L1 ⚛ L1-293 ⊙ Testnet

Subsurface Temperature — geothermal gradient inversion

Geophysics · Borehole temperature geothermal gradient

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⬇ L1-293.md

# ⚛ L1 Principle — Subsurface Temperature — geothermal gradient inversion **ID:** `L1-293` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *Borehole temperature geothermal gradient* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** temperature depth profile > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554066 --- ## 🧠 1. Introduction **Subsurface Temperature — geothermal gradient inversion** is a **linear inverse problem** whose unknown lives in **temperature depth profile** space, within the **Borehole temperature geothermal gradient** sub-domain of **Geophysics**. Measurements consist of thermal radiation / temperature measurements via a **borehole temperature log** sensing mechanism. The forward operator applies, in order: L · 1d heat conduction operator; L · heat flux operator; L · paleoclimate signal 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 · 1d heat conduction → L · heat flux → L · paleoclimate signal → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.paleoclimate_signal` `L.heat_flux` `L.1d_heat_conduction` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.1d_heat_conduction` | L · 1d heat conduction operator | | `L.heat_flux` | L · heat flux operator | | `L.paleoclimate_signal` | L · paleoclimate signal operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | Borehole temperature geothermal gradient | | Carrier | thermal | | Problem class | linear_inverse | | Solution space | temperature_depth_profile | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `subsurface_temp` · **Forward operator:** `subsurface_temp_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 40 | | N depths | — | 500 | | Terrain error | — | 0 | | Surface temp error | — | 0 | | Thermal conductivity error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 10 – 60 | | N depths | — | 10 – 10000 | | Terrain error | — | 0.0 – 0.2 | | Surface temp error | — | 0.0 – 2.0 | | Thermal conductivity error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 26.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x073104cc47cd67eac1a6e82f351c53bbe2d2cb42fce14686412780fe079deb6e` - **Chain tx hash:** `0x59720e45ebc23ef8d267c0abc6eef0ae15d3189ad4712a0ea5e10b45f46e59d8` - **Chain block:** `41554066` --- ## File Mapping This bundle consists of: `L1-293.md`, `L1-293.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-293.md` | Source of truth — edit this | Human or LLM | | `L1-293.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 `L1-293`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-293.md).
Regenerate L1-293.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-293-001 Subsurface Temperature — geothermal gradient inversion Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-293",
  "chain_block": 41554066,
  "chain_hash": "0x073104cc47cd67eac1a6e82f351c53bbe2d2cb42fce14686412780fe079deb6e",
  "chain_tx_hash": "0x59720e45ebc23ef8d267c0abc6eef0ae15d3189ad4712a0ea5e10b45f46e59d8",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 240,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "thermal",
    "difficulty_delta": 3,
    "domain": "Geophysics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.1d_heat_conduction",
      "L.heat_flux",
      "L.paleoclimate_signal",
      "int.spatial"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "borehole_temperature_log",
    "solution_space": "temperature_depth_profile",
    "sub_domain": "Borehole temperature geothermal gradient",
    "title": "Subsurface Temperature \u2014 geothermal gradient inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "subsurface_temp_forward"
    ],
    "allowed_omega_dimensions": [
      "N_depths",
      "SNR_dB",
      "thermal_conductivity_error",
      "surface_temp_error",
      "terrain_error",
      "thermal_conductivity_error",
      "surface_temp_error",
      "terrain_error"
    ],
    "allowed_problem_classes": [
      "subsurface_temp"
    ],
    "center_spec": {
      "epsilon_fn_center": "26.0",
      "forward_operator": "subsurface_temp_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_depths": 500,
        "SNR_dB": 40,
        "surface_temp_error": 0.0,
        "terrain_error": 0.0,
        "thermal_conductivity_error": 0.0
      },
      "problem_class": "subsurface_temp"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_depths": [
        10,
        10000
      ],
      "SNR_dB": [
        10,
        60
      ],
      "surface_temp_error": [
        0.0,
        2.0
      ],
      "terrain_error": [
        0.0,
        0.2
      ],
      "thermal_conductivity_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Borehole temperature geothermal gradient",
  "title": "Subsurface Temperature \u2014 geothermal gradient inversion"
}

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