trend of the sequence of

the autocorrelation coeMcients. The fact may indicate that the trends ofsedimentary

strength of the two parts (3) and (4) do not much resemble each other.

IV. Geologicalconsideration

The trend of particle size changes in lake and bay sediments such as the Osaka

Group is considered to reflect generally the relative expansion and contraction of

sedimentary basins. Therefore, thc trends showing a similar fluctuation to each

other might represent a similar development of the basins.

It is recognized below the boundary C that the trend of SENRIYAMA is dif-

ferent from those OD-1 and OD-2 which resemble each other (Fig. 3). This seemsto suggest that the movement of basin building in Senriyama region differed fromthat in the vicinity of the Osaka City at that time.

It is found between the boundaries A and C that all the trends show almostthe same fluctuation. YoKoyAMA (1969), judging from the extensive distributionof the Osaka Group of this age and common occurrence of marine clay beds, has

" These horizons are according to the references in Tab. 1.

Time Trend Analysis of the Plio-Pleistocene Sequene 61

claimed that the sedimentary basin of the group expanded to its maximum in dimen-sion during this stage. Hence, it is probable that the influence of local movement

then was relatively so weakened and the trend in each location may have become to

show the similar pattern.

The difference in the trends becomes conspicuous again above the boundary A.

This may indicate that the sedimentary basin of the Osaka Group was not only con-tructing but also subdividing during this stage.

The alternation of marine clay beds and nonmarine beds has been consideredto indicate the fluctuation of sea level caused by the climatic change of glacial and

interglacial times.

The periodical oscillation recognized above the boundary B seems to suggestthe periodical sea level changes. According to the resuit mentioned in the preceding

chapter, it is reasonable to consider that the shortest one of its periods spans at least

two marine clay beds. The period, however, could be shorter in reality when taking

into consideration of the influence of the linear trend in the lower part. At the same

time another interpretation is also possible ; the marine regressions which had occurred

twice between Ma 2 and Ma 3, and Ma 4 and Ma 5 might have been larger inscale than those between Ma 3 and Ma 4, and Ma 5 and Ma 6, since the particle size

tends to be coarser in the beds which lie between Ma 2 and Ma 3, and Ma 4 and Ma 5.

In general the Osaka Group has been subdivided at Ma 3 into the two parts,the upper and the lower, using Azuki tuffin it asakey. However, the group couldbe divided at the vicinity of the boundary B, that is, at the upper boundary of Ma 2,

based on the trends obtained by the present investigation.

V. Coneludingremarks

As mentioned in the last chapter, it is evident that a definite pattern of trends

exists in common with all the columns in the region, the Osaka Plain. The factsuggests that a definite sedimentary trend had been preserved in whole the basin

through the development ofthe basin. Consequently, the general correlation amongthe columns can be carried out according to the pattern of the trends, although it

is not much accurate because the influence of oscillative trends in the pattern is

sometimes so intense that it is diMcult to identify the pattern in detail. Therefore,

two of the purposes, (2) and (3), mentioned in the first chapter, are considered to be

almost attained. For the purpose (4), several usefu1 suggestions contributing to the

study of the history of the sedimentary environments are presented in the last chapter.

Several working hypotheses are newly proposed based on the results of the investiga-

tion, in addition to the suggestions consistent with the facts derived from the previous

works. Therefore, it is desired that much more data wili be processed.

The way of processing and its computer program were designed in the study,

62 Kaichiro YAMAM(yro and Yonosuke NAKAGAwA

referring to the method adopted by VisTEuus (1967).

The assumed mean size was defined as a value of sedimentary strength whichquantitatively indicates a certain aspect of sedimentation (see Chapter II). The

procedure computing the value was designed so that the difference of sedimentary

strength would be ekpressed as remarkably as possible, and that the computedvalues would be ranked in as appropriate order among the basic values. For analternation of sand and silt, for example, the assumed mean size will be calculated

as (12+O.5)/2, that is 6.25, assuming that the alternation consists of sand and clay

with a propotion of one to one. The computed value, in this case, slightly exceedsthe basic value 6f silt, 4.

This method might be considered to be very crude. However, the computedvalues obviously show an appropriate order of sedimentary strength together with

four basic values, and, therefore, no serious problems could be found in so far as

the recognition of the general trends of sedimentary strength is concerned. Thevalidity of the argument may be proved by the existence of a definite pattern of trends

cornmon to all the columns. There is, however, no doubt about that any rankingof sedimentary strength with fixed values according to more complete, objectivedescriptions of lithology is much desirable for this kind of analysis.

VisTEuus (!967) has set up those fixed values based on the objective and detailed

standards for the descriptions of lithology. Since such standardized data, however,

have not been available, the computation method described a'bove was employedin the present study.

It may be concluded that 21 terms moving smoothing method is quite effectiveto find a general trend; the Fourier analysis is suitable to investigate the periodical

trends; the run test is not adequate to examine the significance of accepting the

trend obtained as a general one, but is eMcient for avoiding the acceptance of any

trend which is scarce of significance; and the autocorrelation analysis can show the

presence or absence of periodicity and its period, if any.

