Jean-Laurent Mallet. Geomodeling
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578
CHAPTER
10.
DISCRETE SMOOTH PARTITION
Figure
10.20
Tutorial example:
the
conditional probabilities
(A)
denning
the
Association constraints between
the
geophysical fades
G
l
and the
porosity fades
F
v
are
almost
perfectly
reproduced
(B)
when recomputed
from
the
estimated
Mem-
bership
Functions
displayed
in figure
(10.19)
and the
geophysical fades
displayed
in
figure (10.15).
• the
resulting average proportion maps
f^(u,v}
shown
in figures
(10.17)-B1
to
B4
can be
recomputed
as
follows:
• the
resulting average proportion curves
fc(w)
shown
in figure
(10.18)-B
can
be
recomputed
as
follows:
• the
resulting conditional probabilities
P(F
V
\G
1
}
shown
in figure
(10.20)
can
be
recomputed
as
follows:
As
can be
seen
in
these
figures, all the
specified
constraints
are
honored almost
perfectly.
This
is due to the
coherency between these
different
constraints.
Estimation
of the
porosity
facies
The
components
of the
interpolated Membership Function
ip
can be
used
for
estimating
the
facies
in any
cell
a of the
studied domain.
For
this purpose,
and as
explained
on
page
542 and in
section
(10.2.2),
two
strategies
can be
used:
10.6.
CONCLUSIONS
579
Figure
10.21
Tutorial
example:
most
probable
estimated
porosity
fades
(MP)
and
equiprobable
simulation
of
these
fades
(SI),
(S2),
and
(S3).
•
either,
in the
case
where
a
unique
solution
is
sought,
the
most
probable
solu-
tion
shown
in
figure
(10.21)-MP
must
be
used;
• or, in the
case
where
multiple
equiprobable
solutions
are
sought,
simulations
such
as
those
represented
in figures
(10.21)-S1,
S2, and S3
must
be
generated.
The
simulations represented
in figures
(10.21)-S1,
S2, and S3
were generated
thanks
to a
P-Field
technique using
an
exponential covariance model with
ranges
R
u
,
R
v
,
and
R
w
in the
w,
i;,
and w
directions
of the
grid such
that
•
R
u
is
equal
to 22% of the
dimension
of the
domain
under
study
in the u
direction;
•
R
v
is
equal
to 15% of the
dimension
of the
domain
under
study
in the v
direction;
•
R
w
is
equal
to 10% of the
dimension
of the
domain under study
in the w
direction.
The
range
R
w
was
estimated
from
the
observed
facies
along
the
well-paths,
while
the
ranges
in the u and v
directions were
set
arbitrarily.
As can be
seen
in
figure
(10.21)
and as
expected,
the
most probable solution appears
smoother
than
the
simulations, which,
in
turn, appear more like real geological
structures.
10.6
Conclusions
In
this chapter,
a new
method, called
the
"Discrete Smooth Partition"
(DSP)
method, which allows
the set 0 of the
nodes
of a
discrete model
to be
parti-
tioned into
a
series
of
subsets
{F
1
,...,
F
n
},
has
been presented. This method
580
CHAPTER
10.
DISCRETE SMOOTH PARTITION
takes into account
the
relative location
of the
elements
a of the set
£7
and ad-
ditional "structural" information related
to the
shape
and the
distribution
of
the
subsets
{F
1
,...,
F
n
}.
In
practice,
the DSP
method
is
implemented
as a
series
of
specific
constraints processed
by the
DSI
algorithm. This approach
has the
following
advantages:
• The
proposed method
can be
extended very easily;
for
this purpose,
it
suffices
to
"feed"
the DSI
method with additional constraints corresponding
to new
types
of
information.
• If
some constraints
are,
locally
or
globally, contradictory, then
DSI
will
look
for
a
"compromise" solution.
