L1 ⚛ L1-290 ⊙ Testnet

Geothermal Reservoir — coupled thermo-hydraulic inversion

Geophysics · Fractured geothermal reservoir simulation

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⬇ L1-290.md

# ⚛ L1 Principle — Geothermal Reservoir — coupled thermo-hydraulic inversion **ID:** `L1-290` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *Fractured geothermal reservoir simulation* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** permeability temperature 3D > **📡 Carrier:** thermal · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554066 --- ## 🧠 1. Introduction **Geothermal Reservoir — coupled thermo-hydraulic inversion** is a **nonlinear inverse problem** whose unknown lives in **permeability temperature 3D** space, within the **Fractured geothermal reservoir simulation** sub-domain of **Geophysics**. Measurements consist of thermal radiation / temperature measurements via a **well logs tracer** sensing mechanism. The forward operator applies, in order: L · darcy flow operator; L · heat transport operator; L · chem reactive operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · darcy flow → L · heat transport → L · chem reactive → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.chem_reactive` `L.heat_transport` `L.darcy_flow` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.darcy_flow` | L · darcy flow operator | | `L.heat_transport` | L · heat transport operator | | `L.chem_reactive` | L · chem reactive operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | Fractured geothermal reservoir simulation | | Carrier | thermal | | Problem class | nonlinear_inverse | | Solution space | permeability_temperature_3D | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 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:** `geothermal` · **Forward operator:** `geothermal_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N cells | — | 10000 | | N times | — | 500 | | N wells | — | 10 | | Rock cp error | — | 0 | | Porosity error | — | 0 | | Permeability error | — | 0 | | Fracture mapping error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N cells | — | 100 – 1000000 | | N times | — | 10 – 100000 | | N wells | — | 1 – 100 | | Rock cp error | — | 0.0 – 0.1 | | Porosity error | — | 0.0 – 0.1 | | Permeability error | — | 0.0 – 0.3 | | Fracture mapping error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `560` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2df00bf23c2e75617fca596ffabf53ecc9066c00fc8850e01a866be9ab9e73d9` - **Chain tx hash:** `0x822afd28bc37e9206b84fc72073b169da6c121d2f48cae4fbff7839c5a849333` - **Chain block:** `41554066` --- ## File Mapping This bundle consists of: `L1-290.md`, `L1-290.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-290.md` | Source of truth — edit this | Human or LLM | | `L1-290.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 `L1-290`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-290.md).
Regenerate L1-290.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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L2-290-001 Geothermal Reservoir — coupled thermo-hydraulic inversion Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-290",
  "chain_block": 41554066,
  "chain_hash": "0x2df00bf23c2e75617fca596ffabf53ecc9066c00fc8850e01a866be9ab9e73d9",
  "chain_tx_hash": "0x822afd28bc37e9206b84fc72073b169da6c121d2f48cae4fbff7839c5a849333",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 560,
    "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": 3.5,
    "carrier": "thermal",
    "difficulty_delta": 5,
    "domain": "Geophysics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.darcy_flow",
      "L.heat_transport",
      "L.chem_reactive",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "well_logs_tracer",
    "solution_space": "permeability_temperature_3D",
    "sub_domain": "Fractured geothermal reservoir simulation",
    "title": "Geothermal Reservoir \u2014 coupled thermo-hydraulic inversion"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "geothermal_forward"
    ],
    "allowed_omega_dimensions": [
      "N_cells",
      "N_wells",
      "N_times",
      "SNR_dB",
      "permeability_error",
      "porosity_error",
      "rock_cp_error",
      "fracture_mapping_error",
      "permeability_error",
      "porosity_error",
      "rock_cp_error",
      "fracture_mapping_error"
    ],
    "allowed_problem_classes": [
      "geothermal"
    ],
    "center_spec": {
      "epsilon_fn_center": "20.0",
      "forward_operator": "geothermal_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_cells": 10000,
        "N_times": 500,
        "N_wells": 10,
        "SNR_dB": 30,
        "fracture_mapping_error": 0.0,
        "permeability_error": 0.0,
        "porosity_error": 0.0,
        "rock_cp_error": 0.0
      },
      "problem_class": "geothermal"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_cells": [
        100,
        1000000
      ],
      "N_times": [
        10,
        100000
      ],
      "N_wells": [
        1,
        100
      ],
      "SNR_dB": [
        0,
        40
      ],
      "fracture_mapping_error": [
        0.0,
        0.3
      ],
      "permeability_error": [
        0.0,
        0.3
      ],
      "porosity_error": [
        0.0,
        0.1
      ],
      "rock_cp_error": [
        0.0,
        0.1
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Fractured geothermal reservoir simulation",
  "title": "Geothermal Reservoir \u2014 coupled thermo-hydraulic inversion"
}

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