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Title Computer Aided Data Analysis for Geologic Problems : DataAnalysis of Grain-size Distributions of Bottom Sediments

Author(s) Yamamoto, Kaichiro

Citation Memoirs of the Faculty of Science, Kyoto University. Series ofgeology and mineralogy (1977), 44(1): 1-65

Issue Date 1977-08-30

URL http://hdl.handle.net/2433/186619

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

MEMolRs oF THE FAcuLTy oF SclENCE, KYOTO UNIvERslTy, SERIEs oF GEoL. & MINERAL., Vol. XLIV, No. 1, pp. 1-65, 1977

Computer Aided Data Analysis for Geologic Problems ' 'Data Analysis of Grain-size Distributions ofBottom Sediments

By

Kaichiro YAMAMoTo

(Received April 27, 1977)

Abstract

Data analysis of grain-size distribution of the recent sediments in Chijiwa Bay, Nagasaki Prefec-ture, was performed as a case study for showing the usefulness ofcomputer aided data analysis. Multi-

variate analyses discriminated several sediment types which are confirmed to correspond to distinctdepositional environments.

Introduuion

Multivariate analysis was recognized to be one of the most effective methods

for data analysis in order to interpret the complicated geological phenomena. Its

application, however, was not realized until the recent development of the electronic

computer, as it involves complicated and enormous computations. Since then,a number of achievements of data analyses have appeared in many fields of science.

Furthermore, the computer has promoted the development of many unique appli-cations. However, the applicational techniques of the computer analysis have not

yet been settled in geology.

During the last five years I have been developing computer programs at theData Processing Center, Kyoto University, with collaboration of many colleagues.In this paper, I attempt to historically review data analysis in geology, and describe

the outline of the computer supported system which I compiled. Finally I present

a case study which shows the usefulness of computer aided data analysis.

Acknowledgement

I wish to express thank to Prof. KAMADA of Nagasaki University for his kind

offer of the sedimentological data from Chijiwa Bay, Nagasaki Prefecture, to Dr.

Kiyoshi WADATsuMi ofOsaka City University for his financial support and encourage-

ment, and to Dr. Shinjiro MizuTANi ofNagoya University and Dr. Kunihiro IsH:zAKiofTohoku Univeristy for their suggestion especially on analytical techniques. I also

2 Kaichiro YAMAMoTothank Dr. Yasuo NoGAMi of Primate Research Institute, Kyoto University, for his

help with the manuscript.

Special thanks are due to Profi R. REyMENT of Uppsala University (Sweden),ProÅí D. F. MERRiAM of Syracuse University (U. S. A.), Dr. J. E. KLovAN of Univer-

sity of Calgary (Canada), and Dr.J. M. PARKs of Lehigh University (U. S. A.),for their most fruitful suggestion and constructive criticism.

I am also grateful to ProÅí Ichiro MiyAKE ofDoshisha University forpreparation

of the SPSS program in the Data Processing Center, Kyoto University, andintroducing me its procedures.

I wish to thank Prof. Keiji NAKAzAwA of our Department, and Prof. SetsuoOKuDA of Disaster Prevention Institute, Kyoto University for their encouragement

and fruitfu1 discussion during this work.

The work has been performed by using the facility of Data Processing Center,

Kyoto University for the computer analysis. A part ofthe programs was sponceredby the center for preparation.

Historical Review

The electronic computer, which has much higher speed and more reliableperformance than any pre-existed calculator, has made the statistical processing,which involves enormous amount of computations, easier. As the statistical proce-ssing becomes more popular by the advent of computers, the geostatistics dealing

with mainly the multivariate analysis has been rapidly developed. Although theeffectiveness of multivariate analysis was already realized in geology, the analysis

was performed by conventional hand-computation (MrLLER and KAHN, 1962) andless popular than the univariate analysis, because the number of variables and the

amount of data were limited due to a lack of high-speed computers.

Establishment of multivariate analysis for geological use has realized the classi-

fication ofsediments (IMBRiE and PuRDy, 1962) using factor analysis, and numerical

taxonomy using cluster analysis (SoKAL and SNEATH, 1963). Many results fromthese kinds of studies came out in the middle of 60's (McCAMMoN, 1966; PARKs,

1966; WEBB and BRiGGs, 1966). , Although the data analysis using computer enables the composite and ob-jective comprehension ofgeologic information, the application of multivariate analy-

sis was limited in some divisions ofgeology because of the descriptive nature of geolo-

gic data. In other words, the usage of computer and analytical methods requiredthe data of numeric and qualitative nature. Lately, however, statistical methods

dealing with non-parametric data such as original scale and nominal scale have

been invented (KRuscAL, 1964a, 1964b; SAMMoN, 1969; CHEETHAM and HAzEL,1969; HAzEL, 1970), and are applied to the geologic problems (CoLLyER and MER-

Computer Aided Data Analysis for Geologic Problems 3

RIAM, 1973). In addition to the ordinal calculation and geostatistical use, the computer, which

is combined with digital incremental plotters, developed in the late 60's, is utilized

for the spatial data handling; for example, contour mapping and triangular diagrams

(HARBAuGH and MERiAM, 1968; YAMAMoTo and NisHiwAKi, 1975a). It becamecommon to display P-diagram (RoBiNsoN, l963; NoBLE and EBERLy, 1964), T-diagram (WARNER, 1969) and triangular diagram (LuMsDEN, 1973) by computer,Lately the system simulation of sedimentary processes and tectonic movement has

been advanced by Harbaugh and Bonham-Carter (1970), Hattori and MizuTANi(1971), KoMAR (1973), DAvis and Fox (1972), and YAMAMoTo (1974a). MizuTANi (1974) attempted a histrical review of the computer applicationsto geologic problems inJapan and other countries. Many textbooks and introducto-

ry articles are: (1) HARBAuGH and MERRiAM (1968) on computer application;(2) HARBAuGH and BoNHAM-CARTER (l970) on computer simulation; (3) VisTELius(1967) on geomathematics; (4) BLAcKiTH and REyMENT (1971) on morphometrics;and (5) DAvis (1973) on statisticsin geology. From 1966 to 1970, Kansas Geologi-

cal Survey had been publishing the computer contribution series which containcomputer programs and their application examples. Many leading articles in thefield of mathematical geology appear in the Journal of the International Association

for Mathematical Geology that started in 1969, and Computer and Geosciencesbegan in 1975. According to the research survey conducted by MERRiAM (1969), 910/o of scien-

tisbs who answered the questionaire use the computer in some way, and 390/. of

them use KGS (Kansas Geological Survey) computer programs for simulation,plotting, correlation analysis, multivariate analysis, and trend surface anaiysis,

and many of them want to obtain the programs concerning the items mentionedabove. The report indicates that the computer usage for data analysis and plotting

is indespensable in the geological sciences.

Data Analysis in Geology

The problem under study is usually treated through a process shown in Fig.

L

Pr6blem Data Colleetion

{2)tESma•Data Analysis Synthestze

Fig. 1. General process ofdata analysis.

In the process, the data analysis is used to draw a critical information from the

4 Kaichiro YAMAMoTO

input data, and to evaluate it. In practice the procedure consists of selection of

proper method for analysis, calculation, and evaluation of the result. The procedure

is repeated as shown by the arrow in the text-figure, to obtain the final information

several analyses. The whole procedure is called computer aided data analysis. During the procedure, the computer should not only perform the necessaryanalyses, but also manage the data file by storing the data obtained from each analy-

sis, and by feeding them selectively back to the following analyses. The data analy-

sis requires a well designed package program which is composed of a number offunctions to the required procedures and of the function of data management.This demand has promoted the use of SPSS (the Statistical Package for the SocialSciences, NiE et al., 1975), by which the data analysis ofgeologic use can be carried

out (YAMAMoTo and N:sHrwAKi, 1975b; NisHiwAKi and YAMAMoTo, 1975). SPSS is, however, not perfectly applicable to the geological sciences, for the geo-

logic data is somewhat different from that in the social sciences, and most ofstatistical

pracedures are not designed for specifically for geological data analysis. The program

was modefied to be more applicable for the data analysis of geological use.

Data analysis using computer is divided into three categories:

(1) Recognition ofsimirality (classification)

ex, factor analysis, cluster analysis, descriminant analysis, variance analy-

sis, t-test, chi-square test, etc.

(2) Trend analysis ex. trend-surface analysis, time-trend analysis, multi-pass filtering, spectral

analysis, etc.

(3) Plotting and display ex. contour map, block-diagram, triangular diagram, histogram, scatter-

gram, pi and beta diagram, rose diagram, strike-line map, form line

contour, etc.

Computer Supported System for Data Analysis of Geologic Problems

In order data analyses, it is necessary for a package program to have both data

management functions and suMcient variety of the statistical procedures. In addi-tion, these functions must be simple. I have attempted therefore to compile pro-

grams chosen from SPSS, BMD (Biomedical computer Programs Dixon, 1973), BMDP(Biomedical Computer Programs P program, DixoN, 1975) and KGS, in order toachieve more eMcient data analysis. This assemblage of programs works as a single

system in practical use. The system is called "Computer Supported System for Data

Analysis of Geologic Problems" and will be described in the following paragraphs.

The system is designed to fu1fi1 the following requirements:


SuOicient procedare function: The main requirement of data analysis involves the use

of statistical analysis. For the general statistical analysis, I have used programs

in BMD (DixoN, 1973) and SPSS (NiE, l973), which are available at the Data Pro-

cessing Center of Kyoto University. I have also converted three programs,BMDPIM, BMDP2M, and BMDP3M of BMDP (DixoN, 1975), for a FACOM230-75 computer, in order to perform cluster analysis (Yamamoto, 1974c, 1975a),

because no procedure for cluster analysis is available in BMD and SPSS. I haveadded further programs from the KGS for cluster analysis (PARKs, 1970), clusteranalysis of qualitaitive data (BoNHAM-CARTER, 1967), and calculation of n-diagram

(WARNER, 1969). In addition to the programs mentioned, I have included pro-grams designed by myself in the system.

Data mangementfunction: This facility is required to store the analyzed data in data

files, and to maintain them for retrieval and processing. The result ofone analysis

will be registered in data file for the following analysis, if necessary. This ensures

the data management, selection of proper data, and transforming them. It is in-despensable, when we deal with a large amount of data, and operate the reportedfeed-back procedures. SPSS facilitates this ability.

