Magnetic Intensity Ontology

# Magnetic Intensity Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/earth-science-measurements/magnetic-intensity-ontology.html

FLOW MagneticIntensityOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Earth Science Measurements
    -> Magnetic Intensity Ontology

  PURPOSE:
    Represent magnetic intensity measurements in Earth science with explicit distinction between magnetic flux density B and magnetic field strength H, while supporting geomagnetic total-field intensity, vector components, anomalies, temporal variation, magnetometer observations, survey corrections, reference field models, calibration, uncertainty, provenance, and transformations required for consistent AI interpretation.

  ENTITY MagneticFluxDensity {
    TYPE: MagneticFieldQuantity
    SYMBOL: B
    DIMENSION: M*T^-2*I^-1
    SI_UNIT: tesla
    SI_SYMBOL: T

    COMMON_GEOMAGNETIC_UNIT:
      nanotesla
      SYMBOL: nT

    PROPERTIES:
      is_vector
      has_magnitude
      has_direction
      varies_spatially
      varies_temporally
      may_have_uncertainty
  }

  ENTITY MagneticFieldStrength {
    TYPE: MagneticFieldQuantity
    SYMBOL: H
    DIMENSION: I*L^-1
    SI_UNIT: ampere_per_metre
    SI_SYMBOL: A/m

    RULE:
      H_and_B_are_distinct_physical_quantities
  }

  ENTITY TotalFieldIntensity {
    TYPE: MagneticFluxDensityMagnitude
    SYMBOL: F
    SI_UNIT: tesla
    COMMON_UNIT: nanotesla

    FORM:
      F = magnitude(B)
  }

  ENTITY MagneticAnomaly {
    TYPE: DerivedMagneticFieldDifference
    SYMBOL: delta_B

    DEFINITION:
      observed_magnetic_field_minus_declared_reference_or_regional_field
      after_declared_corrections
  }

  UNIT_SYSTEM {
    magnetic_flux_density:
      tesla
      microtesla
      nanotesla

    magnetic_field_strength:
      ampere_per_metre

    conversions:
      1 microtesla = 1000 nanotesla
      1 tesla = 1e9 nanotesla

    RULE:
      B_units_and_H_units MUST_NOT be_interchanged
  }

  TERMINOLOGY_MODEL {
    terms:
      magnetic_intensity
      magnetic_field_intensity
      total_magnetic_intensity
      total_field
      magnetic_flux_density
      magnetic_field_strength

    RULE:
      "magnetic intensity" is_ambiguous
      and MUST be resolved_to_B_magnitude_or_H_using_units_and_domain_context

    geomagnetic_context:
      total_magnetic_intensity commonly_refers_to_total_B_field_magnitude

    electromagnetic_context:
      magnetic_field_intensity MAY refer_to_H
  }

  B_H_RELATION_MODEL {
    general_material_relation:
      B =
        mu_0*(H + M)

    linear_isotropic_medium:
      B =
        mu*H

    vacuum:
      B =
        mu_0*H

    WHERE:
      M = magnetization
      mu = permeability

    RULE:
      conversion_between_B_and_H_requires_material_or_vacuum_context
  }

  VECTOR_MODEL {
    field:
      B = [B_x, B_y, B_z]

    magnitude:
      F =
        sqrt(B_x^2 + B_y^2 + B_z^2)

    RULE:
      total_field_magnitude != individual_vector_component
  }

  GEOMAGNETIC_COMPONENT_MODEL {
    common_local_components:
      X = north_component
      Y = east_component
      Z = vertical_component

    horizontal_intensity:
      H_horizontal =
        sqrt(X^2 + Y^2)

    total_intensity:
      F =
        sqrt(X^2 + Y^2 + Z^2)

    declination:
      D =
        atan2(Y,X)

    inclination:
      I_angle =
        atan2(Z,H_horizontal)

    RULE:
      vertical_sign_and_axis_conventions MUST be preserved
  }

  COORDINATE_FRAME_MODEL {
    possible_frames:
      north_east_down
      north_east_up
      geographic
      geomagnetic
      instrument_frame
      aircraft_frame
      satellite_frame

