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How to make a simple analysis?

All of this begins with a drawing found all over, a simple section of mantle rolls. Basically, those are two circles turning in opposite direction against each other:

From wikipedia: https://en.wikipedia.org/wiki/Mantle_convection

This is simple, accepted as a guess, though. Analysing this is a bit more complicated than one might think at first. Here is an example of how to handle that:

I — FOUNDATIONS


Chapter 1 — The Making of a Model

  • 1.1 Plate tectonics as a descriptive model
  • 1.2 Mantle plumes vs global structure
  • 1.3 Missing geometry in geoscience
  • 1.4 The need for a unifying framework
  • 1.5 Observational inconsistencies

Chapter 2 — First Observations of Order

  • 2.1 Iceland as a key to global structure
  • 2.2 Regular spacing of volcanic zones
  • 2.3 The 30° and 90° patterns
  • 2.4 Symmetry across hemispheres
  • 2.5 The Ring of Fire as a system

Chapter 3 — From Observation to Hypothesis

  • 3.1 Recognizing repeating units
  • 3.2 The idea of convection rolls
  • 3.3 Linking surface features to deep structure
  • 3.4 Early geometric interpretations
  • 3.5 Formulating a testable model

II — THE CONVECTION ROLLS MODEL


Chapter 4 — The Mathematical Framework

  • 4.1 The global equation of mantle rolls
  • 4.2 The 1.5° discretization
  • 4.3 The role of latitude (32°)
  • 4.4 Directional equations
  • 4.5 Spherical corrections

Chapter 5 — Vertical Structure of the Earth

  • 5.1 Earth’s layered structure
  • 5.2 120 km, 410 km, 670 km discontinuities
  • 5.3 Equal height–width condition
  • 5.4 Rayleigh-Bénard convection in Earth
  • 5.5 Stability of convection rolls

Chapter 6 — Global Distribution of Mid-Ocean Ridges

  • 6.1 Ridge alignment and geometry
  • 6.2 Atlantic vs Indian vs Pacific
  • 6.3 90° relationships
  • 6.4 Iceland as a ridge–roll interface
  • 6.5 Implications for seafloor spreading

Chapter 7 — Subduction Zones and the Ring of Fire

  • 7.1 Convergent boundaries as part of the same system
  • 7.2 The Pacific framework
  • 7.3 Mirror symmetry (Japan–New Zealand)
  • 7.4 Andes, Kamchatka, Cascades
  • 7.5 Polygonal structure of volcanic arcs

III — PHYSICS OF THE SYSTEM


Chapter 8 — Convection Physics

  • 8.1 Rayleigh-Bénard convection
  • 8.2 Threshold conditions
  • 8.3 Roll formation and stability
  • 8.4 Laboratory analogues
  • 8.5 Scaling to Earth

Chapter 9 — Rotation and Geometry

  • 9.1 Earth’s rotation and flow alignment
  • 9.2 Coriolis effects
  • 9.3 Spherical geometry constraints
  • 9.4 Energy distribution with depth
  • 9.5 Directional deformation

Chapter 10 — Energy Flow in the Earth

  • 10.1 Heat sources in the Earth
  • 10.2 Radiogenic heat vs primordial heat
  • 10.3 Core–mantle interaction
  • 10.4 Adiabatic gradients
  • 10.5 Energy balance of the system

Chapter 11 — The Core Revisited

  • 11.1 Inner vs outer core
  • 11.2 Problems with crystallization models
  • 11.3 Thermal equilibrium constraints
  • 11.4 Stability of core–mantle boundary
  • 11.5 Alternative energy pathways

IV — SURFACE EXPRESSIONS


Chapter 12 — Iceland as a Natural Laboratory

  • 12.1 Volcanic zones of Iceland
  • 12.2 Reykjanes
  • 12.3 North and East volcanic zones
  • 12.4 Rift shifts and jumps
  • 12.5 Earthquakes and dyke propagation

Chapter 13 — Global Case Studies

  • 13.1 The Great Rift Valley
  • 13.2 Afar Triangle
  • 13.3 Mississippi & global symmetry
  • 13.4 Yunnan rivers
  • 13.5 Mid-ocean ridge systems

Chapter 14 — Volcanic Systems

  • 14.1 Geometry of eruptions
  • 14.2 Icelandic eruptions (Laki, Eldgjá)
  • 14.3 Fagradalsfjall system
  • 14.4 Surtsey and oceanic volcanism
  • 14.5 Global comparisons

Chapter 15 — Geothermal Systems

  • 15.1 Heat distribution
  • 15.2 Vapour reservoirs (Geysir)
  • 15.3 Predicting geothermal locations
  • 15.4 Applications for energy
  • 15.5 Case studies

V — GLOBAL GEOMETRY AND PATTERNS


Chapter 16 — The Geometry of the Earth System

  • 16.1 Polygons and segmentation
  • 16.2 Global symmetry
  • 16.3 Circular vs linear interpretations
  • 16.4 Equatorial structure
  • 16.5 Global mapping

Chapter 17 — Plate Motion Reinterpreted

  • 17.1 Drift as a consequence, not a cause
  • 17.2 Relation to convection rolls
  • 17.3 Symmetry of plate movement
  • 17.4 Transform faults revisited
  • 17.5 San Andreas in context

Chapter 18 — The Ring of Fire Revisited

  • 18.1 Full system perspective
  • 18.2 Energy flow
  • 18.3 Structural consistency
  • 18.4 Predictive implications
  • 18.5 Future research directions

VI — IMPLICATIONS AND FUTURE WORK


Chapter 19 — Predictive Geoscience

  • 19.1 Predicting volcanic zones
  • 19.2 Predicting geothermal resources
  • 19.3 Mapping unknown structures
  • 19.4 Risk assessment

Chapter 20 — Testing the Model

  • 20.1 What must be measured
  • 20.2 Seismic validation
  • 20.3 Laboratory analogues
  • 20.4 Numerical simulations
  • 20.5 Falsifiability

Chapter 21 — A New Framework for Earth Science

  • 21.1 From description to structure
  • 21.2 Implications for geology
  • 21.3 Implications for energy
  • 21.4 Open questions
  • 21.5 Final synthesis

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