Pregram of easl ttsage: It is important that we can prepare, withought diMculty,

the control parameters which inform a program of the contents ofprocedures. Since

data analysis generally involves a considerable number of procedures, this is anessential factor in performing the analysis effectively. I have used the programs

of SPSS and BMDP, as they are designed to require no apecific language for thecontrol parameters, and alllow free format data input.

Interchangeabilit" of data among the Programs: When we perform a series of calcula-

tions, the output of one procedure is often input into the following analysis. This

process requires the interface between SPSS and other programs. I have employed atemporary data file to establish a network among the programs, to make them function

as a system, and I have modified programs which could only use punch cards asIIO (input/output) medium, to utilize the other modes of I/O medium (i. e., tapeor disk).

Throughout the operations, programs from SPSS, BMD, BMDP, and KGS,and the other programs comprise a system. The structure and function of the system

is described in Fig. 2.

The system is composed of two main facilities, as illustrated in Fig. 2 ; the control

of data file which consists of a SPSS system file, and the three subsystems which

perform the data analysis. The data file will be treated by the data processingsubsystem, and the result is displayed by the display subsystem. The data transfor-

6 Kaichiro YAMAMoTo

INPUT

DATATRANSFORMATION

SYSTEM

FrLEMANAGEMENT

SYSTEMDATAFILE

DATAPROCESSINGSYSTEM

DISPLAYSYSTEM OUTPUT

Fig. 2. Schematic illustration ofthe computer supported system for the data analysis of geologic problems.

mation subsystem transforms the data by interpolation, when necessary. Theflow of the data among the subsystem can be seen in Fig. 2.

Since SPSS can only accept the data in matrix form, no program that employsthe data in the other forms can be incorporated in the system. In practice, however,

this limitation poses no serious diMcuity, for the data are usually prepared in matrix

form, and most of data can be described in the form.

The contents of each subsystem are follows:

The dataLlile management subsystem: Functions of the data file management of SPSS

include storage, retrieval, selection and transformation of data (NiE, et al., 1973;

YAMAMoTo and NisHiwAKi, 1975b: NisHiwAK! and YAMAMoTo, 1975). The SPSSsystem file utilized as data file storage consists of two components; reference infor-

mation about the data matrix such as size of the matrix and labels, and raw data

in matrix form i. e. variable by sample <called a case). As the subsystem can accept

data form and provide data to the other programs, it manages the data file for the

whole system (NiE, et aL, 1975, p. 80).

The data processing subs2stem: This is a subsystem to perform mainly the statistical

procedures. It contains the subprograms of statistical procedures of SPSS (NiE,et al., 1975, p. 96), and the statistical package programs of BMD (DixoN,1973) and

BMDP (DixoN, 1975). Besides, the other programs are supplied into the subsystem;

Q-mode cluster analysis using principal component analysis (PARKs, 1970) and clus-

ter analysis of qualitative data (BoNHAM-CARTER, 1967) from KGS, and Q-modefactor analysis for large-scale data (KLovAN and IMBRiE, 1971), and non-linear map-


ping algorithm (SAMMoN, l969; HowARTH, 1973). I have addedafewanalyticpro-grams designed by myself; trend-surface analysis, with polynomial and double Fou-

rier approximations (YAMAMoTo, 1973a), trend-surface analysis with moving averages

and maps of summit and river levels (YAMAMoTo and NisHiwAKi, 1975c), time trendanalysis ofstratigraphic sequences (YAbtAMoTo and NAKAGAwA, 1974).

The disPtay subslstem: The subsystem displays the data in files and output from ana-

lytic procedures, according to the plotting programs, by X-Y plotter, line printer,

typewriter, and other media. The programs in SPSS, BMD, and BMDP, for pre-paring histograms and scattergrams are included in the subsystem. I have designed

the subsystem programs for preparing contour map with an X-Y plotter (YAMAMoToand NisHiwAKi, I975a) and with a line printer (YAMAMoTo, 1976), for checkingthe input data of contour program (YAMAMoTo and NisHiwAKi, l975c), for perspec-tive plotting in three-dimensional space (YAMAMoTo, 1973a), for preparing triangular

contour diagrams, columnar sections, strike-line map, and for estimation of structure

contours from strike-dip data and mapping (YAMAMoTo and NisHiwAKi, 1975d).

Case Study

Data analysis of grain-size distribution of the recent marine sediments was per-

formed by statistical and computer techniques, to evaluate the computer supported

system in practical use. The analytical procedures and results are described and

illustrated as a flow diagram. The results are also compared with those studiedpreviously.

The case study deals with the unconsolidated bottom sediments of the Chijiwa

Bay, Nagasaki Prefecture, southwest Japan. Ali the original data are analyzed

by KAMADA (1966). To show the flow and the results of the analysis as clearly as possible, the pro-

cedures adopted in each step of the analysis are not discussed in detail. Thosewill be published separately. The sedimentary environment is not considered,for it is beyond the scope of the data analysis.

Data Analysig of Grain-size Distribution of the Recent Sediments of Chijiwa Bay

Several papers have been published on the bottom sediments of the Chijiwa(or Tachibana) Bay (see locality map, Fig. 3). KAMADA (1966) classified the bottom

sediments and estimated their sedimentary environments. INouE (1970) discussedthe relation-ship of the bottom sediment distribution to the current system in the

bay. KAMADA, et al. (1973) used the statistical parameters ofgrain-size distribution

8 Kaichiro YAMAMoTo(TRAsK, 1932), and classified the bottom sediments according to the standard of

INMAN and CHAMBERLEiN (1955) into :Type 1: composed of highly sorted fine sand; medium phi 2.0 to 3.0. .Type 2: characterized by sandy constitution; median phi O to 3, sorting coethcient

1.25 to 3.0 in general; subdivided into 2A and 2B.

Subtype 2A: composed ofcoarser grains; median phi about 2.0; skewness

more than 1.0. Subtype 2B: composed of finer grains; containing more than 50/, muddy materials; skewness less than 1.0.

Both types are gradually merge into each other near the point, where skewness is 1.0.

Type 3: muddy sediments; median phi 3.0 to 8.0; subdivided by 4Åë and 6Åë median

into 3A, 3(s-s), and 3B subtypes. It is a character of the sediments

NOMO

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Fig. 3.

x

o" KrLOMETERS

NAGASAKI

MOGI

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s /> ooo ooo

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Location of sampling stations: open circles

solid circles those of No. 2001 to 2160.

eeee A e

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rNDEX MAP

90,100

represent the points of No. 1001 to 1075, and

Computer Aiclcd Datu Analysis Ibr Gcologic Problerns 9

belonging to 3A and 3(s-s) that thc subtypes are less thaJi 1.0 in skewness.

The sorting coefFicient and its deviation increase, correlating to the median

phi, but the sorting coeMcient concentrate in 3.0 to 4.0 near the boundary

between the subtype 3A and type 4.Type 4: containing more than 509/, muddy materials; meclian phi more than 8.0.Type 5: composed ofpebbly material; median phi less than O.O (more than 1.0 mm in diameter) ; generally containing abundant fragments of organic origin.

In addition to recognizing these types of sediments, KAMADA et al., (1973) con-

firmed tlie areal distribution of tl]ese types in the bay, as shown in Fig. 4.

All these data were kindly offered by ProÅí KAMADA for this casc study. Usingmultivariate analyses and several kinds of display teclmiques, data analysis of grain-

size distributions was performcd on Recent bottom sedime.nts in the ChijiwTa Bay.

BOTTOM

NiSEDiMENT

AeNAGASAKI

%'a eb"S "s"s o'S l;'• .I:L;i{.l • I--

TYPES

p" ntzan- TOISHI ENOVPAAeA .. ""lirt •1.; .e ss.. R

- ---• - ---- -1 ''lt 'li'/1."/,''1111" i

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Zi,,?.;l.ti-l:,.t•i'/tiTil,;lr;t;,!i•.',i.l.k.)?2,,/S,11.,i.i./lilltt'S'Si-:...-.:.-tLi-i'ill•iii:3;'iM-

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Fig. 4. Areal distribution of the sedirnent types defined by Kamada et al. (l973).

Procedure

The data analysis on grain-size distribution of tlic Reccnt bottoni sediments

in the Chijiwa Bay was carried out using the computer supported system. Theflow ofwhole procedures and applied methocls are shown in Fig. 5. Main procedurcs

adopted at each step are summarised in Table 1.

10 Kaichiro YAMAMoTo

START s Data Preparation I Description of data pattern I Factor analysis to extract factors as indicators

of the pattern of grain-size

distribution curves, and to

classify sarnples t Cluster analysis for grouping lTest of significance of classification

1 Description of groups defined as result of

classification r Evaluation ofanalytic results l FINISH

Fig. 5 Flow chart ofdata analysis.

Table 1. Summarized table of procedures at each step of data analysis, Chijiwa Bay.

Step l.

*Step 2.

*

* * *Step 3.

* *Step 4.

* *Step 5.

* * *Step 6.

*

*Step 7.

*

Preparation of data, original and transformed

Data transformation

Description of data patternPreparation of scatter diagrams between each pair of statistical ahd compositional

parametersPreparation of histograms on sediment types defined by Kamada et al. (1973)

Preparation of triangular contour diagrams of sand-silt-clay system

Preparation ofcontourmaps ofwaterdepth, median phi, gravel and clay contents Factor analysis

R-mode factor analysis

Q-mode factor analysis

Cluster analysis

Preparation of dendrogram

Simplification of dendrogram

Test of significance of classification

Test for multivariate equality of means among groups

Computation of F-distances among groupsDiscriminant analysis

Description of group

BreakdownPreparation of triangle contour diagram for each group

Evaluation of analytic results

Crosstabulation between two classifications, by Kamada et al. (1973) and this

analysis


Step 1. Preration of orginal and transformed data

The data to be stored in the

SPSS system file should be in"case-variable" matrix form (see

Fig. 6). A case is the basic unit

of analysis for which measure-

ments have been obtained. Inthis study, the cases correspond

to the samples collected from the

bay bottom; No. 1001 to No.1075 and No. 2001 to No. 2160(see locality map Fig. 3). Fig• 6• Data form (matrix form).

Each case is composed of values for one or more measurements that have beentaken. These measurements are termed variables, and each case within a studywill have one value for each of variables. For example, the variables correspond

to the median size, sorting coeMcient, skewness and others in this study.

