Earthquake Magnitude Classification (PWDR) L1-522

GeophysicsEarthquake source-parameter inversion with moment-magnitude / Richter-scale categorical readoutδ=5 · advancedL_DAG = 6.3📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

S t a g e 1 (L 1 - 278) : se i s m o g r a p hn e tw or k \to m o m e n t - t e n sor in v er s i o n \to M_{0}, f oc a l m ec hani s m . S t a g e 2 : M w = (2/3) \cdot lo g_{10} (M_{0}) - 10.7; c a t e g or i c a l = s t e p (M w a t [2, 4, 5, 6, 7, 8]); t s u nam i_{w} a r nin g = s t e p (M w a t [6.5, 7.0, 7.5]) .

Earthquake Magnitude Classification (PWDR): wraps L1-278 Earthquake Source Inversion analytical core with deterministic magnitude-scale formulas. Stage 1 (analytical, from L1-278): recover earthquake source parameters (seismic moment M_0, focal mechanism, fault dimensions L*W, average slip D, hypocenter location, origin time) from seismograph network observations via moment-tensor inversion or finite-fault inversion. Stage 2 (deterministic threshold): apply Hanks-Kanamori formula Mw = (2/3) * log10(M_0) - 10.7 to recover moment magnitude; classify into standard bins or compute alternative scales (ML, mb, Ms). Difficulty tier delta = 5 inherited from L1-278. Mismatch parameters: station_coverage_gap, near_field_truncation, hypocenter_localization_error, velocity_model_uncertainty, instrument_response_uncertainty, magnitude_scale_saturation.

L-DAG

L.seismograph_array -> L.waveform_acquisition -> L.moment_tensor_inversion -> L.fault_dimension_estimation -> L.magnitude_formula -> L.magnitude_threshold_classifier -> int.spatial

L.seismograph_arrayL.waveform_acquisitionL.moment_tensor_inversionL.fault_dimension_estimationL.magnitude_formulaL.magnitude_threshold_classifierint.spatial

Well-posedness W

Existence:: true
Uniqueness:: conditional
Stability:: conditional
κ:: 200

Existence inherited from L1-278. Uniqueness conditional on adequate station coverage (azimuthal gap < 180 degrees) and SNR > 10 dB. Stability dominated by velocity_model_uncertainty (~0.1-0.3 Mw bias) and magnitude_scale_saturation (ML saturates at ~7; Mw is preferred for great earthquakes). Joint Hadamard well-posedness for the source-inversion + magnitude-formula forward established by Hanks-Kanamori 1979 (foundational Mw formula), Richter 1935 (foundational ML), Kanamori 1977 (great-earthquake moment paradox), Aki-Richards 2002 (Quantitative Seismology textbook), Vallee 2013 (SCARDEC moment-tensor algorithm), Duputel et al. 2012 (W-phase moment-tensor inversion for tsunami warning).

Solvability C

Solver class:: linear-operator + convex optimisation [moment-tensor inversion, finite-fault slip inversion] + categorical-readout [magnitude scale + bin] | end-to-end deep neural [DeepShakeNet, MagNet] with explicit physics-informed source-inversion regularization
Convergence rate q:: 1
Complexity:: O(N_stations * N_time_samples * N_focal_mechanism_grid) for grid-search moment tensor; faster O(N_stations * log(...)) for Bayesian inversion (e.g., SCARDEC)

Specs (0)

No L2 specs registered yet for this principle.