Krumbein's Legacy

About Jiri  

Krumbein's Legacy 

Math — my primary love 

In December 1946, I failed mathematics. After my father had forced me to learn all the work I missed by January 6, 1947, math became my primary love: since then, I have used it at every opportunity. For example, while seeking a suitable mixture of my own gun powder to propel my micro-spacecraft in 1948, I optimized its four components by writing four equations for minimum mass of powder and maximum volume of gases. 

Krumbein's Legacy for me

Ten years later, 1958, my paleontologist colleague donated to me the book “Manual of Sedimentary Petrography” by William Christian Krumbein and Francis J. Pettijohn, 1938. The ideas written by Krumbein influenced my work and life. Krumbein's legacy was his showing how easily mathematics can answer questions in sedimentary petrography. 

Krumbein's Legacy for me now 

In the response to my pre-publication review "Sand Texture Sedimentology — 60 Years Research", Robert Folk (his letter dated 2016-Feb-6) was surprised by my impression by Krumbein and was asking what other geologic ideas concerning grain size he invented in addition to the phi scale. You are correct, Bob. However, Krumbein, similarly as me, did not join the crowd of authors seeking solutions based on erroneous input (innatural sieve size as granularity expression and "inexpensive" settling tubes) and using empiricism for higher moment environmental application — correlating magic skewness - kurtosis combination with known environment. Only Gaussian distribution is valid for sedimentary environment in which the source material and forming processes may mix into mixed distributions. This is why I have been seeking a stable algorithm for decomposition of the mixed distributuion into a few Gaussian components. In the year 1965, I found only a very complicated and instable dissection method into two components by Karl Pearson (1894). As late as in the year 1977, I met Isobel and Malcolm Clarks, who developed a unique stable digital solution for decomposition of mixed distributions  (program ROKE) Hyperbolic distribution is adaptable to too many other conditions, Rosin-Rammler-Sperling distribution forms by crushing between two plains, such as in mills and glaciers - it is also not suitable for sedimentary environment. 

My Contacts with Mathematical Geologists 

In the years 1965 - 1968, my contacts with the American founders of Mathematical Geology, such as Daniel Francis Merriam and John Warvell Harbaugh, were illegal for me living in the socialistic Czechoslovakia: the secret police knew about them, passed the information to the communists of my employer, ÚÚG (Central Geological Survey), who prosecuted me as being "suspicious" and "unreliable" for the socialistic regime of that time. I still communicated with the Mathematical Geologists per letters at least. 

In the years 1955 – 1968, while studying thousands samples of sedimentary rocks yearly (mostly from deep boreholes, up to 4.2 km deep), I attempted to find facial and stratigraphic characteristics in the sedimentary basins of the marine Miocene of Moravia and Slovakia (of the West-Carpathian System), and express their relationship mathematically: 

  1. In authigenic minerals, such as glauconites. to identify trace elements and useful ratios from semi quantitative spectral analyses;
  2. Heavy mineral studies enabled me to identify evolution of provenance directions in the sedimentary basins of the marine Miocene in Moravia;
  3. Studying clay minerals, I identified economically important resources of water absorbing montmorillonite clays near Turčianski Svätý Martin, in the Miocene of the Turiec Sedimentary Basin, now Slovakia; their main use was packing industry (as replacement of silicagel) and drying of natural gas;
  4. In thin sections, I found several layers of rhyodacite pyroclastics frequently associated with diatomites; the pyroclastics, even in small admixtures, helped in correlation of leading stratigraphic layers In Moravian Miocene;
  5. In the Lower-Pannonian sediments of the Váh River valley - so called "Piestany beds - I identified haloysite kaolinite mineral by electron microscope and explained the exotic colors of the beds by various particle size of fine hematite crystals; 
  6. To make modal analysis simple, suitable for a few selected mineraly and economic, I developed a Quick Modal Analysis nomograph enabling to identify percentages of individual components, without the need of completing the analyses up to 100 percent - see "A quick method of modal analysis" - "Method of Brezina".
  7. In the year 1957, to better study sandy deposits, I first followed the recently published Woods Hole Rapid Sediment Analyzer, and developed my first settling tube. My instrument was much better than the original: it recorded more sensitively the pressure difference of sedimenting suspension as the Y-axis of an XY-recorder, and — in addition — a special time base drove the X-axis utilizing an old gramophone motor, which rotated a ten-turn- potentiometer, whose changing electrical potential decelerated the X axis so, that it plotted each X-axis value at the required PHI-particle size of the XY plot. The time base enabled to record the PHI-distributions directly. 
  8. In the year 1972, to eliminate asymmetric balance load, I constructed a precision electronic leaf balance (German patent 2251838).
  9. To normalize non-normal distributions, the Dutch astronomer Jacobus C. Kapteyn, 1903, replaced the independent distribution variable by its function such as a logarithm. I applied such an independent distribution variable transformation onto the PHI grain size and transformed the log particle size into log settling rate distributions. I published the idea as Kapteyn's transformation of grain size distributions in Journal of Sedimentary Petrology, 1963. Though the publication was based on falsified data (by A. A. Sarkisian, 1958), the idea was correct (W. C. Krumbein, personal communication 1965) and later, when I had available correct and precise data (from Fort Collins Hydraulic Laboratory, Colorado, and St. Anthony Falls Hydraulic Laboratory, Minnesota), the results were so perfect, that I could use them for the development of my Universal Sedimentation Equation (J. Brezina, 1979). 