To each of variables is given a name which is used as index (see, Table 2).

CASEVARIABLE(Measurement)

(Sample) 1 2 3 4 5 6 7

OOOI 1 .5 A 1 12.3 6 5 AA

OO02 2 .3 A 3 13.5 8 5 AC

OO03 1.4 B 6 23.4 3 6 AD

OO04 o .8 c 2 18.1 2 4 BA

OO05 3 .1 B 8 43.6 9 9 BD

Table 2. Processing steps and data stored into data file of Chijiwa Bay.

Step Procedure Variable Name Attribute

1 Preparation of

original dataSTANOxYDEP

Station number of sampling point

x-coordinate of station

y-coordinate of station

water depth at station

MDMMMDPHsoSK

median diameter in mm

median diameter in phi-scale

sorting coeMcient (Trask, 1932)

skewness (Trask, 1932)

GSASI

CLMUD

gravel contenbs, O/. (SHEpARD, 1954)

sand contents, O/. (SHEpARD, 1954)

silt contents, O/o (SHEpARD, 1954)

clay contents, O/, (SHEpARD, 1954)

mud contents, O/o, SI+CL

VAROO1VARO02VARO03VARO04VARO05

weight O/. ofgrains coarser than -2Åë

between -2ip and -1di

between - 1Åë and Oip

between OÅë and 1ip

between 1ip and 2di


Table 2. Continued.

Step Procedure Variable Name Attribute

VARO06VARO07VARO08VARoo9VARO1OVARO11VARO12VARO13VARO14

between 2Åë and 3Åë

between 3Åë and 4ip

between 4ip and 5Åë

between 5ip and 6ip

between 6ip and 7ip

between 7ip and 8ip

between 8to and 9Åë

between 9Åë and 10Åë or finer than 9ip

finer than 10ip

TYPE sediment type defined by KAMADA et al. (1973)

2 Data transfor-

.matlon

VAR1O1VARl02VARl03VAR104VAR105VAR106VARI07VAR108VARI09VARIIOVAR111VAR112VARI13VAR114

phi percentile of 50/.

of 10 0/.

of 15 0/.

of 20 0/.

of250/.

of 30 0/.

ef 350/.

of tro%

of 45 0/,

of 50 e/,

of 55 0/.

of 60 0/.

of 650/,

of 700/.

3 R-mode factor

analysis

Q-mode factor

analysis

Fl

F2

F3

QFLIQFL2QFL3QFL4

first R-mode factor score

second one

third one

first Q-mode factor loading

second one

third one

fourth one

Classification GROUP code of groups

analysis

defined on the basis of factor

4 Classification by

cluster analysis

CAG3

CAG3D

code of groups defined on the basis of cluster

analysis

code of groups, more detail one of CAG3


In this study, the cases are diveded into two groups termed subfiles, in which the cases

of No. 1001 to 1075 and the cases of No. 2001 to 2160 are stored separately,

The data stored into the file are composed of the following variables.

GeograPhic variables: coordinate value, depth and number of sampling points. The

coordinate value is fixed by the coordinate system (Fig. 3).

Statistical Parameters (KAMADA et al., 1973) : median size (in millimeter and phi scale),

sorting coeMcient and skewness defined by TRAsK (1932). They are not only usedas indices to show some characters of the grain-size distribution, but also in this

instance, for the sake of comparison between the previous and present methods.

ComPositional Parameters (KAMADAetal., 1973): gravel, sand, silt, clay (SHEpARD,

(1954) and mud (silt+clay) contents. They are used to reveal somecharactersof the grain composition.

Sediment tlPes (KAMADA et al., 1973): according to INMAN and CHAMBERLAiN (1955).

Frequenc] scores: percentages of every unit phi, ranging from -2ip to 9 or 10ip and

both tails, by KAMADA. The measurements are analysed in this study.

Phi Percentiles: percentiles of every 50/,, ranging from 5 to 700/.. The values are

computed from the cumulative proportion by linear interpolation. The grain-size distribution was observed on particles up to 10Åë. The percentiles higher than

700/. can not be calculated for most samples.

Step2. Descriptionofdatapattern Several tables and figures are produced to extract some characters from the data

to be analyzed. With the aid of the tables and figures produced, the analytic meth-

ods employed in the following steps are to be selected. In this case study, the follow-

ing ones are prepared (see Table 1).

Scatter diagram: a diagram of data points based on two selected variables as shown

in Fig. 7, In this study, two kinds of scatter diagrams are produced using the SPSS

statistical procedure SCATTERGRAM; one is based on each pair of median, sortingcoefficient and skewness parameters and the other on each pair of sand, silt and clay

content values.

Histogram: an illustration of the absolute or relative frequencies as shown in Fig. 8.

In this case study, three kinds of histograms on the sediment types are obtained using


Frequency

Y

.

.

-e -- -- ' t- . . -- .- --- -- , . . .- -- . --i.

. .

x

30

20

10

Fig. 7. Scatter diagram.o

A B

Fig. 8.

CDECategory

Histogram.

F

the SPSS statistical procedure FREQUENCIES; one dealing with all the cases(samples), the second with the cases of station No. 1001 to 1075, and the third with

the cases ofstation No. 2001 to 2160. Further, the histogram on grain-size distribrtion

is produced for each case by using a specific program prepared for this study.

<1an

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ssathvaZ.x,tli/llll-.S,2•tT,•{•

"fl' a

Fig. 9.

CHIJINA SEDItrIENT COMPONENTS NHOLE ARERTriangular contour diagram, showing concentration pattern of sampleon three variables.

.polnts based

Cornputer Aided Data Analysis for Geologic Problems 15

Tn'angular contour diagram: a contour map showing concentration pattern of data

points in a three component system based on three variables, as shown in Fig. 9.

Contour maP: In this case study, four contour maps are prepared using the CMPP2program (YAMAMoTo and NisHiwAKi, 1975c) ; on the water depth of sampling points,

median Åë, gravel and mud contents.

Step3. Factoranalysis Factor analysis is characterized by distinctive data reduction capavility. Given

an matrix of correlation coeMcients for a set of variables or cases, factor analysis

techniques show whether some underlying patterns of relationships exist, so thatthe data may be reduced to a smaller set of factors or components.

If factor analysis is applied to a matrix of correlations between cases, it is called

Q-mode factor analysis, while the more common variety based on correlations amongvariables is known as R-mode factor analysis.

The factor analysis that subsumes a fairly large variety of procedures is carried

out in four stages: (1) calculation of the correlation matrix, (2) extraction of the

principal factors, (3) rotation to a terminal solution, and (4) estimation of factor

scores.

The first stage involves a calculation of appropriate measures of association for

a set of relevant variables or cases. The second stage is to compute eigenvalues and

eigenvectors of the correlation matrix. The eigenvalue indicates the degree ofrepresentation of the extracted factor to the information exhibited in the original

data. The eigenvalues are cumulated in order of factor extractions and is listedin values relative to the information content of the original data, termed cumulative

proportion of total variance. The eigenvector shows the relation of the extractedfactors to each variable or case. Appropriate factors are then selected, considering

the eigenvalue and the cumulative proportion of total variance. The eigenvectorsof the selected factors are expressed in a "variable/case-factor" matrix form, that

is called the principal factor loading matrix.

In the third stage the matrix is rotated to search for simple and interpretable

factors. Each variable or case is made exclusively related to a specific factor, during

the rotation. The relation between them is shown by a large factor loading. Eachfactor will be more easily interpreted from the variable(s) or case(s) related to it.

The cases can be ciassified into the groups related to factors.

In the fourth stage each factor attribute is numerically estimated, that is termed

factor score. The score is given to each case or variable in R•• or Q-mode factoranalysis.

In this case study, the following factor analyses are carried out (see Table 1).


R-mode factor anal2sis on Phi Percentiles: DAvis (1970)

analysis of frequency scores. The R-mode factorchosen to extract factors, which may adequatelypatterns observed in the cumulative frequency curve

BMD08M program is used for this analysis.

performed analysis on

reflect someof grainsize

the R-mode factor phi percentiles is

characteristics of

distribution. The

(?-modefactor analL),sis onfreeuencLy scores: KLovAN

fomed a classification using the Q-mode factor

this study the same method is adopted, and the

IMBRiE, 1971) is used.

(1966) and DRApEAu (1973)analysis of frequency scores.

CABFAC program (KLovAN

per-

Inand

Factor scores, factor loadings,

analyses are stored in the data file

andto be

the results of the R-

used in the followingandstcps

Q-mode factor (see Table 2).

Step4. Clusteranalysis Cluster analysis is used to classify the cases (Q-mode) or the variables (R-mode)

into groups. Among various methods available procedure was selected in this study,

in order to classify the cases (samples).

The distances (i.e. dissimilarity) among the cases are computed first. Forexample, iftwo cases (ii and i2) have X,,f and X,,d variables (j'-- 1 .vP), respectively,

the distance between two cases is:

dilt2=[t?.1

( Xiil' - Xi2j

l)2 ]2

The distances among the cases are expressed in "case-case" matrix form namedthe distance matrix. Based on the distance matrix, the similarity among the cases

are represented as a hierarchical dendrogram shown in Fig.10. The cases corre-spond to the branches at the left ends of the tree on the dendrogram, and the branches

are united to the root.

//l

Branches- 3 Å~xl

Root

/

Fig. 10. Dendrogram ofcluster analysis. Ends of branches correspohd to the samples (cases).


Cluster analysis has been successfu11y applied not only to paleontology, such

as the numerical taxonomy of species (SoKAL and SNEATH, 1963), classification of

faunal assemblages (HAyAMi and NAKANo, 1968; HAzEL, 1970; UJuE, l973), butalso to sedimentary petrology, such as the classification of limestones (PARKs, 1969).

It has, however, rarely been applied to the grain-size distributions.

In this case study, the chi-square distance based on frequency score is adopted

as a trial, and the computed results are stored into the data file to be used in the

following steps. The results of classification are stored in the data file (see Table 2).

Step5. Testofclassification The results of factor anaiysis and cluster analysis are compared with the interpre-

tation by KAMADA et al. (1973). The classified groups make their own assemblages

in multidimensional space, where each variable used for the classification defines

an axis, as shown diagramatically in Fig. 1l. To test whether the groups are clearly

separated in the space, discriminant analysis is applied to the classification.