    RULE:
      magnetic_vector_components MUST preserve_coordinate_frame
  }

  TOTAL_FIELD_MODEL {
    scalar_magnetometer:
      measures_or_estimates_magnitude_of_B

    total_field:
      F = magnitude(B)

    RULE:
      scalar_total_field_measurement_does_not_by_itself_provide_vector_direction
  }

  MAGNETIC_ANOMALY_MODEL {
    generic:
      anomaly =
        observed_field
        - reference_field
        - declared_temporal_or_platform_effects

    possible_reference:
      IGRF
      regional_field
      local_base_station
      fitted_background

    RULE:
      anomaly_definition_and_reference_field MUST be explicit
  }

  REFERENCE_FIELD_MODEL {
    possible_models:
      International_Geomagnetic_Reference_Field
      World_Magnetic_Model
      regional_geomagnetic_model

    inputs:
      latitude
      longitude
      elevation
      epoch

    output:
      modelled_main_field_components_or_total_field

    RULE:
      reference_model_version_and_epoch MUST be preserved
  }

  DIURNAL_VARIATION_MODEL {
    cause:
      time_varying_external_and_internal_geomagnetic_fields

    correction:
      survey_value_corrected_using_base_station_or_reference_time_series

    generic:
      B_corrected =
        B_survey - delta_B_temporal

    RULE:
      temporal_correction_requires_time_synchronisation
  }

  BASE_STATION_MODEL {
    purpose:
      monitor_temporal_magnetic_variation_during_survey

    REQUIRE:
      base_location
      base_instrument
      timestamp
      sampling_interval
      reference_level

    RULE:
      survey_and_base_station_clocks MUST be_synchronised
  }

  MAGNETOMETER_MODEL {
    possible_instruments:
      proton_precession
      Overhauser
      optically_pumped
      fluxgate
      SQUID
      Hall_effect
      magnetoresistive

    outputs:
      scalar_total_field
      vector_components
      gradient
      instrument_specific_signal

    RULE:
      instrument_type determines_measured_quantity_and_required_calibration
  }

  PROTON_PRECESSION_MODEL {
    principle:
      proton_precession_frequency_related_to_total_field

    relation:
      omega =
        gamma_p*B

    inference:
      B =
        omega/gamma_p

    RULE:
      gyromagnetic_ratio_and_frequency_reference MUST be preserved
  }

  FLUXGATE_MODEL {
    measured:
      vector_field_components

    dependencies:
      sensor_orientation
      scale_factor
      offset
      orthogonality
      temperature

    RULE:
      vector_fluxgate_measurement_requires_orientation_and_axis_calibration
  }

  GRADIOMETER_MODEL {
    magnetic_gradient:
      delta_B/distance

    common_units:
      nT/m

    possible_configuration:
      two_sensors_with_known_separation

    RULE:
      magnetic_gradient != magnetic_field_intensity
  }

  SENSOR_ORIENTATION_MODEL {
    orientation:
      rotation_from_sensor_frame_to_reference_frame

    transformed_vector:
      B_reference =
        R*B_sensor

    REQUIRE:
      rotation_matrix_or_attitude
      axis_definition

    RULE:
      vector_data MUST be_orientation_corrected_before_component_comparison
  }

  CALIBRATION_MODEL {
    parameters:
      scale_factor
      offset
      axis_misalignment
      orthogonality
      temperature_coefficient
      heading_error

    reference:
      calibrated_field
      reference_instrument
      known_orientation

    RULE:
      raw_sensor_output != calibrated_magnetic_field
  }

  HEADING_ERROR_MODEL {
    causes:
      sensor_platform_magnetisation
      orientation_dependent_interference

    correction:
      function_of_heading_and_attitude

    RULE:
      airborne_or_marine_survey_heading_effects MAY require_compensation
  }

  PLATFORM_MAGNETIC_MODEL {
    sources:
      aircraft
      vehicle
      ship
      drone
      electronics
      power_systems

    correction:
      compensation_model

    RULE:
      platform_field MUST be separated_from_Earth_field_when_material
  }

  AIRBORNE_MAGNETIC_MODEL {
    measurements:
      total_field
      vector_field
      altitude
      position
      attitude

    corrections:
      diurnal
      IGRF
      heading
      manoeuvre
      lag
      altitude

