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Publisher: Elsevier   (Total: 3030 journals)

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Showing 1 - 200 of 3030 Journals sorted alphabetically
AASRI Procedia     Open Access   (Followers: 15)
Academic Pediatrics     Hybrid Journal   (Followers: 20, SJR: 1.402, h-index: 51)
Academic Radiology     Hybrid Journal   (Followers: 16, SJR: 1.008, h-index: 75)
Accident Analysis & Prevention     Partially Free   (Followers: 79, SJR: 1.109, h-index: 94)
Accounting Forum     Hybrid Journal   (Followers: 22, SJR: 0.612, h-index: 27)
Accounting, Organizations and Society     Hybrid Journal   (Followers: 27, SJR: 2.515, h-index: 90)
Achievements in the Life Sciences     Open Access   (Followers: 4)
Acta Anaesthesiologica Taiwanica     Open Access   (Followers: 5, SJR: 0.338, h-index: 19)
Acta Astronautica     Hybrid Journal   (Followers: 303, SJR: 0.726, h-index: 43)
Acta Automatica Sinica     Full-text available via subscription   (Followers: 3)
Acta Biomaterialia     Hybrid Journal   (Followers: 25, SJR: 2.02, h-index: 104)
Acta Colombiana de Cuidado Intensivo     Full-text available via subscription  
Acta de Investigación Psicológica     Open Access   (Followers: 2)
Acta Ecologica Sinica     Open Access   (Followers: 8, SJR: 0.172, h-index: 29)
Acta Haematologica Polonica     Free   (SJR: 0.123, h-index: 8)
Acta Histochemica     Hybrid Journal   (Followers: 3, SJR: 0.604, h-index: 38)
Acta Materialia     Hybrid Journal   (Followers: 196, SJR: 3.683, h-index: 202)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5, SJR: 0.615, h-index: 21)
Acta Mechanica Solida Sinica     Full-text available via subscription   (Followers: 9, SJR: 0.442, h-index: 21)
Acta Oecologica     Hybrid Journal   (Followers: 9, SJR: 0.915, h-index: 53)
Acta Otorrinolaringologica (English Edition)     Full-text available via subscription   (Followers: 1)
Acta Otorrinolaringológica Española     Full-text available via subscription   (Followers: 3, SJR: 0.311, h-index: 16)
Acta Pharmaceutica Sinica B     Open Access   (Followers: 2)
Acta Poética     Open Access   (Followers: 4)
Acta Psychologica     Hybrid Journal   (Followers: 21, SJR: 1.365, h-index: 73)
Acta Sociológica     Open Access  
Acta Tropica     Hybrid Journal   (Followers: 5, SJR: 1.059, h-index: 77)
Acta Urológica Portuguesa     Open Access  
Actas Dermo-Sifiliograficas     Full-text available via subscription   (Followers: 4)
Actas Dermo-Sifiliográficas (English Edition)     Full-text available via subscription   (Followers: 3)
Actas Urológicas Españolas     Full-text available via subscription   (Followers: 3, SJR: 0.383, h-index: 19)
Actas Urológicas Españolas (English Edition)     Full-text available via subscription   (Followers: 2)
Actualites Pharmaceutiques     Full-text available via subscription   (Followers: 5, SJR: 0.141, h-index: 3)
Actualites Pharmaceutiques Hospitalieres     Full-text available via subscription   (Followers: 4, SJR: 0.112, h-index: 2)
Acupuncture and Related Therapies     Hybrid Journal   (Followers: 4)
Ad Hoc Networks     Hybrid Journal   (Followers: 11, SJR: 0.967, h-index: 57)
Addictive Behaviors     Hybrid Journal   (Followers: 15, SJR: 1.514, h-index: 92)
Addictive Behaviors Reports     Open Access   (Followers: 5)
Additive Manufacturing     Hybrid Journal   (Followers: 7, SJR: 1.039, h-index: 5)
Additives for Polymers     Full-text available via subscription   (Followers: 20)
Advanced Drug Delivery Reviews     Hybrid Journal   (Followers: 120, SJR: 5.2, h-index: 222)
Advanced Engineering Informatics     Hybrid Journal   (Followers: 11, SJR: 1.265, h-index: 53)
Advanced Powder Technology     Hybrid Journal   (Followers: 16, SJR: 0.739, h-index: 33)
Advances in Accounting     Hybrid Journal   (Followers: 8, SJR: 0.299, h-index: 15)
Advances in Agronomy     Full-text available via subscription   (Followers: 15, SJR: 2.071, h-index: 82)
Advances in Anesthesia     Full-text available via subscription   (Followers: 24, SJR: 0.169, h-index: 4)
Advances in Antiviral Drug Design     Full-text available via subscription   (Followers: 3)
Advances in Applied Mathematics     Full-text available via subscription   (Followers: 6, SJR: 1.054, h-index: 35)
Advances in Applied Mechanics     Full-text available via subscription   (Followers: 10, SJR: 0.801, h-index: 26)
Advances in Applied Microbiology     Full-text available via subscription   (Followers: 21, SJR: 1.286, h-index: 49)
Advances In Atomic, Molecular, and Optical Physics     Full-text available via subscription   (Followers: 16, SJR: 3.31, h-index: 42)
Advances in Biological Regulation     Hybrid Journal   (Followers: 4, SJR: 2.277, h-index: 43)