Equality ofmeans and F-value distances are examined with discriminant analysis.

Testformultivariate equality ofmeans: to test the hypothesis that all the center of groups

are same in the multidimensional space mentioned above, using student t-test.If the hypothesis is verified, the classification is, in turn, considered to be invalid

statistically.

Calculation of F-value distances among the grouPs: to compute the distance of each pair

of assemblages in the space, and in practice, to search for the distance from the

center ofan assemblage to that of the other. The larger the distance value is, the

more suitable the classification is between the two assemblages.

Discn'minant anallsis: to re-classify on the basis of the distance from each case to

the center of each group. The distance is determined taking the group dispersion

Y Y SampleP i •- '':"' 1"'N :'::' '•:';"i•l';'ill:':GroupA /N)•':ii'i,i,1::a'sil.:l.ilil:'l

--- -- . :':':"::::' .'•si!/:•: ' GroupA " GroupB ''' GroupB •x. x Fig. 11. Groups in two dirnensional space. Fig. 12. Descrimination: sample P is classified into the group A, when the group A is larger than the B, even when the distances are same.

18 Kaichiro YAMAMoTointo account. For instance, if the distances from a sample to two groups are sarrle

in absolute value, the sample should be allied to more widely distributed group,

as shown in Fig. 12. According to this standard, each case is discriminated into

the most probable group. The fewer incorrectly discriminated cases, the moresuitable the classification is. Of course, a group from which few cases are re-clas-

sified into another is regarded to be clearly separated.

Step6. Descriptionofgroups According to the clsssification, which is obtained by the cluster analysis, some

groups are defined, and their characteristics are examined. For the purpose areproduced some tables and figures, the breakdown, and the triangle contour mapof each group.

Breakdown: to compute the means and the deviations for statistical parameters andcompositional parameters, and to test the univariate equality of means for F-values,

using SPSS statistical procedure BREAKDOWN. The larger the F-values are, theclearer the differences of the parameters among the groups.

Triangle contour diagram: to search for the concentration pattern ofcases on the sand-

silt-clay triangle diagram for each group, using the TRICON program.

Step 7. Evaluation of analytical results

To compare this classification with that done by KAMADA, et al. (1973), the

crosstabulation table is produced on both Classification A abcd A

CIassi- Bfication

BCFig. 13. Crosstabulation table:joint fre-

quency between two classifications are shown in squares.

27 8 2 3

o 11 5 4

3 1 12 21

classifications by using the SPSS statistical

procedure CROSSTABS. The table indi-cates thejoint frequency of each group for

each classification, as shown in Fig. 13. A

case, which is belonging to the "A" groupby classification B and to the "b" group by

classification A, is printed in the crossing

area of "A" group row and :"b" groupcolumn.

Results of ArLalysis

Description of data pattern

Scatter diagram: In the scatter diagrams based on each pair of median (MDPH),sorting coeMcient (SO) and skewness (SK) (Fig. 14), a positive correlation between


MDPH and SO is confirmed (Fig. 14a), but no definite assemblage is observed. 0n the other hand, in the scatter diagrams based on each pair of compositionsl

parameters, a negative correlation between SA and CL (Fig. 15b) and a positiveone between SI and CL (Fig. 15c) are confirmed. As shown in Figs. 15a and b,the samples contain neither silt nor clay, iftheir sand contents exceed 900/,. They

are almost constant in silt quantity, but increase exceedingly in clay, if their sand

contents are less than 300/,. The SI-CL scatter diagram indicates a tendency that

CHtJltiA, SCATTER6RAM (MOPH, SO,

F:LE CHIJI-A tCREAT:ON DATE .susFILE oNiooe oN2eooSCATTEHGRAM Of CDOvN} MDPH

1,-1 2.10

ss}

HAR,26, 19TS) C-IJS"A.BAY

MEOIAN OIAMETER tN PHI SCALE

2.T) 3.36 1,99

SEDIMtNT STZE

CACROSS)

-.62

APR,24,VATA(WITH TVPE)

SO SORT:NG s,2s s,ee

1"TS PA6E 2

COEFFtCtENT

6,Sl T.1--+"----"-----------+--"+---------+------"----------"-----+-"--------------------+--e-+----+----- :

e,2o . t l 1 s1,16 •

t : i t6,52 . : i l 1S,6S +

t l 1 1-,s- - i l : r-,oo -

l l l t'3,16 . : : : 1-2.32 +

I : t l:,4e + ; I : le.s'- - t t : 1.O,20 •

.

2-t- ---O--2 -232

- •--- -2t e 2-- --- -- . --- --- --2 ;. --

-t2 --2- ----- 22?- --

.

:

--- - "-- -- . -- 2" -- -- -- 3- 3- --- -- " t2-j-2- -2t 2 1- "----- - t-t 2.2 2 -2 22 -- •- --- -

- ?32- -":- - "- 2.

.

.

--

--

'

:--

t

.

.

-:

-- .

.

:

-- -

.

t

.

2

.

2

.

.

.'

.

i I : i ..1 l ; l . I i ; .; . : l i t + : I 1 l + i l z-l • t s l i . : t : 1 + l t ` : . I i : : +

-t----+----+----+--------------+---------+----+----+-e--+------"--------------e-+---------+----+------7.-S

e.20

7,36

6,52

s,es

-'t-

-,eo

3.i6

2.)2

1,-e

O,6-

.O,20

1,IS i,le 2.-1 3.0- 3,67 -.jo -,93 5,5b 6.i9 b.e2

CHIJItiA, SCATTEHGHAM

STATtSTtCS,.

CORRELATION CR).

STO ERR OF EST .

PLOTTEO VALVES .

Fig.

CMDPH, SO,ss)

e,7o3ss

"ssgte2)S

t---------

HSVuAHLD . tNTERCEPr (Al .

[XCLUDEO VALUES.

IS PRINTED IF A COEFFtC:tNT

(a)

O."9-Y9'

O.913T-

o

CANNOT tiE

14. Scatter diagram among statistical parameters:

(b) median against skewness (MDPH-SK) ;

APR,2-, 191S

StGNIFICANCE .

sLopE {e} .MISStNG VALVES -

COMPUTEO,

PAGE 3

o.ooooi

:.t3s2a

e

(a) median against sorting(MDPH-SO);(c) sorting against skewness (SO-SK).


CHtJtWA, SCATTEHGRAN tHOPH, SO,

FTLE CrlJl#k (CREATION DATE .sueFILE oNiooo oN?eooSCATTEHGRAM OF (DO"N) -DPM

e,29 ",62

so}

MAR,26, i9TS) CHiJ:-A.BAV

MLDIAN D:AMETER tN Pttt SCALE

e.g6 i,30 1,b3

SEOIMtNT StZE

"CR05S) 1.97

DATAC-ITH

SK

2,jO

APrt.24, i"7S PAGE -TYPE)

SKE"NESS COEfFIC:ENT

2,6- 2,9e S.Jl-+---------+-----"--+---------+----+d------"+---------+----+----"--tt----+----+---------+-----------

s,20 - t t 1 l7.S6 . I. 1. [ 1-6,S2 . 1 1. I 1s,be . t l l -- :-4-S4 - :" ; t

l4.00 . I t t l),lb . 't t s i2,S? . I 1 t :i.-s . 1 1 l le.b" . 1 : t l.O.20 .

--2:- ;-

.

--.

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. 2.---- t2 2-- -2

.2

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2-

02.

.

.

---2

" --

.

u2-) ---2j-3-

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:

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-- - .

-

-- -

. - -2 2 -- - . ---- - : -: :-

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.

--

.

.

- :: j--- - --2 -3 - -2 -2 - - -t-"- -- - - tt :2 -- : - t- - -2 t--- t-

.

-t-

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.

. i t t `

. I l I :

+ 1 J

t

r+

tt

tI

. 1 1

1

;

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t

t

t

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lt

.-+-------t-t----+---------+"------t-----"-+-------+----+----+-"------+"--+----+---i+----+----+tO,l2 O-b u.19 i.tj i.-b i,so 2.i- 2.-1 2,el ),1- 3-e

e,2o

1,36

6,S2

s,6e

-,e4

-,oo

j,l6

2,32

1.-e

e.s-

.O,20

CHIJ:-A, SCATTLRGRAM CptDPH.

STATISTtCS..

COHHELATiUN CR}.

•STD ERft OF EST .

PLOTTED VKLuES .

SO, 55)

.o,sle61

2,oes"23S

t---------

Fig. J4. Continued (b)

R StsuAREv

INTLHCEPT

EXCLuDED

{A) .VALUES-

:S Plt:NTED IF A COEFFtCIENT

o,uy6-e

S.ISSII

o

CANNOT 6E

APH.24, l97S

StGNIFtCANCE

sLopL (e)

MISStNG VALUES

COMPUTED,

PAGE 5

e,oooe:

.i.?sala

o

the samples concentrate on two lines, which cross each other near a point of 350/,

silt and 150/. clay. The silt contents are mainly increasing, so far as the mud con-

tents are limited within the point. On the other hand, only the clay contents re-

markably increase, if the mud contents exceed the point. These facts suggest that

the bottom sediments are classifiable on the basis of grain-size distribution, and

safely grouped into several assemblages corresponding to sedimenary enviroments.

Histogram: In the histogram of frequency distribution of sediment types (Fig. 16),

(loniputer Aided Data Analysis for Geologic Problems 21

CHIJIWA. $CATTERGRAM CMDPH, SO,

FtLE C":JitA tCREAT:ON DATEsubFILE oNloeo oN2ooo5CATTEHGHAM OF (DO-N} 50

O,2" O,62

ss)

. MAR,2-,

50RTi-G

O;96

1"TSi CHtJIWA-eAY SEVIMLNT SIZE

COEFF:CIENT ("CR05S) 1,)O 1,6S LVI•

OATAC"ITH

s(

2,30

APH,24, 191S PAGE 6TYPE)

SkEWNES5 COEFFICIENT

2.6" 2,9e ).3i---------------------+---------+----+----------t----------"+----i----+---------t------------------+-

T,-S - l I 1 I-,6Z - t I l 16,;9 . 1 1 1 1j.S6 + I I l l.4.93 . t I I I-,oo + I 1 I ;3.6T . I t I 13.04 + t 1 1 12.4i . I 1 : :i.ls . I l i 1i.:b .

