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Fig. 1.10 Intrinsic constraints are controlled by the geometry of the horizons and IPG-lines in the
G-space (Note that the u -lines and v -lines are contained in H t and are tangent to x u and x v ) (Source:
Mallet 2004 , Fig. 7)
“Iso-Paleo-Geographic” (IPG) line for a t -line represented in G-space (Fig. 1.10 ).
T he surface H t in Fig. 1.10 was horizontal in G-space but has become c urv ed in
G-space. The ( u , v ) coordinates have become curved u -lines and v -lines in G-space
that are tangent to the components x u and x v of the 3-D location vector x ,respec-
tively. The x t component is tangent to the IPG-line also called L in Fig. 1.10 .
Mallet ( 2002 , 2004 ) and colleagues (see e.g., Caumon 2010 ) have developed
powerful methods for the analysis of sedimentary rocks that are both folded and
faulted. Most of these techniques have been incorporated in the Gocad software
package ( http://www.gocad.org ) that is used worldwide, especially by oil compa-
nies. Other methods for modeling sedimentary systems are discussed in Harff
et al. ( 1999 ).
1.5
Image Analysis
The theory of textural analysis which deals with the size, shape, orientation and
spatial distribution of objects was advanced significantly by Matheron ( 1975 ). Serra
( 1976 ) implemented these methods on a texture analyzer with hexagonal logic for
the study patterns in the plane. Sagar ( 2013 ) has published a topic on mathematical
morphology with many practical applications to systematically analyze the great
variety of features observed at the surface of the Earth. This includes use of digital
elevation models (DEMs) and digital bathymetric maps (DBMs). The study of
shapes and sizes of objects and their interrelationships has become paramount
in Geoinformation Science (GISci) that is a new flourishing field of scientific
endeavor ( cf . Wu et al. 2005 ).
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