Finally al1 the analyses, being combined and supplemented with each other,were proved to be able to systematically analyze the geological time sequencial

data. And, they were all carried in the computer program designed in the presentinvestigation. Hence, the purpose (1) is considered to have been attained,

Acknowledgments

The authors are indebted to Dr. S. IsH:DA, Department of Geology and Minerl-ogy, Kyoto University, who kindly offered them all the data processed in the present

study and gave them many fruitful suggestions, and to Mr. K. HARADA, Department

of Geology and Mineralogy, Kyoto University, who helped for preparing the manu-script. All computations were done by using the facilities of The Data Processing

Time Trend Analysis of the Plio-Pleistocene Seuqence 63

Center of Kyoto University* . (PROBLEMNO. 5001 CF 653)

Referenoes

HARATA, T. et al. (1963): Plio-Pleistocene deposits in the Izumi region, south of Osaka. Earth Sct'. ("ChikJu Kagaku"), (66), p. 1-8. (in Japanose with English abstract)HARBovGH,J.W., and MERRmM, D. F. (1967): Computer Amplicatiens in StratigraPhic Anallsis. John Willey & Sons.IKEBE, N. et al. (1970) : Quaternary geology of Osaka with special reference to land subsidence. Jrour,

Ceosci., Osaka Citl Univ., 13, p. 39-98.INAi, N., and IsHmA, S. (1966) : Geologic investigations in the cores ofa observation well in Hokusetsu

region, Osaka Pref.. Geol. Surv. JaPan, RePt., 17(3), p. i69-175. (in Japanese)ITiHARA, M. (1961) : Some problems of the Quaternary sedimentarys in the Osaka and Akashi areas. .Ioar. Inst. Pol"tech., Osaks City Univ., ser. Geot., 5. p. 13-30.

ITiHARA, M., and TAKETsuJr, T. (1967) : The Osaka Group in the central part of Senriyama hills. Res. Commtmic. Ostzka GroteP. (1), p. 6-11.

KRuMBErN, W. C,, and GRAyBiLL, F. A. (1965): An introdttctien to statistical models in geotog7. McGraw-

Hill Book Co., New York.MArsusHrTA, S. (1967): Report of the synthetic geological survey of the Sakai-Senboku Littoral Industrial Zones, Geology. (inJapanese)Publishing Committee for the Ground of Osaka (1966): The Ground of Osaka (with collective duta of well-legs). Corona Ltd., Tokyo. (inJapanese)VisTELius, A. B. (1967: Stwdiss in Mathetnatical Ceoleg2. Consultants Bureau, New York.

YAMAMoTo, K. (1972): Development of Program Package for Geological Study. KJoto Univ. Data Processing Center ReP., 5, p. 41 1--413. (in Japanese)

YoKoyAMA, T. (1969) : TephrochronoJogy and Paleogeography of the Plio-Pleistocene in the Eastern Setouchi Geologic Province, Southwest Japan. Mem. Fac. Sci., K7oto Univ., Geol. Mineral., 36, p.

19-85.

1)

and

2)

Appendix; Computer Program**

Contents and procedureThe five kinds ofprocessings as described below are carried out by the program,

its processing flow is illustrated in Appendix-fig. 1.

(a) Convertion of column data to numeric ones.(b) 5 and 21 terms moving smoothing.(c) Fourier analysis.

(d) Run test.(e) Autocorrelation analysis.

InputsAn input data deck is formed as follows:

(a) Controle data for an option of processing and for designations of data kind*** and way of output.

.

*****

FACOM230-75 system is available. TheSee YAMAMoTo (1972) for more detail.TwQ kinds Qf data can be proces$ed; genera

system corresponds to IBM3601195 system,

1 and cplumn Qnes,


START

READCONTROLDATA

GENERAL

KINDOF DATA

WELL DATA

DATA

READ DATA

READDATA

CONVERT

THE DATA

PERFORMMS

MOV!NG

SMOOTHING

PERFORM

NOT PERFORM

FNALYSrS

FOURIER

ANALYSIS

PERFORM

NOT PERFORM

R TEST

RUN TEST

PERFORM

NOT PERFORM

AANALYSIS

AUTO-CORRELAT!ON ANALYSIS

EXIST

NOT PERFORM

NEXTDATA

ABSENT

FINISH

Appendix-fig. 1. Process flowchart ofcomputer program for time

trend analysis.

MS: MOVINGSMOOTHING F: FOURIER R: RUN A: ANALYSIS

(b) Sample source data.

i. General data: arranged in time wise.

ii. Column data: the no., upper boundary depth and litho-facies code*

* A numerical code consists of four digits. The digits indicate gravel, sand, silt and clay propotions

respectivÅëly. 250/. of propotion makes a unity in thedigit. For example, lithology of a sandand gravel bed is represented by a number 2200,


of each bed should be arranged in turn from the top of the column.

(c) A control datum for reporting the existence of following another set of data* to be processed.

3) Outputs (a) Prints ofinput data. (b) Results of the moving smoothings (graphically displayed). (c) Results of the Fourier analysis; Fourier coethcients, power-spectrums and

nonbiased variences (graphically displayed), and curves of Fourier series.

(d) A table resulted from the run test.

(e) Graphs resulted from the autocorrelation analysis.

4) Category for using the program When the program stored in a public file (magnetic disk pack) of The DataProcessing Center ofKyoto University are used, only such a card deck as in Appendix-

fig. 2 is required to be prepared. \NO card** and \KJOB card are requiredfor the informations of accepted and preferential turn and for the identification of

the user respectively. \DPFTRUN card calls out the program stored in the fileand starts it running. \JEND card indicates the end of the deck.

YJEND

data deck

\DPFTRUNVOL=PFO0461 CKA367.TTAN

\KJOB'

YNO

Appendix-fig. 2. Example of computer card setup for time trend

analysis program.

*

**(a) is unnecessary in the following sets.

These cards punched marks "\" onfor IBM360,

the head cQrrespond to JCL cards (Job ContrQl cards)

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