Seismic Wave Ontology

FLOW ALGEBRA
SEISMIC WAVE ONTOLOGY
Kireth Semantic Library | Entity Graph / Physical Entities / Wave Entities
Version: 1.1 | Date: 2026-10-12 | Language: en-GB
Authors: Mark Higgins — Sky (Recursive AI)
Source URL: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/wave-entities/seismic-wave-ontology.html
Source status: Independent scientific synthesis; live page not verified.

01. PURPOSE
Represent seismic disturbances, propagation media, wave modes, observations, and inference as typed, checkable relationships.

02. SCOPE
Covers elastic seismic body waves, surface waves, sources, travel times, attenuation, interfaces, measurement, and inverse problems. Fluid and anisotropic cases require explicit models.

03. CORE TYPES
TYPE PhysicalEntity
TYPE ElasticMedium <: PhysicalEntity
TYPE SeismicSource <: PhysicalEntity
TYPE SeismicWave <: WavePhenomenon
TYPE BodyWave <: SeismicWave
TYPE SurfaceWave <: SeismicWave
TYPE PWave <: BodyWave
TYPE SWave <: BodyWave
TYPE LoveWave <: SurfaceWave
TYPE RayleighWave <: SurfaceWave
TYPE Interface <: PhysicalEntity
TYPE SeismicStation <: MeasurementDevice
TYPE Seismogram <: Observation
TYPE WaveArrival <: Observation
TYPE MaterialParameter
TYPE VelocityModel
TYPE EarthquakeEvent <: SeismicSource
TYPE Uncertainty

04. TYPE CONSTRAINTS
SeismicWave requires a propagation model and a disturbance in a physical medium.
PWave is a compressional mode in isotropic elastic solids; it also propagates in fluids.
SWave is a shear mode in elastic solids; ordinary fluids have no propagating bulk elastic shear waves.
LoveWave requires a suitable layered elastic structure; RayleighWave is a surface mode.
Wave type must not be inferred from frequency alone.

05. RELATIONSHIPS
originates_from(SeismicWave, SeismicSource)
propagates_through(SeismicWave, ElasticMedium)
interacts_with(SeismicWave, Interface)
recorded_by(SeismicWave, SeismicStation)
produces(SeismicWave, Seismogram)
has_arrival(Seismogram, WaveArrival)
constrained_by(SeismicWave, VelocityModel)
characterised_by(SeismicWave, MaterialParameter)
inferred_from(VelocityModel, Observation)

06. QUANTITIES AND UNITS
Displacement u [m]; velocity v [m s^-1]; acceleration a [m s^-2].
Density rho [kg m^-3]; bulk modulus K [Pa]; shear modulus mu [Pa].
P-wave speed alpha [m s^-1]; S-wave speed beta [m s^-1].
Frequency f [Hz]; period T [s]; wavelength lambda [m]; angular frequency omega [rad s^-1].
Travel time t [s]; distance L [m]; attenuation quality factor Q [dimensionless].

07. ELASTIC WAVE EQUATION
In a homogeneous isotropic linear elastic solid with constant parameters:
rho * d2u/dt2 = (lambda_L + mu) grad(div u) + mu laplacian(u) + body_force.
lambda_L is the first Lame parameter, not wavelength.
Assumptions: infinitesimal strain, linear constitutive law, local continuum mechanics.

08. WAVE SPEEDS
alpha = sqrt((K + 4*mu/3)/rho) = sqrt((lambda_L + 2*mu)/rho).
beta = sqrt(mu/rho).
For stable isotropic solids with K>0, mu>0, rho>0: alpha > beta > 0.
For an ideal inviscid fluid, mu=0 and the elastic bulk shear mode does not propagate.

09. MODE DECOMPOSITION
Helmholtz decomposition: u = grad(phi) + curl(psi), with suitable smoothness and boundary conditions.
Compressional potential phi describes P-wave motion; solenoidal potential psi describes S-wave motion in isotropic elastic solids.

10. BODY WAVES
P waves have particle motion parallel to local propagation direction in the ideal isotropic plane-wave case.
S waves have particle motion perpendicular to local propagation direction in the ideal isotropic plane-wave case.
S waves can be resolved into SH and SV components relative to a selected propagation plane.

11. SURFACE WAVES
Rayleigh waves: coupled longitudinal and vertical shear motion with depth-dependent amplitudes.
Love waves: horizontally polarised shear motion supported by appropriate layered media.
Surface-wave speeds and dispersion depend on elastic structure and frequency.
Do not assert a universal Rayleigh/Love speed ordering without specifying a model.

12. WAVE RELATIONS
For a monochromatic plane wave in a nondispersive medium: v_phase = f*lambda = omega/k.
Period T=1/f for f>0; k=2*pi/lambda.
In dispersive media group velocity d(omega)/dk can differ from phase velocity omega/k.

13. SOURCE REPRESENTATION
Earthquake source may be parameterised by origin time, hypocentre, moment tensor, source-time function and uncertainty.
Seismic moment M0 = mu*A*D for a simplified planar shear dislocation with uniform rigidity and average slip.
Moment magnitude Mw = (2/3)*(log10(M0 in N m)-9.1), conventional approximate SI relation.

14. PROPAGATION AND TRAVEL TIME
In a constant-speed medium along a straight path: t = L/v.
In heterogeneous media: t = integral_path ds / v(x) under ray-theory assumptions.
Rays satisfy Fermat's stationary-time principle within an appropriate high-frequency model.

15. INTERFACES
Reflection, refraction and mode conversion can occur at material interfaces.
Snell ray-parameter relation: sin(theta_i)/v_i = sin(theta_t)/v_t for compatible isotropic plane-wave modes.
Critical angles and evanescent fields require physically admissible boundary solutions.

