L1 ⚛ L1-283 ⊙ Testnet

Electrical Resistivity Tomography (ERT) — near-surface

Geophysics · DC-resistivity near-surface imaging

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⬇ L1-283.md

# ⚛ L1 Principle — Electrical Resistivity Tomography (ERT) — near-surface **ID:** `L1-283` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *DC-resistivity near-surface imaging* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D resistivity shallow > **📡 Carrier:** em · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554064 --- ## 🧠 1. Introduction **Electrical Resistivity Tomography (ERT) — near-surface** is a **nonlinear inverse problem** whose unknown lives in **3D resistivity shallow** space, within the **DC-resistivity near-surface imaging** sub-domain of **Geophysics**. Measurements consist of electromagnetic field measurements via a **dc electrodes** sensing mechanism. The forward operator applies, in order: L · current injection operator; L · poisson steady operator; L · regularize operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · current injection → L · poisson steady → L · regularize → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.regularize` `L.poisson_steady` `L.current_injection` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.current_injection` | L · current injection operator | | `L.poisson_steady` | L · poisson steady operator | | `L.regularize` | L · regularize operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | DC-resistivity near-surface imaging | | Carrier | em | | Problem class | nonlinear_inverse | | Solution space | 3D_resistivity_shallow | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.2 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | res_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `ert` · **Forward operator:** `ert_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 32 | | Snr db | dB | 30 | | N electrodes | — | 64 | | N quadrupoles | — | 1000 | | Topography error | — | 0 | | Anisotropy unmodelled | — | 0 | | Electrode contact error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 16 – 1024 | | W | px | 16 – 1024 | | Z | — | 4 – 256 | | Snr db | dB | 0 – 40 | | N electrodes | — | 4 – 1024 | | N quadrupoles | — | 10 – 100000 | | Topography error | — | 0.0 – 0.2 | | Anisotropy unmodelled | — | 0.0 – 0.3 | | Electrode contact error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 6.0 | Metric | Range | |---|---| | Res rel | 0.5 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **res_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:** `0x8c71edc363adfce30932b06cb4847ed79fcf552d0e5bfa557f23a437971b01f8` - **Chain tx hash:** `0x2ea0029752f99ab055ac52493ec723eabb8a24a3ea3cccd7d5a2802e6c99fd71` - **Chain block:** `41554064` --- ## File Mapping This bundle consists of: `L1-283.md`, `L1-283.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-283.md` | Source of truth — edit this | Human or LLM | | `L1-283.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 `L1-283`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-283.md).
Regenerate L1-283.json so every field matches the Markdown.
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L2-283-001 Electrical Resistivity Tomography (ERT) — near-surface Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-283",
  "chain_block": 41554064,
  "chain_hash": "0x8c71edc363adfce30932b06cb4847ed79fcf552d0e5bfa557f23a437971b01f8",
  "chain_tx_hash": "0x2ea0029752f99ab055ac52493ec723eabb8a24a3ea3cccd7d5a2802e6c99fd71",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "res_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "res_rel_error_percent",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "em",
    "difficulty_delta": 5,
    "domain": "Geophysics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.current_injection",
      "L.poisson_steady",
      "L.regularize",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "dc_electrodes",
    "solution_space": "3D_resistivity_shallow",
    "sub_domain": "DC-resistivity near-surface imaging",
    "title": "Electrical Resistivity Tomography (ERT) \u2014 near-surface"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "ert_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_electrodes",
      "N_quadrupoles",
      "SNR_dB",
      "electrode_contact_error",
      "topography_error",
      "anisotropy_unmodelled",
      "electrode_contact_error",
      "topography_error",
      "anisotropy_unmodelled"
    ],
    "allowed_problem_classes": [
      "ert"
    ],
    "center_spec": {
      "epsilon_fn_center": "6.0",
      "forward_operator": "ert_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 128,
        "N_electrodes": 64,
        "N_quadrupoles": 1000,
        "SNR_dB": 30,
        "W": 128,
        "Z": 32,
        "anisotropy_unmodelled": 0.0,
        "electrode_contact_error": 0.0,
        "topography_error": 0.0
      },
      "problem_class": "ert"
    },
    "epsilon_bounds": {
      "res_rel": [
        0.5,
        40.0
      ]
    },
    "omega_bounds": {
      "H": [
        16,
        1024
      ],
      "N_electrodes": [
        4,
        1024
      ],
      "N_quadrupoles": [
        10,
        100000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        16,
        1024
      ],
      "Z": [
        4,
        256
      ],
      "anisotropy_unmodelled": [
        0.0,
        0.3
      ],
      "electrode_contact_error": [
        0.0,
        0.2
      ],
      "topography_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "DC-resistivity near-surface imaging",
  "title": "Electrical Resistivity Tomography (ERT) \u2014 near-surface"
}

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