L1 ⚛ L1-522 ⊙ Testnet

Earthquake Magnitude Classification (PWDR)

Geophysics · Earthquake source-parameter inversion with moment-magnitude / Richter-scale categorical readout

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⬇ L1-522.md

# ⚛ L1 Principle — Earthquake Magnitude Classification (PWDR) **ID:** `L1-522` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *Earthquake source-parameter inversion with moment-magnitude / Richter-scale categorical readout* > **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D magnitude scale categorical > **📡 Carrier:** elastic_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554066 --- ## 🧠 1. Introduction **Earthquake Magnitude Classification (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D magnitude scale categorical** space, within the **Earthquake source-parameter inversion with moment-magnitude / Richter-scale categorical readout** sub-domain of **Geophysics**. Measurements consist of elastic waves recorded by seismometers / geophones via a **seismograph with magnitude classifier** sensing mechanism. The forward operator applies, in order: L · seismograph array operator; L · waveform acquisition operator; L · moment tensor inversion operator; L · fault dimension estimation operator; L · magnitude formula operator; L · magnitude threshold classifier operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. 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). ## ⚙ 2. Forward Model Physical chain: **x** → L · seismograph array → L · waveform acquisition → L · moment tensor inversion → L · fault dimension estimation → L · magnitude formula → L · magnitude threshold classifier → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.magnitude_threshold_classifier` `L.magnitude_formula` `L.fault_dimension_estimation` `L.moment_tensor_inversion` `L.waveform_acquisition` `L.seismograph_array` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.seismograph_array` | L · seismograph array operator | | `L.waveform_acquisition` | L · waveform acquisition operator | | `L.moment_tensor_inversion` | L · moment tensor inversion operator | | `L.fault_dimension_estimation` | L · fault dimension estimation operator | | `L.magnitude_formula` | L · magnitude formula operator | | `L.magnitude_threshold_classifier` | L · magnitude threshold classifier operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | Earthquake source-parameter inversion with moment-magnitude / Richter-scale categorical readout | | Carrier | elastic_wave | | Problem class | linear_inverse_with_categorical_readout | | Solution space | 1D_magnitude_scale_categorical | | Noise model | gaussian | | Integration axis | spatial_temporal | | Difficulty delta | 5 | | L dag | 6.3 | ## 📡 4. Measurement Model 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). | Metric | Value | |---|---| | Metric | categorical_accuracy | | Secondary | RMSE_Mw | ## 📏 5. Operating Range (Ω) **Center problem class:** `earthquake_mw_pwdr` · **Forward operator:** `earthquake_magnitude_pwdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | N stations | — | 30 | | Sampling rate hz | Hz | 100 | | Frequency band hz | Hz | 0.01 – 25 | | Station coverage gap | — | 0 | | Near field truncation | — | 0 | | Station distance km range | — | 0 – 1000 | | Magnitude scale saturation | — | 0 | | Velocity model uncertainty | — | 0 | | Hypocenter localization error | — | 0 | | Instrument response uncertainty | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 3 – 50 | | N stations | — | 3 – 500 | | Sampling rate hz | Hz | 20 – 500 | | Station coverage gap | — | 0.0 – 0.6 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.85_accuracy | Metric | Range | |---|---| | Categorical accuracy | 0.5 – 0.99 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **categorical_accuracy**, with κ = `200` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x77766239d0ed2b70cfeaf020e6742d6bf253792347655b5353a3334248508d27` - **Chain tx hash:** `0x94f5ce0765c0f54904044874b4053d57ca94613587f5e01eafe418156d4880ea` - **Chain block:** `41554066` --- ## File Mapping This bundle consists of: `L1-522.md`, `L1-522.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-522.md` | Source of truth — edit this | Human or LLM | | `L1-522.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-522`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-522.md).
Regenerate L1-522.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-522-001 Earthquake Magnitude Classification (PWDR) — Spec Skeleton

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📋 JSON metadata

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  "chain_block": 41554066,
  "chain_hash": "0x77766239d0ed2b70cfeaf020e6742d6bf253792347655b5353a3334248508d27",
  "chain_tx_hash": "0x94f5ce0765c0f54904044874b4053d57ca94613587f5e01eafe418156d4880ea",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 200,
    "metric": "categorical_accuracy",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "name": "primary",
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    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "categorical_accuracy",
    "regime": "Existence inherited from L1-278. Uniqueness conditional on adequate station coverage (azimuthal gap \u003c 180 degrees) and SNR \u003e 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).",
    "secondary": "RMSE_Mw"
  },
  "physics_fingerprint": {
    "L_DAG": 6.3,
    "carrier": "elastic_wave",
    "difficulty_delta": 5,
    "domain": "Geophysics",
    "integration_axis": "spatial_temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.seismograph_array",
      "L.waveform_acquisition",
      "L.moment_tensor_inversion",
      "L.fault_dimension_estimation",
      "L.magnitude_formula",
      "L.magnitude_threshold_classifier",
      "int.spatial"
    ],
    "problem_class": "linear_inverse_with_categorical_readout",
    "sensing_mechanism": "seismograph_with_magnitude_classifier",
    "solution_space": "1D_magnitude_scale_categorical",
    "sub_domain": "Earthquake source-parameter inversion with moment-magnitude / Richter-scale categorical readout",
    "title": "Earthquake Magnitude Classification (PWDR)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "earthquake_magnitude_pwdr_forward",
      "moment_tensor_pwdr_forward",
      "tsunami_warning_pwdr_forward",
      "earthquake_early_warning_pwdr_forward"
    ],
    "allowed_omega_dimensions": [
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      "station_distance_km_range",
      "frequency_band_Hz",
      "sampling_rate_Hz",
      "SNR_dB",
      "station_coverage_gap",
      "near_field_truncation",
      "hypocenter_localization_error",
      "velocity_model_uncertainty",
      "instrument_response_uncertainty",
      "magnitude_scale_saturation"
    ],
    "allowed_problem_classes": [
      "earthquake_mw_pwdr",
      "earthquake_ml_pwdr",
      "earthquake_tsunami_warning_pwdr",
      "earthquake_early_warning_pwdr"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.85_accuracy",
      "forward_operator": "earthquake_magnitude_pwdr_forward",
      "input_format": "multistation_seismogram_with_magnitude_label",
      "omega": {
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        "SNR_dB": 25,
        "frequency_band_Hz": [
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        "instrument_response_uncertainty": 0.0,
        "magnitude_scale_saturation": 0.0,
        "near_field_truncation": 0.0,
        "sampling_rate_Hz": 100,
        "station_coverage_gap": 0.0,
        "station_distance_km_range": [
          0,
          1000
        ],
        "velocity_model_uncertainty": 0.0
      },
      "problem_class": "earthquake_mw_pwdr"
    },
    "epsilon_bounds": {
      "categorical_accuracy": [
        0.5,
        0.99
      ]
    },
    "omega_bounds": {
      "N_stations": [
        3,
        500
      ],
      "SNR_dB": [
        3,
        50
      ],
      "sampling_rate_Hz": [
        20,
        500
      ],
      "station_coverage_gap": [
        0.0,
        0.6
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Earthquake source-parameter inversion with moment-magnitude / Richter-scale categorical readout",
  "title": "Earthquake Magnitude Classification (PWDR)"
}

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