# ⚛  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._