    RULE:
      navigation_and_platform_corrections MUST be preserved
  }

  MARINE_MAGNETIC_MODEL {
    sensor:
      commonly_towed_away_from_ship

    corrections:
      diurnal
      reference_field
      layback_position
      ship_field

    RULE:
      sensor_position MAY differ_from_vessel_position
  }

  GROUND_SURVEY_MODEL {
    measurements:
      station_or_continuous_traverse

    REQUIRE:
      position
      elevation
      timestamp
      sensor_height
      base_station

    RULE:
      sensor_height_and_station_spacing affect_spatial_interpretation
  }

  SATELLITE_MAGNETIC_MODEL {
    measurements:
      scalar_and_vector_field
      position
      attitude
      time

    separation:
      core_field
      crustal_field
      ionospheric_field
      magnetospheric_field

    RULE:
      satellite_magnetic_products_are_model_decompositions_with_spatial_scale_context
  }

  TEMPORAL_VARIATION_MODEL {
    components:
      secular_variation
      diurnal_variation
      magnetic_storms
      pulsations
      transient_external_fields

    RULE:
      observation_epoch_and_space_weather_context MAY be_material
  }

  MAGNETIC_STORM_MODEL {
    effect:
      large_temporal_field_variation

    RULE:
      survey_data_during_strong_disturbance MAY require_flagging_or_exclusion
  }

  MAGNETIZATION_MODEL {
    material_magnetization:
      M

    components:
      induced_magnetization
      remanent_magnetization

    induced:
      M_induced =
        chi*H
      under_linear_isotropic_approximation

    RULE:
      magnetic_anomaly_interpretation MAY require_susceptibility_and_remanence
  }

  MAGNETIC_SUSCEPTIBILITY_MODEL {
    symbol:
      chi

    dimension:
      dimensionless_in_SI_volume_susceptibility_context

    relation:
      M =
        chi*H

    RULE:
      susceptibility != magnetic_field
  }

  SPATIAL_MODEL {
    field:
      B = B(x,y,z,t)

    REQUIRE:
      latitude
      longitude
      elevation_or_sensor_height
      CRS
      epoch

    RULE:
      magnetic_measurement_is_spatially_and_temporally_specific
  }

  INTERPOLATION_MODEL {
    magnetic_map:
      field_or_anomaly_values_on_grid

    possible_methods:
      minimum_curvature
      kriging
      inverse_distance
      spline

    RULE:
      gridded_magnetic_data MUST preserve_cell_size_interpolation_and_filtering
  }

  FILTERING_MODEL {
    possible_operations:
      despiking
      low_pass
      high_pass
      band_pass
      upward_continuation
      reduction_to_pole
      reduction_to_equator

    RULE:
      processed_magnetic_products MUST preserve_filter_and_transformation_history
  }

  RELATIONSHIPS {
    MagneticFluxDensity -> IS_VECTOR_FIELD -> EarthMagneticField
    TotalFieldIntensity -> MAGNITUDE_OF -> MagneticFluxDensity
    MagneticFieldStrength -> RELATES_TO -> MagneticFluxDensityThroughMaterialRelation
    GeomagneticComponents -> COMPOSE -> TotalField
    Magnetometer -> MEASURES -> MagneticFieldQuantity
    BaseStation -> MONITORS -> TemporalMagneticVariation
    ReferenceFieldModel -> ESTIMATES -> MainGeomagneticField
    MagneticAnomaly -> DIFFERENCE_FROM -> ReferenceField
    SensorOrientation -> MAPS -> InstrumentFrameToReferenceFrame
    PlatformCompensation -> REMOVES_OR_REDUCES -> PlatformMagneticEffect
    MagneticSusceptibility -> RELATES -> MagnetizationAndFieldStrength
  }

  SEMANTIC_EQUIVALENCE {
    "total magnetic intensity" ~= total_magnetic_flux_density_magnitude
      WHEN geomagnetic_context

    "magnetic field intensity" ~= magnetic_field_strength_H
      WHEN electromagnetic_H_context

    magnetic_flux_density_B != magnetic_field_strength_H
    total_field_intensity != horizontal_intensity
    magnetic_anomaly != total_field
    magnetic_gradient != magnetic_field
    raw_sensor_output != calibrated_field
    susceptibility != magnetization
  }