Advances in Botanical Research     Full-text available via subscription   (Followers: 3, SJR: 0.619, h-index: 48)
Advances in Cancer Research     Full-text available via subscription   (Followers: 26, SJR: 2.215, h-index: 78)
Advances in Carbohydrate Chemistry and Biochemistry     Full-text available via subscription   (Followers: 9, SJR: 0.9, h-index: 30)
Advances in Catalysis     Full-text available via subscription   (Followers: 5, SJR: 2.139, h-index: 42)
Advances in Cellular and Molecular Biology of Membranes and Organelles     Full-text available via subscription   (Followers: 12)
Advances in Chemical Engineering     Full-text available via subscription   (Followers: 24, SJR: 0.183, h-index: 23)
Advances in Child Development and Behavior     Full-text available via subscription   (Followers: 10, SJR: 0.665, h-index: 29)
Advances in Chronic Kidney Disease     Full-text available via subscription   (Followers: 8, SJR: 1.268, h-index: 45)
Advances in Clinical Chemistry     Full-text available via subscription   (Followers: 28, SJR: 0.938, h-index: 33)
Advances in Colloid and Interface Science     Full-text available via subscription   (Followers: 18, SJR: 2.314, h-index: 130)
Advances in Computers     Full-text available via subscription   (Followers: 16, SJR: 0.223, h-index: 22)
Advances in Developmental Biology     Full-text available via subscription   (Followers: 11)
Advances in Digestive Medicine     Open Access   (Followers: 4)
Advances in DNA Sequence-Specific Agents     Full-text available via subscription   (Followers: 5)
Advances in Drug Research     Full-text available via subscription   (Followers: 22)
Advances in Ecological Research     Full-text available via subscription   (Followers: 39, SJR: 3.25, h-index: 43)
Advances in Engineering Software     Hybrid Journal   (Followers: 25, SJR: 0.486, h-index: 10)
Advances in Experimental Biology     Full-text available via subscription   (Followers: 7)
Advances in Experimental Social Psychology     Full-text available via subscription   (Followers: 38, SJR: 5.465, h-index: 64)
Advances in Exploration Geophysics     Full-text available via subscription   (Followers: 3)
Advances in Fluorine Science     Full-text available via subscription   (Followers: 8)
Advances in Food and Nutrition Research     Full-text available via subscription   (Followers: 41, SJR: 0.674, h-index: 38)
Advances in Fuel Cells     Full-text available via subscription   (Followers: 14)
Advances in Genetics     Full-text available via subscription   (Followers: 15, SJR: 2.558, h-index: 54)
Advances in Genome Biology     Full-text available via subscription   (Followers: 11)
Advances in Geophysics     Full-text available via subscription   (Followers: 6, SJR: 2.325, h-index: 20)
Advances in Heat Transfer     Full-text available via subscription   (Followers: 18, SJR: 0.906, h-index: 24)
Advances in Heterocyclic Chemistry     Full-text available via subscription   (Followers: 8, SJR: 0.497, h-index: 31)
Advances in Human Factors/Ergonomics     Full-text available via subscription   (Followers: 22)
Advances in Imaging and Electron Physics     Full-text available via subscription   (Followers: 2, SJR: 0.396, h-index: 27)
Advances in Immunology     Full-text available via subscription   (Followers: 33, SJR: 4.152, h-index: 85)
Advances in Inorganic Chemistry     Full-text available via subscription   (Followers: 9, SJR: 1.132, h-index: 42)
Advances in Insect Physiology     Full-text available via subscription   (Followers: 3, SJR: 1.274, h-index: 27)
Advances in Integrative Medicine     Hybrid Journal   (Followers: 4)
Advances in Intl. Accounting     Full-text available via subscription   (Followers: 4)
Advances in Life Course Research     Hybrid Journal   (Followers: 7, SJR: 0.764, h-index: 15)
Advances in Lipobiology     Full-text available via subscription   (Followers: 1)
Advances in Magnetic and Optical Resonance     Full-text available via subscription   (Followers: 8)
Advances in Marine Biology     Full-text available via subscription   (Followers: 16, SJR: 1.645, h-index: 45)
Advances in Mathematics     Full-text available via subscription   (Followers: 10, SJR: 3.261, h-index: 65)
Advances in Medical Sciences     Hybrid Journal   (Followers: 5, SJR: 0.489, h-index: 25)
Advances in Medicinal Chemistry     Full-text available via subscription   (Followers: 5)
Advances in Microbial Physiology     Full-text available via subscription   (Followers: 4, SJR: 1.44, h-index: 51)
Advances in Molecular and Cell Biology     Full-text available via subscription   (Followers: 21)
Advances in Molecular and Cellular Endocrinology     Full-text available via subscription   (Followers: 10)
Advances in Molecular Toxicology     Full-text available via subscription   (Followers: 6, SJR: 0.324, h-index: 8)
