Numerical modelling in applied geodynamics:
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| Format: | Book |
| Language: | English |
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Chichester [u.a.]
Wiley
1998
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV, 966 S. graph. Darst., Kt. |
| ISBN: | 0471974617 |
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| adam_text | NUMERICAL MODELLING IN APPLIED GEODYNAMICS JIF I NEDOMA INSTITUTE OF
COMPUTER SCIENCE PRAGUE, CZECH REPUBLIC JOHN WILEY & SONS CHICHESTER *
NEW YORK * WEINHEIM * BRISBANE * SINGAPORE * TORONTO CONTENTS PREFACE
XVII ACKNOWLEDGEMENTS XXI LIST OF NOTATION XXIII PART I GEODYNAMICS: AN
INTRODUCTION 1 1 GEODYNAMICS OF THE EARTH: GENERAL INTRODUCTION 3 1.1
INTRODUCTION 3 1.2 GLOBAL MODEL OF THE EARTH 8 1.2.1 GEODYNAMIC
PROCESSES IN THE EARTH S CORE AND MANTLE, AND THEIR CAUSES 8 1.2.2
GEODYNAMIC PROCESSES IN THE UPPER PARTS OF THE EARTH 11 REFERENCES 20
PART II TOOLS TO FUCTIONAL AND NUMERICAL ANALYSES 23 2 AN INTRODUCTION
TO VARIATIONAL METHODS AND RELATED PROBLEMS 25 2.1 A BRIEF SURVEY OF
FUNCTIONAL ANALYSIS 25 2.1.1 VECTOR AND METRIC SPACES 25 2.1.2 INNER
PRODUCT, BANACH AND HILBERT SPACES 27 2.1.3 OPERATORS AND FUNCTIONALS 28
2.1.4 DUAL SPACES, WEAK CONVERGENCE AND REFLEXIVITY 30 2.1.5 PHYSICAL
SIGNIFICANCE OF THE INNER PRODUCTS AND THE NORMS 31 2.2 INTRODUCTION TO
THE THEORY OF SPACES 32 2.2.1 HILBERT SPACES 32 2.2.2 OPERATORS AND
FUNCTIONALS IN HILBERT SPACES 34 2.2.3 SOBOLEV SPACES 36 2.2.4 SURVEY OF
THE THEORY OF DISTRIBUTION 44 2.2.5 SOME FUNDAMENTAL THEOREMS 47 2.3
FUNDAMENTALS OF CONVEX ANALYSIS 52 2.3.1 CONVEX SETS AND CONVEX
FUNCTIONS 52 CONTENTS 2.3.2 MINIMIZATION OF FUNCTIONALS 52 2.3.3
MINIMIZATION OF QUADRATIC FUNCTIONALS 56 2.3.4 THEORY OF DUALITY, SADDLE
POINTS AND LAGRANGE MULTIPLIERS 58 2.3.5 PENALTY METHODS 60 2.4
FUNDAMENTALS OF VARIATIONAL EQUALITIES AND INEQUALITIES AND THEIR
NUMERICAL APPROXIMATIONS 61 2.4.1 ELLIPTIC VARIATIONAL INEQUALITIES AND
EQUALITIES * THE CONTINUOUS PROBLEM 61 2.4.2 ELLIPTIC VARIATIONAL
INEQUALITIES AND EQUALITIES * THE APPROXIMATE PROBLEM 65 2.4.3
APPLICATION OF PENALTY METHODS TO VARIATIONAL INEQUALITIES 69 2.5
QUADRATIC FUNCTIONALS IN R N 70 2.5.1 TOOLS FROM THE QUADRATIC
PROGRAMMING 70 2.5.2 MODERN ITERATIVE METHODS 76 2.5.2.1 METHOD OF THE
STEEPEST DESCENT OR THE GRADIENT METHOD 76 2.5.2.2 THE CONJUGATE
GRADIENT METHOD OR THE CG-METHOD 80 2.5.2.3 THE PRECONDITIONED CONJUGATE
GRADIENT METHOD OR THE PCG-METHOD 84 2.5.2.4 CONJUGATE GRADIENT METHODS
FOR NON-SYMMETRIC PROBLEMS 85 2.5.3 THE MULTI-GRID METHOD 88 2.6
