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Workreport 1997-5

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Name:

Application of the POCS Inversion Method to Hydrogeological Characterization

Writer:

Juhani Korkealaakso

Language:

English

Page count:

59

Summary:

Working report: APPLICATION OF THE POCS INVERSION METHOD TO HYDROGEOLOGICAL
CHARACTERIZATION
ABSTRACT
In this report an inversion and interpolation approach is presented for predicting and
systematically handling geoinformation that may be relevant to include and integrate into the
hydrogeologieal characterization process. The Projection Onto Convex Sets (POCS) inversion
is introduced as an technique to reproduce the behavior of the site during some testing phase
(hydraulic interference tests, tracer tests, etc.), and also to interpolate, extrapolate, combine
and integrate in situ point measurements and eross-hole information to the volumetric
properties affecting the behavior of the site. The second and more concrete objective of this
work is to find useful, quantitative methods to improve the inversion results of cross-hole
hydraulic tests that are constructed from liniited data and in this way to be able to apply
tomographic techniques in the hydrogeological conceptualizations.
In the POCS process the image of the subsurface, which is unknown, is viewed as a member
of an infinite set of possible images. The POCS technique incorporates a priori infonnation
into the inverse scheme and its primary advantage is that it can. simultaneously enforce a large
variety of geologically and hydrogeologically useful constraints. POCS also offers an
alternative to a conditional, stochastic interpolation/simulation method and can add even an
inversion option to condi,tional simulations. Instead of "nimizing only the estimation error or
model length, POCS recasts various constraints as convex sets, then applies a procedure
known as a contraction mapping to find a realization that lies in the intersection of all
constraint sets. In the constrained least squares type POCS inversion, the parameter
distribution must lie not only in the intersection but it must also minimize the squared data
error between non-destructive, geohysical and hydrological field observations and simulated,
theoretically calculated, responses.
The different elements of the inverse process and the demonstration of the process flow of the
whole concept are presented through simple synthetic examples. These results show that the
POCS may significantly reduce the artifacts in the general linear/iinearized inversions. A
preliminary, semiquantitative, attempt to apply the technique to the three-dimensional
hydrogeological conceptualization of the NE-1 fracture zone at _sp” Hard Rock Laboratory is
also presented.
APPLICATION OF THE POCS INVERSION METHOD TO HYDROGEOLOGICAL
CHARACTERIZATION
ABSTRACT
In this report an inversion and interpolation approach is presented for predicting and
systematically handling geoinformation that may be relevant to include and integrate into the
hydrogeologieal characterization process. The Projection Onto Convex Sets (POCS) inversion
is introduced as an technique to reproduce the behavior of the site during some testing phase
(hydraulic interference tests, tracer tests, etc.), and also to interpolate, extrapolate, combine
and integrate in situ point measurements and eross-hole information to the volumetric
properties affecting the behavior of the site. The second and more concrete objective of this
work is to find useful, quantitative methods to improve the inversion results of cross-hole
hydraulic tests that are constructed from liniited data and in this way to be able to apply
tomographic techniques in the hydrogeological conceptualizations.
In the POCS process the image of the subsurface, which is unknown, is viewed as a member
of an infinite set of possible images. The POCS technique incorporates a priori infonnation
into the inverse scheme and its primary advantage is that it can. simultaneously enforce a large
variety of geologically and hydrogeologically useful constraints. POCS also offers an
alternative to a conditional, stochastic interpolation/simulation method and can add even an
inversion option to condi,tional simulations. Instead of "nimizing only the estimation error or
model length, POCS recasts various constraints as convex sets, then applies a procedure
known as a contraction mapping to find a realization that lies in the intersection of all
constraint sets. In the constrained least squares type POCS inversion, the parameter
distribution must lie not only in the intersection but it must also minimize the squared data
error between non-destructive, geohysical and hydrological field observations and simulated,
theoretically calculated, responses.
The different elements of the inverse process and the demonstration of the process flow of the
whole concept are presented through simple synthetic examples. These results show that the
POCS may significantly reduce the artifacts in the general linear/iinearized inversions. A
preliminary, semiquantitative, attempt to apply the technique to the three-dimensional
hydrogeological conceptualization of the NE-1 fracture zone at _sp” Hard Rock Laboratory is
also presented.

Keywords:

File(s):

Application of the POCS Inversion Method to Hydrogeological Characterization (pdf) (1.4 MB)


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