Advances in Nanoporous Materials     Full-text available via subscription   (Followers: 3)
Advances in Oncobiology     Full-text available via subscription   (Followers: 3)
Advances in Organometallic Chemistry     Full-text available via subscription   (Followers: 15, SJR: 2.885, h-index: 45)
Advances in Parallel Computing     Full-text available via subscription   (Followers: 7, SJR: 0.148, h-index: 11)
Advances in Parasitology     Full-text available via subscription   (Followers: 7, SJR: 2.37, h-index: 73)
Advances in Pediatrics     Full-text available via subscription   (Followers: 20, SJR: 0.4, h-index: 28)
Advances in Pharmaceutical Sciences     Full-text available via subscription   (Followers: 14)
Advances in Pharmacology     Full-text available via subscription   (Followers: 13, SJR: 1.718, h-index: 58)
Advances in Physical Organic Chemistry     Full-text available via subscription   (Followers: 7, SJR: 0.384, h-index: 26)
Advances in Phytomedicine     Full-text available via subscription  
Advances in Planar Lipid Bilayers and Liposomes     Full-text available via subscription   (Followers: 3, SJR: 0.248, h-index: 11)
Advances in Plant Biochemistry and Molecular Biology     Full-text available via subscription   (Followers: 8)
Advances in Plant Pathology     Full-text available via subscription   (Followers: 5)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Protein Chemistry     Full-text available via subscription   (Followers: 18)
Advances in Protein Chemistry and Structural Biology     Full-text available via subscription   (Followers: 17, SJR: 1.5, h-index: 62)
Advances in Psychology     Full-text available via subscription   (Followers: 56)
Advances in Quantum Chemistry     Full-text available via subscription   (Followers: 5, SJR: 0.478, h-index: 32)
Advances in Radiation Oncology     Open Access  
Advances in Small Animal Medicine and Surgery     Hybrid Journal   (Followers: 1, SJR: 0.1, h-index: 2)
Advances in Space Research     Full-text available via subscription   (Followers: 332, SJR: 0.606, h-index: 65)
Advances in Structural Biology     Full-text available via subscription   (Followers: 7)
Advances in Surgery     Full-text available via subscription   (Followers: 6, SJR: 0.823, h-index: 27)
Advances in the Study of Behavior     Full-text available via subscription   (Followers: 28, SJR: 1.321, h-index: 56)
Advances in Veterinary Medicine     Full-text available via subscription   (Followers: 14)
Advances in Veterinary Science and Comparative Medicine     Full-text available via subscription   (Followers: 12)
Advances in Virus Research     Full-text available via subscription   (Followers: 5, SJR: 1.878, h-index: 68)
Advances in Water Resources     Hybrid Journal   (Followers: 42, SJR: 2.408, h-index: 94)
Aeolian Research     Hybrid Journal   (Followers: 5, SJR: 0.973, h-index: 22)
Aerospace Science and Technology     Hybrid Journal   (Followers: 304, SJR: 0.816, h-index: 49)
AEU - Intl. J. of Electronics and Communications     Hybrid Journal   (Followers: 8, SJR: 0.318, h-index: 36)
African J. of Emergency Medicine     Open Access   (Followers: 4, SJR: 0.344, h-index: 6)
Ageing Research Reviews     Hybrid Journal   (Followers: 7, SJR: 3.289, h-index: 78)
Aggression and Violent Behavior     Hybrid Journal   (Followers: 390, SJR: 1.385, h-index: 72)
Agri Gene     Hybrid Journal  
Agricultural and Forest Meteorology     Hybrid Journal   (Followers: 15, SJR: 2.18, h-index: 116)
Agricultural Systems     Hybrid Journal   (Followers: 29, SJR: 1.275, h-index: 74)
Agricultural Water Management     Hybrid Journal   (Followers: 36, SJR: 1.546, h-index: 79)
Agriculture and Agricultural Science Procedia     Open Access  
Agriculture and Natural Resources     Open Access   (Followers: 1)
Agriculture, Ecosystems & Environment     Hybrid Journal   (Followers: 48, SJR: 1.879, h-index: 120)
Ain Shams Engineering J.     Open Access   (Followers: 5, SJR: 0.434, h-index: 14)
Air Medical J.     Hybrid Journal   (Followers: 3, SJR: 0.234, h-index: 18)
AKCE Intl. J. of Graphs and Combinatorics     Open Access   (SJR: 0.285, h-index: 3)
Alcohol     Hybrid Journal   (Followers: 9, SJR: 0.922, h-index: 66)
Alcoholism and Drug Addiction     Open Access   (Followers: 5)
Alergologia Polska : Polish J. of Allergology     Full-text available via subscription   (Followers: 1)
Alexandria Engineering J.     Open Access   (Followers: 1, SJR: 0.436, h-index: 12)
Alexandria J. of Medicine     Open Access  
Algal Research     Partially Free   (Followers: 7, SJR: 2.05, h-index: 20)
Alkaloids: Chemical and Biological Perspectives     Full-text available via subscription   (Followers: 3)
Allergologia et Immunopathologia     Full-text available via subscription   (Followers: 1, SJR: 0.46, h-index: 29)
