Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys:
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| Format: | Book |
| Language: | English |
| Published: |
1999
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Leizig, Univ., Habil.-Schr., 1999 |
| Physical Description: | 153 Bl. zahlr. Ill. und graph. Darst. |
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MARC
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| 245 | 1 | 0 | |a Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys |c vorgelegt von Klaus Spitzer |
| 264 | 1 | |c 1999 | |
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| adam_text |
CONTENTS
ZUSAMMENFASSUNG 7
SUMMARY 11
1 FINITE DIFFERENCE FORWARD MODELING 15
1.1 INTRODUCTION. 15
1.2 THE EQUATION OF CONTINUITY. 16
1.3 DISCRETIZATION SCHEMES. 18
1.3.1 DISCRETIZATION OF THE PARTIAL DIFFERENTIAL EQUATION ACCORDING TO
BREWITT-
TAYLOR AND WEAVER (1976) [BT&W]. 18
1.3.1.1 CONDUCTIVITIES AT GRID POINTS . 18
1.3.1.2 CONDUCTIVITY GRADIENTS. 19
1.3.1.3 FIRST AND SECOND DERIVATIVES OF THE POTENTIAL.20
1.3.1.4 SOURCE TERMS. 21
1.3.1.5 COEFFICIENTS OF THE LINEAR SET OF EQUATIONS.21
1.3.2 DISCRETIZATION BY POINTS ACCORDING TO DEY
&
MORRISON (1979A) [D&ML] 22
1.3.3 DISCRETIZATION BY VOLUME ACCORDING TO DEY AND MORRISON (1979B)
[D&M2]. 23
1.3.4 DISCRETIZATION ACCORDING TO WURMSTICH & MORGAN (1994) [W&M] . . 25
1.3.5 DISCRETIZATION ACCORDING TO ZHANG ET AL. (1995) [ZM&M].26
1.3.6 THE LINEAR SET OF EQUATIONS AND THE COMPACT STORAGE SCHEME
. 27
1.3.7 ACCURACY OF THE DISCRETIZATION SCHEMES IN COMPARISON.29
1.3.8 CONCLUSIONS. 31
1.4 BOUNDARY CONDITIONS. 31
1.4.1 NEUMANN BOUNDARY CONDITIONS. 32
1.4.2 DIRICHLET BOUNDARY CONDITIONS. 32
1.4.3 MIXED BOUNDARY CONDITIONS . 32
1.5 SINGULARITY REMOVAL AND GRID-INDEPENDENT ELECTRODE POSITIONING.34
2
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/958700028
CONTENTS
3
1.6 ACCURACY ASSOCIATED WITH THE DIFFERENT TYPES OF BOUNDARY CONDITION
AND THE
SINGULARITY REMOVAL. 38
1.6.1 THE RESPONSE ALONG THE SURFACE FOR POLE AND DIPOLE SOURCES.39
1.6.1.1 POLE SOURCE OVER A DIKE MODEL. 39
1.6.1.2 DIPOLE SOURCE OVER A DIKE MODEL .41
1.6.1.3 DIPOLE SOURCE OVER A BURIED CUBE. 41
1.6.2 SUBSURFACE SINGLE-POLE SOURCES. 45
1.6.2.1 BURIED CUBE IN A CROSSHOLE ENVIRONMENT.45
1.6.2.2 HOMOGENEOUS CROSSHOLE ENVIRONMENT. 48
1.7 SPEED OF DIFFERENT EQUATION SOLVERS. 49
1.7.1 CONJUGATE GRADIENT/RESIDUAL EQUATION SOLVERS.51
1.7.2 PRECONDITIONING AND SCALING. 53
1.7.3 THE METHODS. 55
1.7.3.1 CONJUGATE GRADIENTS [CG]
.R.55
1.7.3.2 BI-CONJUGATE GRADIENTS [BICG] . 55
1.7.3.3 CONJUGATE GRADIENTS SQUARED [CGS]. 55
1.7.3.4 BI-CONJUGATE GRADIENTS STABILIZED [BICGSTAB]. 56
1.7.3.5 ORTHOMIN. 56
1.7.4 SUMMARY OF STORAGE REQUIREMENTS AND FLOATING POINT OPERATIONS . .
56
1.7.5 RESULTS. 56
1.7.6 CONCLUSIONS. 59
1.8 MODELING INDUCED POLARIZATION EFFECTS. 59
1.8.1 SHORT INTRODUCTION TO INDUCED POLARIZATION. 59
1.8.2 NUMERICAL IMPLEMENTATION. 62
2 SENSITIVITY STUDIES 64
2.1 CALCULATION OF THE SENSITIVITY. 65
2.1.1 CALCULATION OF THE SENSITIVITY BY DC FORWARD MODELING.66
2.1.2 SENSITIVITY FORWARD MODELING. 67
2.1.3 CALCULATION OF THE SENSITIVITY BY PERTURBATION .68
2.1.4 ANALYTICAL CALCULATION OF THE SENSITIVITY FOR A HOMOGENEOUS
HALFSPACE 68
2.2 THE METHODS IN COMPARISON. 69
2.3 SENSITIVITY DISTRIBUTIONS . 69
2.3.1 POLE-POLE CONFIGURATION. 70
2.3.2 POLE-DIPOLE AND DIPOLE-DIPOLE CONFIGURATIONS. 76
2.4 THE INFLUENCE OF RESISTIVITY CONTRASTS ON THE SENSITIVITY.84
CONTENTS
4
2.4.1 A THREE-LAYER EARTH. 84
2.4.2 A RECTANGULAR PRISMATIC BODY. . 86
2.5 CONCLUSIONS. 90
3 APPLICATIONS 92
3.1 A SURFACE APPLICATION: THE SAINERHOLZ PHONOLITE. 92
3.1.1 INTRODUCTION. 92
3.1.2 THE PHONOLITIC BODY . 93
3.1.3 VERTICAL ELECTRICAL SOUNDINGS. 93
3.1.4 RESISTIVITY FORWARD MODELING. 96
3.1.5 A POSSIBLE 3D MODEL. 96
3.1.6 MODEL STUDIES.101
3.1.7 SENSITIVITY ANALYSIS. 102
3.1.8 CONCLUSIONS.106
3.2 A BOREHOLE APPLICATION: THE CASA BERARDI EXPERIMENT.108
3.2.1 A MODEL STUDY FOR CROSSHOLE ENVIRONMENTS USING STRAIGHT VERTICAL
BOREHOLES .108
3.2.1.1 THE APPARENT RESISTIVITY RESPONSE OF A BURIED CUBE.109
3.2.1.2 OUT-OF-PLANE EFFECTS. 113
3.2.2 A MODEL STUDY USING THE CASA BERARDI BOREHOLE ENVIRONMENT . 114
3.2.3 THE INTERPRETATION OF THE CROSSHOLE POLE-POLE AND SINGLE-HOLE
POLE-
DIPOLE SURVEY AT CASA BERARDI.123
3.2.3.1 MODEL AND GRID.125
3.2.3.2 CROSSHOLE POLE-POLE RESISTIVITY.127
3.2.3.3 SINGLE-HOLE POLE-DIPOLE RESISTIVITY. 128
3.2.3.4 CROSSHOLE POLE-POLE CHARGEABILITY.129
3.2.3.5 SINGLE-HOLE POLE-DIPOLE CHARGEABILITY .130
3.2.3.6 THE CASA BERARDI MODELING PROCESS USING GRID-INDEPENDENT
ELECTRODE LOCATIONS.131
3.23.7 DISCUSSION.135
A EQUATION SOLVERS 138
A.L CONJUGATE GRADIENTS (CG). 138
A.2 BI-CONJUGATE GRADIENTS (BICG). 139
A.3 CONJUGATE GRADIENTS SQUARED (CGS).140
A.4 BI-CONJUGATE GRADIENTS STABILIZED (BICGSTAB).141
A.5 ORTHOMIN.142
CONTENTS
REFERENCES
DECLARATION - ERKLARUNG
CURRICULUM VITAE - LEBENSLAUF |
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| illustrated | Illustrated |
| indexdate | 2024-10-09T18:13:16Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008948928 |
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| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR |
| physical | 153 Bl. zahlr. Ill. und graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| spelling | Spitzer, Klaus Verfasser aut Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys vorgelegt von Klaus Spitzer 1999 153 Bl. zahlr. Ill. und graph. Darst. txt rdacontent n rdamedia nc rdacarrier Leizig, Univ., Habil.-Schr., 1999 Finite-Differenzen-Methode (DE-588)4194626-1 gnd rswk-swf Geoelektrik (DE-588)4156675-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Geoelektrik (DE-588)4156675-0 s Finite-Differenzen-Methode (DE-588)4194626-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008948928&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spitzer, Klaus Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys Finite-Differenzen-Methode (DE-588)4194626-1 gnd Geoelektrik (DE-588)4156675-0 gnd |
| subject_GND | (DE-588)4194626-1 (DE-588)4156675-0 (DE-588)4113937-9 |
| title | Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys |
| title_auth | Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys |
| title_exact_search | Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys |
| title_full | Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys vorgelegt von Klaus Spitzer |
| title_fullStr | Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys vorgelegt von Klaus Spitzer |
| title_full_unstemmed | Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys vorgelegt von Klaus Spitzer |
| title_short | Development of three-dimensional finite difference resistivity, sensitivity, and IP forward modeling techniques and their application to surface and borehole surveys |
| title_sort | development of three dimensional finite difference resistivity sensitivity and ip forward modeling techniques and their application to surface and borehole surveys |
| topic | Finite-Differenzen-Methode (DE-588)4194626-1 gnd Geoelektrik (DE-588)4156675-0 gnd |
| topic_facet | Finite-Differenzen-Methode Geoelektrik Hochschulschrift |
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