.

.

.

.

'

.

-

2

.

.

.

-- . . 2--- -- .2- -) - 2- --- . .2 -")- .-- -- 4 2 2 -- - 4

.

.

.

. --.

.

2-

-- 2 . '2

-- 2 --

.

.

.

-

-

.

.

-----2- -- -

:

-- 2-- S --- -2- . .

::

2:': -; 2:

a2-2:.

-

.

.

-

--

-- --2

-- ---j 2-2--- -j2 .2S2- -"3-2- - .--22

.

`

..

.

.

. t I l 1 . t t t :

. I t l l

. E `

tt

+l

i

`

:.ril

l

.Il

t

I

.I

1

Il

+-t

I

z

1

.I

r

sl

.-+"-----------+----+-"-+-----------"----------""------------tt-------------"------+----------t

2,Si 3.1- }..s

T.4S

6,e2

6,i"

5,S6

-,90

-,so

3,sT

3,e-

2,41

1.IS

i,IS

O.12 O,-6 O,T" 1.1) lt-e i,ee 2,14 2.-T

CHIJIkeA. SCATTERGRAH (HDPH, sO. s))

5TATi5TICS..

COaRELArtON (H). .O.j12o) STD EHR OF E5T. 1.2b"e PLOTTED VALUES . 235

---------- l$

Fig. 14. Continued (c)

H5-uArtLD . O,1)S"2iNTLHCEPT (A) - J.76-i)[XCLUDEO VALUES- O

P"INTED :F A COEFFtCIENT CANNOT SE

-P".24. 19T)

SIGNIFKANCE SLVPE Cb) NTSS:NG VALUES

COMPUTED.

.

PAGL 7

o,eeoo:

.i,29UIT

e

Fig. 16c indicates more variety ofsediment types than Fig. 16b does. The collecting

area ofsamples No. 1001 to No. 1075 seems to be different somewhat in environment

from that of the samples NTo. 2001 to No. 2160.

The figures on grain-size distribution (Fig. I7) illustrate that the samples may

be divided into a few groups on the basis of the curve patterns. Then, the curve

patterns are compared with each other by using the multivariate analysis, in order


SCATTEHSRAM OF cHtJIh'A CSA,Sl,CV APR.IS, 19T4 PAGE 2FILE CH:eOIVi tCRtATION bATE s MA".Z2, ier4)sueFILt oNlooo oraoeoSCATTERGR-M OF COOIN} SA SANO R-TIO tACHOSS) $i SILT R-TIO 3.)" iO.62 1'i,To 24,Te ]1,-6 3e.94 46.u? So.10 60,le 6T.?e -------------t------+---------+--t------------------"+--"-----------------------t-+----+-"-------- ieo,oe .g I l . 90.2S .2 . E I + t'"' 1 ; t t.U2 t [ t I'...- I : t 1 2.. 1 1 1 1. ....t 1 : l, j. I t r :- --2 ..-1 t 1 TO.e4. - ----1 t + :.-..-.-...--..-.".---.9.gg..-9.7.-...h"....-..-..---.-.-.."...-.."""".--."--."-".""1 1 - ---- 1-- t I -2-.- t sl,:2i 'i/-i :-::- i si,., 1/ 'r..: ;: 22. I

: l-1 l t"a .. ; t I -- I-- -"6e! l ----- i- I l " l.• 1----.-----.-----.----.-----.- - -.-.".-.-.-.-.---9.--.-.--V-.-...--..--"-".".--".--."."":

I : . 1 t 1 t . s l : ' . I : t . ' l't 1 . t l l :

-- r : : : .

ioo,oe

90,lt

eo,s-

le,s4

61,12

si,4o

-:.6s

r1;.96 ;

l?2`?4 i

1 i12.S2 i

l 12,eo !

Fig. 15.

1

l

1

t

l

lT

fi1

1

l1

t

!

r

.

.

- ---.

.

. ..

4-.

..

::

:

:

It

t't

l

l

l.tt -'1

t-1.r- --r --: -- 2.3T---- --

.

.

.

.

.

.". I---t

--- - : -

.

.2

.

.

t---------------+----+---------+t-------+-------+----+---------+-"-+----+----+---------+"---------e.o 1.os 14,lb 2i,24 2e.Ot )b"v -2.-S -9.S6 S6,S- el,T2 70,eO

(a)Scatter diagram among compositional parameters: (a) sand vs silt (SA-SI);vs clay(SA-CL) ; (c) silt vs clay (SI-CL).

ls.ge

22,2-

i2,S2

2,tO

(b) sand

to classify the

size.

samples objectively according to the frequency distribution of g rain-

Triangte contour diagram: In the sand-silt-clay contour diagram (Fig. 18), some

concentrated area are confirmed. Fig. 18b is somewhat different in pattern from

Fig. 18c. Namely, the both figures show a common concentrated center, but theother center different; one is situated on the side of less clay content, while the other

is on the side of less sand content. It suggests that the collecting area of the samples

No. 1001 to No. 1075 is not the same in environment as that of the samples No.2001 to No. 2160.

Contour maP: The bathmetric map constructed by computer contouring (Fig. 19)

Clomputer Aided Data Analysis for Geologic Problems

ScATTERGRAM oF cH:JrvS (S-,sl,cL) ApRnS, igT" P-GE 4FiLE CHIoolvi ccREATtoN' DATE = -k.22, lgTg)sueFILE oNloeo oN2oeoSCATTEftGRAM oF (eowN) sA SN,O aATtO CACrt055} CL CLAv RATIO 3.9e il.9S lg,9T 2T,96 3S.9b 4j-94 51,9J S9,92 6r,e: IS.OO -+---+--"-".-.----"---..--"--+----"-+----.----.---+--"i----+.---"-"+---------+-------"--

23

10",OO• .9 r) :4 Il- l- eO,!S .2 1 : I : e",s6 . s l- 1 I Te,e- + t r l el,12 + r : l I s;,4e + ; ; 1 I 41,6S •. r 1 I li.96 . I r 1 r 22,24 . I 1 i I 12,}2 . 1 l 2,SO i

Fig.

shows a ri

and ato No.

from theof the

Themudin

to that

certaln

--•--22-- ----- - -- -- --- - -2- -2- -- - u-- ---

I---.".""-""."-."-9- . -- -• -- - . -

t+----+----+----+----+-------!

I

lt

I

t

lI

l!

lI

I

l;

l

r

I

l

:

t

l!

1I

1I

t1

it

:

l

li

.I1

l1

+l

II

r

.1

l

s

l

•+

l

:.-."....-v99g..-..99.....-..-......h-...".--...-....-."....."-.-.-.-.-"."-..-.".".".-.-.-.I -- ---2 l : 1 ------ ] i l -- ---- l t l }- -f --- 1 l r --2 -- t 1 -: 2- -2 .. I I : --l ; - -,1 1 : ..---1 r : .. .- t I : -2 1• I . ---l I T .-"9.-".."......t

.

2

.-I-

i

1-1-i'-i'1

-:vI.I- ---1

:-I--I-i

l -e1.t-+----+--

----------------------"t-------------------------: 1: I+ I: 1: I1 Ir :1 it 1l 2.-- J !-t--- -! 1 - -2i- -2- --1 l --- -2 --a 21 --+-------+---------------------+--t------+-t---------

ioo,oo

ge,2e

eo,s6

10,e-

61,i2

Sl' ,"O

4i'6e

31,9S

22,24

:2,S2

1,eo +. e.u 7,gg ;).98 2J.91 31.9b j9.9S 47.9- S5,9S 61,g2 li.9! 79,90

15. Continued (b)

dge structure in the central portion of the bay, surrounded a flat bottom,

submarine canyons also along the Nomo Peninsula. The samples No. 1001 1075 are collected from the submarine canyons, and those No. 2001 to 2160

central portion of the bay (see Fig. 3). The geomorphologic defferences bottom for both sampling areas should have influence on the characteristics

of sediments.

contour maps on the distribution of median phi scale, gravel contents and

contents (Figs. 20 to 22) show that the mud contents (Fig. 22) are rather high

the nearshore area, and indicate that an spatial distribution pattern is correlatable

of median phi (Fig. 20). The distribution of gravel contents are pathy in limited areas along the seashore line and the Nomo Peninsula (Fig. 21).

24 Kaichiro 'I'Apt{AMoTo

SCATTERGRAM QF CHrJ:WA CSA,Sl,CL)

FILE Crileelvi cCREATION DATE tsu"FtLE eNlovo ot,2oooSCATTERGRAM OF {:OWN) S[

S.9" 11.9e.++I

ItI

+rt

l!

+I

t

T

:

.I

+ -+- -+-

lApt,2i, 19T4)

S:LT RAT;O

19,97-+

21.g6 3S.9S+ +- -+- : 1 ! t s I t '-- i l ; It- T-- l- - -: - L- -l - I. o

(ACijOSS) CL

.3.9" )1.gS-+----+--d---- +----+i-

APR,iS,

CLAY

S9,-+----+- -

lgT4

RATIO

92 eT,el

PAGE'

IS.90

e

Tu,eo

6j,T2

Sb.6g

49.SS

l1

1

.r

1r

1

.1

::

1

+I

r

I

I

+1!

I

1

.tl

!t

.'l

1

r

+9

o

.

.

-

.

.. .e9

-

•-

.

-

.---. 9

.

-

-- .j

--t 2t

9-.-

2- - -2- - .

2--- ----s9

ts

II

1

I

tl

st1

1

1'

II

,

+- -------+----+----+----+- + I r s I . r ; 1 l + I : : i + I

42,4S

3b.40

2S.12

2- --

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Computer Aided Data Analysis for Geologlc Problems 25,

CHtJtWA TYPE HISTOGRAM

FtLE CH:JtWA CCHEArlON OATEsueF"t e",:eoo eNaaoeVARIASLE TYPE SEDtMENT CObE t 2

tA

2A

?e

3

SA

IB

.

s

VALtO MISSING

Fig. 16.

. SEP,IS, 1914) CHIJtu.8AY SEDIMENT

TYPE

--------e------- { ;S) s,- PcTtl:

-- C 1) O,4 PCT,ttl

---------.- ( ta) 4,) pcr111

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oesERvATIoNsOe5ERVArlONS

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-} i,T PCT

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.1..".""L".".";"""...1,"."."""..",.1",.."..1"..""10 20 3" 40 SO 60 70

.n).o (a) • of the sediment types defined by Kamada et al. (1973): No. 1oo1 to 1075; (c) samples No. 2001 to 2160.

