Depth Ontology

# Depth Ontology — Flow Algebra

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

FLOW DepthOntology {

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

  PURPOSE:
    Represent depth as a vertical or path-related length quantity locating a point, layer, object or measurement below a defined reference surface or datum, including water depth, geological depth, borehole depth, soil depth, ocean depth, ice and snow depth, true vertical depth, measured depth, pressure-derived depth, bathymetry, sounding, remote sensing, coordinate references, sign conventions, transformations, uncertainty, provenance, and strict distinctions between depth, elevation, height, thickness and distance.

  ENTITY Depth {
    TYPE: SpatialLengthQuantity
    SYMBOL: d
    DIMENSION: L
    SI_UNIT: metre
    SI_SYMBOL: m

    DEFINITION:
      depth :=
        distance_or_vertical_position_below_a_declared_reference_surface_or_datum
        according_to_declared_direction_and_measurement_convention

    PROPERTIES:
      has_value
      has_unit
      has_reference_surface
      has_direction_or_sign_convention
      has_spatial_location
      may_be_vertical_or_path_based
      may_be_measured_or_inferred
      may_have_uncertainty
  }

  ENTITY TrueVerticalDepth {
    TYPE: VerticalDepthQuantity
    SYMBOL: TVD
    SI_UNIT: metre

    DEFINITION:
      vertical_distance_below_declared_reference_level
  }

  ENTITY MeasuredDepth {
    TYPE: PathLengthQuantity
    SYMBOL: MD
    SI_UNIT: metre

    DEFINITION:
      distance_measured_along_borehole_well_or_other_defined_path

    RULE:
      measured_depth != true_vertical_depth_for_deviated_path
  }

  ENTITY WaterDepth {
    TYPE: VerticalDepthQuantity

    DEFINITION:
      vertical_distance_from_defined_water_surface_or_datum_to_submerged_point_or_bed
  }

  ENTITY GeologicalDepth {
    TYPE: EarthSubsurfaceDepthQuantity

    DEFINITION:
      depth_of_geological_feature_relative_to_declared_surface_or_datum
  }

  UNIT_SYSTEM {
    canonical_unit:
      metre

    common_units:
      metre
      kilometre
      centimetre
      millimetre
      foot

    conversion:
      1 foot = 0.3048 metre

    RULE:
      depth_unit MUST be preserved_with_reference_and_direction_convention
  }

  TERMINOLOGY_MODEL {
    terms:
      depth
      true_vertical_depth
      measured_depth
      subsea_depth
      water_depth
      soil_depth
      burial_depth
      borehole_depth
      thickness
      elevation
      height

    RULE:
      depth_term MUST be resolved_using_reference_surface_direction_and_path_context
  }

  REFERENCE_SURFACE_MODEL {
    possible_references:
      ground_surface
      land_surface
      sea_surface
      mean_sea_level
      chart_datum
      lake_surface
      river_surface
      borehole_datum
      drilling_rig_datum
      ice_surface
      snow_surface
      sediment_water_interface

    RULE:
      numerical_depth_without_reference_surface
      MAY be semantically_incomplete
  }

  SIGN_CONVENTION_MODEL {
    possible_conventions:
      positive_downward
      negative_vertical_coordinate
      unsigned_magnitude_below_reference

    RULE:
      sign_convention MUST be declared_when_combining_depth_with_elevation_or_coordinates
  }

  ELEVATION_DEPTH_MODEL {
    compatible_reference:
      point_elevation =
        reference_surface_elevation - depth
      under_positive_downward_depth_convention

    inverse:
      depth =
        reference_surface_elevation - point_elevation

    REQUIRE:
      same_vertical_datum
      compatible_units
      defined_sign_convention

    RULE:
      depth_and_elevation MUST_NOT be combined_without_common_vertical_reference
  }

  TRUE_VERTICAL_DEPTH_MODEL {
    TVD:
      vertical_separation_between_reference_level_and_target

    for_deviated_path:
      TVD <= MD
      under_non_self_intersecting_downward_path_geometry
      when_MD_measures_total_path_length_from_same_origin

    RULE:
      TVD_is_vertical_component_not_path_length
  }

  MEASURED_DEPTH_MODEL {
    MD:
      integral_along_path(ds)

    trajectory:
      position = position(MD)

    REQUIRE:
      path_origin
      trajectory
      survey_reference

    RULE:
      MD_requires_path_definition
  }

  BOREHOLE_TRAJECTORY_MODEL {
    survey_parameters:
      measured_depth
      inclination
      azimuth

    derived:
      true_vertical_depth
      northing_offset
      easting_offset

    possible_methods:
      minimum_curvature
      balanced_tangential
      radius_of_curvature

