Earth-Science Reviews 67 (2004) 55 – 89
www.elsevier.com/locate/earscirev
The quantification of geology: from abacus to Pentium
A chronicle of people, places, and phenomena
Daniel F. Merriam *
Kansas Geological Survey, The University of Kansas, Lawrence, KS 66047, USA
Received 17 September 2003; accepted 17 February 2004
Abstract
The geological profession has only recently become numerically literate but highly so in a relatively short time. Mathematics
was applied to geological problems mostly in the fields of hydrology, engineering geology, and geophysics until the past few
decades. Statistics were used by sedimentologists and paleontologists to describe populations with some univariate, bivariate,
and multivariate statistics used by a few avant garde workers. Geocomputing really started in the 1960s but the slow start
became an avalanche in the 1980s with the introduction of microcomputer [personal computer (PC)]. The trend towards
increasing quantification of the discipline is noticeable, and in recent years, this trend has been accelerating. There is seemingly
no limit to the information and communication revolution.
D 2004 Elsevier B.V. All rights reserved.
Keywords: Computers; Statistics; Mathematics; Numerical geology
1. Introduction
The quantitative approach leads in most situations
to a deepened insight into a problem. The Age of
Zap, Richard A. Reyment (1974)
The roots of quantitative geology are deep—deeper
than previously acknowledged (Merriam, 1981a;
Howarth, 2001). Early workers used numbers to
describe and analyze geological conditions as early
as the 17th Century. Agricola (1556) reported the use
of trigonometry in mining surveying in his De Re
Metallica. Numerical methods were also used in
mapping and navigation. Thus, although the beginnings of quantitative studies in geology per se are
* Fax: +1-785-864-5317.
E-mail address: [email protected] (D.F. Merriam).
0012-8252/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.earscirev.2004.02.002
fuzzy, one of the first straightforward publications of
importance was Perraults’ (1674) book that quantitatively related rainfall to runoff. It is true, however, that
practitioners of quantitative methods were few and
unfortunately had little impact on mainstream geology
until much later. From this modest beginning, quantitative geology has grown to where it is today; it is
rare now to read a scientific geological paper with no
numerical computations nor computer processing.
Much of modern geology, such as plate tectonics,
seismic tomography, planetary geology, geostatistiques, remote sensing, geologic simulation, etc.,
would not be feasible without dependence on numerical methods and computers.
. . .when you can measure what you are speaking
about and express it in numbers you know
something about it; but when you cannot measure
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
it, when you cannot express it in numbers, your
knowledge is of a meagre and unsatisfactory kind.
Electrical Units of Measurement, Sir William
Thomson (Lord Kelvin) (1883)
Geology has been mainly a descriptive, historical
science and many of the concepts and features would
be difficult to describe in precise terms (numbers).
Hubbert (1974) questioned ‘Is Being Quantitative
Sufficient?’ and cited numerous examples of advances
in geology made by reasoning (nonquantitative) including the understanding of discordant strata, continental glaciation, and the duration of geologic time.
He further cautioned (p. 34) ‘‘. . .that the application
of quantitative methods. . .do not necessarily lead to
valid results,’’ a comment cogent yet today.
. . .if we are not careful we may easily become
victims of the fallacy that conclusions arrived at in
papers heavily laden with mathematical equations
and numerical data, or with computer results, have,
ipso facto, a higher degree of reliability than those
arrived at by more primitive methods. Is Being
Quantitative Sufficient, M. King Hubbert (1974)
Because the vast majority of archival data in the
geological sciences are of a historic and nonquantitative nature, much will remain ‘lost’; the cost of
converting this enormous amount of data would be
staggering and perhaps would be of doubtful value
anyway. As data capture, storage, and manipulation
became easier, and technology became available to
handle the historical record, the situation has changed,
and, indeed, in the past decade, it has. As noted by
Wadge (1993), ‘‘As professional geologists in the
1990s, we are awash with information.’’ The development in data capture, manipulation, storage, and
display has been termed geoinformatics—a term recently coined by the Japanese.1
Geologists were slow to adopt, and adapt to,
quantitative approaches. That attitude rapidly
1
‘Geoinformatics’ (geology and informatics) apparently was
used in the first circular (1990) for the International Geological
Congress (IGC) in Kyoto. The Japanese Society of Geoinformatics
not only includes Information Technology (IT) in the definition but
also the techniques used in solving geological problems (Kaichiro
Yamamoto, written communication, 2002).
changed as the ever-present microcomputer pervaded
the scene. It is perhaps easy to see why early
workers shunned the use of quantitative descriptions
and computer methods. There was (1) a lack of
support technology, (2) the subject of geology has
a strong background in the arts (see Agterberg,
1974), and (3) methods were lacking for data handling and analysis. These constraints severely limited
the options and possibilities even if the data were in
numeric form and the investigator had a quantitative
bent; the analyses were limited to available mathematical techniques.
Now, of course, the microcomputer is indispensable. Its serves as a secretary in keeping a calendar,
word processor (what used to be termed typing), and
doing correspondence for any and all occasions. It
handles spelling checks, dictionary use, and is a
thesaurus. It is a draftsman—just about any type of
graphics can be accomplished in the way of illustrations and in color. It is a technician, a resident
statistician, and mathematician doing calculations,
and a bookkeeper, maintaining records. It can access
on-line databases anywhere in the world and supply
almost immediately an infinite amount of data. It can
do library work by accessing bibliographic databases
and do reference searches. It serves as a communication device via e-mail and fax, allowing correspondence with other workers all over the world (see
Leblanc, 1993 for a summary on the use of computers
in writing and communication). What a labor- and
time-saving device, and it is limited essentially only
by the inventiveness of the user!
By the mid-20th Century, practitioners were using
mathematics to solve geological problems, especially
in the fields of geohydrology (Matalas, 1969), geophysics (Landsberg, 1958), geochemistry (Krauskopf,
1967), structural geology (Whitten, 1966), mineralogy
(Dana, 1932), and engineering geology (Johnson,
1970). In the Preface to their book on Statistical
Analysis in the Geological Sciences, Miller and Kahn
(1962) give a brief history on the application of
statistics in the earth sciences and divide the history
into three periods: 1890 to 1930s; 1930s to WWII,
and post-WWII (to the early 1960s). The development
of the field of quantitative geology, which includes
mathematics and statistics applied to geological problems, has progressed through several phases to today’s
modern, integrated state where the new generation of
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
57
investigators have at their fingertips the tremendous,
in fact, almost unlimited, amount of brain power
through the use of the computer.
People who are thinking about what they are doing
are using computers. P.C. Hammer (personal
communication, 1966)
The introduction of computers that ushered in the
space age also brought about a new set of problems,
as with the introduction of any new technology. There
has been an invasion of privacy, many trades and
practices have been declared obsolete and redundant,
and an impersonal touch has been added to an everincreasing complex society. There is a tendency to
regard any database on-line as high quality, but
depending on the source, this may or may not be
true. Computer viruses and worms also have added
another dimension to the new way of life. The way in
which geologists think and accomplish things have
radically changed as traditional approaches have been
altered as the science transforms from a qualitatively
to quantitatively oriented one.
Since the end of the last millennium, the computer
revolution has marched on. As predicted a decade
ago, computers have gotten yet smaller in size, larger
in capacity, and faster in operation than ever imagined2 (Fig. 1). It is noted that the speed of computers
has increased by a factor of about 1 million, whereas
the cost has decreased by a factor of about 20,000.
Supercomputers now can calculate at a speed of about
12.3 trillion calculations/s.
With the introduction of Pentium 4 processor, the
supercomputer (workstation) is now on your desktop,
and with the Internet connections, the world is at your
fingertips. One of the fears (if there is one) is that a
generation of geologists now are dependent on databases of perhaps questionable quality or at least
without the user’s verification. No longer does the
geoscientist necessarily collect his/her own data, but
can search the net for ‘suitable’ data sets. Nevertheless, the Information Age is here and the revolution is
2
The limits of technology, however, may be close (Normile,
2001). According to Moore’s Law (the doubling of the number of
transistors on a chip every 18 months with an increase in
performance and a corresponding decrease in price), this limit
could be reached as early as 2014, or will it? (Lundstrom, 2003).
Fig. 1. Graph of computer power as viewed in Sejnowski’s (1987)
review of Computing and Connections by W.D. Hillis. Speed
increases as log per second through time. CM is Connection
Machine and GF-11 is IBM experimental machine. As noted by this
illustration and later by Normile (2001), limits to increase computer
power may be near or not near depending (Lundstrom, 2003).
based on the technology of electronics and material
science—we must make the best of it. This communication or information revolution is taking place as a
result of the computer, especially the microcomputer
or as it is affectionately known—the personal computer (PC).
Chronicled here then is the story of the beginnings
of part of that revolution in one branch of science—
geology—for according to the old adage, those who
do not know history are destined to repeat it.
2. Background and history
There have been several major conceptual revolutions in geology that accompanied or followed
technological advances of the time, allowing for
rapid developments of science. The first revolution
was the result of Copernicus’ discovery that the Sun,
not the Earth, was the center of the solar system. The
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
second from the work of James Hutton and Charles
Lyell, founders of modern geology, in their elucidation of time and processes (‘no vestiges of a beginning and no prospect of an end’; and ‘the present is
the key to the past,’ uniformitarianism). The third
was Darwin’s revelation of man’s place; the fourth
was the integrated theory of plate tectonics, and the
fifth?
Many of the conceptual revolutions were dependent on advances in technology, such as the wheel
(Mechanized Age), compass (Exploration Age), telescope (Discovery Age), steam engine (Industrial Revolution), and computer (Information Age), which
allowed quantum leaps in changes. Invention of the
compass allowed exploration of the globe and recognition of the world’s geography (Aczel, 2001). In the
17th Century, Galileo (1564 – 1642) and Johannes
Keppler (1571 –1630) utilized the telescope, invented
in the previous century, to make observations that led
to the verification of Copernicus’ (1473 – 1543) ideas.
Invention and development of the steam engine by
James Watts (1736 –1819) in the later part of the 17th
and early part of the 18th Century allowed the
massive changes in manufacturing and transportation
in the 19th Century, which was instrumental in the
creation of leisure time so necessary for scientific
pursuits. The computer, which dates from Charles
Babbages’ work in the 19th Century, allows the
massive digestion of data and information on a
worldwide basis. Each subsequent advance was built
on the previous one(s) and only time will tell what
good will be wrought from the information revolution
but the possibilities seem unlimited.
[The] computer [is] one of the very most important
mathematical events of all time. Historiography: a
Perspective for Computer Scientists, K.O. May
(1980)
Howarth (2002) has documented in detail the
history of importance of graphic displays from the
hand-drawn illustrations of the early 1800s to the
intensive application of computers to the design and
presentation of illustrations today. Included in his
coverage are maps, graphs, scatterplots, diagrams,
bar charts, and pie diagrams, as well as a description
of statistical thinking, mathematical modeling, and
geostatistiques, all in relation to the utilization of the
all-powerful computer. This history gives evidence of
major technological and conceptional advances and
one reason for the rapid acceptance and adoption of
the computer and computer methods by the geological
community.
The ability to acquire, manipulate, and analyze
massive amounts of data facilitated the acceptance
of plate tectonics in a matter of just a few years. In
each instance, the technological product was an extension of a human faculty—the compass: orientation;
the telescope: sight; the steam engine: muscle; and the
computer: the mind. The power of the computer was
recognized early by many and best said by P.C.
Hammer.
A computer is an intelligence amplifier. P.C.
Hammer (personal communication, 1966)
How prophetic!
The use of computers obviously is linked closely
with developments and availability of hardware and
software. The dawn of the computer age in geology
usually is dated as starting from the publication in
1958 of a geologically oriented computer program in
a recognized journal by W.C. Krumbein (1902 – 1979)
Father of Computer Geology and his coworker, L.L.
Sloss (1913 – 1996) (Table 1). Advances in many
aspects of geology since that time have been dependent on utilization of computers.
The origins of modern geology and the computer
both date back to the early part of the 19th Century
where an amazing group of far-sighted scientists
lived in London. Included in this group was Charles
Lyell (geology), Charles Babbage (mathematics),
Charles Darwin (biology), Humphrey Davy and
Notes to Table 1:
IAMG: International Association for Mathematical Geology.
IUGS: International Union of Geological Sciences.
AAPG: American Association of Petroleum Geologists.
MGUS: Mathematical Geologists of the United States.
COGS: Computer-Oriented Geologists Society.
SEPM: Society of Economic Paleontologists and Mineralogists.
COGEODATA: Committee on Storage, Automatic Processing, and
Retrieval of Geologic Data.
IGC: International Geological Congress.
KGS: Kansas Geological Survey.
C&G: Computers & Geosciences.
Sources: Merriam (1975a,b, 1980).