In
addition
to the DSP
method, another method based
on
Moving-Centers
has
been proposed
and can be
used either independently
or in
association
with
the DSP
method.
Bibliography
[1]
Abraraovitz,
M., and
Stegun,
I.,
(1972).
Handbook
of
Mathematical Functions:
with Formulas,
Graphs,
and
Mathematical Tables. Dover,
New
York,
NY, 9th
(revised)
printing.
[2]
Ahlfors,
L.,
and
Sario,
L.,
(1960).
Riemann
Surfaces.
Princeton University
Press,
Princeton,
New
Jersey, 1960,
371p.
[3]
AitEttajer,
T.,
(1995).
Modelisation
de
Surfaces
Geologiques
Complexes sous
Contraintes
Geometriques.
Ph.D.
thesis, Institut National Polytechnique
de
Lorraine, Nancy, Prance.
[4]
Akima,
H.,
(1978).
A
Method
of
bivariate interpolation
and
smooth
surface
fitting
for
irregularly distributed data points.
ACM
Trans.
Math. Software,
V.
4, pp.
56-76.
[5]
Allan,
U.S.,
(1989).
Model
for
hydrocarbon migration
and
entrapment within
faulted
structures. AAPG Bull.
V. 73, No. 7, pp.
803-811.
[6]
Aminzadeh,
P.,
Burkhard,
N.,
Nicoletis,
L.,
Rocca,
P.,
and
Wyatt,
K.,
(1994).
SEG/EAEG
3-D
modeling project:
2nd
update.
The
Leading Edge, Sept
1994,
V.
13, No. 9, pp.
949-952.
[7]
Angelier,
J.,
(1994). Fault
Slip
Analysis
and
Palaeostress Reconstruction.
Con-
tinental
Deformation, Hancock,
P.
(ed.), Pergamon
Press,
pp. 53
100.
[8]
Armstrong,
M.A.,
(1983). Basic
Topology.
Springer-Verlag,
New
York,
251 p.
[9]
Arthur, D.W.G., (1965). Interpolation
of a
function
of
many variables.
Pho-
togrammetric Engineering
and
Remote Sensing,
V. 31, No. 2, pp.
348-349.
[10]
Aziz,
K.,
and
Settari,
A.,
(1979). Petroleum reservoir simulation. Elsevier,
New
York,
476 p.
[11]
Balas,
E., and
Padberg,
M.W.,
(1976).
Set
Partitioning:
A
survey.
SIAM
ReV.,
V.
18-4,
pp.
710-760.
[12]
Barnhill,
R.E.,
(1974). Smooth interpolation over triangles. Computer-Aided
Geometric Design,
R.E.
Barnhill
and
R.F.
Riesenfeld (eds.), Academic
Press,
New
York,
pp.
45-70.
[13]
Barnhill,
R.E.,
(1985).
Surfaces
in
Computer-Aided
geometric design:
a
survey
with
new
results. Computer-Aided Geometric Design,
V. 2, pp.
1-17.
[14]
Bass,
J.,
(1968). Cours
de
mathematiques, tome
1.
Masson
et
Cie,
Paris,
682
P-
[15]
Bass,
J.,
(1971). Cours
de
mathematiques, tome
3:
topologie, integration,
dis-
tributions, equations
integrales,
analyse
harmonique.
Masson
et
Cie,
Paris,
389
p.
581
582
BIBLIOGRAPHY
[16]
Baumgart,
B.,
(1974). Geometric
Modeling
for
Computer Vision. Ph.D. the-
sis,
Stanford University, Also
as
Tech. Rep. CS-463.
[17]
Baumgart,
B.,
(1975).
A
polyhedron
representation
for
computer vision.
Na-
tional Computer Conference,
AFIPS
Conf.
Proc.,
pp.
589-596.
[18]
Bellman, R.E., (1957). Dynamic Programming. Princeton University
Press,
Princeton,
New
Jersey.
[19]
Bellman, R.E., (1960). Introduction
to
Matrix Analysis.