  CONSTRAINTS {
    magnetic_quantity_type_must_be_defined = true
    B_and_H_must_be_distinguished = true
    unit_must_match_magnetic_quantity = true
    coordinate_frame_must_be_defined_for_vector_components = true
    spatial_location_and_epoch_should_be_defined = true
    total_field_and_vector_components_are_not_semantically_equivalent = true
    anomaly_requires_reference_field_definition = true
    raw_sensor_output_requires_calibration = true
    temporal_and_platform_corrections_should_be_preserved = true
    uncertainty_should_include_instrument_orientation_reference_and_temporal_components = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      MagneticFluxDensity
      MagneticFieldStrength
      TotalFieldIntensity
      MagneticAnomaly
      MagneticGradient

    COMMON_METHODS:
      proton_precession_magnetometry
      Overhauser_magnetometry
      optically_pumped_magnetometry
      fluxgate_magnetometry
      SQUID_magnetometry
      gradiometry
      airborne_magnetic_survey
      marine_magnetic_survey
      satellite_magnetometry

    RECORD:
      magnetic_quantity_type
      numerical_value
      unit
      total_or_component
      coordinate_frame
      X_component
      Y_component
      Z_component
      horizontal_intensity
      declination
      inclination
      latitude
      longitude
      elevation
      sensor_height
      coordinate_reference_system
      timestamp
      epoch
      instrument
      sensor_orientation
      sampling_rate
      raw_signal
      calibration_state
      base_station
      temporal_correction
      reference_field_model
      platform_correction
      processing_history
      quality_flag
      uncertainty
      provenance

    UNCERTAINTY:
      measured_or_inferred_magnetic_quantity =
        best_estimate +/- uncertainty
  }

  UNCERTAINTY_MODEL {
    sources:
      sensor_noise
      scale_factor
      offset
      axis_misalignment
      orientation
      temperature
      timing
      position
      sensor_height
      base_station
      diurnal_variation
      reference_field_model
      platform_compensation
      heading_error
      magnetic_storm
      interpolation
      filtering

    PROPAGATION:
      magnetic_measurement_uncertainty
      <- sensor_orientation_spatial_temporal_reference_and_processing_uncertainties
  }

  REASONING_RULES {
    IF vector_components_X_Y_Z_known
      THEN total_field =
        sqrt(X^2+Y^2+Z^2)

    IF X_and_Y_known
      THEN horizontal_intensity =
        sqrt(X^2+Y^2)

    IF X_and_Y_known
      THEN declination =
        atan2(Y,X)

    IF Z_and_horizontal_intensity_known
      THEN inclination =
        atan2(Z,horizontal_intensity)

    IF B_known AND vacuum_context
      THEN H =
        B/mu_0

    IF H_known AND vacuum_context
      THEN B =
        mu_0*H

    IF observed_field_and_reference_field_known
      THEN magnetic_anomaly =
        observed_field-reference_field
      after_declared_corrections

    IF survey_and_base_station_time_series_known
      THEN apply_temporal_correction
      using_synchronised_timestamps

    IF proton_precession_frequency_known
      AND proton_gyromagnetic_ratio != 0
      THEN total_field =
        angular_frequency/proton_gyromagnetic_ratio

    IF sensor_vector_and_orientation_matrix_known
      THEN reference_frame_vector =
        rotation_matrix*sensor_frame_vector
  }

  VALIDATION {
    CHECK magnetic_quantity_type
    CHECK B_vs_H
    CHECK unit_consistency
    CHECK total_vs_component_field
    CHECK coordinate_frame
    CHECK axis_and_vertical_sign_convention
    CHECK spatial_location
    CHECK elevation_or_sensor_height
    CHECK timestamp_and_epoch
    CHECK sensor_orientation
    CHECK calibration_state
    CHECK base_station_and_time_sync
    CHECK temporal_correction
    CHECK reference_field_model_and_version
    CHECK platform_or_heading_correction
    CHECK magnetic_storm_or_disturbance
    CHECK processing_history
    CHECK quality_flag
    CHECK uncertainty_representation
  }