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table 1
Important events in computer applications in geology (adapted from
Merriam, 1975a,b, 1980)
1642
1694
1804
1812
1822
1834
1842
1890
1941
1943
1944
1945
1946
1949
1951
1952
1953
1954
1958
1961
1963
1964
1966
1967
1968
1969
Blaise Pascal devised a calculating machine
Leibniz’s machine to multiply and divide
Jacquard loom used punched cards
Charles Babbage gets the idea of calculating machines
First working model of Babbage’s Difference Engine
Babbage starts work on his Analytical Engine
Ada Augusta ‘writes’ the first program
Punched-card system developed by Herman Hollerith
Z3, first electronic computer
Colossus, the first programmable electronic computer
Mark 1, the decimal electromechanical calculator put
into operation at Harvard
John von Neumann’s idea of stored memory
ENIAC, built at the University of Pennsylvania, the first
large, general-purpose electronic computer
EDSAC, the first stored-program, digital computer
UNIVAC, the first commercial computer
Digital plotters introduced
First FORTRAN compiler written
IBM 650, the first mass-produced computer
W.C. Krumbein and L.L. Sloss publish the first
geologically oriented computer program in a major
geological journal
Transistorized second-generation computers introduced
Establishment of GeoRef
Arizona’s ‘Computer Applications in the Mineral
Industries’
Announcement of third-generation microcircuit
computers
Kansas Geological Survey ‘Special Distribution
Publications’
More than 100 papers on computer applications in
geology
BASIC introduced
Time-sharing successfully used at Dartmouth University
Kansas Geological Survey ‘Computer Contributions’
Kansas’ ‘Computer Applications in the Earth Sciences’
Colloquia
AAPG appoints an associate editor for computer
applications
AAPG Committee on Storage, Automatic Processing,
and Retrieval of Geologic Data formed (later the
Committee on Computer Applications)
COGEODATA (IUGS) formed
IAMG founded in Prague at the XXIII IGC
‘Journal of Mathematical Geology’ of IAMG
inaugurated
‘Geocom Bulletin’ published
USGS starts a ‘Computer Contribution’ series
‘Computer Applications in the Earth Sciences,’ a book
series initiated by Plenum Press (New York)
First issue of ‘Journal of Mathematical Geology,’
sponsored by the IAMG
Table 1 (continued )
1970
1971
1972
1973
1975
1976
1977
1978
1979
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
SEPM Computer Technology Group
First fourth-generation machines utilizing VM
More than 500 papers published on computer
applications in geology
First Geocom Program published (successor to KGS
Computer Contributions and later merged with C&G)
Syracuse University establishes a series of
Geochautauquas
GeoRef goes online on SDC ORBIT
First release in a series ‘Informatique Geologique,’ a
new section of ‘Sciences de la Terre’
The first issue of ‘Computers & Geosciences’ sponsored
by IAMG
Indiana Geological Survey publishes first ‘Geophysical
Computer Programs’
Pergamon’s book series on ‘Computers and Geology’
The Apple II microcomputer
First year more than 1000 papers on computer
applications in geology reported
Supercomputers, Cray-1, Cyber 205, and BSP are
available
Word-processing software and spreadsheets introduced
MGUS holds their first meeting
Announcement of fifth-generation computers with AI
functions
The IBM PC microcomputer introduced
‘Computer Methods in the Geosciences,’ a VNR book
series
COGS formed in Denver
Denver GeoTech83 sponsored by COGS
Lotus 1 – 2 – 3 spreadsheet software introduced
Apple introduces the Macintosh with its graphic-based
operating system
‘Geobyte,’ a new publication by AAPG
COGS membership surpasses 1000
BITNET comes into general use
IAMG inaugurates a memoir series
SEPM forms a Computer Applications Committee
First geological oriented paper using a supercomputer
FAX come into general use
The i486 chip is introduced
First geological computer program published on softstrip
Meta-analysis becomes available
COGS ‘Computer Contributions’ merged with
‘Computers & Geosciences’
SEPM introduces its ‘Computer Contribution’ series
Microsoft 3.0 ‘Windows’ software unveiled
The super supercomputer, Touchstone Delta, is installed
Geobyte suspends publication
Palmtop systems generally available
AAPG announces the ‘Computer Applications in
Geology’ series
The Pentium chip is introduced
The IAMG celebrates its 25th Silver Anniversary in
Prague
59
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Michael Faraday (chemistry), and John Herschel
(astronomy). These men, following on the Scientific
Revolution of the 18th Century, took an active part
in the Industrial Revolution and contributed to a
scientific golden age laying the foundations for
modern science.
Sir Charles Lyell (1797 – 1875), formulator of the
Principle of Uniformitarianism, and one of the first to
use statistics in geology, and Charles Babbage (1791 –
1871), mathematician and creator of the Difference
and Analytical Engines, were good friends (Fig. 2).
They were acquainted professionally through the
Royal Society and the Geological Society of London
and, in addition, entertained each other and were
entertained by mutual friends. It is likely that they
shared ideas and problems of work as both were
Fig. 2. (Upper) Babbage’s Analytical Engine and (lower) punched cards used with the ‘computer’ (photo from British National Museum in
London).
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
ingenious and inquisitive researchers. Although
Lyell’s work forms much of the basis for modern
geology and he was recognized for his contributions,
Babbage’s calculating machines were destined for
failure for lack of at-the-time-technology and, therefore, he was not given due recognition in his time
(Merriam, 1983).
Not much happened in the next 100 years from this
modest beginning. Ada Augusta, Lady Lovelace and
daughter of Lord Byron, ‘wrote’ the first computer
program, which was a series of steps to compute
Bernoulli numbers using Babbage’s Analytical Engine. This program was patterned after the series of
card instructions used to control the weaving patterns
on Jacquard looms. Later, at the turn of the 20th
Century, Herman Hollerith at the U.S. Census Bureau
utilized the idea of punch cards for tabulating census
data (Fig. 2). Punch cards also were used in precomputer days for routinely sorting bibliographic and
other large data sets; it is not surprising then that
punch cards were used as input/output (I/O) for the
first computers.
There is a definite lack of quantitatively oriented
publications in the early days and only a few
applications between 1830 and 1958 can be cited
from the literature. Some applications of trigonometry and geometry were made in crystallography and
computations made on age determinations and heat
61
flow in the Earth. Statistics were applied to sedimentological and paleontological problems (Cubitt
and Henley, 1978). Geophysicists, geochemists, engineering geologists, and hydrologists applied mathematics in solving their problems. Observations and
data had been collected for 100 years and the
numerical data was processed with abaci, slide rules,
and calculators. Introduction of the computer ushered
in the automated era where complex problems could
be solved easily and quickly, large amounts of data
manipulated, and data acquisition was automated; it
was the harbinger of the development of French
geostatistiques, applications of sophisticated techniques to geological problems, use of large realistic
data sets, and development of simulation and model
studies, especially those involving time (Merriam,
1981a).
As with any history, this story is best told through
individuals and their contributions. The story is punctuated into chapters by an event that changed the
direction or acceleration of the story. As with most
stories, it starts slowly and gains momentum so that
events happen more frequently and are more drastic
with the passage of time (Fig. 3). It may be that this
acceleration is only perceived by the recentness and
quickness of the passage of time, such as the Doppler
effect, but, on the other hand, it maybe real and
actually accelerating.
Fig. 3. Stages of development of quantitative geology, 1650 – 1995.
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table 3
Selected papers on mathematics and statistics in geology
3. Quantitative geology
The genuine goal of scientific computation in
geology should be insight, not numbers. Geology
and Mathematics, H. Schaeben (1988)
As with any multidisciplinary science, quantitative
geology is the result of an interplay of several specialties and it is difficult, if not impossible, to separate
them. First, there were the contributions of mathematicians, followed by those of the statisticians after the
development of the subject (Tables 2 and 3). These
methods were enhanced and furthered by computer
scientists in the mid-1950s and beyond. This symbiotic relationship between mathematicians, statisticians, computer scientists, and geologists has
resulted in major advances in the earth sciences in
the past four decades with promised exciting discoveries yet to come (Fig. 4).
There has been a discussion of the definition of
mathematical geology or geomathematics. The successful application of mathematics in geology via
computer applications in the 1960s rivals the development of geophysics in the 1940s and geochemistry in the 1950s. Again, the practical (and
successful) applications in numerical exploration
and exploitation was foremost in promoting interest
in, and development of, the subject (Merriam,
Table 2
Mathematicians who contributed to geology
Simon Stevin
(1548 – 1620)
Belgian
Gottfried Leibnitz
(1646 – 1716)
John Playfair
(1748 – 1819)
German
Pierre de Laplace
(1749 – 1847)
Charles Babbage
(1790 – 1871)
John Henry Pratt
(1811 – 1871)
Charles S. Peirce
(1839 – 1914)
Karl Pearson
(1857 – 1936)
Scot
French
English
English
American
English
systematic studies of agents
effecting changes on the
Earth’s surface
physical properties of the Earth
1674
1757
1762
Pierre Perrault
M. Adanson
Paola Frisi
1801
Abbe Hauy
1802
John Playfair
1824
William
Whewell
1830 – 1833 Charles
Lyell
1832
R. Everest
1837
1846
James D.
Dana
Samuel
Haughton
1848
M.A. Delesse
1870
J. Clerk
Maxwell
T.M. Reade
1885
1895
1908
1909
1914
1921
1930
1935
computing dips to project at
depth; application of calculus
to stream transport problems
planetary system calculations
1936
heat flow and competency of
the Earth’s crust
geodetic surveys in the
Himalaya Mountains
geodetic and geophysics of the
Earth
statistical principles applied to
geology
1948
1941
1958
1958
De l’Origine des Fontaines
Histoire Naturelle du Senegal. . .
A Treatise on the Rivers and
Torrents. . .
Traite de Mineralogie,
Tome Premier
Illustrations of the Huttonian
Theory. . .
General Method of Calculating
the Angles Made by Any
Planes of Crystals. . .
Principles of Geology, 3 volumes
A Quantitative Study of
Stream Transportation
A System of Mineralogy With
an Appendix. . .
On the Laws of Equilibrium
and Motion of Solids and
Fluid Bodies
Procede Mecanique pour
Determiner al Composition
des Roches
On Hills and Dales
The Importance of Solution
as a Factor in Erosion
K. Pearson
Contributions to the Mathematical
Theory of Evolution
H.C. Sorby
On the Application of
Quantitative Methods to the
Study of the Structure and
History of Rocks
J. Joly
Radioactivity and Geology
J.A. Udden
Mechanical Composition of
Clastic Sediments
W. Penck
Morphologische Analyse
A.E. Trueman
Results of Some Recent
Statistical Investigations of
Invertebrate Fossils
C. Eisenhart
A Test for the Significance
of Lithological Variation
William C.
Application of Logarithmic
Krumbein
Moments to Size Frequency
Distributions in Sediments
A.N.
The Lognormal Law of
Kolmogorov
Distribution of Particle Sizes....
Benjamin H.
First of Three Studies in
Burma
Quantitative Paleontology, II
John C.
Petrographical Investigations
Griffiths
of the Salt Wash Sediments
W.C. Krumbein/ High-Speed Digital Computers
L.L. Sloss
in Stratigraphic and Facies
Analysis
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
63
Fig. 4. Tree of quantification showing some names of those involved early with interrelations of mathematics, statistics, and computer science.
64
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
1982). Just as geostatistics can be defined as
statistics applied to geology (Bates and Jackson,
1980), geomathematics can be simply defined as
mathematics applied to geology. Some would even
say that geomathematics is what geomathematicians
do. More formal definitions include those by Vistelius (1967):
definitions are essentially the same again but have
been expanded to:
Mathematical geology [has] posed as its goal the
elucidation and solution of those problems in
geology that require the development of specific
mathematical methods.
The simplest definition may be the best and most
descriptive.
It has been proposed that geomathematics be
recognized as a scientific discipline in its own right
with a status and importance equal to the other
interdisciplinary subjects of geophysics, geochemistry, paleobiology, engineering geology, etc. (Merriam,
1982). However, much of the subject has been incorporated now into mainstream geology, and thus considered a stand-alone subject by only a few, although
there are many corollaries of geomathematics (sensu
stricto) with the other subdisciplines. This is probably
because the subject (when analyzed in the broadest
sense) is basic and is simply the use of mathematics to
solve geological problems.
It is unclear who first used the hybrid term geomathematics, but according to Hatten Yoder (written
communication, 2000), the term was first used in
1941, although this could not be confirmed. It was
used, however, by Rasmussen (1952) in a study of
groundwater reservoirs; the other hybrid names came
earlier—geophysics (1834), geochemistry (1838), and
geobiology (1939). Mathematical geology was the
name preferred by the organizing committee for the
International Association for Mathematical Geology
(IAMG) in 1968, largely at the insistence of Andrew
Vistelius (Merriam, 1978, 2001).
The quantification of geology that has taken place
in several stages, which have been punctuated by
certain events and certain persons, are given in Table
4 and relationships are shown in Fig. 4.
and, again, by Vistelius (1968):
Mathematical geology is the scientific discipline
which deals with the establishment of mathematical models of geological processes; geological
processes are classified according to the type of
stochastic processes that—with the fundamental
objective of investigating geology with mathematics—exhibit probability distribution functions with
the necessary values chosen appropriately. All
other applications of mathematics to geology,
although they may have practical importance, are
special cases or particular instances of solutions to
problems that use mathematics in geology or
geomathematics.
and Agterberg (1974):
Geomathematics, in its broadest sense, includes all
applications of mathematics to studies of the
earth’s crust.
and in the Glossary of Geology (Gary et al., 1972),
both terms are defined the same:
Mathematics as applied to geology.
but in the 2nd edition (Bates and Jackson, 1980), they
are slightly different:
Geomathematics: All applications of mathematics
to studies of the Earth’s crust. Mathematical
Geology: Mathematics as applied to geology.
and in the 3rd and 4th editions of the Glossary
(Bates and Jackson, 1987; Jackson, 1997), the
Geomathematics: All applications of mathematics
to studies of the Earth’s crust. Mathematical
Geology: Mathematics, especially statistics and
probability theory, as applied to geology.
3.1. Origins Stage (1650 –1833)
Because some aspects of mathematical applications to geological problems have been with us for a
long time, it is difficult to pinpoint the beginnings of
quantitative geology. For example, in (1802), John
Playfair (1748 – 1819) used what has been termed as
quasimathematical methods for computing dips and
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table 4
Stages in development of quantitative geology
1650 – 1833
Origins stage Rudimentary applications of
mathematics to geological problems
in the areas of hydrogeology,
geophysics, structural geology, and
mineralogy.
1833 – 1895 Formative
Application of trigonometry and
stage
geometry to crystallography,
computations on age determinations,
heat flow, etc.