QUADRATIC FUNCTIONALS WITH CONSTRAINTS IN R 91 2.6.1 INTRODUCTION , 91
2.6.2 PROBLEMS OF QUADRATIC PROGRAMMING 91 2.6.3 LAGRANGE MULTIPLIERS
AND DUAL PROBLEM 97 2.6.4 THE GENERALIZED GRADIENT METHOD AND THE
GRADIENT PROJECTION METHOD 100 2.6.5 THE ACTIVE SET METHOD 101 2.7
NONQUADRATIC FUNCTIONALS IN R AND ITERATIVE METHODS FOR THE SOLUTION OF
SYSTEMS OF NON-LINEAR EQUATIONS 102 2.7.1 INTRODUCTION 102 2.7.2 THE
NEWTON METHOD AND ITS MODIFICATIONS 103 2.7.3 GENERALIZED LINEAR METHODS
105 2.7.4 NON-LINEAR JACOBI-, GAUSS-SEIDEL-, SOR-,
PEACEMAN-RACHFORD-NEWTON METHODS 107 2.7.5 MODERN NON-LINEAR ITERATIVE
METHODS 109 2.7.5.1 INTRODUCTION 109 2.7.5.2 DESCENT METHODS 110 2.7.5.3
CONJUGATE GRADIENT METHOD 112 2.7.5.4 THE GAUSS-NEWTON METHOD 112
REFERENCES 113 PART III NUMERICAL MODELS OF REFORMATION OF GEOLOGICAL
BODIES 117 3 DEFORMATION OF GEOLOGICAL BODIES AND STRESS-STRAIN
MEASUREMENTS IN SITU 119 3.1 INTRODUCTION TO THE MATHEMATICAL THEORY OF
CONTINUUM MECHANICS 119 3.1.1 BRIEF SURVEY OF MATHEMATICAL
THERMODYNAMICS 119 3.1.1.1 THE FIRST LAW OF THERMODYNAMICS 120 CONTENTS
IX 3.1.1.2 PRINCIPLE OF CARATHEODORY AND FORMULATION OF THE SECOND LAW
OF THERMODYNAMICS 124 3.1.1.3 THE REVERSIBLE AND IRREVERSIBLE STATES 130
3.1.1.4 SOME THEOREMS 136 3.1.1.5 PHASE CHANGES OF THE FIRST AND SECOND
ORDERS 140 3.1.2 INTRODUCTION TO THE TENSOR ANALYSIS 143 3.1.3 FIELD
EQUATIONS OF CONTINUUM MECHANICS 146 3.1.3.1 KINEMATICS OF DEFORMABLE
CONTINUUM 146 3.1.3.2 CONSERVATION LAWS IN THEIR INTEGRAL AND
DIFFERENTIAL FORMS 149 3.1.3.3 STRESS TENSOR 154 3.1.3.4 STRAIN AND
STRAIN RATE TENSORS 160 3.1.4 CONSTITUTIVE LAWS IN THE THEORY OF
ELASTICITY AND VISCO-ELASTICITY 163 3.1.4.1 CONSTITUTIVE LAWS OF HOOKEAN
ELASTICITY 163 3.1.4.2 CONSTITUTIVE LAWS OF LINEAR VISCO-ELASTICITY 166
* 3.1.5 CONSTITUTIVE LAWS IN THE THEORY OF PLASTICITY 167 3.1.6 BASIC
BOUNDARY VALUE PROBLEMS OF THE LINEAR THEORY OF ELASTICITY 170 3.1.7
VARIATIONAL PRINCIPLES IN THE THEORY OF ELASTICITY 171 3.1.8 THE SPACE
OF FUNCTIONS WITH FINITE ENERGY AND SOME THEOREMS 174 3.2 DEFORMATION OF
GEOLOGICAL BLOCKS AND THEIR LOCAL REGIONS: APPLICATIONS IN PRACTICE 176
3.2.1 SIMPLE MODELS OF DEFORMATION OF GEOLOGICAL BLOCKS BASED ON
BOUNDARY VALUE PROBLEMS OF LINEAR ELASTICITY 176 3.2.2 SIMPLE MODELS OF
DEFORMATION OF GEOLOGICAL BLOCKS BASED ON BOUNDARY VALUE PROBLEMS IN THE
DEFORMATION THEORY OF THERMO-PLASTICITY 179 3.2.2.1 FORMULATION OF THE
PROBLEM 179 3.2.2.2 VARIATIONAL FORMULATION OF THE PROBLEM 180 3.2.2.3
NUMERICAL SOLUTION 187 3.3 STRESS-STRAIN MEASUREMENT IN SITU AND