McGraw
Hill,
New
York,
275 p.
[20]
Bennis,
C.,
Vezien, J.M.,
and
Iglesias,
G.,
(1991).
Piece-wise
surface
flattening
for
nondistorted texture mapping. Computer Graphics,
V. 25, No. 4,
July,
pp.
237-246.
[21]
Bergthorsson,
P., and
Doos, B.R., (1955). Numerical weather
map
analysis.
Tellus VII,
V. 3, pp.
329-340.
[22]
Bertrand
Y.,
(1992).
Specification
algebrique
et
realisation d'un modeleur
in-
teractif
d'objets
geometriques volumiques.
Ph.D. thesis, Louis
Pasteur
Uni-
versity,
Strasbourg, France.
[23]
Bertrand
Y.,
Dufourd, J.F.,
Francon,
J., and
Lienhardt,
P.,
(1993). Algebraic
Specification
and
Development
in
Geometric Modeling.
Proc.
TAPSOFT,
Or-
say,
LNCS
668,
Springer-Verlag,
pp.
75-89.
[24]
Bertrandias,
J.P.,
(1971). Analyse fonctionnelle. Armand Colin,
Paris,
230 p.
[25]
Bezier,
P.,
(1967). Definition numerique
des
courbes
et
surfaces
I.
Automa-
tisme,
No. 11, pp.
625-632.
[26]
Bezier,
P.,
(1967). Definition numerique
des
courbes
et
surfaces
II.
Automa-
tisme,
No. 12, pp.
17-21.
[27]
Bezier,
P.,
(1974). Mathematical
and
practical possibilities
of
UNISURF.
Computer-Aided Geometric Design, R.E.
Barnhill
and
R.F. Riesenfeld (eds.),
Academic Press,
New
York,
pp.
127-152.
[28]
Bloomenthal,
J.,
Bajaj
C.,
Blinn,
J.,
Cani-Gascuel,
M.P.,
Rockwood,
A.,
Wyvill,
B.,
and
Wyvill,
G,
(1997). Introduction
to
Implicit
Surfaces.
Morgan
Kaufmann
Publisher,
San
Francisco,
332 p.
[29]
Boissonat, J.D., (1984). Geometric structures
for
three-dimensional
shape
rep-
resentation.
ACM
Trans.
Graph.,
V. 3, No. 4, pp.
266-286.
[30]
Boissonat, J.D., (1988).
Shape
reconstruction from planar cross sections. Com-
puter Vision Graphics
and
Image Processing,
V. 44, pp.
1-29.
[31]
Boissonat, J.D.,
and
Yvinec,
M.,
(1995).
Geometric
Algorithmique. Ediscience
International, Paris,
540 p.
[32]
Bombarde,
S., and
Basire,
C.,
(1997). Building
stratigraphic
surfaces
tied
to
well
markers using
a
morphing
like
approach.
15th gOcad meeting report,
16
P-
[33]
Bowyer,
A.,
(1981). Computing
Dirichlet
tesselations. Comput. Journal,
V.
24,
No. 2, pp.
162-166.
[34]
Briggs,
I.C.,
(1974). Machine contouring using minimal curvature. Geophysics,
V.
39, No. 1, pp.
39-48.
BIBLIOGRAPHY
583
[35]
Brisson,
E.,
(1989). Representing Geometric Structures
in d
dimensions:
topol-
ogy
and
order. Proc.
5th ACM
Symposium
on
Computational Geometry,
Saar-
brucken,
Germany, June 1989,
pp.
187-196.
[36]
Brisson,
E.,
(1990). Representation
of
d-Dimensional
Geometric
Objects.
Ph.D. thesis, Dept.
of
Compt. Sci.
and
Eng., University
of
Washington,
Seat-
tle,
WA.
[37]
Brisson,
E.,
(1993). Representing Geometric Structures
in d
dimensions:
topol-
ogy
and
order. Discrete Comput.
