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.

Publisher EAGE
Language ENGLISH
Publish year 2014
Pages 388 pages


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.

The first part of this book is dedicated to a theoretical presentation of the GeoChron model. The second part presents applications of this model such as seismic interpretation, fault property modeling, fractured reservoirs characterization, geometrical uncertainties, property modeling, paleo-bathymetry estimation and permeability upscaling. To make this book ‘self sufficient’, the third part consists of annexes presenting the notions of tensors, differential geometry and Discrete Smooth Interpolation (DSI).

About the author:
In 2006, professor Mallet retired from Lorraine-University and became emeritus professor of the Nancy School of Geology. Currently, he enthusiastically continues to develop the mathematical theory of the ‘GeoChron’ model and the associated uvt-transform® that he introduced for the first time in 2004. In 2006, professor Mallet was nominated ‘senior research fellow’ by Paradigm® where he helps developers to implement the many applications of the GeoChron model and uvttransform ® in Paradigm’s SKUA® software.

For his contribution to research, during his carrier Professor Mallet was awarded a series of prizes and awards, in particular:
– in 1997 the ‘ENI Prize’,
– in 2000 the ‘SPE Anthony Lucas Gold Medal’
– in 2003 the ‘Grand Prix Dolomieux’ (French Academy of Sciences),
– in 2005 the ‘Marcel Roubault’ prize (French Geologists Society – SGF),
– in 2009 the ‘SEG Distinguished Achievement Award’ for the gOcad project,
– in 2011 the ‘EAGE Erasmus Award’.

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