.1so

".-""u"",,.,s go leo

'(a) whole samples;


CH:JIWA TYPE HISTOGRAM

FiLE CHtJIWA CCREAT;ON VATESUBFLLE ONZOOO

VARtAeLE TYPE SEDIMENT CODE l 1 ...{ 1) 1,3 1 T 1 2A --------- t 4) 1 : :

2B

. SEP,iS,

TYPE

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197-) CHIJIbuA.SAY

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1

IA

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----------------------t---------t---------------'------------------------- : : s""."":""," Db FREauENcY

oesERvAnoNs .OBSERVATtONS .

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CHIJIWA TYPt H;STOGRAM

FILE CH:JtWA (CHEATiON DATEsuBF:LL oN2oeo

VARIABLE TYPE SED:MENT COOE 1 1 --------------- ( r s l IA .-{ 1) O,6 : : : 2A -------{ b} r : l

?B

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VAL:D OeSERVAT:ON5 - 160 MZSSING OSSERVATIONS . OFig. 16. Continued (c)

. ,,.1,,".",.1.-."".1"""".T","H"1"".""t so 60 70 eO 9e :oo

Computer Aid ed Data Analysis for Geolog ic Problems

Åë

o

5

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-L..-Tt.-

1-li l-tt 1-1- l"-

tes-

-10Sl

10Se

101t

-

10 se m le co m

1{" 1-i-

Fig .17. Frequenc y distribution

to co se to sm to s s" w (a)

of grainsize, samples from the bottom of the

eo og

Chijiwa Bay.

27


Åë

o

5

10

o

5

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lele

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Computer Aidec l Data Analy sis for Geolog ic Problems

Åë

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10

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29


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Computer Aid ed Data Analysis for Geologic Problems 31

SAND

C)•/kZ&-$sw

1

?

'

[1'x<

c2

1

7

1

SILT CLRY

Fig.

CHIJINR SEDIMENT COMPeNENTS inHOLE AREg

(a)

18. Triangular contour diagrams, showing concentration pattern of samples diagram of sandsilt-clay three components system. (a) all sampies; (b) 1001 to 1075; (c) samples No. 2001 to 2160.

on triangular samples No.


SAND

<atÅíxl$lisx

-y fZziLltsZf7/zk21?t

!s //

/

"

SILTCHIJINAONIOOO AREA

SEDIMENTCOMPONENTSCLA\

Fig. 18. Continued (b)


SA Ni D

N

Å~

XXkx

'NS,g.

va

ISiuilSl,,,,lliZZ/,,,,t,•t".' }'gg'N {"s}slil; %Z N,

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(Å~

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x

CHIJINAON2000 PREA

SE [] IMENT coMpertiENTsCLAY

Fig. 18. Continued (c)

su KaichirD YAMAMoTo

taI `r

NOM8

NAGgS"Kl

"o r' T

Fl

AB"

c--y.it

ICTSH!rk: 'j

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id

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Fig. 19. Contour map of water depth (DEP) in meter.


o s"p

NOMO

/

NRGRSRKI

MO I

PENINSUTRpt sHZI

TOISHf

ulRBR d..

Åëb5.

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by

f3

CHIJIWA

I'

BAQ•

Y

tr

EH

.

1,

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KPZUS

KUCH

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Fig. 20. Distribution of median ip (MDPH).

ss Kaichiro YAMAMoTO'

e-w

NeMo

.

NRGRSRK!

MO

PENINSTR" SHI •

--.lli;/-

5•

I

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of•

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'

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ng •

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KRZUS

Kucn

JIHR

NOTSU

Fig. 21. Contour map of gravel contents (G) in weight percent.

Ciotnputer Aided Data Analysis for Geologic Problems 37

1"V rt#

CH JrNA

V NPGRspKI

! MONeMO PENINSU TRpt SHI/

.Z'X.

"o

I

n

gBg

TOISHI

o

`ep

o

0

20

o

.

CHIJINA BAY .

KAZUS

KUCH

.

NOT•SU

Fig. 22. Contour map ofmud contents (MUD) in weight percent.

Factor analysis

R-mode factor anal)sis: Three factors are extracted, judging from the eigenvalue

and cumulative proportion of total variance. To obtain the final factor loadingmatrix, three principal components are rotated (Table 3). The values are diagram-matically shown in Fig. 23. As the result suggests, the factors seem to have the fol-

lowing attributes on the cumulative curve pattern of grain-size distribution.

Fi...Size factor. Position of curve, for the factor Ioadings are positive and almost

same.F2,..Shape factor. Range ofthe curve.

F3,..Shape factor. Distortion of the curve. The negative score means that thecurve is distorted on the larger side of the proportion (O/,). The positive means the

contrary case, though the distortion will be smaller than that of the negative.


The correlation of factor scores to each statistical parameters (MDPH, SOand SK) are shown in Fig. 24a-c. Fig. 24a indicates strongly high correlationbetween Fi and MDPH, but Figs. 24b and 24c do not illustrate any one. Factor scores are plotted to investigate the relations among newly extractedfactors, Fi, F2, and F3, and among the samples based on the factor scores (Fig. 25a-

c). On the basis of the scattered diagram of Fi and F2 factor scores, the samplesare tentatively classified into four groups named A, B, C, and D, which seem to take

their positions parallel with each other on the diagram. The cumulative curves of

several representative samples of the four groups are shown in Fig. 26a, and their

positions on the scattered diagram of Fi and F2 in Fig. 26b.

The cumulative curves are reconstructed using the model obtained as the result

of the factor analysis. Although those of the samples which show unimodality offrequencies of grain-size distribution are well reconstructed, those of showing multi-

modality are not well reconstructed.

e-mode factor anatmsis: The computed eigenvalues and cumulative proportion oftotal variance are shown in Table 4a. Four factors are extracted, and they explain

94.70/. of total variance. The eigenvectors (the principal factor loading matrix

Table 3. Results of R-mode factor analysis using correlation matrix.

Variable F,Initial

F2 Fa Quartimax rotated

Ft F2 FsVARIOI (di 5)

VARI02 (ip10)

VARI03 (Åë15)

VARI04 (Åë20)

VARI05 (e25)VARI06 (Åë30)

VARI07 (ip35)

VARI08 (Åë40)

VARI09 (Åë45)

VARI10 (e50)VARI11 (ip55)

VARI12 (Åë60)

VARI13 (Åë65)

VARI 14 (e70)

O.892

O.950

O.974

O.987

O.993

O.995

O.996

O.994

O.992

O.988

O.983

O.978

O.970

O.962

O.409 O.313

O.219

O.146 O.087

O.028-O.023

-O.os8-O.107

-O.141

-O.173

-O.202

-O.219-O.226

O.104 O.059

-O.OOI

-o.oro-O.067

-O.086

-O.087

-e.o74

-O.022

-O.022 e.oll

O.055

O.103

O.119

O.885

O.945

O.971

O.985

O.991

O.995

O.996

O.995

O.993

O.990

O.986

O.980

O.973

O.964

-O.435-O.332-O.229-O.149-O.086-O.025 O.026 O.067 O.101 O.128 O.153 O.172 O.179 O.183

O.020-O.O03

-o.o"-O.067-O.082-O.088-O.080-O.057-O.029 O.oo9 O.048 O.096 O,I46 O,164

EIG*CUM•PCT**

13.32

95.2

O.55

99.1

O.07

99.6

(l3.32

95.1

O.53

98.9

O.09 )

99.6

***

Eigenvalue. Sum of squares offactor loadings in the parentheses

Cumulative proportion of total variance (O/,)


1.0

o.

o

Fl-t

: : : :i::::"'----- ':":'::i:': ;•::-:•::••• :- :-t::s.----lt•:,f,:.:. :.:.:,::d--. .i:I.:.:i: :t---:-:--:-;:-i-i-- -:t:-:J:-

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:.t::.:

i:::::':"tt t t+ tt

i.::'U

O.1

o.o

-O.1

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>

.9gs6 NeE 'et-

gsFig. 23.

u) oeomomo Ln omo"N pa th mev ut ut eo "`gsvngvnsg" fi amc u} eN co aOrN th eeoeooeor"-r-e. e e e- r-. e- e- t- t- r- r e-ct ae cx a ee ac et ac et tr at ntq(<<q(((q rt qq)>>>>)>)))>> Final factor loadings of R-mode factor analysis.

of these factors) are rotated by the varimax method. Then, the samples are plotted

in a coordinate, where each pair of vectors define X- and Y-axes (Fig. 27). Fig.

27 indicates that most samples are concentrated near the factor axes.

KLovAN (1966) employed the Q-mode factor analysis for grain-size frequencydistribution data and classified recent sediments into four groups on the basis of

grain-size characters. According to his procedure most of the samples are wellclassified into any of four groups, named 1, 2, 3, and 4, each of which is related to

one of four factors. There are, however, still remaining several samples which have

not any significant relation to each factor.

4Q Kaichiro YsxMAMoTo . By factor scores of Q-rnode analysis, variable(s) is/are selected, which is/are

closely related to each group, as shown in Table 4b. The group 1 is especially re-

lated to the 7th variable (frequency of3 to 4ip), the group 2 the 13th' variable (fre-

quency of 9Åë +), the group 3 the 4th variable (frequency of O to 1ip), and thegroup4 the 6th variable (frequency of 2 to 3Åë). Namely, the groups 1 to 4 areconsidered to be constituted from the silt, clay, gravel and sand rich samples,

respectively.

Ce"HELArtLN bF.T-Et- F4LTe-, ;CL'-tS

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-----t--------i-+-----------------------------+----+----+---------+-------------------"--------ny+------.c.2o u.)) it)u 2.eS 2.ev 3.)ti -.je ).oS .).eO (a)Scatter diagrams between each pair of factor $cores of R-modeparameters: (a) first factor score vs median (Fi-MDPH);coeMcient (Fs-SO).; (c) third vs skewness (Fs-SK).

d,)) . T.ju

analysis and(b) second

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ComputerAided Data Analysis .for Geologic Problems 4I

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.

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.