  CONFIDENCE {
    definition_confidence: 1.00
    B_H_distinction_confidence: 1.00
    vector_relationship_confidence: 1.00
    total_field_relationship_confidence: 1.00
    geomagnetic_anomaly_confidence: 0.98
    temporal_correction_confidence: 0.97
    platform_compensation_confidence: 0.96
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when quantity type, coordinate frame,
      orientation, epoch, calibration, base correction,
      reference field, platform effect or uncertainty is missing or ambiguous
  }

  UPDATE_MODEL {
    ON new_measurement:
      identify_B_H_total_component_or_gradient_quantity
      validate_unit
      attach_location_and_CRS
      attach_elevation_or_sensor_height
      attach_timestamp_and_epoch
      identify_instrument
      attach_sensor_orientation
      preserve_raw_signal
      apply_calibration
      transform_vector_to_reference_frame_when_required
      apply_temporal_and_platform_corrections
      attach_reference_field_model
      compute_anomaly_when_requested
      attach_quality_flag
      attach_uncertainty
      update_magnetic_state

    ON base_station_update:
      append_base_field_observation
      synchronise_with_survey_time
      recompute_temporal_correction
      update_corrected_survey_values

    ON orientation_revision:
      preserve_sensor_frame_vector
      update_rotation_model
      recompute_reference_frame_components
      update_uncertainty

    ON reference_field_revision:
      preserve_observed_field
      preserve_previous_model
      attach_new_reference_model_and_version
      recompute_anomaly
      update_provenance

    ON platform_compensation_revision:
      preserve_raw_platform_measurement
      update_heading_or_manoeuvre_model
      recompute_corrected_field
      update_uncertainty
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_domain: MagneticIntensity
    canonical_B_entity: MagneticFluxDensity
    canonical_H_entity: MagneticFieldStrength
    geomagnetic_total_entity: TotalFieldIntensity

    interpretation_order:
      identify_magnetic_quantity_as_B_H_total_component_anomaly_or_gradient
      identify_value
      identify_unit
      identify_total_or_vector_component
      identify_coordinate_frame
      identify_location_elevation_and_sensor_height
      identify_timestamp_and_epoch
      identify_instrument_and_orientation
      identify_raw_or_calibrated_status
      identify_base_station_and_temporal_correction
      identify_reference_field_model
      identify_platform_heading_or_manoeuvre_correction
      identify_processing_history
      identify_quality_flag
      identify_uncertainty
      normalize_units
      validate_magnetic_semantics
      infer_vector_and_anomaly_relationships

    ambiguity_controls:
      distinguish_magnetic_flux_density_B_from_field_strength_H
      distinguish_total_field_from_horizontal_intensity
      distinguish_total_field_from_individual_components
      distinguish_observed_field_from_magnetic_anomaly
      distinguish_magnetic_gradient_from_field_intensity
      distinguish_raw_sensor_output_from_calibrated_field
      distinguish_susceptibility_from_magnetization
      preserve_quantity_frame_location_epoch_orientation_reference_and_processing_context
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_Earth_science_magnetic_intensity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Earth Science Measurements
      -> Magnetic Intensity Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_domain
      ontology_path
      terminology_model
      B_H_relation_model
      vector_model
      geomagnetic_component_model
      coordinate_frame_model
      total_field_model
      magnetic_anomaly_model
      reference_field_model
      diurnal_variation_model
      base_station_model
      magnetometer_model
      proton_precession_model
      fluxgate_model
      gradiometer_model
      sensor_orientation_model
      calibration_model
      heading_error_model
      platform_magnetic_model
      airborne_magnetic_model
      marine_magnetic_model
      ground_survey_model
      satellite_magnetic_model
      temporal_variation_model
      magnetic_storm_model
      magnetization_model
      magnetic_susceptibility_model
      spatial_model
      interpolation_model
      filtering_model
      relationships
      constraints
      measurement_model
      uncertainty_model
      reasoning_rules
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      magnetic_quantity_definition_changes
      B_H_semantic_model_changes
      vector_or_coordinate_frame_changes
      reference_field_or_anomaly_model_changes
      temporal_or_base_station_correction_changes
      calibration_or_orientation_model_changes
      platform_compensation_model_changes
      processing_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW