L1 ⚛ L1-274 ⊙ Testnet

Surface Wave Dispersion — shallow Vs profile inversion

Geophysics · Rayleigh/Love wave phase-velocity dispersion

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⬇ L1-274.md

# ⚛ L1 Principle — Surface Wave Dispersion — shallow Vs profile inversion **ID:** `L1-274` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *Rayleigh/Love wave phase-velocity dispersion* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 1D shear velocity > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554051 --- ## 🧠 1. Introduction **Surface Wave Dispersion — shallow Vs profile inversion** is a **nonlinear inverse problem** whose unknown lives in **1D shear velocity** space, within the **Rayleigh/Love wave phase-velocity dispersion** sub-domain of **Geophysics**. Measurements consist of acoustic pressure waves recorded by transducers via a **geophones** sensing mechanism. The forward operator applies, in order: L · mass stiffness 1D operator; L · eigenvalue operator; L · dispersion match operator; integration over a band of frequencies. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · mass stiffness 1D → L · eigenvalue → L · dispersion match → Frequency integration → **y** (detector). ``` y = ∫dω `L.dispersion_match` `L.eigenvalue` `L.mass_stiffness_1D` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.mass_stiffness_1D` | L · mass stiffness 1d operator | | `L.eigenvalue` | L · eigenvalue operator | | `L.dispersion_match` | L · dispersion match operator | | `int.frequency` | Integration over a band of frequencies | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | Rayleigh/Love wave phase-velocity dispersion | | Carrier | acoustic | | Problem class | nonlinear_inverse | | Solution space | 1D_shear_velocity | | Noise model | gaussian | | Integration axis | frequency | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | Vs_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `masw` · **Forward operator:** `masw_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | N freqs | — | 60 | | N layers | — | 10 | | Vp prior error | — | 0 | | Density prior error | — | 0 | | Higher mode contamination | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N freqs | — | 10 – 500 | | N layers | — | 2 – 100 | | Vp prior error | — | 0.0 – 0.2 | | Density prior error | — | 0.0 – 0.1 | | Higher mode contamination | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 4.0 | Metric | Range | |---|---| | Vs rel error | 0.5 – 30.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **Vs_rel_error_percent**, with κ = `400` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7601231eefd5fa4fb5049dd796a20ce6098d58c50d7aca10ae839cfdcdc640fe` - **Chain tx hash:** `0x1d67b90b95c8e1dc970adcb7495b08364611afc2a4c8e6f79779e9b50df4d84b` - **Chain block:** `41554051` --- ## File Mapping This bundle consists of: `L1-274.md`, `L1-274.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-274.md` | Source of truth — edit this | Human or LLM | | `L1-274.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 `L1-274`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-274.md).
Regenerate L1-274.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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L2-274-001 Surface Wave Dispersion — shallow Vs profile inversion Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-274",
  "chain_block": 41554051,
  "chain_hash": "0x7601231eefd5fa4fb5049dd796a20ce6098d58c50d7aca10ae839cfdcdc640fe",
  "chain_tx_hash": "0x1d67b90b95c8e1dc970adcb7495b08364611afc2a4c8e6f79779e9b50df4d84b",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 400,
    "metric": "Vs_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "Vs_rel_error_percent",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Geophysics",
    "integration_axis": "frequency",
    "noise_model": "gaussian",
    "primitives": [
      "L.mass_stiffness_1D",
      "L.eigenvalue",
      "L.dispersion_match",
      "int.frequency"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "geophones",
    "solution_space": "1D_shear_velocity",
    "sub_domain": "Rayleigh/Love wave phase-velocity dispersion",
    "title": "Surface Wave Dispersion \u2014 shallow Vs profile inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "masw_forward"
    ],
    "allowed_omega_dimensions": [
      "N_layers",
      "N_freqs",
      "SNR_dB",
      "vp_prior_error",
      "density_prior_error",
      "higher_mode_contamination",
      "vp_prior_error",
      "density_prior_error",
      "higher_mode_contamination"
    ],
    "allowed_problem_classes": [
      "masw"
    ],
    "center_spec": {
      "epsilon_fn_center": "4.0",
      "forward_operator": "masw_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_freqs": 60,
        "N_layers": 10,
        "SNR_dB": 25,
        "density_prior_error": 0.0,
        "higher_mode_contamination": 0.0,
        "vp_prior_error": 0.0
      },
      "problem_class": "masw"
    },
    "epsilon_bounds": {
      "Vs_rel_error": [
        0.5,
        30.0
      ]
    },
    "omega_bounds": {
      "N_freqs": [
        10,
        500
      ],
      "N_layers": [
        2,
        100
      ],
      "SNR_dB": [
        0,
        40
      ],
      "density_prior_error": [
        0.0,
        0.1
      ],
      "higher_mode_contamination": [
        0.0,
        0.3
      ],
      "vp_prior_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Rayleigh/Love wave phase-velocity dispersion",
  "title": "Surface Wave Dispersion \u2014 shallow Vs profile inversion"
}

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