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.--

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i

: I

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tl I

l

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1,42

t e.s-

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i.Te

Continued

2,4i

(b)

j.e- 3.bT ".JO -.?3 b,)6 S,1" -.bZ T.-S

42 Kaichiro YAMAMOTO

COIIRELATION bFT.Ef.N FACTCk bCOHES

FtLE IEMF, tCRLATION L,ATt .sue-ILE vN!ooe ot,2eooSCATTEHgNAM OF CDO") VO

O,29 O.ts2-+----+----+---------

-hv STArl.SrtLAL V".uEb

JAN.1ts,!,)IS) LHIJI-A.-AY

rHl-•i fl.CTvl:

e."" i.3,J "bS-."--"+ -------

1 t 1 t : t l I 1, t : 1 : : : : t

-----+-

SEDIktLNT btl.E

CA[HtjSSJ

1.g'l

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bk

2.30----------+--t

JAN.29. i91) FA3E 2- TTPO

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a,6- 2.9s 3,)i),gT

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:

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Fig.

o.iu

24.

----------- e.-e v.'tg

Continued (c)

1.i3---------+

1.-e i--O 1.1- i.-1 i,el 3,1- s.-e

ComputerAided Data Analysis for Geologic Problems 43

CHIJIdA.CU.H.FA

elLE TCMPsueFILE oNieooSCATTERGRAM OF

2,li

i.66

1,?i

O.T6

O,Jl

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F.SCORES AbDeTION

tCRE-TION OATE . oNaeoo (OOtN) Fl

-i,13 -i.i6

JAN,tS, 1"IS}

FIRST fACTeR

-O,S9

CHtJl.A.eAV

.o,o2 e,ss

JkN.ie, 1915

SEVtMENT StiL bAT"-ITH TVPU "eRoss} n sLcoND -AcroH

i,ij 1.10 a,2e 2,1}

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CHtJ:dA,CU-H.FA F-5COReS ADb:TION JAN,le, 1915 PA"E 3 ' STATISTICS..

CeltRELATION tR). .e.O03eT HSuuSRLD . U.OOeUi S:GNtHCANCE . O,-T"-- STV ERR OS EST. 1,Oe292 SNTEHCEPT ") . O.SeSOiO.Ub SLePE (B} . .O,OOM5 PLOTrED vALu[S. i9- EtCLvDED vALuES. O MtSSiN" vALutS- o ,...-".., IS pR:NTED IF A CeEFFLcSENT CANNeT bL co-puTtO.

(a)

Fig. 25. Scatter diagram among factor scores of R-mode analysis: (a) first vs second factor

(FrF2); (b) first vs third (FrFs); (c) second vs third (F2-Fe).

I . i l l i . I i :. : . : : l i . .J.Ti

2tl:

1!6e

:,21

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score


CHtJl-A,CU.R.FA

FtLE TEMPsveFILE oNloeoSCATTERGnAM OF

F.SCORt5 APDrrION

tCREAT:ON DATE . ON2000 (DOhN) fi

-S,06 .2!S2

JAN,le, i91S}

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JAN,ie, i91STH TVPtS

rH:HD FACTeH

2,12t--"--t------------------+------e"----------+---------------"------+

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I t O,Sl . t i t l.e.1- . 1 i 1 t.e,s9 - : :

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CHSJI-A,CU-R.FA F.SCORE5 ADblTtON

STATISTIC5,.

CORRELATION CR). O,eOl-6 STD ERR OF ESt. 1.00a"V PLOTTED VALUES - iV-

"---------


.i,2i .o," u,21 i'.ui

RSeuAREO . e,ooOob INTERCEPT {A} - e,-93b2D.OS

EXCLUDEb VALUES. OT$ pRINTED LF A COEFFIclENT "kNol ot

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ComputerAided Datac Analysis for Geologic Problems 45

CH:JI".CU.H.FA

FILE TEMPSU8FtLE ONiOeeSCArTERGRAM CF

F.SCORES ADVITSVN

(CREAT:ON vAlt - ON2000 tOO-N) f2

.1,06 .2,J2

JAN.le, 197S)

SEtONO FACTOR

.i,se

CH:Jl-A.BAY

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(ACH05S}

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1

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CHIJtptA,CU.H-FA F.SCORES ADD[TloN

sTAnsrtcs••

CORRELATiON (R). .O,Ob3S" STD ERR OF E5T. LO]3eO PLOrTED VALUES . i--

--------{

Fig. 25. Contuned (c)

RsteuAREo . e,ou-be INTEHCEPT (A} . .e,2]eS9V.Ub

EXCLuDEV vAL"ES. O

, ]S PHrNTEP IF A COtFFICILNI LANNVI et

JAr,,ls, lg7S

St"N]HCANCE SLOPL tv)

MISSiNb VALUtS

CvMPblLD.

eAGt 't

O,ISS2h

.v.ebl:e

u

46 Kaich iro YAMAMoTo

dtemeter(6)

8-

7-

6 --

5 --

4-

3 --

2-

1-

o --

-1 --

t

.

LEGEND

.-----•----• e2 Group

------ A2 Group s•- c

GrovpGroup

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:.:.;.:',.-E{{.Jvii-:':'..----".-

' /::

.- ----- i-lt- - e-" --- --- .. t- t--- .-t . e- - .- -- -i -- ----t - .- .--l -- --tT- --i-

l / tt t- t -t tt /t tt -t t-tt t- tt tt';"'t::';"':';t..t".F :-tt "--

-.

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1

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t

xle23

tlO19

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t tl064

103]200B1021

c2053 2156

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7 / /` '

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// 2013 !.-:-.2iS7'

/• t---2oe6

Fig

•/••/•l

10

/. 26. (a) Cumulative curves analysis, and (b) where arrows show ascend

ltltll 2o 3o 4o so se 7o cumulative propartien {X)

(a)

of representative samples of groups defined by factortheir points plotted on Fi-F2 diagram of R-mode factor scores,

ing order of cumulative curves in (a).

Computer Aid ed Data Analysis for Geologic Problems 47

2oete 2 e21e4

2013e

1 LEGEND

eD26roup

OMGroup

102 OB Group

ec Group

1019

-1 104S 1

2ooe

10 1 i064

1033 21S6

21S4

2147 lo4e-1

21S7

20i3

-2 2ee6

F2

Fl


Table 4.

(a)

Results of Q-mode factortion of total variance; (b)

analysis: (a) Eigenvaluevarimax factor scores.

and cumutative propor-

Factor Eigenvalue Cumulative Proportion

1

2

3

4

5

6

7

133.12

53.76

25.65

10.05

4.46 3.17 1.45

56.65

79.53

90."94.72

96.62

97.97

98.58


Table 4. Continued (b)

Variable1 2

Factor3 4

VAROOIVARO02VARoo3VARO04VARoo5VARO06VARoo7VARoo8VARO09VAROIOVAROI1VARO12VARO13

O,OOI

O.O07

O.O19-;-O.O12

-O.139

O.344

O.840

O.318

O.208

O.053

-O.O13

O.053-O.077

-O.oo1

-O.O05-O.O13

-o.oos O.044-O.042

-O.039 O.155

O.233

O.327 O.287

O.146 O.8tro

O.031

O.140 O.433 O.741 O.439-O.158 O.073 O.096 O.087 O.Ol2-O.Oll

-O.OOI-O.057

-O.O02 O.O19 O.080 O.036-O.525-O.808 O.150 O.154 O.118 O.O02-O.023-O.Oll

-O.056

C-1"--, e.FA AeDtllON

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(a)Fig. 27. Scatter diagrams among factor loadings ofQ-mode analysis: (a) first vs second factor loading (QFLI-QFL2); (b) first vs third (QFLI-QFL3); (c) first vs fourth (QFLI-QFL4); (d) second vs third (QFL2-QFL3); (e) second vs fourth (QFL2-QFL4); (f) third vs fourth (QFL3-QFL4).


CHIJIvA. e.FA ADDIT:ON

FILE CHIJt-A (CHEATION PATE .sveFtLe oNleoo os2eeoSCATTE-GftA- OS tDevN) eFLI

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Cluster analysis

Several methods of the cluster analysis were carried out, and it was clarified

that the cluster analysis based on chi-square distance of frequency scores is the most

suitable in this case. The analyzed results are discussed below.

Four major branches are observed in the simplified figure (Fig. 28). Theupper branch is further subdivided into three subbranches. As the samples be-longing to the lowest branch are rather limited, the branch is omitted in this case

study. The second and fourth major branches are subdivided into two subbranchesrespectively. Thereby, seven clusters are observed in the figure, and named as the

Ai, A2, D2, Di, C, B2, and Bi group in descending order. The group names corre-spond to the classification by the factor analysis. By using the dendrogram of the

original outputs (Fig. 29), the more detailed classification is attained, as shown in

the figure.

The convergence of each cluster is very good, and the separation of one cluster

from the other is also good. It is rather easy to recognize the cluster structure.

52 Kaichiro YAMAMOTO

A.i

A2

D

Di

c

a(

Bi

Fig. 28. Simplified dendrogram of output shown in Fig. 29.

Q-modecluster analysis, compiled from original


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More


Statistical significance of classification

Classi cation b] thefactor analysis: As shown in Tabs. 5a and 5b, the distance between

each pair of groups is significant at 1O/, significant level, and the equality of means

among the groups is rejected 10/. significant level, so that the multivariate means

of the groups are different each other. As shown in Tab. 5c, the discriminationof each sample is excellent, for almost all samples are discriminated into correct

group.

Table5. Discriminant analysis of groups defined by factoranalysis with frequency scores and phi values: (a) Test for multivariate equality of means; (b) F-distance matrix (D. F.=14, 172); (c) Re-classification by discriminant analysis. (a)

U-statistic

Approximate F

O.02927 ,17.72478

D. F.=14, 4, 185

D. E = 56, 671.22

(b)

GroupA B C Dl

Group

BCDID2

15.24

47.29

14.44

tlO.05

9.66

30.02

62.26

58.37

104.13 7.94

(c)

D2Number of cases classified into group

Dl A B c

Original group

D2DlABC

22

2

o

o

o

4

21

4

o

1

o

1

67

1

o

o

o

3

28

2

oo

o

2

32

Classi cation by the cluster anatmsis: As shown in Tables. 6a and 6b, both the distances

among the groups and the rejection of a null hypothesis on the equalty of means are

significant at10/, significant level, The discrimination of each sample is also very

good (Table 6c). Several samples of the Ai group are, however, discriminated into

the Di or A2 group. The fact suggests that the Ai group is situated between the

Di and A2 groups in the space, based on the variables used for the classification,

and that the Ai group is a transitional or overlapping of the latter groups in the dis-


tribution pattern of grain-size. Judging from the distance, the groups may be ar-ranged in the order: the Di, Ai, A2, Bi, and C group, on the basis of the similarity

among them. Examining each neibouring pair of the groups, the distance betweenthe B2 and B! groups is especially small (4.14), in comparison with the others having

usually 11.85 to 18.11. The division between the B2 and Bi groups is more detailed

than those of the other pairs.