Allergology Intl.     Open Access   (Followers: 5, SJR: 0.776, h-index: 35)
ALTER - European J. of Disability Research / Revue Européenne de Recherche sur le Handicap     Full-text available via subscription   (Followers: 6, SJR: 0.158, h-index: 9)
Alzheimer's & Dementia     Hybrid Journal   (Followers: 45, SJR: 4.289, h-index: 64)
Alzheimer's & Dementia: Diagnosis, Assessment & Disease Monitoring     Open Access   (Followers: 5)
Alzheimer's & Dementia: Translational Research & Clinical Interventions     Open Access   (Followers: 3)
American Heart J.     Hybrid Journal   (Followers: 45, SJR: 3.157, h-index: 153)
American J. of Cardiology     Hybrid Journal   (Followers: 47, SJR: 2.063, h-index: 186)
American J. of Emergency Medicine     Hybrid Journal   (Followers: 34, SJR: 0.574, h-index: 65)
American J. of Geriatric Pharmacotherapy     Full-text available via subscription   (Followers: 6, SJR: 1.091, h-index: 45)
American J. of Geriatric Psychiatry     Hybrid Journal   (Followers: 14, SJR: 1.653, h-index: 93)
American J. of Human Genetics     Hybrid Journal   (Followers: 32, SJR: 8.769, h-index: 256)
American J. of Infection Control     Hybrid Journal   (Followers: 25, SJR: 1.259, h-index: 81)
American J. of Kidney Diseases     Hybrid Journal   (Followers: 31, SJR: 2.313, h-index: 172)
American J. of Medicine     Hybrid Journal   (Followers: 48, SJR: 2.023, h-index: 189)
American J. of Medicine Supplements     Full-text available via subscription   (Followers: 3)
American J. of Obstetrics and Gynecology     Hybrid Journal   (Followers: 174, SJR: 2.255, h-index: 171)
American J. of Ophthalmology     Hybrid Journal   (Followers: 51, SJR: 2.803, h-index: 148)
American J. of Ophthalmology Case Reports     Open Access   (Followers: 2)
American J. of Orthodontics and Dentofacial Orthopedics     Full-text available via subscription   (Followers: 6, SJR: 1.249, h-index: 88)
American J. of Otolaryngology     Hybrid Journal   (Followers: 22, SJR: 0.59, h-index: 45)
American J. of Pathology     Hybrid Journal   (Followers: 23, SJR: 2.653, h-index: 228)
American J. of Preventive Medicine     Hybrid Journal   (Followers: 21, SJR: 2.764, h-index: 154)
American J. of Surgery     Hybrid Journal   (Followers: 32, SJR: 1.286, h-index: 125)
American J. of the Medical Sciences     Hybrid Journal   (Followers: 13, SJR: 0.653, h-index: 70)
Ampersand : An Intl. J. of General and Applied Linguistics     Open Access   (Followers: 5)
Anaerobe     Hybrid Journal   (Followers: 4, SJR: 1.066, h-index: 51)
Anaesthesia & Intensive Care Medicine     Full-text available via subscription   (Followers: 52, SJR: 0.124, h-index: 9)
Anaesthesia Critical Care & Pain Medicine     Full-text available via subscription   (Followers: 3)
Anales de Cirugia Vascular     Full-text available via subscription  
Anales de Pediatría     Full-text available via subscription   (Followers: 2, SJR: 0.209, h-index: 27)
Anales de Pediatría (English Edition)     Full-text available via subscription  
Anales de Pediatría Continuada     Full-text available via subscription   (SJR: 0.104, h-index: 3)
Analytic Methods in Accident Research     Hybrid Journal   (Followers: 2, SJR: 2.577, h-index: 7)
Analytica Chimica Acta     Hybrid Journal   (Followers: 38, SJR: 1.548, h-index: 152)
Analytical Biochemistry     Hybrid Journal   (Followers: 154, SJR: 0.725, h-index: 154)
Analytical Chemistry Research     Open Access   (Followers: 7, SJR: 0.18, h-index: 2)
Analytical Spectroscopy Library     Full-text available via subscription   (Followers: 10)
Anesthésie & Réanimation     Full-text available via subscription  
Anesthesiology Clinics     Full-text available via subscription   (Followers: 21, SJR: 0.421, h-index: 40)
Angiología     Full-text available via subscription   (SJR: 0.124, h-index: 9)
Angiologia e Cirurgia Vascular     Open Access  
Animal Behaviour     Hybrid Journal   (Followers: 143, SJR: 1.907, h-index: 126)
Animal Feed Science and Technology     Hybrid Journal   (Followers: 5, SJR: 1.151, h-index: 83)
Animal Reproduction Science     Hybrid Journal   (Followers: 5, SJR: 0.711, h-index: 78)
Annales d'Endocrinologie     Full-text available via subscription   (SJR: 0.394, h-index: 30)
Annales d'Urologie     Full-text available via subscription  
Annales de Cardiologie et d'Angéiologie     Full-text available via subscription   (SJR: 0.177, h-index: 13)
Annales de Chirurgie de la Main et du Membre Supérieur     Full-text available via subscription  
Annales de Chirurgie Plastique Esthétique     Full-text available via subscription   (Followers: 2, SJR: 0.354, h-index: 22)
Annales de Chirurgie Vasculaire     Full-text available via subscription   (Followers: 1)

