By William Haneberg

**Computational Geosciences with Mathematica** is the single booklet written by way of a geologist in particular to teach geologists and geoscientists the right way to use Mathematica to formulate and remedy difficulties. It spans a huge variety of geologic and mathematical issues, that are drawn from the author's wide event in examine, consulting, and instructing. The reference and textual content leads readers step by step via geologic purposes corresponding to customized pix programming, info enter and output, linear and differential equations, linear and nonlinear regression, Monte Carlo simulation, time sequence and photograph research, and the visualization and research of geologic surfaces. it's jam-packed with real Mathematica output and contains boxed computing device Notes with counsel and exploration feedback.

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**Sample text**

The preservation of area can be demonstrated using a Schmidt equal area net from a structural geology lab manual such as Marshak and Mitra (1988, p. 146). Mark off several 10 by 10 areas on different parts of the net. All of them will be, within the limits of experimental accuracy, identical. Likewise, line segments of a given angular dimension will be equal in length regardless of their position on a Schmidt equal area net. , 1976). It is more difﬁcult to calculate the equal area projection of a plane than the stereographic projection of a plane because the arc of the former is a portion of an ellipse rather than a circle.

03 0 270 90 180 Out[35]= -Graphics- The difference between the stereographic (equal angle) and equal area projections of the diplines can be illustrated by using Show to superimpose the two plots. The ﬁlled circles are the equal area projections and the open circles are the stereographic projections. 2 Contouring Equal Area Projections One of the principal uses of equal area projections is to analyze the angular distribution of large numbers of linear elements. These can be elements that are actually linear— for example, elongated mineral grains or clasts in a metamorphic rock, crystals in glacial ice, fault plane striations, fold axes— or elements such as dip lines or poles that are unique linear representations of planes.

In[67]:= aquifer Table 0, sp i, 2 , i, npts 2 54 2 Special Plots for Geoscience Data Then, replace 0 with 1 for each depth at which all three of the criteria are satisﬁed. In[68]:= Do If sp i, 1 nphi i, 1 i, npts 2 80. && sflu i, 1 > ild i, 1 && dphi i, 1 , aquifer i, 1 1 , Now create, but do not display, a plot of the potential aquifer quality. 2 , 580, 615 FrameLabel "aquifer", "Depth" , DisplayFunction Identity , Out[69]= -Graphics- Finally, show the aquifer quality plot next to the three geophysical log plots for comparison.