    RULE:
      trajectory_calculation_method MUST be preserved
  }

  SOIL_DEPTH_MODEL {
    reference:
      ground_or_soil_surface

    possible_targets:
      sampling_interval
      horizon_boundary
      root_depth
      sensor_depth
      bedrock_depth

    interval:
      depth_top
      depth_bottom

    thickness:
      depth_bottom-depth_top
      under_positive_downward_common_reference

    RULE:
      soil_sample_depth_interval != layer_thickness_without_reference_context
  }

  STRATIGRAPHIC_DEPTH_MODEL {
    possible_bases:
      measured_depth
      true_vertical_depth
      stratigraphic_thickness
      depth_below_surface

    RULE:
      stratigraphic_position_and_geometric_depth
      MUST be distinguished_when_bedding_is_inclined_or_deformed
  }

  BURIAL_DEPTH_MODEL {
    quantity:
      vertical_or_modelled_depth_of_geological_unit_below_surface

    temporal:
      may_change_through_deposition_erosion_uplift_or_compaction

    RULE:
      present_depth != maximum_burial_depth
  }

  WATER_DEPTH_MODEL {
    depth:
      vertical_distance_from_reference_water_surface_or_datum_to_bed_or_target

    dependencies:
      tide
      water_level
      waves
      datum
      vessel_motion

    RULE:
      water_depth MUST preserve_reference_water_level_or_chart_datum
  }

  BATHYMETRY_MODEL {
    bathymetry:
      spatial_field_of_underwater_depth_or_seafloor_elevation

    possible_sources:
      single_beam_echo_sounder
      multibeam_echo_sounder
      lidar_bathymetry
      sonar
      satellite_derived_bathymetry

    RULE:
      bathymetric_depth_and_seafloor_elevation
      require_explicit_vertical_reference
  }

  ACOUSTIC_SOUNDING_MODEL {
    travel_time:
      delta_t

    sound_speed:
      c_s

    simple_two_way_depth:
      d =
        c_s*delta_t/2

    REQUIRE:
      sound_speed_profile_or_assumption
      transducer_draft
      travel_time
      geometry

    RULE:
      sound_speed_variability_and_refraction MAY require_ray_path_correction
  }

  PRESSURE_DEPTH_MODEL {
    hydrostatic:
      delta_P =
        rho*g*d

    inferred_depth:
      d =
        delta_P/(rho*g)
      WHEN rho != 0 AND g != 0

    REQUIRE:
      pressure_reference
      fluid_density
      gravity
      hydrostatic_assumption

    RULE:
      pressure_depth_is_model_derived_and_requires_fluid_and_reference_context
  }

  OCEAN_PRESSURE_DEPTH_MODEL {
    pressure:
      increases_with_depth

    high_accuracy_conversion:
      may_require
        latitude
        seawater_density_or_equation_of_state
        local_gravity
        pressure_reference

    RULE:
      pressure_in_dbar_or_Pa MUST_NOT be relabelled_as_metres_without_conversion_model
  }

  ICE_DEPTH_MODEL {
    possible_quantities:
      ice_thickness
      depth_below_ice_surface
      depth_below_ice_water_interface

    RULE:
      ice_thickness != depth_below_ice_surface
  }

  SNOW_DEPTH_MODEL {
    snow_depth:
      vertical_distance_from_ground_or_reference_surface_to_snow_surface

    RULE:
      snow_depth != snow_water_equivalent
  }

  SEDIMENT_DEPTH_MODEL {
    reference:
      sediment_water_interface
      ground_surface
      core_top

    possible_targets:
      sample
      layer
      horizon
      buried object

    RULE:
      compaction_and_core_recovery MAY affect_depth_interpretation
  }

  CORE_DEPTH_MODEL {
    possible_scales:
      depth_below_seafloor
      depth_below_surface
      core_section_depth
      composite_depth

    RULE:
      core_depth_scale_and_correlation_method MUST be identified
  }

  REMOTE_SENSING_MODEL {
    methods:
      lidar
      radar
      photogrammetry
      satellite_bathymetry

    derived_depth:
      sensor_observation -> retrieval_model -> depth

    RULE:
      remote_sensing_signal != depth_without_geolocation_calibration_and_retrieval
  }

  SPATIAL_MODEL {
    depth_field:
      d = d(x,y)

    gridded_depth:
      bathymetric_or_subsurface_raster

    attributes:
      CRS
      vertical_datum
      horizontal_resolution
      vertical_accuracy
      acquisition_time

    RULE:
      gridded_depth MUST preserve_spatial_reference_and_resolution
  }

  TEMPORAL_MODEL {
    depth_may_change_due_to:
      erosion
      deposition
      sedimentation
      water_level_change
      tide
      glacier_change
      subsidence
      uplift
      excavation