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Journal Cover Advances in Exploration Geophysics
  [3 followers]  Follow
    
   Full-text available via subscription Subscription journal  (Not entitled to full-text)
   ISSN (Print) 0921-9366
   Published by Elsevier Homepage  [3030 journals]
  • Introduction
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • I Acoustic Waves
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • II Elastic Waves
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • III Acoustic Two-Way and One-Way Wave Equations
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • IV Elastic Two-Way and One-Way Wave Equations
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • V Acoustic Forward Wave Field Extrapolation
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • VI Elastic Forward Wave Field Extrapolation
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • VII Acoustic Inverse Wave Field Extrapolation in Low Contrast Media
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • VIII Elastic Inverse Wave Field Extrapolation in Low Contrast Media
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • IX Acoustic Inverse Wave Field Extrapolation in High Contrast Media
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • X Elastic Inverse Wave Field Extrapolation in High Contrast Media
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • XI Acoustic Redatuming of Single-Component Seismic Data
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • XII Elastic Redatuming of Multi-Component Seismic Data
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • APPENDIX A Matrix Notation
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • APPENDIX B Interactions of One-Way Acoustic Wave Fields
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • APPENDIX C Interactions of One-Way Elastic Wave Fields
    • Abstract: Publication date: 1989
      Source:Advances in Exploration Geophysics, Volume 2