Geom.,
V. 9, pp.
387-426.
[38]
Brunet,
P.,
(1929).
Maupertuis:
L'oeuvre
et sa
place dans
la
pensee
scientifique
et
philosophique
du
XVIII
e
siecle.
Blanchard,
Paris.
[39]
Caers,
J.,
and
Journel,
A.G.,
(1998). Stochastic simulations using neural net-
works
trained
on
outcrop data.
SPE
annual conference
and
technical exhibi-
tion,
New
Orleans, 1998.
[40]
Catmull,
E.,
(1974).
A
Subdivision Algorithm
for
Computer
Display
of
Curved
Surfaces.
Ph.D. thesis, Dept.
of
Computer Sciences, University
of
Utah,
De-
cember 1974.
[41]
Gavin,
X.,
(1996). Intersection
de
surfaces
triangulees: amelioration
du
mail-
lage.
DEA
report, Centre
de
Recherche
en
Informatique
de
Nancy, Nancy,
France,
60 p.
[42]
Cerveny,
V.
(1985).
The
application
of ray
tracing
to the
numerical modeling
of
seismic wave
fields in
complex structures. Geophysical press, London,
Part
A,
pp.
1-124
[43]
Cheimanoff,
N.,
(1985). Modelisation tridimensionnelle d'un gisement
minier
non
tabulaire.
DEA
report,
Ecole
Nationale
Superieure
des
Mines
de
Paris,
Paris,
France, 70p.
[44]
Cherfils,
C., and
Hermeline,
F.,
(1990). Diagonal
Swap
procedures
and
charac-
terization
of
2D-Delaunay triangulations. Rairo, Math. Mod.
and
Num. Anal.
V.
24, No. 5, pp.
613-626.
[45]
Chiles,
J.P.,
and
Delfiner,
P.,
(1999). Geostatistics
—
Modeling
Spatial
Uncer-
tainties. Wiley, series
in
Prob.
and
Stat.,
New
York,
615 p.
[46]
Chipot,
Y.,
(1991). Generation
et
Modification
de
Surfaces
Triangulees. Ph.D.
thesis, Institut National Polytechnique
de
Lorraine, Nancy, France.
[47]
Chiyokura
H., and
Kimura
F.
(1983). Design
of
solids with
free-form
surfaces.
ACM
Computer Graphics,
V. 17, No. 3, pp.
289-298.
[48]
Christakos,
G.,
(1992).
Random Field
Models
in
Earth Sciences. Academic
Press,
San
Diego, 1992,
474 p.
[49]
Cognot,
R.,
Thore,
P., and
Hass,
A.,
(1994).
Tying
seismic
to
well
data using
structural uncertainties.
S.E.G.
proceedings
of the
64th Annual Meeting.
[50]
Cognot,
R.,
(1996).
La
Methode
DSI:
Optimisation, implementation
et
appli-
cations. Ph.D. thesis,
Institut
National Polytechnique
de
Lorraine, Nancy,
France.
[51]
Conraud,
J.,
(1997).
Generation
de
maillages
de
simplexes pour
la
modelisation
d'objets
naturels. Ph.D. thesis, Institut National Polytechnique
de
Lorraine,
Nancy,
France.
584
BIBLIOGRAPHY
[52]
Conreaux,
S.,
(2001).
Modelisation
de
3-varietes
a
base
topologique:
applica-
tion
a la
geologic.
Ph.D. thesis,
Institut
National
Polytechnique
de
Lorraine,
Nancy,
France.
[53]
Dahlstrom,
C.,
(1969). Balanced Cross Sections. Canadian Journal
of
Earth
Sciences,
No. 6, pp.
743-757.
[54]
de
Boor,
C.,
(1972).
On
calculating with
B-Splines.
Journal
of
Approximation
Theory,
No. 6, pp.
50-62.