My Research at Technical University Karlsruhe

In the years 1968 - 1971, in Germany — at the beginning of my life in freedom — during my postdoctoral studies at the Institute for Mechanical Engineering (Prof. Dr.-Ing. Hans Rumpf), Technical University of Karlsruhe, I investigated the stratified sedimentation above the Stokes' law range hrtp://www.granometry.com/index.php/en/biography/1968-72 : 

  1. I focused my experiments onto two types of the particle concentration effects: (a) suspension density streaming, (b) mutual influence of sedimenting particles. My study of both these effects showed, that the sand particle centers must be at least 3.4 mm apart from each other.
  2. This defines the maximum sample size W to be about 18,000 particles for 20 cm sedimentation column diameter, quartz particle density, medium particle shape (SF = 0.65), distilled water at about 20°C and standard gravity acceleration. In grams, the maximum sample-size is: W = 25 dc3, where dc is the critical particle diameter in millimeters equaling to the tenth percentile of a distribution; 
  3. If the maximum sample size is maintained, then the particle settling velocities are not influenced by collective sedimentation (J. Brezina, 1971b, 1972a). These particle colletives sediment as their individual particles would do;  
  4. However, that small sample size sets the highest requirements for the Analyzer's Underwater Balance: sensitivity, S/N (signal to noise) ratio, and the weighing response speed.

My Private Research

In the years 1972 - 1979, I assembled the world best data including nominal grain size, particle density and shape and settling velocity. Some included also the sedimentation drag coefficient and Reynolds' number; otherwise I calculated the values myself and started developing a universal sedimentation equation by a non-linear regression analysis in a 3D-space. 

Having the above listed prerequisites, I developed also an instrument for analysis of the sand settling rate distribution, correctly: Sand Sedimentation Analyzer™, the last pre-requisite needed to study particle distribution of sands. 

In the years 1987 - 1988, I developed also a Sand Sedimentation Separator™ - unique instrument with many uses. For example, from a narrow sieve fraction, it isolates density fractions, otherwise hardly obtainable by toxic heavy liquids (inaccurately and discontinuously). Similarly, from a narrow sieve fraction, the Separator™ isolates also porous microfossils, otherwise obtainable manually only and important for detailed stratigraphy, especially of petroleum promising sediments and sedimentary rocks. 

Motivating Students in Mathematics - the Queen of Science  

Since January 1973, while having taught geological and astronomical sciences (Physical and Environmental Geologies, Astronomy, and Intro to Physical Science) more than 7000 U.S.A. students in Germany, I always motivated them in mathematics - the queen of science, as referred to by Carl Friedrich Gauss

In 2012, I introduced teaching Planetology for Geologists at Charles University, Faculty of Natural Science, Prague, Czech Republic. And - against the opinion of the faculty colleagues - students like it and the course became one of the most popular at the Geology Section. Of course, they like also my showing them the power and simplicity of mathematics in solving space questions. And - they agree that the modern geologist should understand the Earth's geology from the wider view of Planetology. To see the Earth's minerals and rocks as result of planetological processes. For example, impact processes must be considered also on the Earth, the role of the magnetic field and solar wind applied in understanding of the past life, gravity influence of the Moon, tidal heating affecting especially the Earth's volcanism at subduction zones etc..