      PubDate: 2013-09-01T11:04:55Z
       
  • Chapter 1 Geophysical potential fields
    • Abstract: 1998
      Publication year: 1998
      Source:Advances in Exploration Geophysics, Volume 5



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 2 Potential field signals and models
    • Abstract: 1998
      Publication year: 1998
      Source:Advances in Exploration Geophysics, Volume 5



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 3 Power spectrum and its applications
    • Abstract: 1998
      Publication year: 1998
      Source:Advances in Exploration Geophysics, Volume 5



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 4 Digital filtering of maps I
    • Abstract: 1998
      Publication year: 1998
      Source:Advances in Exploration Geophysics, Volume 5



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 5 Digital filtering of maps II
    • Abstract: 1998
      Publication year: 1998
      Source:Advances in Exploration Geophysics, Volume 5



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 6 Parameter estimation
    • Abstract: 1998
      Publication year: 1998
      Source:Advances in Exploration Geophysics, Volume 5



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 1 Preliminary statistics
    • Abstract: 1995
      Publication year: 1995
      Source:Advances in Exploration Geophysics, Volume 4



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 2 Direct, linear and iterative-linear inverse methods
    • Abstract: 1995
      Publication year: 1995
      Source:Advances in Exploration Geophysics, Volume 4

      In this chapter we reviewed direct, linear and iterative linear inverse methods in geophysics. Most direct methods are not robust for incomplete data in the presence of noise and are consequently not very useful. Therefore model based inversion methods have gained much popularity. Based on the nature of the forward problem, we followed the commonly accepted definition [e.g., Tarantola, 1987] to classify inverse problems into linear, weakly nonlinear, quasi-linear and highly nonlinear problems. These definitions may at times be somewhat misleading in that it is very difficult to say under what condition a problem can be classified as a weakly nonlinear or quasi-linear problem. The facts are straightforward in that we know that most forward modeling operators are nonlinear and the success of an inverse method is usually judged by how well we explain the observed data given their uncertainty. Thus a probabilistic theory as developed by Tarantola or based on Bayes' rule, seems to be adequate to describe the inverse problem. Their solution, however, is the most difficult aspect. If a problem can be linearized, i.e., if under some restrictive set of conditions a forward modeling operator can be reduced to a linear operator, the solution becomes fairly straightforward. Otherwise, one needs to at least try to use gradient based methods in solving the inverse problem. The gradient based methods suffer from the following limitations: • Gradient based methods will often find a minimum in the close neighborhood of the starting solution. In situations where the error function may have several secondary minima, one needs to either start very close to the global minimum or try several starting points hoping that one of them will lead to the best solution. • Most of these methods require that a gradient and sometimes a curvature (second derivative) matrix be computed at each point during the iteration process. Although for some geophysical applications analytical expressions for the gradient and curvature can be derived, it is not possible in general. For example, for wave propagation problems in laterally varying media, the forward calculation is done most accurately with methods such as finite differences. In such a case, the gradient can only be computed numerically—a computationally formidable task. • Almost all of these methods require computing the inverse of a large matrix. Fortunately, in many situations several known methods such as Cholesky decomposition can be used for this purpose. Inverting a large matrix even with well known techniques is not necessarily a very easy computational task. Using a statistical framework, the solution of an inverse problem is described by the PPD. If the forward modeling is nonlinear, clearly the PPD is not Gaussian and the analysis of the solution is not straightforward. Even in the case of a highly nonlinear problem, if one can start at a point very close to the peak of the PPD, the MAP point can be reached by gradient methods. But, using this approach one would still only approximate the PPD by a Gaussian around the MAP point, even though the true PPD may be highly complicated in shape. The only way to truly estimate the PPD is to evaluate the error function at each point in model space which is in general an impossible task. Therefore, practical ways need to be sought that can sample several points near the peak of the PPD such that the most significant part of the PPD can be approximately constructed by direct sampling rather than fitting a presumed shape around the MAP point.