    RULE:
      observation_time SHOULD be preserved_when_reference_or_surface_changes
  }

  THICKNESS_DISTINCTION_MODEL {
    depth:
      position_relative_to_reference

    thickness:
      separation_between_two_boundaries

    layer_thickness:
      may_equal depth_bottom-depth_top
      only_under_compatible_vertical_reference_and_geometry

    RULE:
      depth != thickness
  }

  DISTANCE_DISTINCTION_MODEL {
    depth:
      reference_oriented_spatial quantity

    distance:
      separation_or_path_length_without_necessarily_implying_below_reference

    RULE:
      depth != generic_distance
  }

  RELATIONSHIPS {
    Depth -> HAS_DIMENSION -> Length
    Depth -> MEASURED_IN -> Metre
    Depth -> REFERENCED_TO -> SurfaceOrDatum
    Depth -> MAY_RELATE_TO -> Elevation
    TrueVerticalDepth -> VERTICAL_COMPONENT_OF -> SubsurfacePosition
    MeasuredDepth -> FOLLOWS -> BoreholeOrWellPath
    BoreholeTrajectory -> MAPS -> MeasuredDepthToSpatialPosition
    WaterDepth -> REFERENCED_TO -> WaterSurfaceOrChartDatum
    AcousticTravelTime -> MAPS_TO -> WaterDepthThroughSoundSpeed
    Pressure -> MAPS_TO -> DepthThroughHydrostaticModel
    Bathymetry -> REPRESENTS -> UnderwaterDepthField
    LayerThickness -> RELATES_TO -> BoundaryDepthDifference
  }

  SEMANTIC_EQUIVALENCE {
    "depth" ~= distance_below_declared_reference_under_defined_convention
    "TVD" ~= true_vertical_depth
    "MD" ~= measured_depth

    depth != elevation
    depth != height
    depth != thickness
    depth != generic_distance
    measured_depth != true_vertical_depth
    water_depth != seafloor_elevation_without_reference_conversion
    pressure != depth
    snow_depth != snow_water_equivalent
  }

  CONSTRAINTS {
    depth_dimension = L
    reference_surface_or_datum_must_be_defined = true
    sign_or_direction_convention_must_be_defined = true
    spatial_location_should_be_defined = true
    measured_and_true_vertical_depth_are_not_semantically_equivalent = true
    depth_and_elevation_require_common_vertical_reference_for_conversion = true
    pressure_derived_depth_requires_density_gravity_and_reference_pressure = true
    acoustic_depth_requires_sound_speed_and_travel_time_geometry = true
    thickness_and_depth_are_not_semantically_equivalent = true
    uncertainty_should_include_reference_measurement_and_model_components = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      Depth
      TrueVerticalDepth
      MeasuredDepth
      WaterDepth
      SoilDepth
      GeologicalDepth

    COMMON_METHODS:
      direct_scale_measurement
      borehole_survey
      drilling_measurement
      acoustic_sounding
      pressure_sensor
      lidar
      radar
      photogrammetry
      core_logging
      excavation_or_profile_measurement

    RECORD:
      numerical_value
      unit
      depth_type
      reference_surface
      vertical_datum
      sign_convention
      horizontal_coordinates
      horizontal_CRS
      path_or_trajectory_when_relevant
      measurement_method
      instrument
      pressure_reference_when_relevant
      sound_speed_model_when_relevant
      observation_time
      spatial_resolution_when_gridded
      calibration_state
      uncertainty
      provenance

    UNCERTAINTY:
      measured_or_inferred_depth =
        best_estimate +/- uncertainty
  }

  UNCERTAINTY_MODEL {
    sources:
      instrument_precision
      reference_surface
      vertical_datum
      positioning
      trajectory_survey
      sound_speed
      acoustic_travel_time
      pressure_sensor
      fluid_density
      gravity
      tide_or_water_level
      core_recovery
      surface_classification
      spatial_resolution
      retrieval_model

    PROPAGATION:
      depth_uncertainty
      <- measurement_reference_geometry_environment_and_model_uncertainties
  }

  REASONING_RULES {
    IF reference_surface_elevation_and_depth_known
      AND compatible_datum_and_positive_downward_convention
      THEN point_elevation =
        reference_surface_elevation-depth

    IF reference_surface_elevation_and_point_elevation_known
      AND compatible_datum
      THEN depth =
        reference_surface_elevation-point_elevation

    IF acoustic_two_way_travel_time_and_sound_speed_known
      THEN simple_depth =
        sound_speed*travel_time/2
      UNDER simple_vertical_path_conditions

    IF pressure_difference_density_and_gravity_known
      AND density != 0 AND gravity != 0
      THEN hydrostatic_depth =
        pressure_difference/(density*gravity)

    IF borehole_trajectory_known
      THEN derive_true_vertical_depth_from_measured_depth_inclination_and_azimuth
      USING declared_trajectory_method

    IF layer_top_and_bottom_depth_known
      AND common_reference_and_positive_downward_convention
      THEN vertical_layer_thickness =
        bottom_depth-top_depth

    IF depth_grid_known
      THEN spatial_statistics_or_gradients
      MUST preserve_CRS_vertical_datum_resolution_and_sign_convention
  }

  VALIDATION {
    CHECK depth_type
    CHECK length_unit
    CHECK reference_surface_or_datum
    CHECK sign_convention
    CHECK spatial_location
    CHECK horizontal_CRS
    CHECK depth_vs_elevation
    CHECK depth_vs_thickness
    CHECK measured_vs_true_vertical_depth
    CHECK path_origin_and_trajectory
    CHECK water_level_or_chart_datum_for_water_depth
    CHECK sound_speed_for_acoustic_depth
    CHECK pressure_density_gravity_for_pressure_depth
    CHECK temporal_context
    CHECK spatial_resolution
    CHECK calibration_state
    CHECK uncertainty_representation
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    reference_surface_confidence: 1.00
    elevation_depth_relationship_confidence: 0.99
    acoustic_depth_confidence: 0.98
    pressure_depth_confidence: 0.98
    borehole_trajectory_confidence: 0.97
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when reference surface, sign convention,
      vertical datum, trajectory, sound speed, fluid density,
      observation time, calibration or uncertainty is missing or ambiguous
  }

  UPDATE_MODEL {
    ON new_measurement:
      identify_depth_type
      validate_unit
      attach_reference_surface_or_datum
      attach_sign_convention
      attach_spatial_location_and_CRS
      identify_measurement_method
      attach_path_or_trajectory_when_relevant
      attach_environmental_model_when_relevant
      preserve_original_value_and_reference
      attach_observation_time
      attach_uncertainty
      update_depth_state

    ON reference_surface_change:
      preserve_original_depth
      update_reference_surface
      recompute_depth_or_elevation_when_valid
      record_reference_transformation
      propagate_uncertainty

    ON borehole_survey_update:
      preserve_measured_depth
      update_inclination_and_azimuth
      recompute_true_vertical_depth_and_spatial_position
      preserve_trajectory_method

    ON acoustic_model_revision:
      preserve_raw_travel_time
      preserve_previous_sound_speed_model
      recompute_depth
      update_uncertainty
      update_confidence

    ON pressure_model_revision:
      preserve_raw_pressure
      update_reference_pressure_density_or_gravity
      recompute_depth
      update_uncertainty
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Depth
    canonical_symbol: d
    canonical_dimension: L
    canonical_SI_unit: metre

    interpretation_order:
      identify_depth_quantity
      identify_value
      identify_unit
      identify_reference_surface_or_datum
      identify_sign_or_direction_convention
      identify_spatial_location_and_CRS
      identify_true_vertical_measured_water_soil_or_geological_depth
      identify_path_or_trajectory
      identify_measurement_method
      identify_pressure_or_acoustic_model_when_relevant
      identify_observation_time
      identify_spatial_resolution_when_gridded
      identify_calibration
      identify_uncertainty
      normalize_units
      validate_reference_context
      infer_depth_relationships

    ambiguity_controls:
      distinguish_depth_from_elevation
      distinguish_depth_from_height
      distinguish_depth_from_thickness
      distinguish_depth_from_generic_distance
      distinguish_measured_depth_from_true_vertical_depth
      distinguish_water_depth_from_seafloor_elevation
      distinguish_pressure_from_pressure_derived_depth
      distinguish_snow_depth_from_snow_water_equivalent
      preserve_reference_surface_datum_sign_CRS_trajectory_method_and_time_context
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_Earth_science_depth_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      terminology_model
      reference_surface_model
      sign_convention_model
      elevation_depth_model
      true_vertical_depth_model
      measured_depth_model
      borehole_trajectory_model
      soil_depth_model
      stratigraphic_depth_model
      burial_depth_model
      water_depth_model
      bathymetry_model
      acoustic_sounding_model
      pressure_depth_model
      ocean_pressure_depth_model
      ice_depth_model
      snow_depth_model
      sediment_depth_model
      core_depth_model
      remote_sensing_model
      spatial_model
      temporal_model
      thickness_distinction_model
      distance_distinction_model
      relationships
      constraints
      measurement_model
      uncertainty_model
      reasoning_rules
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      depth_type_definition_changes
      reference_surface_or_datum_changes
      sign_convention_changes
      borehole_trajectory_model_changes
      acoustic_or_pressure_depth_model_changes
      bathymetric_or_remote_sensing_model_changes
      spatial_or_temporal_reference_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW