Kinematic and stochastic fault modeling from sparse data for structural uncertainty analysis

Gabriel Godefroy. ( 2018 )
University of Lorraine

Abstract

The sparsity and the incompleteness of geological data sets lead geologists to use their prior knowledge while modeling the Earth. Uncertainties in the interpretation are an inherent part of geology. In this thesis, I focus on assessing uncertainties related to the modeling of faulted structures from sparse data. Structural uncertainties arise partly from the association of fault evidence explaining the same structure. This occurs especially while interpreting sparse data such as 2D seismic lines or limited outcrop observations. I propose a mathematical formalism to cast the problem of associating fault evidence into graph theory. Each possible scenario is represented by a graph. A combinatorial analysis shows that the number of scenarios is related to the Bell number and increases in a non-polynomial way. I formulate prior geological knowledge as numerical rules to reduce the number of scenarios and to make structural interpretation more objective. I present a stochastic numerical method to generate several interpretation scenarios. A sensitivity analysis, using synthetic data extracted from a reference model, shows that the choice of the interpretation rules strongly impacts the simulated associations. In a second contribution, I integrate a quantitative description of fault-related displacement while interpreting and building 3D subsurface models. I present a parametric fault operator that displaces structures closely surrounding a fault in accordance with a theoretical isolated normal fault model. The displacement field is described using the maximum displacement (dmax), two profiles on the fault surface (DX and DZ), and a third profile representing the displacement attenuation in the normal direction to the fault surface. These parameters are determined by numerical optimization from the available structural observations. This kinematic fault operator ensures the kinematic consistency of structural models built from sparse data and/or in polyphasic deformation contexts. These two modeling methodologies are tested and discussed on two data sets. The first one contains nine seismic lines imaging a faulted and fractured basement in the Ifni Margin, offshore Morocco. The interpretation of these lines is guided by orientation measurements coming from a nearby onshore field analog. However, uncertainties remain on the association of observations and on the structure chronology. The second data set is located in the Santos Basin, offshore Brazil. A seismic cube exhibits normal faults within a layered sedimentary sequence. I build a reference structural model from this high quality seismic data. The kinematic and stochastic methodologies can be tested and discussed on synthetic sparse data extracted from this known reference model.

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BibTeX Reference

@PHDTHESIS{,
    author = { Godefroy, Gabriel },
     title = { Kinematic and stochastic fault modeling from sparse data for structural uncertainty analysis },
      year = { 2018 },
    school = { University of Lorraine },
  abstract = { The sparsity and the incompleteness of geological
data sets lead geologists to use their prior knowledge while
modeling the Earth. Uncertainties in the interpretation are an inherent
part of geology. In this thesis, I focus on assessing uncertainties
related to the modeling of faulted structures from sparse
data.
Structural uncertainties arise partly from the association of
fault evidence explaining the same structure. This occurs especially
while interpreting sparse data such as 2D seismic lines or
limited outcrop observations. I propose a mathematical formalism
to cast the problem of associating fault evidence into graph
theory. Each possible scenario is represented by a graph. A combinatorial
analysis shows that the number of scenarios is related
to the Bell number and increases in a non-polynomial way. I formulate
prior geological knowledge as numerical rules to reduce
the number of scenarios and to make structural interpretation
more objective. I present a stochastic numerical method to generate
several interpretation scenarios. A sensitivity analysis, using
synthetic data extracted from a reference model, shows that the
choice of the interpretation rules strongly impacts the simulated
associations.
In a second contribution, I integrate a quantitative description
of fault-related displacement while interpreting and building 3D
subsurface models. I present a parametric fault operator that displaces
structures closely surrounding a fault in accordance with a
theoretical isolated normal fault model. The displacement field is
described using the maximum displacement (dmax), two profiles
on the fault surface (DX and DZ), and a third profile representing
the displacement attenuation in the normal direction to the fault
surface. These parameters are determined by numerical optimization
from the available structural observations. This kinematic
fault operator ensures the kinematic consistency of structural
models built from sparse data and/or in polyphasic deformation
contexts.
These two modeling methodologies are tested and discussed
on two data sets. The first one contains nine seismic lines imaging
a faulted and fractured basement in the Ifni Margin, offshore
Morocco. The interpretation of these lines is guided by
orientation measurements coming from a nearby onshore field
analog. However, uncertainties remain on the association of observations
and on the structure chronology. The second data set
is located in the Santos Basin, offshore Brazil. A seismic cube
exhibits normal faults within a layered sedimentary sequence. I
build a reference structural model from this high quality seismic
data. The kinematic and stochastic methodologies can be tested
and discussed on synthetic sparse data extracted from this known
reference model. }
}