[55]
de
Boor,
C.,
(1978).
A
practical guide
to
splines. Springer Verlag, Applied
Mathematical Sciences,
No. 27, 245 p.
[56]
Delaunay,
B.,
(1934).
Sur la
sphere
vide.
Bui.
Acad. Sci. URSS, Class. Sci.
Nat.,
pp.
793-800.
[57]
DeRose,
T., and
Mann,
S.,
(1992).
An
approximately
G
l
cubic
surface
inter-
polant. Academic
Press,
Mathematical methods
in
Computer-Aided
Geometric
Design
II,
Lyche,
T. and
Schumaker,
L.
(eds.),
pp.
185-196.
[58]
Deutsch, C.V.,
and
Journel, A.G., (1998).
GSLIB:
Geostatistical
Software
Li-
brary
and
User's
Guide
(second
edition). Oxford University
Press,
New
York,
369
p.
[59]
Diday
E.,
(1971).
La
methode
des
Nuees
dynamiques.
Revue
des
Statistiques
Appliquees,
V. 19, No. 2, pp.
19-34.
[60]
Dieudonne
J.A.,
(1994).
A
History
of
Algebraic
and
Differential
Topology.
Birkhauser, Boston, Massachusetts.
[61]
DoCarmo,
M.,
(1976).
Differential
Geometry
of
Curves
and
Surfaces.
Prentice
Hall,
Englewood,
New
Jersey,
503 p.
[62]
Doob, J.L., (1953). Stochastic Processes. John Wiley,
New
York.
[63]
Doyen, P.M.,
den
Boer, L.D.
and
Pillet, W.R., (1996). Seismic porosity map-
ping
in the
Ekofisk
field
using
a new
form
of
collocated
coKriging.
SPE
article
36498, Annual Technical Conference, Denver, Colorado,
pp.
21-30.
[64]
Du,
W.H., (1988). Etude
sur la
representation
de
surfaces
complexes:
Ap-
plication
a la
reconstruction
de
surfaces
echantillonnees.
Ph.D. thesis,
Ecole
Nationale
Superieure
des
Telecommunications,
Paris,
France.
[65]
Du,
W.H.,
and
Schmitt, F.J., (1990).
On the
G
l
continuity
of
piecewise Bezier
surfaces:
a
review with
new
results. Computer-Aided Design Journal,
V. 22,
No.
4,
April 1990,
pp.
556-573.
[66]
Dufourd, J.F., (1989). Algebraic Map-Based
Topological
Kernel
for
Polyhedron
Modellers.
Proc. Eurographics, Hamburg, Germany, September 1989,
pp.
649-662.
[67]
Dufourd,
J.F., (1991). Formal
specifications
of
topological
subdivisions using
hypermaps.
C.A.D.,
V. 23, No. 2, pp.
99-116.
[68]
Dufourd,
J.F., (1991).
An
OBJ3 Functional
Specification
for the
Boundary
Representation.
Proc.
ACM
Symp.
on
Solid Modeling, Austin,
Texas,
pp.
61-72.
[69]
Duvinage,
L,
Mallet, J.L.,
and
Dulac,
J.C., (1999). Constructing structural
models
without computing intersections. Int. Assoc. Math.
Geol.
5th
Confer-
ence.
Ed. by S. J.
Lippard
S.J.,
Naess,
A. and
Sinding-Larsen
R.,
Trondheim,
Norway,
August 1999,
V. 2, pp.
609-614.
BIBLIOGRAPHY
585
[70]
Ecoule,
A.B.,
Peyrin, F.C.,
and
Odet, C.L., (1991).
A
triangulation
algorithm
for
arbitrary
shaped
multiple planar contours.
ACM
Trans.
Graph.,
V. 10 No.
2,
pp.
182-199.
[71]
Edelsbrunner,
H., and
Mucke,
E.P.,
(1994). Three-dimensional
alpha-shapes.