      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 3 Monte carlo methods
    • Abstract: 1995
      Publication year: 1995
      Source:Advances in Exploration Geophysics, Volume 4



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 4 Simulated annealing methods
    • Abstract: 1995
      Publication year: 1995
      Source:Advances in Exploration Geophysics, Volume 4

      Since the work of Kirkpatrick et al. [1983], the optimization method now known as SA has been applied to several problems in science and engineering. Following the work of Rothman [1985, Rothman 1986], the method has gained popularity in the geophysical community and has been applied to a wide variety of problems in geophysics. Many geophysical inverse problems are nonlinear and due to the availability of high speed computers, SA is now being applied to these problems. In this chapter, we reviewed starting with classical SA, several variants of SA that are aimed at making the algorithm computationally efficient. Most of these algorithms are statistically guaranteed to attain equilibrium distribution and possibly reach the global minimum of an error or energy function and are thus suitable in MAP estimation. We also note that they can be used as importance sampling algorithms to estimate the uncertainties and the marginal posterior probability density function for each parameter in model space. In practice, however, these algorithms cannot be expected to always perform flawlessly since care needs to be taken in parameter selection which is problem dependent. For example, it is important to choose the starting temperature and cooling schedule properly. One obvious omission in this chapter is a discussion of cooling schedules. There has been some theoretical work on choosing a cooling schedule. However, the problem with theoretical cooling schedules is that your computer budget will quickly be exceeded. For this reason, we found VFSA very useful in many applications. The SA's that use fast cooling schedules are often called simulated quenching (SQ) [Ingber, 1993]. One variant of SQ is to find the critical temperature and either run the algorithm at that constant temperature [Basu and Frazer, 1990] or anneal slowly by starting slightly above the critical temperature [Sen and Stoffa, 1991]. However, a substantial amount of computer time can be spent finding the critical temperature. The MFA algorithm appears promising in that an approximate value of the critical temperature can be found analytically. SA at a constant temperature of one avoids the issues of selecting a suitable starting temperature and a cooling schedule and enables us to use SA as an importance sampling technique in the efficient evaluation of multidimensional integrals. These concepts will be illustrated in Chapter 7. In MAP estimations, however, choice of the proper cooling schedule is critical to the design of an efficient algorithm. In practice, an SQ method that uses a cooling schedule which is faster than a theoretical cooling schedule can be determined by trial and error.