1895 – 1941 Exploration The use of uni- and bivariate statistics
stage
to geological problems and the
deterministic approach. Provided the
basis for advancement in all
geological fields as techniques
became available; continued
development of mathematical
applications especially in geophysics.
1941 – 1958 Development Introduction of multivariate statistics
stage
which allowed an expansion into
most fields of geology. Rapid
development of the probabilistic
approach to problem solving.
1958 – 1982 Automated Or the application of computers.
stage
Development of the French
geostatistics; practical applications of
sophisticated techniques to geological
problems involving large realistic
data sets; development of simulation
and model studies, especially those
involving time.
1982 – present Integration
Use of microcomputers (PCs) in all
stage
aspects of data capture, manipulation,
and analysis. PCs used for number
crunching, word-processing, drafting,
communication, and bibliographic
work. PCs are being replaced by the
more powerful workstations.
other surface measurements to project the depth at
which beds would occur downdip, calculated areas
that rock types occupied in certain areas, and applied
the idea of integration of small changes to the
problem of gradual changes in stream valleys (Rudwick, 1972). At the turn of the 18th Century, other
quantitative measurements were being made such as
the determination of specific gravity of minerals,
subsurface temperature gradients and heat flow in
the Earth, and the estimation of volume of blocks of
material being transported by streams and glaciers
(which was used as evidence that streams cut their
own valleys).
65
Most of these applications were arithmetic or geometric, with the exception of the application of calculus by Playfair. Other applications of calculus to
geological problems were being made at that time by
astronomers and physicists who were calculating planetary motions. One of the foremost problems that faced
workers at that time in applying their mathematical
expertise was stated aptly by Playfair (1802, p. 457)
‘‘. . .where every object changes, it is difficult to find a
measure of change, or a fixed point from which the
computation may begin. The astronomers already feel
this inconvenience, and when they would refer their
observations to an immoveable plane, that shall preserve its position the same in all ages, they meet with
difficulties, which cannot be removed but by a profound mathematical investigation. In geology, we
cannot hope to be delivered from this embarrassment
in the same manner; and we have no resource but to
multiply observations of the difference of level: to
make them as exact as possible, and to select points of
comparison that have a chance of being long distinguished.’’ This plea was in response to the efforts at the
time to determine apparent changes in sea level.
John Playfair, a friend of James Hutton (1728 –
1799), was professor of mathematics and later held the
chair of natural philosophy at the University of Edinburgh. It was through Playfair’s Illustrations of the
Huttonian Theory that Hutton’s work was recognized
(McIntyre and McKirdy, 1997). Hutton (1788) wrote
in an awkward and heavy style that Playfair rewrote
into prose along with added interpretations of some of
his friend’s ideas. Therefore, it was only natural that he
use mathematical concepts in explaining the Huttonian
Theory, and in fact, he may have been responsible for
modifying some of Hutton’s original ideas.
At about the same time, another mathematician,
Paolo Frisi (1728 – 1784), in his mathematical discourses (1782 – 1785), was considering the problem
of change in position of masses of transported sediment
in effecting the motion of the Earth. He calculated how
much waste might be eroded from the continents and
deposited in the sea per unit of time and then determined what change in motion of the globe should be as
a result and concluded that the change ‘‘. . .exceeds
more than ten times the age of any historical record.’’
He based his conclusion on his premise that ‘‘. . .if any
considerable mass of matter were accumulated in the
interior of the ocean, the diurnal motion of the globe
66
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table 5
Some early quantitative papers, 1674 – 1833 (Origins stage)
P. Perrault
M. Adanson
Abbe Hauy
John Playfair
1674
1757
1801
1802
P. Frisi
1818
De l’Origine des Fontaines
Histoire Naturelle du Senegal
Traite de Mineralogie
Illustrations of the Huttonian
Theory of the Earth
A Treatise on the Rivers and Torrents;
With the Method of Regulating Their
Course and Channels
would be disturbed, and consequently, it would be
perceptible. . .’’
As early as 1762, Frisi (1818) described and
measured attributes of rivers including calculations
of velocity and quantity of water per second, etc., in
a study of transportation of material and hydraulics.
In this study, which is one of the first quantitative
studies on sediment transport, Frisi postulated several
principles of water flow.3 Some of these ideas may
have come from the French naturalist Pierre Perrault
(1611 –1680) and his early quantitative work on De
l’Origine des Fontaines (The Source of Water in
Springs and Rivers), which was published in 1674
(Mather and Mason, 1939); he related rainfall to
stream flow (Table 5). In fact, Ellenberger (1996, p.
109) credits Perrault with being the pioneer of
modern hydrogeology. According to von Zittel
(1901, p. 186), Simon Stevin, a Belgian mathematician, also carried out systematic studies in the 17th
Century of agents effecting changes on the Earth’s
surface.
At about this same time, geophysicists were busy
making contributions on calculations of the terrestrial
magnetism and density of the Earth (see Howarth,
2001). John Mitchell (1724? – 1793), an English
astronomer, developed the first torsion balance and
methods for reducing the data. These early quantitative studies were carried on and enhanced by the
French geophysicist, Pierre Bouguer (1698 –1758).
An English clergyman, Robert Everest (c. 1805 –
1875), who was surveyor-general of India; John Pratt
(1811 – 1871), an English mathematician; George
Airy (1801 – 1892), an English astronomer; and
3
Everest (1832) continued this line of study on sediment
transport as well as other studies in his paper on ‘‘A Quantitative
Study of Stream Transport.’’
Charles Babbage, the English mathematician, all
contributed to the background for C.E. Dutton’s
(1841 –1912) principle of isostasy, proposed much
later. While the geophysicists were making their
calculations, the experimental chemists Lazarro Spallanzani (1729 – 1799) and later, Sir James Hall
(1761 –1832) were perfecting their methods for the
analysis of rocks. Some of them were highly quantitative requiring carefully controlled conditions, so
by the mid- and late 18th Century, mineralogists had
developed blowpipe analysis and chemical analyses
to the point where the analytical tests for identification were standardized and there were established
classification schemes.
3.2. Formative Stage (1833 – 1895)
As soon as an Analytical Engine exists, it will
necessarily guide the future course of science.
Passages from the Life of a Philosopher, Charles
Babbage (1864)
Thus, while crystallographers and microscopists
were busy with their calculations, Charles Lyell came
along with his proposal on how to subdivide the
Tertiary. In 1828, Lyell, visiting Paris on his way home
from an extensive trip in Europe, part of which was in
the company of Sir Roderick I. Murchison (1792 –
1871), met the conchologist Paul Deshayes (1795 –
1875), who was busy describing and sorting his extensive mollusk collections. Lyell stayed and worked with
Deshayes to learn more of his methods and ideas and in
doing so, apparently, reinforced his own ideas on
uniformitarianism and developed and refined a scheme
of subdividing the Tertiary on the basis of percentage of
living vs. extinct fossil forms (Fisher, 1953, pp. 2– 3).
Geologists prior to Lyell had recognized the
sequences of strata, which we know as Primary and
Secondary, using in the first place the regularity of
order of superposition at the same locality. They also
observed that particular components of these formations could be recognized, although far apart, by their
characteristic fossils.4 They could not, by these
4
See, for example, Torrens (2003) on Phillips’ 1844 memoirs of
William Smith and Simon Winchester’s (2001) description of
William [Strata] Smith’s discoveries and accomplishments as a
surveyor and mapmaker.
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
means, recognize or establish the order among the
Tertiary rocks, for, in the part of the world then
accessible, these occur in patches and not over wide
areas overlying one another. Lyell determined the
order and assigned to the successive rock masses the
names they now bear by a purely statistical argument.
A rich group of strata might yield so many as 1000
recognizable fossil species, mostly marine mollusks.
A certain number of these might be still living in the
seas of some part of the world or at least be morphologically indistinguishable from such a living species.
It was as though a statistician had a recent census
record without recorded ages, and a series of undated
records of previous censuses in which some of the
same individuals could be recognized. A knowledge
of the Life Table would then give him estimates of the
dates, and, even without the Life Table, he could set in
chronological order, merely by comparing the proportion in each of those who were still living.
With the aid of the eminent French M. Deshayes,
Lyell proceeded to list the identified fossils occurring
in one or more strata and to ascertain the proportions
now living. To a Sicilian group with 96% surviving, he
later gave the name of Pleistocene (mostly recent).
Some sub-Appennine Italian rocks, and the English
Crag with about 40% of survivors, were called Pliocene (majority recent). Forty percent may seem to be a
poor sort of majority but no doubt scrutiny of the
identifications continued after the name was first
bestowed, and the separation of the Pleistocene must
have further lowered the proportion of the remainder
(Fisher, 1953). The Miocene, meaning ‘minority recent,’ had 18%, and the Eocene, ‘the dawn of the
recent,’ only 3% or 4% of living species. Not only did
Lyell immortalize these statistical estimates in the
names used for the great divisions of the Tertiary
Series, but in an Appendix in his third volume, he
occupies no less than 56 pages with details of the
classification of each particular form and of the calculations based on the numbers counted. There can be no
doubt that, at the time, the whole process, and its
results, gave Lyell the keenest intellectual satisfaction.
According to his own account, Lyell (1863, p. 3)
conceived the idea in 1828 for ‘‘. . .classing the
whole of this series [the Tertiary] of strata according
to the different degrees of affinity which their fossil
testacea bore to living fauna.’’ He proposed this
statistical technique to help interpret the chronology
67
Table 6
1833 – 1895 Formative stage
Charles Lyell
R. Everest
1830 – 1833
1832
James Dana
Samuel Haughton
1837
1846
J. Clerk Maxwell
1870
Principles of Geology
Quantitative Study
of Stream Transportation
System of Mineralogy
On the Laws of
Equilibrium and
Motion of Solid and
Fluid Bodies
On Hills and
Dales
of the Tertiary by punctuating ‘‘. . .a uniform overall
rate of change in the organic world’’ (Rudwick,
1972, p. 183).
Lyell’s (1830 – 1833) efforts appeared as an Appendix in volume 3 in the first edition of the Principles of Geology (published as Table 6 in 1833).5 No
less than 56 pages on the classification of each
particular form and of the calculations based on the
numbers counted were detailed. Lyell later (1863)
used this same idea in determining the age of Pliocene
deposits in marine terraces when illustrating a point
on climate changes.
While Lyell worked with Deshayes, he seemingly
was not aware of similar work by a German paleontologist, Heinrick Bronn (1800 – 1862). In Heidelberg,
Bronn independently proposed a similar but broader
classification scheme in his work of 1831 (Rudwick,
1972, p. 190). Nor does Lyell seem to have known of
the work done in numerical taxonomy by the great
French botanist Michael Adanson, which is strange
considering his extensive travels and interest in others
work. Adanson (1757) used unweighted characters to
determine similarity between taxa of mollusks. With
few exceptions (e.g., Whewell, 1840), Adanson’s
work was not followed up until an upsurge of activity
in the 1950s spearheaded by R.R. Sokal and P.H.A.
Sneath. Sokal and Sneath (1963) published their
5
The data tables incidentally were not included in future
editions of Principles and there has been some discussion as to
whether the concepts on the Tertiary subdivision was original with
Lyell. Paul Tasch in an unpublished manuscript concluded that
‘‘. . .the achievement of bringing the total data to a ‘gestalt,’ living
and fossil mollusks and geological field evidence from different
basins, belongs to Lyell. . .Lyell had no coequals in the matter of
priority in delineation of the definitive Tertiary epoch.’’
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
definitive work on numerical taxonomy that resulted
in a rapid advance of the field of biometrics.
It is interesting to speculate whether Charles Babbage influenced his friend Lyell’s thinking on quantification. Babbage, Lucasian Professor of Mathematics
at Cambridge, published several papers on geology
(Van Sinderen, 1980; Merriam, 1983). Lyell and Babbage attended geological meetings together and sometimes social functions. Lyell (1881, v. 1, p. 363) noted
that Babbage ‘‘ . . .unconsciously jokes and reasons in
high mathematics, talks of the ‘algebraic equation’ of
such a one’s character, in regard to the truth of his
stories, & c.’’. Although there is no evidence of
cooperation or exchange of ideas specifically on the
application of mathematics to geological problems, it
is highly likely that, now and then, the two discussed
problems of mutual interest including Lyell’s proposed
subdivision of the Tertiary.6
Another interesting suggestion at this time was
the proposal by H.H. Hayden in 1820 for a series of
questions—the first field coding form—for ‘‘Geologists, mineralogists, and other persons of correct
observation, as being intimately connected with the
subjects contained in his work, and calculated to and
assist in all future researchers of a number kind.’’
The checklist of 100 questions served as a prompter
for a systematic examination of an area and recording the data (Merriam, 1981b). (The list could have
been set up as in binary form for use with a
portapunch.) Interestingly enough, little or nothing
was done about coding forms in geology from Hayden’s time until Parker (1946) proposed a form for
recording well data in Illinois. However, automatic
data collection, coding, and processing developed
rapidly after introduction of the computer, and
resulted in the development of large integrated data-management systems such as G-EXEC, SAFRAS,
GIPSY, etc.
In other areas and nearly simultaneously, J.D.
Dana (1813 – 1895), in his first edition of System of
6
At about the same time Lyell was developing his ideas,
Charles Babbage was formulating his, but seemingly there was no
connection between Babbage’s interest in geology and his work on
his calculating engine. He saw the application of his Analytical
Engine to mathematical pursuits of all types but primarily in the
fields of astronomy, statistics, navigation, and pure mathematics
(see Merriam, 1981a).
Mineralogy (Dana, 1837), included An Appendix
Containing the Application of Mathematics to Crystallographic Investigations. This Appendix is essentially the application of analytical geometry to
crystallography. Dana also cites the work of C.F.
