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Elements of Mathematical Sedimentary Geology

the GeoChron Model


The purpose of this book is to offer a mathematically well-defined unified framework to model sedimentary terrains. The core of this framework, named 'GeoChron', consists of a curvilinear coordinate system (u,v,t) which superimposes on the rectilinear coordinate system (x,y,z) commonly used to locate particles of sediment in the subsurface. For each particle of sediment observed today at location (x,y,z), coordinate (t) represents the geologicaltime ('Chron' in GeoChron) at which this particle was deposited whilst (u,v) represent the paleo-geographical coordinates ('Geol' in GeoChron) of this particle when it was deposited. The u (x,y,z), v (x,y,z) and t (x,y,z) functions link the geological space (x,y,z), as it is observed today, to the depositional-space (u,v,t) and the 'uvt-transform®' thus defined plays a central role in using GeoChron to model the subsurface. In the (u,v,t) space, the image of each horizon is a horizontal plane where seismic attributes are easier to interpret and where reservoir properties are more accurately modeled.


Theoretical presentation of the GeoChron model
1-58Introducing the GeoChron model
59-96Deformations of sedimentary terrains
97-124Curvature of sedimentary terrains
125-146Stratigraphic distance & riemannian G̃-space
Applications of the GeoChron model
149-166Property modeling
167-182Upscaling permeability
183-196Modeling fault properties
197-220Modeling fault properties
221-240Geometricals uncertainties
241-252Seismic interpretation
253-268Estimating the paleo-bathymetry
305-338Differential geometry
339-360Discrete smooth interpolation

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