16. ATTENUATION
Amplitude decreases through geometrical spreading, scattering and intrinsic absorption.
For a simple constant-Q plane-wave approximation: A(x) ~ A0*exp(-pi*f*x/(Q*v)).
This approximation must not be substituted for a general attenuation law.

17. OBSERVATION MODEL
recorded_trace(t) = instrument_response * ground_motion(t) + noise(t).
The asterisk denotes convolution here, not scalar multiplication.
A seismic station may record displacement, velocity or acceleration depending on instrumentation and processing.

18. ARRIVAL PICKING
Arrival pick = estimated onset or phase arrival with time uncertainty.
P arrival often precedes S arrival for common solid-Earth paths, but observed phase order depends on source, path and phase definitions.
Phase classification requires waveform and travel-time evidence.

19. INFERENCE RULES
RULE R01: isotropic_solid(m) AND rho(m)>0 AND mu(m)>0 -> supports_bulk_S_wave(m).
RULE R02: fluid(m) AND mu(m)=0 -> NOT supports_bulk_elastic_S_wave(m).
RULE R03: same_straight_path(P,S) AND alpha>beta -> travel_time(P)<travel_time(S).
RULE R04: recorded_arrival(a) AND model_consistent(a,phase) -> candidate_phase(a,phase), not confirmed_phase.
RULE R05: interface_crossing(w,i) -> evaluate_reflection_refraction_mode_conversion(w,i).
RULE R06: layered_elastic_medium(m) -> surface_wave_dispersion_possible(m).
RULE R07: insufficient_station_geometry -> location_nonunique_possible.

20. WORKED EXAMPLE: VELOCITIES
Assume rho=2500 kg/m^3, K=40 GPa, mu=30 GPa.
alpha=sqrt((40e9+40e9)/2500)=sqrt(32e6)=5656.85 m/s.
beta=sqrt(30e9/2500)=sqrt(12e6)=3464.10 m/s.
For L=100 km straight paths: tP~17.68 s; tS~28.87 s.
Difference ~11.19 s. Values are idealised and not an earthquake-location solution.

21. WORKED EXAMPLE: FREQUENCY
If v_phase=3000 m/s and f=5 Hz in a nondispersive model, lambda=600 m.

22. CONSERVATION AND BOUNDARIES
At a welded solid-solid interface, displacement and traction continuity apply in the ideal elastic model.
Energy flux accounting must include reflected, transmitted and converted modes.
Absorption and inelastic processes require an extended energy balance.

23. NUMERICAL METHODS
Finite difference, finite element, spectral element and pseudo-spectral methods approximate wave equations.
Numerical stability, dispersion, absorbing boundaries and mesh resolution require validation.
Synthetic seismograms must declare model, source, discretisation and solver assumptions.

24. INVERSE PROBLEMS
Seismic tomography infers velocity or related parameters from travel times or waveforms.
Inversion is generally nonunique and sensitive to regularisation, data coverage and modelling error.
Do not treat inferred subsurface structure as direct observation.

25. SEMANTIC EQUIVALENCE
P-wave ~ primary/compressional body wave, context dependent.
S-wave ~ secondary/shear body wave, context dependent.
Seismogram != seismic wave; observation differs from physical process.
Seismic moment != moment magnitude; related by a logarithmic convention.
Phase velocity != group velocity in general.

26. KNOWLEDGE GRAPH ASSERTIONS
PWave SUBCLASS_OF BodyWave.
SWave SUBCLASS_OF BodyWave.
RayleighWave SUBCLASS_OF SurfaceWave.
LoveWave SUBCLASS_OF SurfaceWave.
SeismicWave RELATED_TO ElasticMedium.
Seismogram OBSERVES SeismicWave.
VelocityModel CONSTRAINS TravelTime.

27. VALIDATION
CHECK dimensional_consistency for all equations.
CHECK source_event has explicit temporal and spatial reference if location claims are made.
CHECK material parameter units and positivity constraints.
CHECK wave mode is physically supported by medium.
CHECK arrival uncertainty and phase evidence are retained.
CHECK numerical result states approximations and boundary conditions.
CHECK measured, inferred and hypothetical assertions remain distinct.

28. CONFIDENCE
CONFIDENCE is evidence-specific, not a universal fixed score.
Represent: confidence(value:0..1, basis, calibration_method, uncertainty, provenance).
Do not assign empirical confidence without supporting measurements or calibrated inference.

29. FLOW_HASH
FLOW_HASH.algorithm = SHA-256.
FLOW_HASH.canonicalisation = UTF-8, LF newlines, stable field ordering, exclude mutable hash field.
FLOW_HASH.value = COMPUTE_ON_INGEST; no fabricated digest.

30. UPDATE_MODEL
Track semantic version, change log, reviewed equations, source provenance and superseded assertions.
On model changes, recompute derived results and invalidate dependent claims where necessary.

31. AI_CONSUMPTION
Inputs: source parameters, medium properties, model geometry, observations and uncertainties.
Outputs: typed graph assertions, derived travel times, candidate wave phases and traceable inferences.
Require assumption disclosure, unit checking, uncertainty preservation and provenance links.
Reject unsupported categorical claims and extrapolation outside the model domain.

32. RELATED ONTOLOGIES
Wave Ontology; Mechanical Wave Ontology; Sound Wave Ontology; Water Wave Ontology;
Elastic Body Ontology; Deformable Body Ontology; Physical Interaction Ontology;
Earthquake, Geophysics, Seismology, Measurement and Scientific Metadata ontologies.

33. COMPLETENESS
Sections 01 through 33 present. Scientific claims are model-scoped.
END FLOW ALGEBRA — SEISMIC WAVE ONTOLOGY