Naumann of 1830 in this field as well as in Abbe
Hauy’s (1743 – 1822) application of plane trigonometry to crystallography (Abbe Hauy, 1801). Another
mineralogist, Delesse (1848), determined that relative
volumes of minerals in rocks could be measured
from random sections. Other examples of mathematical applications in this period include Haughton’s
(1846) On the Laws of Equilibrium and Motion of
Solid and Fluid Bodies, published in the Cambridge
and Dublin Mathematical Journal. A contemporary
of Haughton’s was William Hopkins, a mathematician at Cambridge. Hopkins’ main contribution was
through his students—several of whom gained prominence in science—including Lord Kelvin (1824 –
1907) and James Clerk Maxwell (1838 – 1879)
(Cockbain, 1980).
The influence of mathematicians, and those with
a strong background in mathematics, thus perhaps
may have been more widespread than heretofore
realized or admitted. Some workers were trained as
philosophers or clergymen; others had solid backgrounds in mathematics and the physical sciences—
astronomy, chemistry, and physics—or medicine.
During the 19th Century, much speculation on the
age of the Earth and climatic changes were made
based on mathematical calculations. In addition,
geodesy, experimental petrology, and chemical
applications required a certain amount of mathematical expertise. Several mathematicians were active in
the early and formative years of quantitative geology including Robert Hooke, Baron von Leibnitz,
Laplace, and of course, John Playfair and Charles
Babbage.
Understandably, some misunderstandings must
have occurred and, therefore, suspicions between
mathematicians and geologists arose to such an extent
that by 1869, Charles Darwin (1809 – 1882), in a letter
to J.D. Hooker, advised his colleagues to beware of
trusting mathematicians (Darwin and Seward, 1903,
p. 314). Part of this cautiousness undoubtedly was the
result of criticism he received from mathematically
oriented scientists about his book, The Origins of
Species (Hull, 1973).
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
The latter part of the 19th Century saw other
advances and retreats in quantification. Advances
include Thomas Reade’s (1832 – 1909) quantitative
work (Reade, 1885) on solution as a factor of erosion,
and Clarke Maxwell’s On Hills and Dales (Clerk
Maxwell, 1870). Also at this time, much effort was
being put into calculation of the age of the Earth. Lord
Kelvin’s (Sir William Thomson) attempt was one of
those that, if not regressive, was certainly no help—
his calculations were far too conservative because
they were based on a fatal flaw in the inferences. It
was not the conservative estimates that were so
detrimental, but the considerable creditability given
them by the fact they had been determined by Lord
Kelvin. Therefore, it took years to dispel the erroneous ages.
So, too, were other calculations based on the
amount of salt in the oceans or sediment accumulation rates by Sam Haughton in 1878 (Holmes, 1965,
p. 351). Although the ‘sodium method’ was suggested by Edmund Halley in 1715, it was not until
1898 that John Joly was able to collect the data
necessary for a reasonable value on age, and even
that value, as Kelvin’s, was an underestimate because
of faulty assumptions (Joly, 1909). It was not until
radioactive-age dating, which was developed in the
early part of the 20th Century, that calculations could
be made accurately, calculations which incidentally
required considerable computations. Therefore, at the
turn of the 19th Century, marked changes were
taking place in geology and the Formative Stage in
the development of quantitative geology drew to a
close.
The close of the Formative Stage was punctuated
in 1895 by publication of a paper on Contributions
to the Mathematical Theory of Evolution by the great
statistician and founder of modern statistics Karl
Pearson (Cubitt and Henley, 1978). The scattered
papers on application of trigonometry and geometry
to solving geological problems published up to this
time seemingly had little effect on later workers and
in most aspects of geology. Part of the problem was
the education of geologists, and as aptly noted by
Van Bemmelen (Agterberg, 1974), geologists can be
categorized into two types: artists and scientists, and
the artistic side (qualitative aspects) developed faster
and more broadly in scope than the scientific side
(quantitative aspects). Porter (1977, p. 4) notes that,
69
‘‘There was continuous pressure to render the pursuit
more ‘scientific,’ while criteria of the ‘scientific’
themselves developed in course of time. Methods,
techniques and standards were forged which were
claimed to be more rigorous, philosophically sophisticated and appropriate to the object. Pragmatically
speaking, these moves bore fruit.’’ This quantification is taking place yet today and the wide use of
computer techniques has accelerated the process.
Therefore, it is interesting to note that Lyell’s statistical contribution based on ratios was made even
prior to the formalization to the subject of statistics,
and the basis on which one of his major contributions was made was lost subsequently and its impact
limited (Fisher, 1953).
Thus, the point is that the statistical argument by
which one of the revolutions in geological sciences
was affected was almost immediately forgotten. In
later editions of the Lyell’s Principles, this great
Appendix, in which so much labor had been
expended, disappeared; it survived, indeed, only 2
years (until publication of the 2nd edition). It had
served its purpose, but the ladder by which the height
had been scaled was kicked down.
3.3. Exploration Stage (1895 –1941)
In the case of nearly all branches of science a great
advance was made when accurate quantitative
methods were used instead of merely qualitative.
On the Application of Quantitative Methods to the
Study of Structure and History of Rocks, H.C.
Sorby (1908)
There was little improvement during the next
half-century during the Exploration Stage, but Karl
Pearson’s (1857 – 1936) paper on Mathematical
Contributions. . .signaled a definite change (Pearson,
1895). The subject of Pearson’s paper was elicited
in the subtitle On a Form of Spurious Correlation
Which May Arise When Indices are Used in the
Measurement of Organs. A few numerically inclined
workers pioneered the application of the new field
of statistics to geology. Paleontologists (see especially Rowe, 1899; Trueman, 1930; Brinkmann,
1929) and sedimentologists (Sorby, 1908; Udden,
1914; Wentworth, 1929; Krumbein, 1936) made use
of statistical techniques to summarize and present
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table 7
1895 – 1941 Exploration stage
Karl Pearson
1895 Contributions to the Mathematical
Theory of Evolution
J.A. Udden
1898 The Mechanical Composition of
Wind Deposits
A.W. Rowe
1899 An Analysis of the Genus Micraster,
as Determined by Rigid Zonal Collecting
From the Zone of Rhynchonella cuvieri
to That of Micraster coranairinum
H.C. Sorby
1908 On the Application of Quantitative
Methods to the Study of the
Structure and History of Rocks
J. Joly
1909 Radioactivity and Geology, an
Account of the Influence of Radioactive
Energy on Terrestrial History
W. Penck
1921 Morphologische Analyse
W.A. Richardson 1923 The Frequency-Distribution of Igneous
Rocks
C.K. Wentworth 1929 Method of Computing Mechanical
Composition Types in Sediments
A.E. Trueman
1930 Results of Some Recent Statistical
Investigations of Invertebrate Fossils
W.C. Krumbein 1934 The Probable Error of Sampling
Sediment for Mechanical Analysis
C. Eisenhart
1935 A Test for Significance of Lithological
Variation
W.C. Krumbein 1936 Application of Logarithmic Moments to
Size Frequency Distributions of
Sediments
H. Korn
1938 Schechtung und Absolute Zeit
their enormous amounts of data on populations
(Table 7).
Henry Clifton Sorby (1826 – 1908) published his
classic paper, On the Application of Quantitative
Methods to the Study of the Structure and History
of Rocks in 1908 (Sorby, 1908). His purpose was to
apply quantitative methods to the mass of data
accumulated in his stream experiments and investigations of slaty cleavage. His last paper, perhaps
his most important one geologically, set the stage for
additional advances in quantitative geology by suggesting additional studies and lines of inquiry. Many
examples of univariate and bivariate statistical applications could be given for the early part of the 20th
Century. In petrology, studies could be cited starting
with Reyer (1877) and extended to Richardson’s
(1923) paper, in stratigraphy by Eisenhart (1935)
and Korn (1938), and in geomorphology by Penck
(1921).
3.4. Development Stage (1941 –1958)
Many geologists have been caught short in the
computer revolution: educated in a tradition
which emphasized the qualitative at the expense
of the quantitative, they are inadequately prepared
in mathematics, unfamiliar with statistics. Statistics and Data Analysis in Geology, J.C. Davis
(1973)
The next stage comes with another statistician’s
contribution, Kolmogorov (1941), who introduced
probability methods into geology (Table 8). These
types of academic studies, however, were interrupted
by WWII. Nevertheless, the definitive paper by Bagnold (1941) on The Physics of Blown Sand and Desert
Dunes, which was a highly quantitative analysis of the
subject, appeared just about the time of the war. This
stage continued after the war but was really underdeveloped in the strictest sense because of the laborious
calculations necessary to do anything meaningful.
About this time, Ben Burma initiated his multivariate
studies in paleontology, resulting in his trilogy of
contributions on ‘Studies in Quantitative Paleontology’ (Burma, 1948, 1949, 1953). [Burma] ‘‘. . .was a
pioneer in the study of quantitative invertebrate paleontology in the days when the involved and tiresome
mathematical calculations were performed by hand
Table 8
1941 – 1958 Development stage
A.N. Kolmogorov
1941
H.E. Horton
1945
A.B. Vistelius
1947
A.H. Strahler
H.J. Pincus
1952
1952
R.L. Miller
1953
W.C. Krumbein
1955
A.H. Strahler
F. Chayes
L.H. Ahrens
1956
1956
1957
The Lognormal Law of Distribution
of Particle Sizes During Crushing
Erosional Development of
Streams and Their Drainage Basins
Stochastic Basis of a O.V.
Sarmanov Geologically Important
Probability Distribution
Dynamic Basis of Geomorphology
Some Methods for Operating on
Orientation Data
Introduction to Special Issues on
Statistics in Geology
Experimental Design in the Earth
Sciences
Quantitative Slope Analysis
Petrographic Modal Analysis
Lognormal-type Distributions
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
71
Fig. 5. (Upper) G. Baily Price worked in Operations Research (OR) unit in Bletchley Park, England, during WWII from 1943 to 1945, where
Colossus was located. Price visited Bletchley again in 2002 where a replica of Colossus was on display (he is on the right, caretaker on the left).
Price was head of KU Department of Mathematics and Chairman of University Committee that recommended KU secure its first computer—
IBM 650. Early experience with computers at KU is similar to other American academic institutions. (Lower) IBM 650 at University of Kansas,
ca. 1957, with the first director of ‘computer center,’ Urs Hochstrasser of the Department of Mathematics.
72
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
rather than on a pocket or desktop calculator’’ (Kaska,
1986).
WWII was the time of accelerated development of
automated methods and development of computers to
deal with problems of the war effort, a push in the
development of technology (Table 1; Fig. 5). After the
war, as things gradually changed, these advances and
developments were made available commercially. In
1954, IBM unveiled its 650 computer that used
punched cards for input/output, and results were
printed by specially designed wired-print boards on
another machine. Calculations were made using ma-
Fig. 6. Computer program written in machine language SOAP for IBM 650 (from Krumbein and Sloss, 1958).
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
73
Fig. 6 (continued ).
chine language or the programming language SOAP
(Fig. 6).
The early computers (the IBM 650 and later IBM’s
700 series) used vacuum tubes, which were subject to
failure because of the heat generated and because
there were so many tubes in a unit, the failures came
often. (The airconditioners typically occupied more
space than the computer.) This problem was solved
74
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
after ‘invention’ and use of transistors in place of
vacuum tubes, and, in addition, transistors facilitated
calculations (Fig. 7).
The early quantitatively oriented workers were
viewed with some suspicion and were not accepted
widely by fellow workers because of some feeling of
distrust in mathematical and computer-oriented studies—this was mainly because the ‘artistic ones’ did
not comprehend the basics of the different approach.
The Development Stage offered some interesting
geological papers, but the real impetus for accelerated
development was the introduction of the computer.
All at once, difficult or impossible things were available easily and, therefore, progress towards quantification took a real leap forward and the computer age
was upon us (Merriam, 1981b). The IBM 650 (Fig. 5),
thus, set the stage for the automation of geology
which was announced to the geologic public via
Krumbein and Sloss’ (1958) paper; Babbage’s prediction of 1864 was fulfilled.
3.5. Automated Stage (1958 – 1982)
Among the earliest uses of the digital computer in
geology was its application to relatively simple
statistical analysis. . .then to map studies and
multiple regression. From these beginnings. . .use
of the computer spread into virtually all fields of
geology. . .. The Computer in Geological Perspective, William C. Krumbein (1969)
3.5.1. Early developments
The conceptual stage of computer applications in
geology took place during the 1950s. The story is told
well by perusing the Bibliography of Computer Applications in the Earth Sciences, 1948– 1970 compiled
by Merriam (1988). Early workers include W.C.
Krumbein (1902 – 1979), J.C. Griffiths (1912 – 1992),
A.B. Vistelius (1915 – 1995), Felix Chayes (1916 –
1993), and Georges Matheron (1930 – 2000); all had a
profound affect on the development of the subject. It
was during this time that geologists recognized the
potential of the new tool as an extension of the mind
(Merriam, 1981b). Early applications were mainly
calculations that had been done previously by hand
or by calculator. Geophysicists, geochemists, engineering geologists, and others, who were quantitatively inclined, simply exchanged their calculators and
slide rules for computers where computation was
speeded up and fewer errors were made—hallmark
of computers: reliability and reproducibility. Many
papers were published containing suggestions of possibilities, and the literature was long on ideas but short
on meaningful applications (Table 9).
Fig. 7. IBM 1620, second-generation machine at University of Kansas, ca. 1966.
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table 9
1958 – 1982 Automated stage
W.C. Krumbein/
L.L. Sloss
R.R. Sokal/
P.H.A. Sneath
G. Matheron
D.F. Merriam/
J.W. Harbaugh
W.C. Krumbein/
F.A. Graybill
A.B. Vistelius
J.C. Griffiths
1958
1963
1963
1964
1965
1967
1967
J.W. Harbaugh/
D.F. Merriam
J.E. Robinson/
H.A.K. Charlesworth/
M.J. Ellis
J.W. Harbaugh/
G.F. Bonham-Carter
F. Chayes
J.C. Davis
1968
1971
1973
F.P. Agterberg
W. Schwarzacher
1974
1975
K.G. Jöreskog/
J.E. Klovan/
R.A. Reyment
I. Clark
J.E. Robinson
1976
1979
1982
R.W. LeMaitre
1982
1969
1970
High-Speed Digital Computers in
Analysis Stratigraphic and Facies
Principles of Numerical
Taxonomy
Principles of Geostatistics
Trend-Surface Analysis of
Regional and Residual
Components of Geologic
Structure in Kansas
An Introduction to Statistical
Models in Geology
Studies in Mathematical Geology
Scientific Method in Analysis of
Sediments
Computer Applications in
Stratigraphic Analysis
Structural Analysis Using Spatial
Filtering in Interior Plains of
South-Central Alberta
Computer Simulation in Geology
Ratio Correlation
Statistics and Data Analysis in
Geology
Geomathematics
Sedimentation Models and
Quantitative Stratigraphy
Geological Factor Analysis
Practical Geostatistics
Computer Applications in
Petroleum Geology
Numerical Petrology
It was also a time when a number of textbooks on
the subject were published. Following the lead of
Miller and Kahn’s (1962) book on statistics in the
geological sciences, Krumbein and Graybill (1965)
published An Introduction to Statistical Models in
Geology. Griffiths (1967) looked into sampling and
statistics in the analysis of sediments in his authoritative book on the subject. And in (1968), Harbaugh
and Merriam summarized the use of computers in
stratigraphy.
Part of the problem in the early days was simply
the limit of the machines; the amount of data that
could be processed was limited by storage space and
run time. Only the simplest computations could be
done and those only with difficulty. Programming was
extremely awkward and tedious, for example, in
75
machine language and cards or paper tape because
input had to be punched; run time was long and many
errors could occur during processing time; and the
vision of applications mainly was limited by the user
and the technology to analytical techniques. In addition, most geologists were cautious and even suspicious of computers which no doubt dated from the
time of Darwin and his warning to beware of trusting
mathematicians (and by extension, to computers).
To process large databases, it was necessary to
analyze available geological data and determine how
they could be stored and retrieved in machines with
limited capacity (Hubaux, 1969, 1970). To handle the
enormous amount of accumulated data in the early
days, it was necessary to code them with semantic
symbols (Dixon, 1970). A good summary of data
processing and databases used in geology as of the
early 1970s is given by Bergeron et al. (1972). This
approach was difficult and awkward and was fortunately superseded shortly by machines with larger
memories, making it possible to use full citations.
It was at this time that the petroleum and mining
companies became interested in using computers for
both exploration and exploitation (in addition to bookkeeping chores; see, for example, Dillon, 1964). IBM
formed a group headed by Bill Peikert, one of Krumbein’s students, to promote the use of their computers
in the petroleum industry (Peikert, 1969). Their published computer programs and instructions served as a
model for the Kansas Geological Survey Special
Distribution Publications and later, the Computer
Contributions (Merriam, 1999). Mining companies
were concerned mainly with ore-reserve estimations
and Georges Matheron and Danie Krige pioneered
these efforts. Because companies could afford real
computing power, their numerically oriented geologists often were miles ahead of the academics and thus
could and did make numerous notable contributions.
3.5.2. A decade of rapid development
Toward the end of the 1950s, 2nd-generation
computers (Fig. 8) and higher-level languages were
introduced. Programming became easier; machines
were made accessible; and computing became more
economical. As a result, geologists branched out into
modifying statistical techniques and mathematical
procedures to solve their problems; algorithms were
borrowed form other disciplines; and many papers
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Fig. 8. (Upper) IBM 7040 at University of Kansas, which replaced IBM 1620 in ca. 1968, and (lower) IBM 7090 at Stanford University in 1963.
Both second-generation machines used transistors.
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
were published demonstrating the use of different
techniques (Table 10). In the 1960s, multivariate
statistical techniques, such as trend analysis, were
applied (Fig. 9). Trend analysis, separating a largescale effect from the local effects, became popular
because it was a technique that geologists could
understand and interpret the results; they had been
using such a procedure and computing and plotting
the data by hand (Fig. 10). The concept of simulation
(modeling) was introduced early (see Chapter 8 of
Harbaugh and Merriam, 1968; and later, Whitten,
1983; Schaeben, 1988); Harbaugh and Bonham-Carter’s (1970) book on geologic simulation was a decade
or so ahead of its time but a forerunner of things to
come.
In analyzing the subject matter of some of these
early papers, it is interesting to note that certain
nationalistic trends occur. For example, geologists in
Germany, France, Canada, and Czechoslovakia were
concerned with data, its collections, and treatment.
Geologists in other countries were more concerned
with applications—in the United Kingdom, to sedimentological, paleontological, and geomorphological
problems; in India, to petrological ones; in Italy, to
geochemical problems; and in the USSR, to sedimentological and petrological problems. Much work was
done on structural and tectonic problems by the Germans, hydrology by the French, and mineral exploration by the Canadians, South Africans, and Czechs.
Trend analysis was popular in the UK, India, and
Australia; factor analysis in France; power-spectra
studies in Romania; and simulation in the United
States. These generalities reflected to some extent
Table 10
Some techniques available to geologists
Sequential
Power spectrum
Variograms
Cross-correlation
Autocorrelation
Cross-association
Autoassociation
Markov chains
Spatial
autocorrelation
2D power strata
kriging
bicubic spline
trend analysis
2D Fourier analysis
3D trend analysis
discriminant functions
Fourier analysis
spatial filtering
Moving averages fractals
Time trend
Dimension-free
correlation coefficients
regression analysis
cluster analysis
principal components
factor analysis
canonical correlation
77
the availability of hardware, workable software, local
problems, and interest of those geologists working
with computers (Merriam, 1974a).
Rapid growth and accelerated interest in computer
use occurred during the 1960s as many saw the
potential of this powerful tool. Dissemination of
information was paramount and had to be timely. In
pre-Internet time, dissemination was by hardcopy.
GeoRef, the leading bibliographic database was established, Computer Applications in the Mineral Industries (APCOM), a series of meetings in the mineral
industries, and the Kansas Colloquia were established
(with accompanying proceedings), and the Kansas
Computer Contributions made their debut (Merriam,
1999).
The International Association for Mathematical
Geology (IAMG) was founded at the ill-fated International Geological Congress in Prague in 1968,
largely at the instigation of Richard A. Reyment
(Merriam, 1978). The IAMG, affiliated both with
the International Union of Geological Sciences
(IUGS) and the International Statistical Institute
(ISI), in a few short years, established three international journals [Mathematical Geology, 1969; Computers & Geosciences, 1975; and Natural Resources
Research (formerly Nonrenewable Resources), 1992]
and a newsletter, sponsored numerous meetings, and
fostered and facilitated an exchange of ideas on a
worldwide basis.
For a time, in the late 1970s and 1980s, a group of
interested workers formed a society in Denver
concerned with microcomputing—Computer-Oriented Geological Society (GOGS). They were successful
in disseminating information to interested workers
through publications and a series of meetings.
The status of computer use in the different geological disciplines was summarized in a collection of
papers published in 1969 (Merriam, 1969) and
updated a decade later (Merriam, 1981d). By the
1980s, however, the proliferation of the hardware
and software was so widespread in the geosciences,
making assessment of the status in subdisciplines of
geology difficult, and the surveys were not continued.
Some workers at this time in the field began to
publish their works including F.P. Agterberg (mineral
resources), G.F. Bonham-Carter (mineral resources/
pollution), F. Chayes (petrology), J.M. Forgotson, Jr.
(petroleum), W.T. Fox (sedimentology), G.M. Fried-
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Fig. 9. (A) Subset of geological subjects, methods of data analysis, and time in 2-year periods. (B) Horizontal slice to show time of entry of
computer applications in stratigraphy. Dashed lines indicate precomputer applications of methods shown. (C) Vertical slice cut to show spread of
Markov models into various geological fields by year (from Krumbein, 1969).
man (sedimentology), J.W. Harbaugh (petroleum), J.
Imbrie (paleoecology), R.L. Kaesler (paleontology),
G.S. Koch, Jr. (mining), D.G. Krige (mining), T.V.
Loudon (structure), G. Matheron (mining), R.B.
McCammon (stratigraphy), D.B. McIntyre (petrology),
D.F. Merriam (stratigraphy), A.T. Miesch (geochemistry), R.A. Reyment (paleontology), W. Schwarzacher
(stratigraphy), and E.H.T. Whitten (structure).
3.5.3. Pervasion of computers in geology
By the 1970s, computers had become available
and were easier and economical to use (Merriam,
1981c). High-level symbolic languages were available with the 3rd-generation machines and interactive systems forecasted the demise of cards and
paper tape; terminals were everywhere. Sequential
and spatial analysis were being used extensively and
Fig. 10. Example of early computer graphics—lineprinter output of: (A) first-, (B) second-, and (C) third-degree trend surfaces representing
regional geologic structure in Kansas (from Merriam and Harbaugh, 1964; made with BALGOL computer program on Stanford IBM 7090,
Harbaugh, 1963).
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
79
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
dimension-free methods were gaining popularity
(Table 10). Simulation was introduced and the
modeling of geological processes now was realistic.
GeoRef and GeoArchives both went on-line. In
addition, meetings were held on the subject first
with the Kansas Geological Survey Colloquia followed by the Syracuse University Geochautauquas,
which, in the early days, were the longest lasting
and most effective forum for disseminating information on geomathematics and geocomputing.
Databases proliferated and were accessible through
timesharing networks. Different countries, especially
Canada, Romania, and Czechoslovakia, worked towards development of large archival files; others
toward special files for mapping, mineral resources,
geochemistry, paleontology, well information, etc.
(Merriam, 1974b). GEOMAP was developed in Sweden for field mapping data and GRENVILLE in
Canada. CRIB contained the mineral-resource data of
the U.S. Geological Survey and RASS contained their
geochemical data. COGEODATA (a committee of the
IUGS) looked after standards and quality control for
the international exchange of data. Database Management Systems (DBMS) came into being to handle
these databases. G-EXEC, GIPSY, SASFRAS,
GRASP, and CLAIR (all acronyms for their specialties) were just a few of the DBMS which came into
existence at this time. The large databases and sophisticated programs available set the stage for the supercomputer (Bethke et al., 1988).
The journal Mathematical Geology, the premier
hardcopy computer publication disseminating geomathematical information, was joined by the IAMG
journal, Computers & Geosciences (C&G). C&G is
devoted to the rapid publication of computer programs in widely used languages and their applications (Merriam, 1992). C&G was the successor to
GEOCOM Bulletin, which took over publishing
computer programs in 1971 at the conclusion of
the Kansas Geological Survey’s series of successful
Computer Contributions. In 1990, C&G took over
publication of the COGS software and, in 1993,
assumed the papers from the demise of the American Association of Petroleum Geologists’ Geobyte.
The aim of C&G is to serve as a public medium for
exchange of ideas between the geological and
computer sciences—a concise statement as to an
interdisciplinary venture approximately 150 years
after constitution of the parent bodies (geology
and computer science).
Interestingly, in a study of specialized journals,
Payne and Merriam (1992, 1993) determined that the
C&G was cited more than anticipated, and that more
authors outside the geosciences cited the journal than
expected.
An experiment in publishing computer programs
on softstrip was initiated for C&G, but this unique
system did not gain acceptance. Although softstrip
was permanent, durable, and easy to reproduce and
distribute, it required special equipment to produce
and read. Thus, the user could not ‘translate’ the bar
code easily. This problem was solved by floppy disks
(initially 5 1/4 in., and later 3 1/2 in. ones), which
were readable almost anywhere. The 3 1/2-in. floppy
has a capacity of 720K and is readily portable, and
thus became the preferred method of hardcopy communication. Now, CDs are used for storage and
distribution of all types of computer-oriented data
(Merriam, 1991).
A new generation of workers appeared in the late
1970s. Their foundation in mathematics and statistics was solid, along with their good geological
background. Just a few of the many outstanding
workers to be mentioned include J.C. Brower, Isobel Clark, J.M. Cubitt, Michel David, J.C. Davis,
J.H. Doveton, P.A. Dowd, Steve Henley, Michael
Ed. Hohn, Richard J. Howarth, A. Journel, and
Donald E. Myers.
3.6. Integration Stage (1982 – present)
Like a canal navigator watching an iron horse
steam by, like a railroad engineer sighting a
horseless carriage, the geologist viewing images
on computer screen is witness to a paradigm shift.
Unrecognized assumptions lose their validity, and
things will never be the same again. Geoscience
after IT, T.V. Loudon (2000)
3.6.1. The PC era
In the fourth decade of computer applications,
the physical size of the machines decreased enormously and they became user-friendly. These attributes were the result of advances in technology
(Table 11; McIntyre, 1981). Such developments as
virtual memory (VM), bubble memory, memory
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
81
Table 11
Progression of computer development to present
1950s
1960s
1970s
1980s
1990s
Time technology
Software
Orientation
1st-generation
machines—vacuum tubes
2nd-generation
machines—transistors
3rd-generation machines—
integrated circuits—minis
Machine language
Cards and paper tape
Low-level symbolic languages, e.g., SOAP,
ALGOL, COBOL
High-level symbolic-languages, e.g.,
macroassembler; BASIC, Pascal, USP:
Database management e.g., ADABAS;
Database languages, e.g., IMS
Virtual memory; special high-level
languages; user friendly spreadsheets, e.g.,
VisaCalc and Lotus 1,2,3, query languages
Cards, RJEs, magnetic tape, batch
Windows; specialist languages for data
manipulation and graphics
CD-ROMs, communications, laser
disks, optic scanners
4th-generation machines—VLSI
circuits, micros (PCs),
supercomputers neXT computers,
Hypercubes
5th-generation machines—parallel
processing – —workstations/RISC,
Palmtops
FORTRAN,
chips, optical fibers, large-scale and very large scale
integrated (LSI and VLSI) circuits revolutionized
the hardware.7 Microcomputers became ubiquitous.
The personal computer (PC), because of its low cost
and user orientation, was almost instantly accepted
(Krajewski, 1986).
Software was improved with fast algorithms such
as the fast Fourier transform (FFT), user-friendly
languages, and telecommunications. Networking became ubiquitous. The invention of metalanguage(s)
for solving geological problems was proposed by
Griffiths (1982). To date, however, none have been
forthcoming, with the exception of geostatistiques, a
development of the French school, which is the only
technique developed expressibly for solving geological problems (Matheron, 1962, 1963). Synthesizers
were introduced so that it was possible to transmit
instructions to computer vocally.
3.6.2. The Pentium
Developments now are literally taking place faster
than they can be chronicled. New and more powerful
mainframe computers have been introduced including
the IBM 9000 series and super supercomputers. There
is an increase in use of optical scanners. The i486 chip
is obsolete and its successor, the Pentium, which has
been incorporated into the new computer lines,
7
The latest development is the terabyte disk drive with
anticipation of petabyte drives in the near future (Hayes, 2002).
Interactive sharing disks, CRTs
Networking, floppy disks, smart
terminals, interactive, and color
graphics
improves speed and capacity. Palmtop systems have
been introduced and the trend is to be even smaller
and faster (Merriam, 1991).
In software, there has been an improvement and
introduction of new and better operation systems.
DOS and UNIX are used widely; Windows has
proven popular. An extensive use has been made of
high-level and specialized languages such as LISP,
Turbo-Pascal, PROLOG, C, and J (Table 12). Geographic Information Systems (GIS) have become
widely used (Bonham-Carter, 1994). New mathematical/statistical techniques have become available including chaos theory, fractals, and meta-analysis;
these trends as noted by Cox (1991) continue. FORTRAN is declining if compared with other languages
(from 100% in 1975 to 50% in 1992). APL, PL/1, and
ALGOL essentially are gone and have been for
several years. BASIC seems to have peaked in the late
1980s as other new and specialist languages, such as
PROLOG, LISP, and C, took over. Recently, there has
been an increase in the use of spreadsheets and
specialist languages for data manipulation and
graphics. These trends are likely to continue in the
future.
New approaches have been developed, paralleling the advances in hardware/software. Workstations give geologist an integrated look at their
problems (Table 13). Compact discs with read-only
memory (CD-ROMs) put tremendous amounts of
data at their fingertips; networks connect electronic
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table 12
Numbers of articles listing programs in various languages in Computers & Geosciences, Volumes 1 – 18, 1975 – 1992 (adapted from Cox, 1991)
Year
Volume
FORTRAN
1975 – 1976
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
Total
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
20
17
23
20
13
16
27
20
18
17
31
31
23
20
32
36
36
25
425
a
APL
1
1
BASIC
Pl/1
ALGOL
PASCAL
C
LISP
PROLOG
Othersa
Total
1
9
9
19
20
21
26
20
21
20
29
21
21
22
40
40
40
38
66
57
69
49
620
3
1
7
3
1
1
1
2
1
1
1
7
1
3
4
8
7
11
9
20
5
12
6
99
1
1
3
6
8
4
6
1
30
1
3
2
1
2
1
3
7
6
7
27
1
1
2
3
1
3
5
Others include mostly spreadsheets and specialist languages for data manipulation and graphics.
mail to supercomputers and on-line databases (both
factual and bibliographical). Along with e-mail, fax
transmission has improved our ability to communicate and communicate fast (Merriam, 1990).
Much of our ‘substantial’ information exchange
now takes place through these communication
networks before hardcopy publication. It is necessary to be linked into the communications network
to be fully aware of current happenings. New
journals are on-line (no hardcopy) and established
journals are being put on-line. Most journals ask
for digitized text and illustrations along with the
hardcopy, or require authors to submit the manuscript directly via e-mail. It is now possible to
submit a paper for publication and have the
review, revision, editing, typesetting, and publication all take place electronically with no hardcopy
involved.
Table 13
Examples of generations of microcomputers (adapted from Barr, 1985)
1977
1979
1981
1983
1991
1st generation,
8 bit
2nd generation,
8 bit
3rd generation,
8/16 bit
4th generation,
16/32 bit
5th generation,
32 bit
Examples
Dominant
processor
Operating
system
Apple II, PET, TRS 80, BBC
Micro, Commodore 64
Superbrain, RML 380 Z,
Osborne, Epson QX 10
Sirius 1, IBM PC, DEC
Rainbow 100, ACT Apricot
Apple Lisa, Sage
6502
Z80
Apple DOS, Commodore,
Tandy, Acorn
CP/M
8088
CP/M 86, MS-DOS
68000
UNIX?
88000
80386SX
i486
Pentium
UNIX and Microsoft OS/2
Sun workstations
SiliconGraphics
Macintosh
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Undoubtedly, there will be more hardware/software
creations, changes, and improvements. Machines will
become faster, more compact, and more portable
(Table 14). Software will become more user-friendly,
more easily available, and more powerful. Communications will continue to improve and program/data
exchange will be almost instantaneous and available
to anyone desiring or needing it. Large databases
are accessible to the users that are tied into networks; bulletin boards serve as newsletters for
organizations. Off-line CD-ROMs provide an enormous amount of instantly available data/information.
Manuscripts, as noted, are being submitted via the
network. All phases of science will be faster, more
intense, more focused, and require better education
and background than required of geologists today. It
will be a challenge for users to stay aware of these
new hardware/software advances and innovative
applications.
Loudon (2000) took a look into the future with
his predictions in Geoscience After IT, IT being
Information Technology. He notes that IT handles
tools for information, computers, and networks, and
IT, which is more efficient, allows a better expression of concepts and an exchange of ideas. IT is how
geoscientists investigate the real world, how they are
organized, and what they know and how they think.
His summary, therefore, is IT is the way of the
future.
In 1972, I predicted (in general terms; Merriam, 1972) that ‘‘Computers undoubtedly will be
Table 14
A. Computation speeds (modified from Knuth, 1976)
Man (pencil and paper)
Man (abacus)
Mechanical calculator
Medium-speed computer
Fast computer
Super fast computer
0.2/s
1/s
4/s
200,000/s
200,000,000/s
32,000,000,000/s
1,000,000,000,000/s
B. Cubic feet/1 million characters of storage (data from IBM)
1953
1959
1970
1976
1979
1991
400 ft3
100 ft3
8.0 ft3
0.3 ft3
0.03 ft3
0.00003 ft3
83
easier to communicate with and become faster
and larger (in capacity). Graphic displays will
be more sophisticated and realistic. Programs will
be easier to use and available through various
exchanges developed on national and international
levels. Programs will be thoroughly tested, thus
reliable, increasing the credibility of the results.
Databases will be compatible and available
through national and international organizations.
Cooperation among geologists will increase as
they strive to fully use their data for all the
information it contains.’’
All of these predictions have come to pass and
exceed expectations. The next 20 years is most
likely to see a continuation of these trends and
even an acceleration! As implied by Vic Loudon,
one of the few things that we can be sure of in this
world is change, only the rate is unknown.
Acknowledgements
I would like to thank Alan P. Brynes of the
Kansas Geological Survey, John C. Davis of Baker
University, John W. Harbaugh of Stanford University, Richard J. Howarth of Imperial College
(London), Richard A. Reyment of the University
of Uppsala (Sweden), Donald B. McIntyre, formerly of Pamona College, now residing in Perth,
Scotland, Floyd W. Preston of the University of
Kansas, and Gerry Friedman of the Rensselaer
Center of Applied Geology for reading a preliminary version of the manuscript and offering
helpful, insightful suggestions. As usual, I was
abetted in many ways by the Survey’s information
specialist Janice Sorensen; I owe her undue thanks
for help.
Appendix A . Kansas Geological Survey Colloquia
The first colloquium was organized and held at
the Kansas Geological Survey, The University of
Kansas in 1966. This series of meetings was
organized to fulfill a definite need to disseminate
information on the latest developments in quantitative geology and computer applications. All eight
meetings that were held are shown in Table A1. In
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D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table A1
List of colloquia hosted by the KGS (from Merriam, 1999)
Table A2
Geochautauquas
1st
2nd
3rd
4th
5th
6th
7th
8th
Classification Precedures (KGS/CC7)
Trend Analysis (KGS/CC12)
Time-Series Analysis (KGS/CC18)
Simulation (KGS/CC22)
Sampling (KGS/CC30)
Computer Applications (CAES/1)a
Optical-Data Processing (no publication)
Geostatistics (CAES/2)a
1
1972
Syracuse
2
1973
Syracuse
3
4
5
1974
1975
1976
Syracuse
Syracuse
Syracuse
KGS/CC: Kansas Geological Survey Computer Contributions.
CAES: Computer Applications in the Earth Sciences, a book series
sponsored by the IAMG and published by Plenum Press.
a
Cohosted by the IAMG.
6
7
1977
1978
Syracuse
Syracuse
8
1979
Syracuse
1971, the meetings at KGS/KU were continued as
the Geochautauquas at Syracuse University.
9
1980
Miami
10
1981
Ottawa
11
1982
Urbana
12
1983
Lawrence
13
1984
Morgantown
14
1985
Wichita
15
1986
Calgary
16
17
1987
1988
Pribram
Tucson
18
19
1989
1990
Newark
Freiburg
20
1991
Denver
21
1992
Kyoto
22
1993
Prague
23
1994
Mt. Tremblant
24
1995
Osaka
1966
1967
1967
1968
1968
1969
1970
1970
Colloquium
Colloquium
Colloquium
Colloquium
Colloquium
Colloquium
Colloquium
Colloquium
on
on
on
on
on
on
on
on
Appendix B . Syracuse University Geochautauquas
The Geochautauquas were the follow-up organized
meetings of the KGS Colloquia. The first one was held
at Syracuse University in the fall of 1972 and others
were held yearly after that (Table A2). In 1980, the
meetings started to rotate to interested organizations
that wanted to host the group. In 1986, the meetings
went international with the first meeting outside the
United States in Calgary, Canada. Starting in 1991.
The meetings consisted of a session in conjunction
with another meeting and continued in that venue until
discontinuance in 1997 after the establishment of the
IAMG’s Annual Meetings in 1994.
Appendix C . International Association for
Mathematical Geology (IAMG) Annual Meetings
In 1994, IAMG decided to hold annual stand-alone
meetings with the exception of those years of the IGC
when they would have sessions in conjunction with
the Congress (Table A3). These meetings have been
successful and a publication has resulted from each.
Appendix D . APCOM Meetings
The first meeting in the APCOM (APplication of
COMputers and operational research in the mineral
industries) series was initiated and sponsored by the
The Impact of Quantification on
Geology
Geologic Data Analysis with
Computers
Computers and Mineral Resources
CAI in Geology
Computer Software in the
Geosciences
Quantitative Stratigraphic Correlation
Mathematical Models in the Earth
Sciences
Computer Applications in the Earth
Sciences, an Update of the 1970s
Climate Models and the Past, The
Role of Oceans on Geochemical
Cycles, and Natural Resource
Discovery and Models
Use of computers in MineralResources Evaluation
New Developments in Quantification
of Coal Geology
Think Deep: Computer Methods in
the Subsurface
Big Programs on Small Machines:
Research Methods on Mini and
Microcomputers
Computer Applications in Petroleum
Exploration and Development
Computers in the Petroleum Industry:
‘‘Integrated Approaches’’
Mathematical Methods in Geology
Computers for the Analysis of
Geochemical and Hydrogeochemical
Data
Mineral-Resource Assessment
Three-Dimensional Computer
Graphics in Modeling Geologic
Structures and Simulating Geologic
Processes
Mapping algorithms and applications
(with Denver GeoTech ’91)
Mathematical and statistical analyses
of geological data (with 29th
International Geological Congress)
Mathematical, statistical, and
computing problems in the geological
sciences (with 25th Silver
Anniversary Meeting of IAMG)
Basin analysis (with IAMG Annual
Meeting)
Mathematical Methods in the Earth
Sciences (with 2nd Annual Meeting
of IAMG)
(continued on next page )
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Table A2 (continued )
25
26
1996
1997
Beijing
Barcelona
Mathematical and Statistical Data
Analysis in Geology (with 30th IGC,
session 19-5)
Quantitative Methods in the Earth
Sciences (in conjunction with 3rd
IAMG Annual Meeting-IAMG’97)
Meetings and session superseded by IAMG Annual Meetings.
University of Arizona College of Mines at Tucson,
AZ, in 1961 (Table A4). (The acronym APCOM was
originated by the organizers of the 10th symposium in
Johannesburg, South Africa, in 1972.) The conferences are organized by an informal council composed
of past and future hosts of the meeting. Jay C. Dotson
was editor of a 2-volume proceedings entitled as a
Short Course on ‘‘Computers and Computer Applications in the Mineral Industries.’’ Most of the papers in
this softback publication were concerned with an
introduction to computing and related problems, business and accounting, and applications in mining. The
IBM 650 was the machine used in the short course and
SOAP the programming language. From this modest
beginning, the meetings expanded to their present-day
international coverage. The second meeting was held
the next year because of the success of the first meeting
and again was held in Tucson. Subject matter included
in addition was papers on geostatistics, a subject which
has been emphasized ever since. John C. Griffiths,
Danie Krige, and George Koch and Dick Link were
among those on the conference program.
By 1963, the conference sponsorship was expanded to include the Stanford University School of Earth
Sciences. The subject matter was also expanded to
Table A3
IAMG Annual Meetings
1
2
3
1994
1995
1996
4
5
6
7
1997
1998
1999
2000
8
9
10
11
2001
2002
2003
2004
Mt. Tremblant, Quebec, Canada
Osaka, Japan
Beijing, Peoples Republic of China (in
conjunction with 30th IGC)
Barcelona, Spain
Ischia, Italy
Trondheim, Norway
Rio de Janeiro, Brasil (in conjunction with
31st IGC)
Cancun, Mexico
Berlin, Germany
Portsmouth, England
Florence, Italy (in conjunction with the 32nd IGC)
85
Table A4
List of APCOM meetings and international symposia
1
1961
Tucson, AZ
2
1962
Tucson, AZ
3
1963
Stanford, CA
4
1964
Golden, CO
5
1965
Tucson, AZ
6
1966
7
1968
University
Park, PA
Golden, CO
8
1969
9
1970
10
1972
11
1973
12
13
1974
1975
Golden, CO
Clausthal,
Germany
14
1976
15
1977
University
Park, PA
Brisbane,
Australia
16
17
1979
1982
Tucson, AZ
Golden, CO
18
1984
London,
England
19
1986
20
1987
21
22
23
1989
1990
1992
University
Park, PA
Marshalltown,
Transval,
South Africa
Golden, CO
Berlin, Germany
Tucson, AZ
Salt Lake
City, UT
Montreal,
Canada
Johannesburg,
South Africa
Tucson, AZ
Computers and computer
applications in the Mineral
Industries
Mathematical techniques and
computer applications in mining
and exploration
Computers in the mineral
industries
Applications of statistics,
operations research, and
computers in the mineral
industries
Computers and computer
applications in mining and
exploration
Computers and operations
research in mineral industries
Symposium on OR and computer
applications in the mineral
industries
A decade of digital computing in
the mineral industries
Techniques for decision-making in
the mineral industries
Application of computer methods
in the mineral industries
Computer applications in the
mineral industries
Application of computer and
mathematics for decision-making
in the mineral industries
Application of computers and
operations research in the mineral
industries
Application of computers and
operations research in the mineral
industry
Application of computers and
mathematics in the mineral
industries
Application of computers and
operations research in the mineral
industry
86
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
include petroleum. There were sessions on geophysics
and petroleum exploration and production. Paper were
presented by John P. Dowds, J.L. Morrison, Ed. L.
Dillon, John C. Griffiths, Robert L. Miller, D.F.
Merriam, John W. Harbaugh, Floyd W. Preston, Z.V.
Jizba, and D.R. Ojakangas.
In 1964, the Colorado School of Mines was the host
and numerous papers were included on geology and
geophysics. Back in Tucson for the 5th (1965) meeting, they included sessions on Exploration, Exploitation and Geology, and Exploration and Geophysics,
plus short courses, demonstrations, and exhibits. Familiar names showed up on the program including
DeVerle Harris, John W. Harbaugh, Floyd W. Preston,
Scott W. Hazen, Vaclav Nemec, Frits P. Agterberg,
John C. Griffiths, and Larry Drew. In 1966, the
meeting moved to the Pennsylvania State University
and some of the same participants were on the program
again including Krige, Agterberg, Griffiths, Harris,
and Harbaugh. The meetings went international with
the Johannesburg, South Africa meeting in 1972.
The publications, for the most part, are softback,
unedited, and author-prepared. However, they give a
good account of the development of computers and
computer applications in the mining industry especially. Certain names reoccur throughout the history of
the organization. Danie Krige and John C. Griffiths
both have been honored by the group for their support
and contributions during the years.
The meetings have emphasized geostatistiques in
all phases of the mining industry from an early time.
This is understandable because the subject was largely
developed by mining geologists and engineers from
the French School of Geostatistiques in Fontainebleau, France. The very first meetings lacked geological sessions, but in the late 1960s, 1970s, and 1980s,
there have been many sessions on geology, geophysics, and exploration and development in both mining
and petroleum. Recent meetings, however, have not
emphasized these subjects.
References
Abbe Hauy, R.J., 1801. Traité de Minéralogie, Tome Premier. Chez
Louis Libraire, Paris, 494 pp.
Aczel, A.D., 2001. The Riddle of the Compass: The Invention that
Changed the World. Harcourt, New York, 178 pp.
Adanson, M., 1757. Histoire naturelle du Senegal. Coquillages.
Avec la relation abrégée d’un royage fait en ce pays, pendant
les années 1749, 50, 51, 52, et 53. Bauche, Paris, 175 pp.
Agricola, G., 1556. De re Metallica: Froben, Basel (transl. from
Latin by Hoover, H.C., Hoover, L.H., 1912, and reproduced
by Dover Publ., New York, 1950).
Agterberg, F.P., 1974. Geomathematics. Elsevier, Amsterdam,
596 pp.
Babbage, C., 1864. Passages from the Life of a Philosopher. Longman, Green, London. Reprinted in 1968 by Dawsons of Pall
Mall, London, 496 pp.
Bagnold, R.A., 1941. The Physics of Blown Sand and Desert
Dunes. William Morrow and Co, New York. Reprinted by
Methuen & Co., London, 1954, 265 pp.
Barr, R., 1985. Thematic mapping on microcomputers: the hardware and software environments. Comput. Geosci. 11 (3),
283 – 289.
Bates, R.L., Jackson, J.A., 1980. Glossary of Geology, 2nd ed.
Am. Geol. Inst., Alexandria, VA, 749 pp.
Bates, R.L., Jackson, J.A., 1987. Glossary of Geology, 3rd ed.
Am. Geol. Inst., Alexandria, VA, 788 pp.
Bergeron, R., Burk, C.F., Robinson, S.C. (Eds.), 1972. ComputerBased Storage, Retrieval and Processing of Geological Information. 24th Intern. Geol. Cong. Sect. (Montreal), vol. 16.
222 pp.
Bethke, C.M., Harrison, W.J., Upson, C., Altaner, S.P., 1988. Supercomputer analysis of sedimentary basins. Science 239
(4837), 261 – 267.
Bonham-Carter, G.F., 1994. Geographic Information Systems for
Geoscientists: Modelling with GIS. Pergamon, Oxford, 398 pp.
Brinkmann, R., 1929. Statistisch-biostratigraphische Unterschungen an mittel-jurassischen Ammoniten uber Art-begriff und
Stammes-entwicklung. abhandlungen der Gesellschaft der Wissenschaften zu Gottingen, mathematisch physikalische Klasses.
Neue Folge Bd, vol. 13. Weidmannsche Buchhandlung, Berlin,
249 pp.
Burma II, B.H., 1948. Studies in quantitative paleontology: I. Some
aspects of the theory and practice of quantitative paleontology.
J. Paleontol. 22 (6), 725 – 761.
Burma II, B.H., 1949. Studies in quantitative paleontology: II.
Multivariate analysis—a new analytical tool for paleontology
and geology. J. Paleontol. 23 (1), 95 – 103.
Burma II, B.H., 1953. Studies in quantitative paleontology: III. An
application of sequential analysis to the comparison of growth
states and growth series. J. Geol. 61 (6), 533 – 543.
Clerk Maxwell, J., 1870. On hills and dales. Rep. Meeting Br.
Assoc. Adv. Sci. (Liverpool) Trans., 17 – 18.
Cockbain, A.E., 1980. James Clerk Maxwell, the first quantitative
geomorphologist. J. Math. Geol. 12 (6), 615 – 616.
Cox, N.J., 1991. Programming languages in Computers & Geosciences, 1975 – 1989. Comput. Geosci. 17 (4), 595.
Cubitt, J.M., Henley, S., 1978. Statistics in Geology. Dowden,
Hutchinson & Ross, Stroudsburg, PA, 340 pp.
Dana, J.D., 1837. A System of Mineralogy with an Appendix Containing the Application of Mathematics to Crystallographic
Investigations, and a Mineralogical Bibliography. Durrie & Peck
and Herrick & Noyes, New Haven, 571 pp.
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Dana, E.S., 1932. A Textbook of Mineralogy. Wiley, New York,
851 pp.
Darwin, F., Seward, A.C., 1903. More Letters of Charles Darwin. D
Appleton and Co, New York, 508 pp.
Davis, J.C., 1973. Statistics and Data Analysis in Geology. Wiley,
New York, 550 pp.
Delesse, M.A., 1848. Procede mecanique pour determiner al composition des roches. Ann. Mines (4th Ser.) 13, 379 – 388.
Dillon, E.L., 1964. Electronic storage, retrieval, and processing of
well data. Am. Assoc. Pet. Geol. Bull. 48 (11), 1828 – 1836.
Dixon, C.J., 1970. Semantic symbols. Math. Geol. 2 (1), 81 – 87.
Eisenhart, C., 1935. A test for the significance of lithological variations. J. Sediment. Petrol. 6 (1), 35 – 47.
Ellenberger, F., 1996. History of Geology, v. 1. From Ancient Times
to the First Half of the XVII Century. A.A. Balkema, Rotterdam,
299 pp.
Everest, R., 1832. A quantitative study of stream transportation.
J. Asiat. Soc. Bengal 1, 238 – 240.
Fisher, R.A., 1953. The expansion of statistics. J. R. Stat. Soc., Ser.
A Stat. Soc. 116 (Pt. 1), 1 – 6.
Frisi, P., 1818. A Treatise on the Rivers and Torrents; with the
Method of Regulating Their Course and Channels. Longman,
Hurst, Rees, Orme, and Brown, London, 184 pp. (transl. by
Major-General John Garstin; 1st ed. 1782 printed at Lucca;
2nd ed., 1770, Florence).
Gary, M., McAfee Jr., R., Wolf, C.L. 1972. Glossary of Geology.
Am. Geol. Inst., Washington, DC, 805 pp.
Griffiths, J.C., 1967. Scientific Method in Analysis of Sediments.
McGraw-Hill, New York, 507 pp.
Griffiths, J.C., 1982. Mathematics in geology: new languages, new
perspectives. Nat. Resour. 28 (4), 14 – 17.
Harbaugh, J.W., 1963. BALGOL program for trend-surface mapping using an IBM 7090 computer. Kansas Geol. Surv. Spec.
Dist. Publ. 3, 17 pp.
Harbaugh, J.W., Bonham-Carter, G.F., 1970. Computer Simulation
in Geology. Wiley, New York, 575 pp.
Harbaugh, J.W., Merriam, D.F., 1968. Computer Applications in
Stratigraphic Analysis. Wiley, New York, 282 pp.
Haughton, S., 1846. On the laws of equilibrium and motion of solid
and fluid bodies. Camb. Dublin Math. J. 1, 173 – 182.
Hayes, B., 2002. Terabyte territory. Am. Sci. 90 (3), 212 – 216.
Holmes, A., 1965. Principles of Physical Geology. The Ronald
Press, New York, 1288 pp.
Howarth, R.J., 2001. A history of regression and related modelfitting in the Earth sciences (1636?) – 2000). Nat. Resour. Res.
10 (4), 241 – 286.
Howarth, R.J., 2002. From graphical display to dynamic model: mathematical geology in the Earth sciences in the
nineteenth and twentieth centuries. In: Oldroyd, D.R. (Ed.),
The Earth Inside and Out: Some Major Contributions to Geology in the Twentieth Century. Spec. Publ.-Geol. Soc., vol.
192, pp. 59 – 97.
Hubaux, A., 1969. Archival files of geological data. Math. Geol. 1
(1), 41 – 52.
Hubaux, A., 1970. Description of geological objects. Math. Geol. 2
(1), 89 – 95.
Hubbert, M.K., 1974. Is being quantitative sufficient? In: Merriam,
87
D.F. (Ed.), The Impact of Quantification on Geology. Syracuse
Univ. Geol. Contrib., vol. 2, pp. 27 – 49.
Hull, D.L., 1973. Darwin and His Critics. Harvard Univ. Press,
Cambridge, MA, 473 pp.
Hutton, J., 1788. Theory of the earth, or an investigation of the laws
observed in the composition, dissolution, and restoration of land
upon the globe. R. Soc. Edinb. Trans. 1, 209 – 304.
Jackson, J.A., 1997. Glossary of Geology, 4th edn. Am. Geol. Inst.,
Alexandria, VA, 769 pp.
Johnson, A.M., 1970. Physical Processes in Geology. Freeman
Cooper & Co, San Francisco, 577 pp.
Joly, J., 1909. Radioactivity and Geology, an Account of the Influence of Radioactive Energy on Terrestrial History. Archibald
Constable, London, 287 pp.
Kaska, H.V., 1986. Benjamin Harrison Burma II, 1917 – 1992.
Mem.-Geol. Soc. Am. 16, 3 pp.
Knuth, D.E., 1976. Mathematics and computer science: coping with
finiteness. Science 194 (4271), 1235 – 1242.
Kolmogorov, A.N., 1941. The lognormal law of distribution of
particle sizes during crushing. Dokl. Akad. Sci. (USSR) 31
(2), 99 – 101.
Korn, H., 1938. Schechtung und absolute zeit. Neues Jahrb. Mineral., Geol. Paläontol., Abh., Abt. A 74 (1), 51 – 188.
Krajewski, S.A., 1986. Past, present and future trends in microcomputing. Computer-Aided Methods in Geology and Engineering: Denver GeoTech ’86, Denver, CO, pp. 123 – 131.
Krauskopf, K.B., 1967. Introduction to Geochemistry. McGrawHill, New York, 721 pp.
Krumbein, W.C., 1936. Application of logarithmic moments to size
frequency distributions of sediments. J. Sediment. Petrol. 6 (1),
35 – 47.
Krumbein, W.C., 1969. The computer in geological perspective. In:
Merriam, D.F. (Ed.), Computer Applications in the Earth Sciences. Plenum, New York, pp. 251 – 275.
Krumbein, W.C., Graybill, F.A., 1965. An Introduction to Statistical
Models in Geology. McGraw-Hill, New York, 475 pp.
Krumbein, W.C., Sloss, L.L., 1958. High-speed digital computers
in stratigraphic and facies analysis. Am. Assoc. Pet. Geol. Bull.
42 (11), 2650 – 2669.
Landsberg, H.E., 1958. Data processing in geophysics. In: Benioff,
H., Ewing, M., Howell, B.F., Press, F. (Eds.), Contributions to
Geophysics (In Honor of Beno Gutenberg). Pergamon, New
York, pp. 210 – 227.
Leblanc, P.J., 1993. Re-inventing writing in the virtual age. Educ.
Tech. Exch. 1 (4), 6 – 13.
Loudon, T.V., 2000. Geoscience After IT: a View of the Present
Future Impact of Information Technology on Geoscience. Pergamon, Amsterdam, A142 pp.
Lundstrom, M., 2003. Moore’s law forever? Science 299 (5604),
210 – 211.
Lyell, C., 1830 – 1833. Principles of Geology. John Murray, London, 3 volumes.
Lyell, C., 1863. The Geological Evidences of the Antiquity of Man.
John Murray, London, 520 pp.
Lyell, Mrs. K.M. (Ed.), 1881. Life, Letters and Journals of Sir Charles
Lyell, Bart., John Murray, London, v. 1, 475 pp.; v. 2, 489 pp.
Matalas, N.C., 1969. Systems analysis in water-resources investi-
88
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
gations. In: Merriam, D.F. (Ed.), Computer Applications in the
Earth Sciences. Plenum, New York, pp. 143 – 159.
Mather, K.F., Mason, S.L., 1939. A Source Book in Geology.
McGraw-Hill, New York, 702 pp.
Matheron, G., 1962. Traité de géostatistique appliquée, tome I.
Mem.-Bur. Rech. Géol. Min. (14) (333 pp.).
Matheron, G., 1963. Traité de géostatistique appliquée, tome II.
Mem.-Bur. Rech. Géol. Min. (24) (171 pp.).
May, K.O., 1980. Historigraphy: a perspective for computer scientists. In: Metropolis, N., Howlett, J., Rota, G.C. (Eds.), A History of Computing in the Twentieth Century. Academic Press,
Orlando, 693 pp.
McIntyre, D.B., 1981. Developments at the man – machine interface. In: Merriam, D.F. (Ed.), Computer Applications in the
Earth Sciences, an Update of the 70s. Plenum, New York,
pp. 23 – 42.
McIntyre, D.B., McKirdy, A., 1997. James Hutton, the founder of
modern geology. The Stationary Office, Edinburgh, 51 pp.
Merriam, D.F. (Ed.), 1969. Computer Applications in the Earth
Sciences. Plenum, New York, 281 pp.
Merriam, D.F., 1972. Introduction to ‘the impact of quantification
on geology’. Syracuse Univ. Geol. Contrib. 2, 1 – 3.
Merriam, D.F., 1974a. Introduction. In: Merriam, D.F. (Ed.), The
Impact of Quantification on Geology. Syracuse Univ. Geol.
Contrib., vol. 2, pp. 1 – 3.
Merriam, D.F., 1974b. Resource and environmental data analysis.
Earth Science in the Public Service. U. S. Geol. Surv. Prof. Pap.,
vol. 921, pp. 37 – 45.
Merriam, D.F., 1975a. Computer Fundamentals for Geologists.
COMPTE, Dartmouth, NH, 305 pp.
Merriam, D.F., 1975b. Computer perspectives in geology. In:
McCammon, R.B. (Ed.), Concepts in Geostatistics. SpringerVerlag, New York, pp. 138 – 149.
Merriam, D.F., 1978. The International Association for Mathematical Geology—a brief history and record of accomplishments.
In: Merriam, D.F. (Ed.), Geomathematics: Past, Present, and
Prospects. Syracuse Univ. Geol. Contrib., vol. 5, pp. 1 – 6.
Merriam, D.F., 1980. Computer applications in geology—two decades of progress. Proc. Geol. Assoc. 91 (1 – 2), 53 – 58.
Merriam, D.F., 1981a. A forecast for use of computers by geologists
in the coming decade of the 80’s. In: Merriam, D.F. (Ed.), Computer Applications in the Earth Sciences—an Update of the 70’s.
Plenum, New York, pp. 369 – 380.
Merriam, D.F., 1981b. Roots of quantitative geology. In: Merriam,
D.F. (Ed.), Down-to-Earth Statistics: Solutions Looking for
Geological Problems. Syracuse Univ. Geol. Contrib., vol. 8,
pp. 1 – 15.
Merriam, D.F., 1981c. Computer applications in geology—two decades of progress. Proc. Geol. Assoc. 91 (1 – 2), 53 – 58.
Merriam, D.F. (Ed.), 1981d. Computer Applications in the Earth
Sciences, an Update of the 70s. Plenum, New York, 385 pp.
Merriam, D.F., 1982. Development, significance, and influence of
geomathematics: observations of one geologist. J. Math. Geol.
14 (1), 1 – 10.
Merriam, D.F., 1983. The geological contributions of Charles Babbage. Compass 61 (1), 31 – 38.
Merriam, D.F., 1988. Bibliography of computer applications in
the earth sciences, 1948 – 1970. Comput. Geosci. 14 (6),
719 – 964.
Merriam, D.F., 1990. Digital decade deserves soft and hard copy.
Geobyte 5 (6), 14.
Merriam, D.F., 1991. FAX, e-mail, diskettes, softstrip, and CD
ROMs. . .our communication revolution. Proc.-Geosci. Inf.
Soc. 21, 23 – 33.
Merriam, D.F., 1992. Computers & geosciences: an editorial. Comput. Geosci. 18 (1), v – viii.
Merriam, D.F., 1999. Reminiscences of the editor of the kansas
geological survey computer contributions, 1966 – 1970 and a
byte. Comput. Geosci. 25 (4), 321 – 334.
Merriam, D.F., 2001. Andrei Borisovich Vistelius: a dominant figure in 20th Century mathematical geology. Nat. Resour. Res. 10
(4), 297 – 304.
Merriam, D.F., Harbaugh, J.W., 1964. Trend Surface Analysis of
Regional and Residual Components of Geologic Structure in
Kansas. Kansas Geol. Surv. Spec. Dist. Publ., vol. 11. 27 pp.
Miller, R.L., Kahn, J.S., 1962. Statistical Analysis in the Geological
Sciences. Wiley, New York, 483 pp.
Normile, D., 2001. The end—not here yet, but coming soon. Science 293 (5531), 787.
Parker, M.A., 1946. Use of International Business Machine techniques in tabulating drilling data. Ill. State Acad. Sci. Trans. 39,
92 – 95.
Payne, K., Merriam, D.F., 1992. Use of the proceedings of international conferences and symposia in geology as determined by
citation analysis: a preliminary report. Proc.-Geosci. Inf. Soc.
22, 165 – 173.
Payne, K., Merriam, D.F., 1993. Impact of geoscience specialist
journals: a study in use patterns. Proc.-Geosci. Inf. Soc. 23,
23 – 33.
Pearson, K., 1895. Contributions to the mathematical theory of
evolution: 2. Skew variation in homogeneous materials. Philos.
Trans. R. Soc. London Ser. A: Math. Phys. Sci. 186, 343 – 414.
Peikert, E.W., 1969. Developments at the man – machine interface.
In: Merriam, D.F. (Ed.), Computer Applications in the Earth
Sciences. Plenum, New York, pp. 1 – 11.
Penck, W., 1921. Morphologische Analyse. Verhandl. Dtsch. Geograph. 20, 122 – 128 (see Penck, W., 1953, Morphological
Analysis of Landforms, Macmillan, London, 429 pp.).
Perrault, P., 1674. De l’Origine des Fontaines. Pierre le Petit, Printer
& Bookseller, Paris. trans. by LaRocque, A., 1967. On the
Origin of Springs, Hafner Publ. Co., New York, 209 pp.
Playfair, J., 1802. Illustrations of the Huttonian Theory of the Earth,
Cadell and Davies, London, and William Creech, Edinburgh.
528 pp. (reprinted 1956 by Dover Publ., New York, with Introduction and biographical notes by G.W. White).
Porter, R., 1977. The Making of Geology, Earth Science in Britain
1660 – 1815. Cambridge Univ. Press, Cambridge, 288 pp.
Rasmussen, W.C., 1952. Yield of ground-water reservoirs calculated by geo-mathematical analogy. Proc. Md. – Del. Water Sewage
Assoc. 25th Ann. Conf. (Washington, DC), pp. 42 – 62.
Reade, T.M., 1885. The importance of solution as a factor in erosion. Am. J. Sci. (3rd Ser.) 29, 290 – 300.
Reyer, E., 1877. Beitrage zur Fysik der Eruptionen und der Eruptivgestine: Vienna, 225 pp.
D.F. Merriam / Earth-Science Reviews 67 (2004) 55–89
Reyment, R.A., 1974. The age of zap. In: Merriam, D.F. (Ed.), The
impact of quantification on geology. Syracuse Univ. Geology
Contrib. vol 2, pp. 19 – 26.
Richardson, W.A., 1923. The frequency-distribution of igneous
rocks: Part II. The laws of distribution in relation to petrographic
theories. Min. Mag. 20 (pt. 100), 1 – 4.
Rowe, A.W., 1899. An analysis of the genus Micraster, as determined by rigid zonal collecting from the zone of Rhynchonella
cuvieri to that of Micraster corangirinum. Q. J. Geol. Soc.
London 55, 494 – 547.
Rudwick, M.J.S., 1972. The Meaning of Fossils. Macdonald, London, 287 pp.
Schaeben, H., 1988. Geology and mathematics: progressing mathematization of geology. Geol. Rundsch. 77 (Heft 2), 591 – 607.
Sejnowski, T.J., 1987. Review of ‘Computing with Connections’.
J. Math. Psychol. 31 (2), 203 (and following pages).
Sokal, R.R., Sneath, P.H.A., 1963. Principles of Numerical Taxonomy. Freeman, San Francisco, 359 pp.
Sorby, H.C., 1908. On the application of quantitative methods to the
study of the structure and history of rocks. Q. J. Geol. Soc.
London 64, 171 – 233.
Thomson, W., 1883. Electrical units of measurement. Popular Lectures and Addresses, vol. 1. Macmillan, New York, pp. 73 – 136.
Torrens, H., 2003. Memoirs of William Smith, LLD The Bath
Royal Literary and Scientific Institution, Bath, England, 230
pp. (first published in 1844, by J. Phillips) with an introduction
to the Life and Times of William Smith.
Trueman, A.E., 1930. Results of some recent statistical investigations of invertebrate fossils. Biol. Rev. Biol. Rev. Cambr. Philos.
Soc. 5 (4), 296 – 308.
Udden, J.A., 1914. Mechanical composition of clastic sediments.
Geol. Soc. Am. Bull. 25, 655 – 744.
Van Sinderen, A.W., 1980. The printed papers of Charles Babbage.
Ann. Hist. Comput. 2 (2), 169 – 185.
Vistelius, A.B., 1967. Studies in Mathematical Geology. Consultants Bureau, New York, 294 pp.
Vistelius, A.B., 1968. Mathematical geology: a report of progress.
Geocom Bull. (unpaginated).
von Zittel, K.A., 1901. History of Geology and Paleontology to
the End of the Nineteenth Century. Walter Scott, London,
562 pp.
89
Wadge, G., 1993. Computers and geological information: the depth
and the width of it. Geoscientist 3 (2), 10 – 13.
Wentworth, C.K., 1929. Method of computing mechanical composition types in sediments. Geol. Soc. Am. Bull. 40 (4), 771 – 790.
Whewell, W., 1840. The philosophy of the inductive sciences,
founded upon their history, 2 vols. Parker, London and Deighton, Cambridge.
Whitten, E.H.T., 1966. Structural Geology of Folded Rocks. Rand
McNally, Chicago, 663 pp.
Whitten, E.H.T., 1983. Twenty-five years of mathematical geology:
a new threshold. Math. Geol. 15 (2), 237 – 243.
Winchester, S., 2001. The Map that Changed the World. Harper
Collins, New York, 329 pp.
Daniel F. Merriam is a Senior Research Scientist (emeritus) with
the Kansas Geological Survey at the University of Kansas. He
received his BS, MS, and PhD from the University of Kansas, and
MSc and DSc from Leicester University (England). He was with
the KGS from 1953 to 1971, serving as Chief of Geologic
Research in his last position. From 1971 to 1981, he was the
Jessie Page Heroy Professor of Geology and head of the Department of Geology at Syracuse University. In 1981, he returned to
Wichita State University as Endowment Association Distinguished
Professor of the Natural Sciences and chairman of the Department
of Geology and Geography. He rejoined the Survey in 1991 and
retired in 1997 but remains active. He has been a Visiting
Research Scientist at Stanford University, a Fulbright – Hays Senior Research Fellow to the United Kingdom, Director of the
American Geological Institute’s International Field Institute to
Japan, an American Geological Institute’s Visiting Geological
Scientist, a Participant in Project COMPUTe, Dartmouth College,
an Esso Distinguished Lecturer at the University Sydney (Australia), a Visiting Professor at the Centre d’Informatique Geologique, Ecole des Mines de Paris (Fontainebleau), and a Visiting
Scientist at the GeoForschungsZentrum Potsdam (Germany). His
interests are mainly in late Paleozoic, Mesozoic, and Cenozoic
stratigraphy in the Midcontinent area including petroleum geology,
plains-type folds and structural development of cratonic basins,
geothermics, Pennsylvanian cyclic sedimentation, computer applications in geology, spatial analysis, information studies and
dissemination, and history of geology.