      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 5 Genetic algorithms
    • Abstract: 1995
      Publication year: 1995
      Source:Advances in Exploration Geophysics, Volume 4

      GA is a novel and interesting approach to optimization problems. Unlike SA, the commonly used GA still lacks a rigorous mathematical basis. Its innovative appeal lies in its analog with natural biological systems and the fact that even a simple GA can be applied to find many good solutions quickly. We have shown how some aspects of GA, e.g., stretching the objective function, can be replaced by incorporating the concept of temperature to the probabilities for the selection process. Also, the genetic concept of heredity can be replaced with the Metropolis criterion to decide if each new model should be replaced by its predecessor. The modification to a classical GA allows the algorithm to be viewed as either an analog to biological reproduction or as an approximation to parallel Metropolis SA. In either case, the principal distinction is the introduction of the crossover operator which allows the models in the distribution to share information. This is an advantage, since the information common to good models propagates to the next generation more efficiently, and a disadvantage since premature convergence can occur. Each model of a given generation can be evaluated independently and each run can be made independently. This makes GA's ideally suited for implementation in parallel computer architectures.

      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 6 Geophysical applications of SA and GA
    • Abstract: 1995
      Publication year: 1995
      Source:Advances in Exploration Geophysics, Volume 4



      PubDate: 2012-12-15T09:29:34Z
       
  • Chapter 7 Uncertainty estimation
    • Abstract: 1995
      Publication year: 1995
      Source:Advances in Exploration Geophysics, Volume 4

      It is now well recognized that the results of geophysical inversion may have uncertainties for several reasons. Bayes' rule offers an elegant description of the solution for the geophysical inverse problem in terms of the posterior probability density function in the model space. Because the model space is highly multidimensional, a complete display of the PPD is not possible and therefore, we seek quantities such as the posterior marginal density functions, mean, covariance, etc. to describe the solution of our inverse problems. Derivation of these quantities is not a trivial task because they involve numerical evaluation of integrals with a large number of variables. One additional difficulty is that for most geophysical inverse problems the data have a nonlinear relationship with the model parameters resulting in error functions which may have multiple extrema. The PPD may therefore be highly complicated, and methods that require prior assumptions about the shape of the PPD may not be adequate. These methods attempt to locate the maximum of the PPD and the Hessian computed at the MAP point is used to estimate the covariance; thus a Gaussian is completely described. We described several computationally intensive sampling based approaches to derive quantities such as the posterior marginal PPD, mean and covariance. Six different methods have been tested and compared by application to synthetic resistivity sounding data where the number of model parameters were only five, such that the forward modeling was computationally tractable. Methods such as GS and PGS agree well with grid search integration. The results from multiple MAP algorithms are quite encouraging because even though the estimated variances were lower than those estimated by GS, PGS, and grid search, the correlations were in very good agreement. Of course for very complicated PPD's, the multiple MAP algorithms may not perform equally well, but for many applications, they will help in getting approximate estimates of these quantities quite rapidly. The SA method is guaranteed to asymptotically converge to a Gibbs' distribution. We showed numerically that a steady state distribution can be achieved in a finite number of iterations. Thus a GS requires much less computation time than a complete grid search in the evaluation of multidimensional integrals. Running SA at a constant temperature of 1.0 appears to be feasible for many practical problems. Although our PGS is not based on a mathematical model as rigorous as SA, we showed numerically that the results from GS and PGS are nearly identical. The PGS, however, offers the advantage of running the algorithm on parallel computer architectures. The use of stochastic inversion methods based on statistical models, has been criticized primarily because of the requirement that the prior distribution of noise in the data and theory error be known. Often the prior noise pdf is assumed Gaussian. In practice, it is never possible to estimate the true noise distribution with a small and finite number of repeated measurements, since the classical definition of probability requires that an experiment be repeated an infinite number of times under identical conditions. The use and specification of the prior pdf has long been a subject of dispute and the use of a statistical approach has often been criticized by classical inverse theorists. There exist several definitions of probability. Besides the classical definition which is based on relative frequency of occurrence, the Bayesian interpretation defines probability as a degree of belief [Bayes, 1763]. The only requirement is that the axioms of probability theory are not violated. Again, in the subjective Bayesian interpretation, the degree of belief is a personal degree of belief. Thus a priori distribution may simply reflect an expert's opinion. We therefore recommend that a simple and practical approach be taken to characterize the prior distribution of noise in the data. For any practical problem, we need to carefully analyze the data and explore the sources of error in the data in order to arrive at some way of characterizing the uncertainty.

      PubDate: 2012-12-15T09:29:34Z
       
 
 
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