ACM
Trans,
on
Graphics,
V. 13, No. 1, pp.
43-72.
[72]
Edmonds,
J.,
(1960).
A
combinatorial representation
for
polyhedral
surfaces.
Notices
Araer.
Math. Soc.,
V. 7,
1960.
[73]
Elter,
H.,
(1991). Chaines
de
Cartes
et
Complexes Cellulaires. Ph.D. Thesis,
Louis
Pasteur University, Strasbourg, France.
[74]
Euler,
N.,
(1999).
Modelisation
volumique
de
reservoirs
petroliers:
construc-
tions
et
operations
de
mise
a
jour.
Ph.D. thesis,
Institut
National Polytech-
nique
de
Lorraine, Nancy,
France.
[75]
Farin,
G.,
(1986). Triangular
Bernstein-Bezier
Patches.
Computer-Aided
Ge-
ometric Design,
V. 6, pp.
83-127
[76]
Farin,
G.,
(1988). Curves
and
surfaces
for
Computer-Aided
Geometric Design.
In
Geometric Modeling: Algorithms
and New
Trends, Farin G.E. (ed.),
SIAM
Publ.
Co.,
pp.
235-245.
[77]
Farin,
G.,
(1988). Curves
and
surfaces
for
Computer-Aided geometric design,
A
Practical Guide. Academic
Press,
San
Diego,
334 p.
[78]
Feller,
W.,
(1966).
An
introduction
to
probability theory
and its
applications.
V.
1 and 2.
John Wiley,
New
York,
669 p.
[79]
Fisher,
R.A.,
(1936).
The use of
multiple Measurements
in
Taxonomic Prob-
lems. Ann. Eugenics,
V. 7, pp.
179-188.
[80]
Fitchtl,
P.,
Fournier,
F., and
Royer, J.J., (1997).
Cosimulations
of
lithofacies
and
associated reservoir properties using
well
and
seismic data. Proceedings
of
the
72nd
SPE
conference,
San
Antonio, article
No.
38680, Soc.
of
Pet. Eng.,
pp.
810-823.
[81]
Fletcher,
R., and
Reeves, C.M., (1964). Function Minimization
by
Conjugate
Gradients. Computer
J.,
No. 7, pp.
149-154.
[82]
Foley,
J.D.,
and Van
Dam,
A.,
(1982). Fundamentals
of
Interactive Computer
Graphics.
Addison Wesley, Reading, Massachussets.
664 p.
[83]
Forgy, E.W. (1965). Cluster Analysis
of
multivariate data:
Efficiency
versus
interpretability
of
classifications.
Biometrics,
V. 21, pp.
768-769.
[84]
Fourgeaux,
C., and
Fuchs,
A.,
(1972). Statistique. Dunod, Monographies
Universitaires
de
mathematiques,
V. 24,
Paris,
334 p.
[85]
Froideveaux,
R.,
(1992). Probability Field
Simulation.
Proceedings
of the
Fourth International Geostatistics Congress,
Scares,
A.
(ed.),
Geostatistics
Troia,
Quantitative Geology
and
Geostatistics,
V. 1,
Kluwer, Dordrecht, Hol-
land,
pp.
73-83.
[86]
Fuch,
H.,
Kedem,
Z.M.,
and
Ulselton,
S.P.,
(1977). Optimal
surface
recon-
struction from planar contours. Commun. ACM,
V. 20, pp.
793-702.
[87]
Gastinel,
N.,
(1970). Mathematiques pour
I'informatique:
equations
differentielles.
Armand Colin,
Paris.
[88]
George, P.L., Borouchakri,
H.,
(1997). Triangulation
de
Delaunay
et
maillage.
Hermes,
Paris,
432 p.
586
BIBLIOGRAPHY
[89]
Gibbs,
A.,
(1983). Balanced cross sections construction from seismic sections
in
area
of
extensional tectonics.
Journ.
of
Struct.
Geol.,
V. 5, No. 2, pp.
153-160.
[90]
Gill, P.E., Murray,
W., and
Wright, M.H.,
(1981).
Practical optimization.
Academic
Press,
San-Diego,
401 p.
[91]
Gingerich, P.D., (1969). Markov analysis
of
cyclic alluvial sediments. Journ.
Sedimentary
Petrology,
V. 39, No. 1, pp.
330-332.
[92]
Gomez,
J., and
Journel,
A.G.,
(1993). Joint Sequential Simulation
of
Multi-
Gaussian Fields.
Geostatistics
Troia,
A
Scares
(ed.), Kluwer, Dordrecht, Hol-
land,
pp.
493-506.
[93]
Gonzales, R.C.,
and
Woods, R.E., (1993). Digital Image Processing. Addison
Wesley,
New
York,
716 p.
[94]
Goovaerts,
P.,
(1997). Geostatistics
for
Natural Resources Evaluation. Oxford
Univ.
Press,
New
York,
481 p.
[95]
Gratier,
J.P.,
Guillier,
B.,
Delorme
A.,
and
Odonne,
F.,
(1991).
Restoration
and
balance
of a
folded
and
faulted
surface
by
best-fitting
of finite
elements:
principles
and
applications. Journal
of
Structural Geology,
V. 13, No. 1, pp.
111-115.
[96]
Gregory,
J.A.,
(1974). Smooth interpolation without twist constraints.
Computer-Aided
Geometric Design, R.E.
Barnhill
and
R.F. Riesenfeld (eds.),
Academic Press,
New
York,
pp.
71-88.
[97]
Gregory,
J.A.,
(1980). Triangular Interpolation Patch
for
CAGD.
In:
Com-
puter Graphics
and
Image Processing.
V. 13. pp.
80-87.
[98]
Guiziou, J.L., Mallet, J.L.,
and
Madariaga,
R.,
(1996).
3D
seismic
reflection
tomography
on top of the
gOcad
depth
modeler. Geophysics,
V. 61, No. 5, pp.
1499-1510.
[99]
Gutjar,
A.,
(1989). Fast Fourier transform
for
random
fields.
Technical report
No.
4-R58-2690R,
Los
Alamos, N.M.
[100]
Haas, M.H.,
and
Dubrule,
O.,
(1994). Geostatistical Inversion:
a
sequential
method
of
stochastic modeling constrained
by
seismic data.
First
Break,
V. 12,
No.
11, pp.
561-569.
[101] Halmos, P.R.,
(1950).
Measure theory.
Van
Nostrand,
Princeton,
New
Jersey.
[102]
Harder, R.L.,
and
Desmarais,
R.N., (1972). Interpolation using
surface
splines.
J.
Aircraft,
V. 9, No. 2, pp.
189-191.
[103]
Hartigan,
J.,
(1975).
Clustering Algorithms. Wiley,
New
York.
[104]
Hassoun,
A.,
(1995).
Fundamentals
of
Artificial
Neural Networks.
MIT
Press,
Cambridge, Massachussetts,
511 p.
[105]
Henle,
M.,
(1979).
A
Combinatorial Introduction
to
Topology.
Dover Publica-
tions inc.,
New
York,
NY, 310 p.
[106]
Hildebrandt,
S., and
Tromba,
A.,
(1996).
The
Parsimonious Universe. Coper-
nicus
Springer-Verlag,
New
York,
330 p.
[107]
Horton, R.E., (1923).
Rainfall
interpolation. Mon. Wea. Rev.
, V. 51, No. 6,
pp.
291-304.
[108] Hoschek,
J.,
and
Lasser,
D.,
(1993).
Fundamentals
of
Computer-Aided Geo-
metric Design.
A.K.
Peters
Wellesley, Massachusetts,
727 p.
BIBLIOGRAPHY
587
[109]
Huang,
Y.,
(1990).