ANALYSIS OF THE MEASURED DATA 194 3.3.1 PROBLEMS, APPROACHES, AND A
SHORT SURVEY OF INSTRUMENTATION 194 3.3.2 ON THE SENSIBILITY OF THE
STRING TENSOMETRIC METHOD FOR THE STRESS-STRAIN MONITORING IN SITU AND
THE OVERCORING METHOD 197 3.3.2.1 INTRODUCTION 197 3.3.2.2 PRINCIPLE OF
THE STRING TENSOMETRIC METHOD, AND SENSITIVITY OF THE METHOD 197 3.3.2.3
INFLUENCES ACTING ON THE SENSITIVITY OF THE STRING 199 3.3.2.4 EXCITING
FORCE WITH A RANDOM PHASE 207 3.3.2.5 PROBLEM OF THE RELIABILITY OF
MEASURING ELEMENTS 207 3.3.2.6 IN-SITU STRESS MEASURING SYSTEM BASED ON
STRING TENSOMETRY 208 3.3.3 MATHEMATICAL MODELS OF IN-SITU STRESS-STRAIN
MEASUREMENTS BASED ON THE METHOD OF HOMOGENIZATION 211 3.3.3.1
INTRODUCTION 211 3.3.3.2 FORMULATION OF THE PROBLEM AND THE MAIN RESULTS
211 REFERENCES 246 PART IV NUMERICAL MODELS OF PLATE TECTONICS 251 4
MATHEMATICAL MODELS OF GEODYNAMIC PROCESSES IN THE LITHOSPHERE AND OF
PLATE TECTONICS 253 4.1 INTRODUCTION 253 CONTENTS 4.2 GEODYNAMIC
PROCESSES IN THE UPPER PARTS OF THE EARTH: AN INTRODUCTION 256 4.2.1
RHEOLOGY OF THE LITHOSPHERE AND OF THE UPPER MANTLE 257 4.2.2 TECTONIC
EVOLUTION OF RIFT ZONES 271 4.2.3 TECTONIC EVOLUTION OF COLLISION ZONES
278 4.2.3.1 MECHANICS OF SUBDUCTED LITHOSPHERE 280 4.3 MODEL PROBLEMS OF
PLATE TECTONICS 299 4.3.1 INTRODUCTION 299 4.3.2 ELASTIC, THERMO-ELASTIC
AND THERMO-VISCO-ELASTIC STRESS-STRAIN ANALYSIS OF THE GEODYNAMIC
MECHANISM 300 4.3.2.1 ELASTIC AND THERMO-ELASTIC CASES 300 4.3.2.2 THE
THERMO-VISCO-ELASTIC CASE 309 4.3.3 THERMO-ELASTO-VISCO-PLASTIC
STRESS-STRAIN ANALYSIS OF THE GEODYNAMIC MECHANISM 311 4.3.3.1
ELASTO-PLASTIC ROCKS: DEFORMATION THEORY OF THERMO-PLASTICITY 312
4.3.3.2 PERFECTLY PLASTIC AND RIGID PERFECTLY PLASTIC ROCKS UNDER
GEOTHERMAL FIELD 313 4.3.3.3 ELASTO-VISCO-PLASTIC ROCKS UNDER GEOTHERMAL
FIELD 314 4.3.3.4 LITHOSPHERIC AND UPPER MANTLE ROCKS AS A RIGID
VISCO-PLASTIC FLUID UNDER THE GEOTHERMAL FIELD 316 REFERENCES 318
MATHEMATICAL MODELS OF THE RIFT ZONES 323 5.1 INTRODUCTION 323 5.2
MODELS BASED ON THERMO-BINGHAM RHEOLOGY 323 5.2.1 MATHEMATICAL MODEL OF
THE RIFT ZONE BASED ON THE THERMO-ELASTO-VISCO-PLASTIC BINGHAM FLUID
WITHOUT MELTING AND RECRYSTALLIZATION 323 5.2.1.1 MATHEMATICAL
FORMULATION AND VARIATIONAL SOLUTION OF THE PROBLEM 325 5.2.1.2 FINITE
ELEMENT APPROXIMATION 333 5.2.1.3 ALGORITHM 338 5.2.2 MODELS BASED ON
THE STEFAN-LIKE PROBLEM AND VISCO-PLASTIC BINGHAM 339 RHEOLOGY: THE CASE
WITH MELTING AND SOLIDIFICATION REFERENCES 341 SIMPLE MODELS OF
COLLISION AND SUBDUCTION ZONES 343 6.1 INTRODUCTION 343 6.2 MATHEMATICAL
MODELS BASED ON LINEAR ELASTICITY 343 6.3 SIMPLE MODELS OF COLLISION AND
SUBDUCTION ZONES BASED ON THE BASIC BOUNDARY VALUE PROBLEMS OF
ELASTICITY 346 6.3.1 FORMULATION OF THE MODEL PROBLEM 346 6.3.2
VARIATIONAL FORMULATIONS AND WEAK SOLUTIONS OF PRIMARY AND DUAL PROBLEMS
IN LINEAR ELASTICITY 348 6.4 MODELS BASED ON THE ANALYSIS OF PERIODIC
GEOLOGICAL STRUCTURES: METHOD OF HOMOGENIZATION 354 6.4.1 FORMULATION OF
THE PROBLEM AND THE MAIN RESULTS 354 CONTENTS XI 6.5 MODELS OF COLLISION
ZONES BASED ON THE BASIC INITIAL BOUNDARY VALUE PROBLEMS OF
THERMO-VISCO-ELASTICITY 359 6.5.1 INTRODUCTION 359 6.5.2 MODELS BASED ON
LINEAR THERMO-VISCO-ELASTICITY WITH SHORT MEMORY 359 6.5.2.1 DYNAMIC
CASE 359 6.5.2.2 QUASI-STATIC CASE 364 REFERENCES 367 7 REALISTIC
MATHEMATICAL MODELS OF COLLISION ZONES BASED ON VARIATIONAL INEQUALITIES
369 7.1 MODELS OF COLLISION ZONES BASED ON CONTACT PROBLEMS WITH OR
WITHOUT FRICTION IN LINEAR ELASTICITY 369 7.1.1 INTRODUCTION 369 7.1.2
THE MODELS 370 7.1.3 BOUNDARY CONDITIONS 371 7.1.4 CLASSICAL FORMULATION
OF THE PROBLEM 373 7.1.5 VARIATIONAL FORMULATION AND WEAK SOLUTION 375
7.1.6 NUMERICAL SOLUTION 384 7.1.7 CONSTRUCTION OF THE STIFFNESS MATRIX
AND OF THE RIGHT HAND SIDE VECTOR 393 7.2 MATHEMATICAL MODELS OF PLATE
TECTONICS BASED ON CONTACT PROBLEMS WITH FRICTION IN THERMO-ELASTICITY
399 7.2.1 QUASI-COUPLED PLATE TECTONIC MODELS BASED ON CONTACT PROBLEMS
WITH FRICTION: THE COERCIVE CASE 399 7.2.1.1 INTRODUCTION 399 7.2.1.2
FORMULATION OF THE PROBLEM 400 7.2.1.3 VARIATIONAL SOLUTION OF THE
PROBLEM 405 7.2.1.4 NUMERICAL SOLUTION 410 7.2.1.5 ALGORITHM 414 7.2.2
QUASI-COUPLED PLATE TECTONIC MODELS BASED ON CONTACT PROBLEMS WITH
FRICTION: THE SEMI-COERCIVE CASE 418 7.2.2.1 INTRODUCTION 418 7.2.2.2
VARIATIONAL FORMULATION AND WEAK SOLUTION 420 7.2.2.3 FINITE ELEMENT
APPROXIMATION 425 7.3 MATHEMATICAL MODELS OF PLATE TECTONICS BASED ON
COUPLED CONTACT-TWO-PHASE STEFAN-LIKE PROBLEMS IN LINEAR
THERMO-ELASTICITY: PROBLEMS OF RECRYSTALLIZATION OF ROCKS IN SUBDUCTION
AND COLLISION ZONES 429 7.3.1 INTRODUCTION 429 7.3.2 NUMERICAL SOLUTIONS
OF COUPLED TWO-PHASE STEFAN-LIKE-CONTACT PROBLEMS WITH FRICTION ARISING
FROM AN IMPLICIT TIME DISCRETIZATION: 430 THE COERCIVE CASE 7.3.2.1 THE
MODEL PROBLEM 430 7.3.2.2 VARIATIONAL FORMULATION OF THE ELLIPTIC
PROBLEM ARISING FROM AN IMPLICIT TIME DISCRETIZATION 434 7.3.2.3 THE
FINITE ELEMENT APPROXIMATION 437 7.3.2.4 ALGORITHM 444 7.4 MODELS OF
COLLISION ZONES BASED ON A COUPLED CONTACT-STEFAN-LIKE PROBLEM ARISING
FROM THE TIME DISCRETIZATION IN DEFORMATION THEORY OF THERMO-PLASTICITY
449 7.4.1 INTRODUCTION 449 7.4.2 FORMULATION OF THE COUPLED FIELD
PROBLEM 449 CONTENTS 7.4.3 VARIATIONAL FORMULATION OF THE PROBLEM 454
7.4.4 NUMERICAL SOLUTION 461 7.5 COMPUTER IMPLEMENTATION OF THE
ALGORITHMS FOR CONTACT PROBLEMS 471 7.5.1 INTRODUCTION 471 7.5.2
CONJUGATE GRADIENT METHOD WITH CONSTRAINTS 473 7.5.3 ELIMINATION METHOD
478 7.6 COMPUTER IMPLEMENTATION OF THE ALGORITHMS FOR COUPLED
CONTACT-STEFAN-LIKE PROBLEMS 482 7.6.1 INTRODUCTION 482 7.6.2 ALGORITHM
483 7.6.2.1 BASIC IDEA OF THE ALGORITHM 483 7.6.2.2 NON-LINEAR SOLUTION
FOR THE STEFAN PART OF THE PROBLEM BASED ON NON-LINEAR CONJUGATE
GRADIENT METHODS 485 7.6.2.3 SOLUTIONS FOR THE CONTACT PART OF THE
PROBLEM BASED ON CONSTRAINED CONJUGATE GRADIENT METHODS 488 REFERENCES
489 NUMERICAL SIMULATION OF TECTONIC EVOLUTION OF COLLISION AND
SUBDUCTION ZONES 493 8.1 SIMULATION OF TECTONIC PROCESSES IN THE TIME
DOMAIN: ORIGIN OF THE EARTHQUAKE 493 8.1.1 INTRODUCTION 493 8.1.2 THE
MODEL AND CONSTITUTING EQUATIONS 494 8.1.3 VARIATIONAL SOLUTION OF THE
PROBLEM WITH THE GIVEN FRICTION 499 8.1.4 NUMERICAL MODEL: NUMERICAL
SOLUTION OF DISCRETIZED COUPLED EQUATIONS 501 8.1.5 ALGORITHM AND
MECHANISMS OF EARTHQUAKES 503 8.1.5.1 THE CASE OF A CRACK PROPAGATION
505 8.1.5.2 THE CASE OF COULOMBIAN FRICTION FORCES ACTING ON THE CONTACT
BOUNDARY 506 8.2 NUMERICAL MODELLING OF INTERPLATE DEFORMATION IN THE
CENTRAL ALEUTIAN ARC SYSTEM: TECTONIC STRESSES IN THE LITHOSPHERE 507
8.2.1 INTRODUCTION 507 8.2.2 NUMERICAL RESULTS 510 8.2.3 VERTICAL
MOTIONS 512 8.2.4 INTERPLATE STRESSES 512 8.3 MODEL OF THE CARPATHIAN
CONTINENT/CONTINENT COLLISION 514 8.3.1 GEODYNAMIC MODEL OF TECTONICS OF
THE WESTERN CARPATHIANS 514 8.3.1.1 INTRODUCTION 514 8.3.1.2 MODEL OF
THE WESTERN CARPATHIANS 519 8.3.2 NUMERICAL VERIFICATION OF GEODYNAMIC
PROCESSES IN THE WESTERN CARPATHIANS 521 8.4 GEODYNAMIC EVOLUTION OF THE
HIMALAYAN COLLISION REGION AND THE INTRAPLATE TECTONICS IN THE NORTHERN
INDIAN OCEAN, AND GEODYNAMIC MODELS OF THE HIMALAYA AND THE INDIAN PLATE
MARGIN 522 8.4.1 INTRODUCTION 522 8.4.2 GEOLOGICAL AND TECTONIC
CHARACTERIZATION OF THE HIMALAYAS AND THE TIBETAN PLATEAU 526 8.4.2.1
THE SIWALIK BELT 526 8.4.2.2 THE LESSER AND HIGH HIMALAYAS 527 8.4.2.3
THE TIBETAN PLATEAU 530 8.4.3 GEODYNAMIC MODEL OF THE HIMALAYAS, PROFILE
* NANDA DEVI 531 CONTENTS XIII 8.5 EASTERN HIMALAYA AND NORTHERN BURMA,
AND SURROUNDING REGIONS 540 8.5.1 INTRODUCTION 540 8.5.2 SEISMO-TECTONIC
ACTIVITY OF THE NE INDIAN PLATE 541 8.5.3 SEISMO-TECTONIC ACTIVITY OF
THE EASTERN HIMALAYAN AREA AND SURROUNDING AREAS 543 8.5.4
SEISMO-TECTONIC ACTIVITY IN BURMA 544 8.5.5 SEISMO-TECTONIC ACTIVITY IN
THE AREA OF SOUTH CHINA 546 8.5.6 GEODYNAMIC MODEL OF THE ANDAMAN ARC
SYSTEM: PROFILE ACROSS NORTH ANDAMAN ISLAND, BARREN-NARCONDAM VOLCANIC
ARC SYSTEM AND BURMESE PLATE 547 8.6 GEODYNAMIC PROCESSES IN SOME
VOLCANICALLY ACTIVE AREAS 553 8.6.1 INTRODUCTION 553 8.6.2 MECHANICS OF
THE SUBDUCTED LITHOSPHERE IN THE HOT SPOT AREAS, MEDITERRANEAN AREA AND
JAPANESE AREA 554 8.7 PROGRAMME ON THE ASSESSMENT OF EARTHQUAKE HAZARD
FOR AREAS OF CATASTROPIC EARTHQUAKES 560 8.7.1 SOME RUDIMENTARY
DEFINITIONS AND PRESENT STUDIES OF SEISMIC HAZARD 560 8.7.2 OBJECTIVES
QUALIFYING THE PROGRAMME 561 8.7.3 ASSESSMENT OF SEISMIC HAZARD AND
EARTHQUAKE PREDICTION-PROPOSED PROGRAMME 561 8.7.4 ASSESSMENT OF HAZARD
OF CRITICAL STRUCTURES-PROPOSED PROGRAMME 563 8.7.5 MITIGATION OF RISK *
564 REFERENCES 565 PART V SOME MATHEMATICAL PROBLEMS OF GEOPHYSICAL
FIELDS 573 9 MATHEMATICAL MODELS OF THE GEOTHERMAL FIELD OF THE EARTH
575 9.1 INTRODUCTION 575 9.2 THERMAL PROPERTIES OF ROCKS AND THERMAL
REGIME INSIDE THE EARTH 575 9.3 STEADY-STATE THERMAL FIELD OF THE EARTH
597 9.3.1 INTRODUCTION 597 9.3.2 THE LINEAR STEADY-STATE CASE 599
9.3.2.1 INTRODUCTION 599 9.3.2.2 NUMERICAL SOLUTION 603 9.3.2.3
ALGORITHM 606 9.3.3 THE NON-LINEAR STEADY-STATE GEOTHERMAL MODELS OF THE
EARTH 609 9.3.3.1 INTRODUCTION 609 9.3.3.2 NUMERICAL SOLUTION 613 9.4
EVOLUTION MODELS OF THE GEOTHERMAL FIELD OF THE EARTH 620 9.4.1
INTRODUCTION 620 9.4.2 THE MODEL GOVERNING EQUATIONS AND INITIAL AND
BOUNDARY VALUE CONDITIONS 621 9.4.3 GEOTHERMAL MODELS: LINEAR CASE 623
9.4.3.1 MATHEMATICAL ANALYSIS OF THE CONTINUOUS PART OF THE PROBLEM 623
9.4.3.2 NUMERICAL SOLUTION 628 9.4.4 EVOLUTION GEOTHERMAL MODELS:
NON-LINEAR CASE 635 9.4.4.1 MATHEMATICAL ANALYSIS OF THE CONTINUOUS PART
OF THE PROBLEM 635 9.4.4.2 NUMERICAL SOLUTION 637 CONTENTS 9.5 THERMAL
MODELS OF THE EARTH S INTERIOR WITH PHASE TRANSITION ZONES 642 9.5.1
INTRODUCTION 642 9.5.2 CLASSICAL FORMULATION OF THE NON-LINEAR TWO-PHASE
STEFAN PROBLEM 643 9.5.3 VARIATIONAL FORMULATION 646 9.5.4 NUMERICAL
SOLUTION 653 REFERENCES 658 10 MATHEMATICAL PROBLEMS OF THE EARTH S
ELECTROMAGNETIC FIELD. NUMERICAL ANALYSES OF THE MAGNETO-TELLURIC MODELS
OF THE EARTH 663 10.1 INTRODUCTION 663 10.2 VARIATIONAL PROBLEMS IN THE
THEORY OF MAGNETO-TELLURIC FIELD AND DEEP GEOMAGNETIC SOUNDING. MODEL
PROBLEMS 667 10.2.1 INTRODUCTION 667 10.2.2 PHYSICAL FORMULATION.
MATHEMATICAL MODELS IN FREQUENCY AND TIME DOMAINS 667 10.2.2.1 THE
FREQUENCY DOMAIN APPROACH 673 10.2.2.2 TIME VARIABLE INDUCING MAGNETIC
FIELD AND THE TIME DOMAIN APPROACH 680 10.2.3 MAGNETO-TELLURIC FIELD.
MATHEMATICAL MODELS AND VARIATIONAL SOLUTIONS 682 10.2.3.1 MATHEMATICAL
FORMULATION OF THE PROBLEM IN THE FREQUENCY AND TIME DOMAINS 682
10.2.3.2 VARIATIONAL FORMULATION. EXISTENCE AND UNIQUENESS OF THE
SOLUTION OF A MODEL MAGNETO-TELLURIC PROBLEM. THE FREQUENCY AND TIME
DOMAINS 683 10.2.3.3 NUMERICAL SOLUTIONS OF MAGNETO-TELLURIC MODEL
PROBLEMS. THE FREQUENCY AND TIME DOMAIN 691 10.3 VARIATIONAL PROBLEMS IN
THE THEORY OF ELECTROMAGNETIC FIELD. ELECTROMAGNETIC INDUCTION 702
10.3.1 INTRODUCTION 702 10.3.2 ELECTROMAGNETIC INDUCTION IN A CONDUCTIVE
LAYER 707 REFERENCES 712 11 SOME MATHEMATICAL PROBLEMS OF SEISMIC WAVE
PROPAGATION 715 11.1 INTRODUCTION 715 11.2 THEORY AND PHYSICAL
FORMULATION OF THE PROBLEM 718 11.3 PROPAGATION OF PSEUDO P AND SV WAVES
IN AN INHOMOGENEOUS, GENERALLY ANISOTROPIC MEDIA GENERATED BY HARMONIC
LINE SOURCES 732 11.3.1 INTRODUCTION 732 11.3.2 FORMULATION OF THE
PROBLEM 732 11.3.3 VARIATIONAL FORMULATION AND WEAK SOLUTION 734 11.3.4
NUMERICAL SOLUTION 735 11.3.5 ALGORITHM 737 11.3.6 MODELS AND THEIR
CLASSIFICATION 743 11.3.6.1 MODEL ML * THE ASTHENOSPHERE 743 11.3.6.2
MODEL M2 * THE ASTHENOSPHERE BETWEEN 744 TWO HALFSPACES CONTENTS XV
11.3.6.3 MODEL M3*THE EXPLORATION OF SEISMOLOGICAL PRACTICE 745 11.3.6.4
MODEL M4 * THE LAYER OF SEDIMENTS BETWEEN TWO HALFSPACES 745 11.4
PROPAGATION OF SEISMIC SH WAVES IN UNBOUNDED DOMAINS 758 11.5
PROPAGATION OF PULSE SEISMIC WAVES IN INHOMOGENEOUS MEDIA 760 REFERENCES
763 12 MATHEMATICAL PROBLEMS OF GLOBAL GEODYNAMIC, GEOMAGNETIC,
GEOTHERMAL AND GRAVITY MODELS OF THE EARTH AND PLANETS AND A GLOBAL
PLATE TECTONIC HYPOTHESIS 767 12.1 INTRODUCTION 767 12.2 GLOBAL
GEODYNAMIC, GEOMAGNETIC, GEOTHERMAL AND GRAVITY MODELS OF THE EARTH 768
12.2.1 INTRODUCTION 768 12.2.2 THE FUNDAMENTAL EQUATIONS OF THE
GEODYNAMIC MECHANISMS 772 12.2.3 DISCUSSION OF EQUATIONS, LIMITS OF
THEIR VALIDITY AND THEIR PHYSICAL CONSEQUENCES 780 12.2.3.1 THE CASE OF
GEODYNAMIC PROCESSES IN THE CORE 780 12.2.3.2 THE CASE OF GEODYNAMIC
PROCESSES IN THE MANTLE 783 12.2.3.3 THERMAL REGIME IN THECORE AND IN
THE MANTLE OF THE EARTH AND THEIR STRUCTURE 788 12.3 GEODYNAMIC
PROCESSES IN THE MANTLE 791 12.3.1 INTRODUCTION 791 12.3.2 MATHEMATICAL
MODELS BASED ON THE LINEAR AND NONLINEAR NEWTONIAN FLUID RHEOLOGY 792
12.3.2.1 INTRODUCTION 792 12.3.2.2 MODELS OF MANTLE CONVECTION BASED ON
NUMERICAL ANALYSES OF THE NAVIER-STOKES PROBLEM IN THE BOUSSINESQ
APPROXIMATION 796 12.3.3 MATHEMATICAL MODELS BASED ON THE THERMO-BINGHAM
RHEOLOGY 807 12.3.3.1 INTRODUCTION 807 12.3.3.2 ANALYSIS OF GEODYNAMIC
PROCESSES IN THE MANTLE BASED ON THERMO-BINGHAM APPROXIMATION 811
12.3.3.3 ANALYSIS OF GEODYNAMIC PROCESSES IN THE EARTH BASED ON COUPLED
STEFAN-LIKE PROBLEMS IN A THERMO-VISCO-PLASTIC BINGHAM RHEOLOGY 859 12.4
MATHEMATICAL ANALYSIS OF GEODYNAMIC PROCESSES IN THE EARTH S AND
PLANET S 893 INTERIOR. GLOBAL GEODYNAMIC, GEOMAGNETIC AND GRAVITY MODELS
12.4.1 GOVERNING EQUATIONS OF MAGNETODYNAMICS OF INCOMPRESSIBLE
THERMO-BINGHAM S FLUID UNDER THE GRAVITY EFFECT 893 12.4.1.1
INTRODUCTION 893 12.4.1.2 VARIATIONAL FORMULATION OF THE PROBLEM 896
12.5 GENERALIZED THERMO-MAGNETODYNAMIC PROBLEM. A NEW APPROACH TO
MANTLE-CORE COUPLING STUDIES. PROBLEMS OF IONIZATION AND METALLIZATION
OF THE EARTH ROCKS 911 12.5.1 INTRODUCTION 911 12.5.2 THE MODEL:
DISCUSSION OF PROPERTIES OF ROCKS INSIDE THE EARTH 912 12.5.3 THE MODEL:
THEORY 917 12.5.3.1 INTRODUCTION 917 CONTENTS 12.5.3.2 DERIVATION OF THE
SYSTEM OF EQUATIONS 917 12.5.3.3 BOUNDARY CONDITION 923 12.6 SECOND
PHASE-CHANGE TRANSITION AND THE PLANET URANUS MAGNETIC FIELD ANOMALY 926
12.6.1 INTRODUCTION 926 12.6.2 MATHEMATICAL MODEL 926 12.6.3 VARIATIONAL
FORMULATION AND WEAK SOLUTION OF THE PROBLEM 928 12.7 GLOBAL GRAVITY
MODEL OF THE EARTH AND OF PLANETS 935 12.7.1 INTRODUCTION 935 12.7.2
GENERALIZED THEORY OF GRAVITY 937 12.7.2.1 INTRODUCTION 937 12.7.2.2
LEVEL SURFACES AND PLUMB LINES 941 12.7.2.3 INTEGRAL EQUATION FOR THE
GRAVITY POTENTIAL 943 12.7.2.4 THE ANOMALOUS GRAVITY FIELD 945 12.7.3
GRAVITY FIELD OUTSIDE THE EARTH 946 REFERENCES 947 INDEX 955
|
| any_adam_object | 1 |
| author | Nedoma, Jiří 1934- |
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| building | Verbundindex |
| bvnumber | BV012173206 |
| callnumber-first | Q - Science |
| callnumber-label | QE501 |
| callnumber-raw | QE501.4.M38 |
| callnumber-search | QE501.4.M38 |
| callnumber-sort | QE 3501.4 M38 |
| callnumber-subject | QE - Geology |
| classification_rvk | RB 10103 |
| ctrlnum | (OCoLC)36877489 (DE-599)BVBBV012173206 |
| dewey-full | 551.1/015194 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology |
| dewey-raw | 551.1/015194 |
| dewey-search | 551.1/015194 |
| dewey-sort | 3551.1 515194 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geologie / Paläontologie Geographie |
| format | Book |
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| id | DE-604.BV012173206 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:23:00Z |
| institution | BVB |
| isbn | 0471974617 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008247681 |
| oclc_num | 36877489 |
| open_access_boolean | |
| owner | DE-703 DE-706 |
| owner_facet | DE-703 DE-706 |
| physical | XXIV, 966 S. graph. Darst., Kt. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Wiley |
| record_format | marc |
| spelling | Nedoma, Jiří 1934- Verfasser (DE-588)143757296 aut Numerical modelling in applied geodynamics Jiří Nedoma Chichester [u.a.] Wiley 1998 XXIV, 966 S. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Géodynamique - Modèles mathématiques ram Mathematisches Modell Geodynamics Mathematical models Geodynamik (DE-588)4020212-4 gnd rswk-swf Numerisches Modell (DE-588)4338132-7 gnd rswk-swf Geodynamik (DE-588)4020212-4 s Numerisches Modell (DE-588)4338132-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008247681&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nedoma, Jiří 1934- Numerical modelling in applied geodynamics Géodynamique - Modèles mathématiques ram Mathematisches Modell Geodynamics Mathematical models Geodynamik (DE-588)4020212-4 gnd Numerisches Modell (DE-588)4338132-7 gnd |
| subject_GND | (DE-588)4020212-4 (DE-588)4338132-7 |
| title | Numerical modelling in applied geodynamics |
| title_auth | Numerical modelling in applied geodynamics |
| title_exact_search | Numerical modelling in applied geodynamics |
| title_full | Numerical modelling in applied geodynamics Jiří Nedoma |
| title_fullStr | Numerical modelling in applied geodynamics Jiří Nedoma |
| title_full_unstemmed | Numerical modelling in applied geodynamics Jiří Nedoma |
| title_short | Numerical modelling in applied geodynamics |
| title_sort | numerical modelling in applied geodynamics |
| topic | Géodynamique - Modèles mathématiques ram Mathematisches Modell Geodynamics Mathematical models Geodynamik (DE-588)4020212-4 gnd Numerisches Modell (DE-588)4338132-7 gnd |
| topic_facet | Géodynamique - Modèles mathématiques Mathematisches Modell Geodynamics Mathematical models Geodynamik Numerisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008247681&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nedomajiri numericalmodellinginappliedgeodynamics |