Symmetries in geology and geophysics

Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth’s topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters.

Scaling in geology: landforms and earthquakes.

Landforms and earthquakes appear to be extremely complex; yet, there is order in the complexity. Both satisfy fractal statistics in a variety of ways. A basic question is whether the fractal behavior is due to scale invariance or is the signature of a broadly applicable class of physical processes. Both landscape evolution and regional seismicity appear to be examples of self-organized critical phenomena. A variety of statistical models have been proposed to model landforms, including diffusion-limited aggregation, self-avoiding percolation, and cellular automata. Many authors have studied the behavior of multiple slider-block models, both in terms of the rupture of a fault to generate an earthquake and in terms of the interactions between faults associated with regional seismicity. The slider-block models exhibit a remarkably rich spectrum of behavior; two slider blocks can exhibit low-order chaotic behavior. Large numbers of slider blocks clearly exhibit self-organized critical behavior.

Models of blast furnaces for smelting iron / by Henry W. Nichols, Assoc. Curator of Geology.

no.2(1922)

Longiscitula houghae; a new genus of dissorophid amphibian from the Permian of Texas / Robert E. DeMar, Asst. Professor of Geology, University of Illinois, Chicago Circle Campus.

v.16:no.2(1966)

Famous diamonds/ by Oliver C. Farrington, Curator of Geology.

no.10(1929)

A classification of the Conularida / G. Winston Sinclair, Dept. of Geology, University of Michigan.

v.10:no.13(1952)

Amber: its physical properties and geological occurrence / by Oliver C. Farrington, Curator of Geology.

no.3(1923)

Meteorites / by Oliver C. Farrington, Curator of Geology.

no.4(1923)

Introduction and index to Fieldiana: Geology volume 33 / Eugene S. Richardson, Jr. -- William D. Turnbull --.

v.33:no.31(1981)

Cement / by Henry W. Nichols, Assoc. Curator of Geology.

no.12(1929)

The Mammalian faunas of the Washakie Formation, Eocene Age, of Southern Wyoming. Introduction: The geology, history, and setting / William D. Turnbull --.

v.33:no.30(1978)