Modelisation
et
manipulation
des
surfaces
triangulees.
Ph.D. thesis,
Institut
National Polytechnique
de
Lorraine, Nancy, Prance.
[110]
Hubral,
P., and
Krey,
T.,
(1980). Interval velocities from seismic
reflection
time measurements. Society
of
Exploration Geophysicists, P.O.
Box
3098,
Tulsa,
Oklahoma,
203 p.
[Ill]
Isaaks,
E.H.,
and
Srivastava, R.M., (1989).
An
Introduction
to
Applied
Geo-
statistics.
Oxford University
Press,
New
York.
[112]
Jacques,
A.,
(1971). Constellations
et
graphes
topogiques.
Colloque Math.
Soc.
Janos
Bolyai, Budapest,
pp.
657-672.
[113]
Jardine,
N., and
Sibson,
R.,
(1971). Mathematical Taxonomy. Wiley,
New
York,
230 p.
[114]
Journel,
A.G.,
and
Huijbregt, C.J., (1978). Mining Geostatstics. Academic
Press,
New
York,
600p.
[115]
Journel,
A.G.,
(1980).
The
lognormal
approach
to
predicting
local
distributions
of
selective mining unit grades. Journal
of
Mathematical Geology,
V. 12, No.
4,
pp.
285-303.
[116]
Journel,
A.G.,
(1982).
The
indicator
approach
to
estimation
of
spatial
dis-
tributions
of
selective mining unit grades. Proceedings
of the
17th APCOM
International Symposium, T.B. Johnson
and
R.J. Barnes, eds. Society
of
Min-
ing
Engineers
of the
AIME,
New
York,
pp.
793-806.
[117]
Journel,
A.G.,
(1983). Nonparametric estimation
of
spatial
distributions. Jour.
Math.
Geology,
V. 15, No. 3, pp.
445-468.
[118]
Journel,
A.G.,
(1986). Constrained interpolation
and
qualitative information:
The
soft
Kriging
approach.
Jour. Math. Geology,
V. 18, No. 3, pp.
269-286.
[119]
Journel,
A.G.,
(1989). Fundamentals
of
geostatistics
in five
lessons. Short
course
presented
at the
28th International Geological Congress, Washington
D.C., American Geophysical Union,
40 p.
[120]
Journel,
A.G.,
(1993).
Modeling
uncertainties: Some conceptual thoughts.
In
R.
Dimitrakopoulos, editor, Geostatistics
for the
next century, Kluwer,
Dordrecht, Holland,
pp.
30-43.
[121]
Kent, J.R., Carlson, W.E.,
and
Parent, R.R., (1992).
Shape
transformation
for
polyhedral
objects.
In
SIGGRAPH92 Proceeding Conference, ACM,
V.
26,
pp.
47-54.
[122]
Kerr, H.G., White,
N.,
and
Brun, J.P., (1993).
An
automatic method
for
determining three-dimensional normal faults geometries.
J.
Geophysical
Res.,
V.
98, pp.
17837-17857.
[123]
Knuth, D.E., (1972).
The Art of
Computer Programming.
Addison-Wesley
Publishing Company, Reading, Massachusetts.
V.
3.,
722 p.
[124]
Launay,
L.,
Bouchet,
P., and
Mallet, J.L., (1996).
3D
reconstruction
of
cerebral
vessels
and
pathologies from
a few
biplane
digital
angiographies.
In
visualiza-
tion
in
Biomedical
Computing
-
Hamburg, 1996. Lecture notes
in
Computer
Sciences,
pp.
379-391.
[125]
Launay,
L.,
Bouchet,
P.,
Maurincomme,
P.,
Berger, M.O.,
and
Mallet, J.L.,
(1996). Reconstruction from X-Ray Projections.
In
Proceedings
of
13th Inter-
national Conference
on
Pattern
Recognition
-
ICPR
1996, Vienna, Austria,
pp.
513-517.