Fractals and Chaos in Geology and Geophysics - download pdf or read online

By Donald L. Turcotte

Now in a drastically extended moment variation, this publication relates fractals and chaos to quite a few geological and geophysical purposes and introduces the elemental ideas of fractal geometry and chaotic dynamics. during this re-creation, Turcotte expands insurance of self-organized criticality and comprises information and time sequence to supply a large historical past for the reader. subject matters contain drainage networks and erosion, floods, earthquakes, mineral and petroleum assets, fragmentation, mantle convection, and magnetic box iteration. the writer introduces all innovations on the lowest attainable point of arithmetic in step with their figuring out, in order that the reader calls for just a historical past in easy physics and arithmetic. He contains difficulties for the reader to resolve. This e-book will entice a extensive variety of readers attracted to complicated ordinary phenomena.

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Gaps in the sedimentary record are recognized on a global basis, and these gaps form the boundaries of various geological epochs. But these gaps appear at all time scales and can be attributed to periods dominated by erosion or lack of deposition. We will introduce a simple model, based on fractal concepts, for sediment deposition. The basis of this model is the devil's staircase. 11, has the same fractal dimension as the Cantor set. Instead of removing the middle third of each line segment at each order, it is retained as a horizontal segment.

The center square and four corner squares are retained and the construction is repeated. This is known as a Koch snowflake. , consider i = 1,2. (b) Determine N,, N,, N,, r,, r,, r,. (c) Determine the fractal dimension. 9. A unit square is divided into nine smaller squares of equal size and the four corner squares are discarded. The construction is repeated. (a) Illustrate the construction to second order. (b) Determine N,, N,, N,, r,, r,, r,. (c) Determine the fractal dimension. 10. A unit square is divided into 16 smaller squares of equal size.

8(c). The shaded areas are the boxes required to cover the coastline. 5 km to cover the coastline. 9. 4. This is somewhat higher than the values given above for other examples. But this is due to the extreme roughness of the coastline used in this example. When the ruler method is applied to this coastline, the same fractal dimension is found. The statistical number-size distribution for a large number of objects can also be fractal. A specific example is rock fragments. For the distribution to be fractal, the number of objects N with a characteristic linear dimension greater than r should satisfy the relation where D is again the fractal dimension.

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