Table 6. Discriminant analysis of groups defined bycluster analysis with chi-square distance of frequency data: (a) Test of multivariate equality of means; (b) F distance matrix (D. F.=14, 174); (c) Re-classification by discriminant analysis.

(a)

U-statistic

Approximate F

O.02048

l5.02178

D. F.=:14, 5, 187

D. F. == 70, 832.49

(b)

Al A2Group Bl B2 c

A2 BlGroup B2 c Dl

l1.85

30.72

21.39

82.12

18.77

12.68

10.90

54.29

34.43

4.14

14.41

64.34

17.12

46.39 127.73

(c)

Dl Number of cases classified into groups

Al A2 B2 Bl C

Dl AlOriginal A2 groUP B2 Bl C

25

4

o

o

o

o

1

41

1

o

o

o

o

8

39

3

o

o

o1

2

13

1

o

o

o

o

2

25

o

o

o

o

o

o

27

Ctasst:tiication made b" Kamada et al. (1973): As shown in Tables. 7a and 7b, a null

hypothesis on the multivariate equality of means is rejected at 10/. significantlevel. The distance between each pair of groups is significant at 10/. Ievel, except

for that between the 2A and 2B groups, which is not significant. Combining the2A and 2B groups into a group, five groups are tested by discriminant analysis.

The result (Table 7c) shows that many of the samples belonging to the 2A and 2Bgroups are re-classified into the group 1, and that some samples of the group 3 are

56 KaichiroYAMAMoTo 're-classified into the group 3A. Therefore, this classification is indistinct especially

in the separation between each pair of the groups 1, 2A and 2B.

Table 7. Discriminant analysis of sediment types defined by Kamada et al. (1973) : (a)Test of multivariate equality of means; (b) F distance rnatrix (D. F.=8, 215) ;

(c) Re-classification by discriminant analysis.

(a)

U-statistic

Approximate F

O.03000

29.03202

D. F.==8, 5, 222

D. F.=40, 939.96

(b)

1 2AGroup 2B 3 3A

2A 2BGroup 3 3A 3B

5i13

7.38 5Lll21.14

106.51

2.42

27.18

11.67

60.90

82.21

35.58

216.34

22.88

40.25 109.80

(c)

1Number of cases classified into groups

2A,B - 3A - 3 3B, 4

Original

group

1

2A, B

3A3

3B, 4

14

12

o

1

o

2

ca

o

o

o

o

5

39

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o

o

o

1

381

o1

o

2

56

Description of groups

Breakdown: The general statistics of each group, which is classified by KAMADAet al. (1973) and the cluster analysis, are shown in Tables 8 and 9. The tables describe

the mean and standard deviation of the statistical parameters for each group.

Table 10 illustrates the difference of each parameters among the groups. Themedian, sand, silt, clay and mud contents are remarkably different among the groups.

The difference between two classifications is tested by the F-values of gravel contents

(G), sorting coethcient (SO) and water depth (DEP).

Triangle contour diagram: A

is produced for each group,

the original dendrogram (Fig

triangle

which is. 29).

contourdefined

diagram ofby the cluster

sand-silt-clay

analysis and

(Fig. 30)

shown in

L

Cornputer Aided Data Analysis for Geologic Problems 57

All

mean

the groupslocations are

except for the

different fromgroupeach

Ao show good iso

other as shown

lation

in Fig.

in the figures.

3LThe

Table 8. Description of groups definedcompositional parameters.

by cluster analysis, concermngstatistical and

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Table 9. Description ofstatistical and

sediment types definecl by

compositional parameters.Kamada et al. (1973), concernlng

PltE"OU.N OF C":Jt{A

FrLt cHIJh4 (cStATteN )41E .SudFILL oklouo eN2oco

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---------------t--------------------d-v-LVF- L-ftE: bU-

9-s."leJ

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ComputerAided Data Analysis for Geologic Problems 59

CRITEqtO- enokE-i

vAVIAULL O:ptr- By

GTVPt

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vAHIAtiLt ceoL ViLL[ LlbU su" -E-H STC utv vAeli-cE -

se" i-T:HE PcPuL"IUK tn).edov )T. ITCt 1-.-leb 2T--11o2 ` 1)J)

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1-t-lej1-j-`'

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60

Table

Kaichiro YAMAMoTo

10. Univariate variance analysis of compositional parameters.

statistical and

Procedure TYPE CAG3Degrees of

Freedom

8

226

6

228

MDPHsoSKGSASI

CLMUDDEP

251.1

39.6

ILI 24.0

224.4

131.7

117.5

213.2

4.9

341,8

51.6

11.5

l2.6

399.8

228.2

166.4

389.6

17.2

t-kn snNo 5A,,O

#t.

1/.

't

.tt/-' i7•""

t

=-'

S/LrS:tSirJ-".l -EomENT, tecH ceoup e-sEo eN cL

s--o

SILTSraiJUn SEPS"EliT, E"H OReue e"sEo ok cL

snNo

SILT L esJy- sEoleEHT, tAcH onyoup eqsiv eH cL

S-NO

Sl{T L, iH.:J;,-.t SEOLHtNl, cncH pteup tAsto o" [L

SnNO ss as li'x

tl.

SILTS:SiJl,-- SEOIMENT, EgcH atovp e-sco o" tL

S-NO

S:LT L scSiJL"n SEU:"E-T. EAcH a-OuF epsED e- tL

sn-o

Sl:t SUt E• :Si"1Jit-P S[Dr"tNT, t"CH Gtou- egsEo ek cL

Fig. 30. Triangle contour diagrams, diagram of sand-silt-clay.

Al-1; Al-2; A2; AO;

t StLT Tsnl-Jwa sEolHE-T. Eat" oeeue lAsEo oN cL Åí:sti.lw- sEvmEe4T, Ea[- a-c:" eqsEo o- [L

showing concentration pattern of samples on a triangleProduced for each group defined by cluster analysis:

Bl; B2; C; Dl; D2group.


SAND

Al-1

1-7

,N

e

BtB c

e-

c

s.

A2&

Al`2

AO

"

Ol

&

Fig. 31

Dl D2 SlLT. Configuration ofconcentration centers ofgroups defined by also Fig. 30.

CLAYcluster analysis, see

Evaluation of analytical results

The crosstabulation table between the two classification by KAMADAetal.(1973) and by the multivariate techniques demonstrated in this study are given in

Table 11. According to this table, the sum of the groups Dr and D2 in this study

corresponds to the group 3B by KAMADA et al., the sum of the groups Ai and A2to that of the groups 3 and 3A. But the groups containing coarser grains have no

clear correspondence between the two classifications.

This may influence the interprepation of the sedimentary environments of the

Chijiwa Bay. As shown in this case study, the cluster analysis and factor analysis can classify

the samples easily, definitely and in more detail, and the multivariate disciminant

analysis can reveal the characterisrics of classified groups and the relation among

them.

62

Table

Kaichiro YAMAMoTo

11. Crosstabulation table between two classification by Kamada et al. (1973) (across side) and by cluster analysis (down side). Numbers in each cell indicate count, row percent, column percent and total percent in descending

order.

CHIJt-A

f:LLSUtsFILE

----- CAG3""---

CAts3

A;

A2

-ts--

e2

c

Ol

bl

CH:CRAMER,S

KENDALL,SKENDALL,SGAMMA .SOMER,S D

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SeuARE vCONTIN6ENCY

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l "i Ll u; eE ei vl 2Sl -1 O: } v.o L o.c, l o.{J i e.e s v,o t o.o t es.2 t 1-,e 1 o.o 1 i v.o i u,u l b.e l v.u t L•.o l o,o l -o.- liuo,o t o,o 1 I u.o l u,L 1 u." i e.o : o,v : e.u ; g.s i 1.7 : o,o l .i.-..."-;..-.""t".--..1.--..".l-"--".1--".-.-l".-.."S"--...-1-.""..lCOLUMN i> 1 i" -e -O )b ST - 2 TCTAL b.- O.4 lt,3 i"." IT,O 24,'t ;-.3 "7 O.9s )3b.yg7u6 w;Th -6 VLGREtS vF FNEEVcM Si""IFiCAI"cE . b,O. O.PiT;3

CCtFFICILhT . O,e)-V2TAv ti . O.2v)bl S:GNiHCAr`CL . o,euouTAu C s O.IV54S SIGNIFtCANCE i O.eQooo.22elT

. o.2ue5b

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1

Conclusion

In the case study mentioned above, the grain-size distribution data are analyzed

using the computer supported system. Namely, factors are extracted and theirmeanings are examined by R-mode factor analysis; samples are classified into several

groups by the Q-mode factor analysis and cluster analysis; of their significance, the

given classifications are tested by the discriminant analysis; and the results are also

shown in several types of diagrarns using the display programs. In the course ofthese studies the data file system is used forthestorage, retrieval, selection, transfor-

mation, and display of data.

The results are well concordant with those which are concluded from the ex-


cellent studies of ordinal geologic techniques. Therefore, the validity of the data

analysis in geology is confirmed. Simultaneously the usefulness of the computersupported system presented here is shown in the smooth processing of thses studies.

The size ofgeologic data is generally larger than those used in this study, and the

data analysis for such data is hardly performed without the help of computer. The

computer supported system presented here can treat such a large amount of data,and is available for any geologists with a little knowledge on the computer.

In this study mainly numeric data are used, though large amounts of geologic

data are nonmetric, nominal, and nonquantitative. The computer supported systemcan treat only a part of such data. By the improvement of the system, however,nonquantitative geologic data will be treated in near future.

I have studied not only the computer supported system, but also the mathematical

and statistical techniques to treat geologic data. Some of the contributions on these

aspects will be reported in future.

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