L1 ⚛ L1-279 ⊙ Testnet

Gravity Field Inversion — density imaging

Geophysics · 3D gravity inversion for subsurface density

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⬇ L1-279.md

# ⚛ L1 Principle — Gravity Field Inversion — density imaging **ID:** `L1-279` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *3D gravity inversion for subsurface density* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D density anomaly > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554063 --- ## 🧠 1. Introduction **Gravity Field Inversion — density imaging** is a **linear inverse problem** whose unknown lives in **3D density anomaly** space, within the **3D gravity inversion for subsurface density** sub-domain of **Geophysics**. Measurements consist of mechanical vibrations or strain signals via a **gravimeter** sensing mechanism. The forward operator applies, in order: L · newton gravity operator; L · linear forward operator; L · regularize operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Non-unique (Coulomb's inverse potential); requires smoothness/sparsity priors. ## ⚙ 2. Forward Model Physical chain: **x** → L · newton gravity → L · linear forward → L · regularize → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.regularize` `L.linear_forward` `L.newton_gravity` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.newton_gravity` | L · newton gravity operator | | `L.linear_forward` | L · linear forward operator | | `L.regularize` | L · regularize operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | 3D gravity inversion for subsurface density | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | 3D_density_anomaly | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Non-unique (Coulomb's inverse potential); requires smoothness/sparsity priors. | Metric | Value | |---|---| | Metric | density_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `gravity_inversion` · **Forward operator:** `gravity_inversion_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 64 | | Snr db | dB | 30 | | Tidal error | — | 0 | | N observations | — | 1024 | | Background error | — | 0 | | Terrain correction error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Z | — | 8 – 512 | | Snr db | dB | 0 – 40 | | Tidal error | — | 0.0 – 0.2 | | N observations | — | 64 – 100000 | | Background error | — | 0.0 – 0.3 | | Terrain correction error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 4.0 | Metric | Range | |---|---| | Density rel | 0.5 – 30.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **density_rel_error_percent**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x15850d9e58b36d8250c531c5eb127e483c2e7eb40cdb7d431dcd9100df9310ba` - **Chain tx hash:** `0x0e86fd111978b84a8c945285ec30fa19d47e8c817cc965e7f21caed0d504262f` - **Chain block:** `41554063` --- ## File Mapping This bundle consists of: `L1-279.md`, `L1-279.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-279.md` | Source of truth — edit this | Human or LLM | | `L1-279.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 `L1-279`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-279.md).
Regenerate L1-279.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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📋 JSON metadata

{
  "artifact_id": "L1-279",
  "chain_block": 41554063,
  "chain_hash": "0x15850d9e58b36d8250c531c5eb127e483c2e7eb40cdb7d431dcd9100df9310ba",
  "chain_tx_hash": "0x0e86fd111978b84a8c945285ec30fa19d47e8c817cc965e7f21caed0d504262f",
  "domain": "Geophysics",
  "hardness_fn": {
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    "regime": "Non-unique (Coulomb\u0027s inverse potential); requires smoothness/sparsity priors.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Geophysics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
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      "L.linear_forward",
      "L.regularize",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "gravimeter",
    "solution_space": "3D_density_anomaly",
    "sub_domain": "3D gravity inversion for subsurface density",
    "title": "Gravity Field Inversion \u2014 density imaging"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "W",
      "Z",
      "N_observations",
      "SNR_dB",
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      "background_error",
      "terrain_correction_error",
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    ],
    "allowed_problem_classes": [
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    "center_spec": {
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      "forward_operator": "gravity_inversion_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_observations": 1024,
        "SNR_dB": 30,
        "W": 256,
        "Z": 64,
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        "tidal_error": 0.0
      },
      "problem_class": "gravity_inversion"
    },
    "epsilon_bounds": {
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        30.0
      ]
    },
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      "H": [
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        2048
      ],
      "N_observations": [
        64,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "Z": [
        8,
        512
      ],
      "background_error": [
        0.0,
        0.3
      ],
      "terrain_correction_error": [
        0.0,
        0.2
      ],
      "tidal_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "3D gravity inversion for subsurface density",
  "title": "Gravity Field Inversion \u2014 density imaging"
}

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