# ⚛  L1 Principle — Controlled-Source EM (CSEM) — resistivity for hydrocarbons

**ID:** `L1-282` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geophysics — *Marine CSEM for hydrocarbon reservoirs*
> **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D resistivity field
> **📡 Carrier:** em · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554064

---

## 🧠 1. Introduction

**Controlled-Source EM (CSEM) — resistivity for hydrocarbons** is a **nonlinear inverse problem** whose unknown lives in **3D resistivity field** space, within the **Marine CSEM for hydrocarbon reservoirs** sub-domain of **Geophysics**.

Measurements consist of electromagnetic field measurements via a **marine emf receivers** sensing mechanism.

The forward operator applies, in order: L · em dipole source operator; L · diffuse through seafloor operator; L · frequency domain operator; integration over a band of frequencies.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · em dipole source → L · diffuse through seafloor → L · frequency domain → Frequency integration → **y** (detector).

```
y = ∫dω `L.frequency_domain` `L.diffuse_through_seafloor` `L.em_dipole_source` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.em_dipole_source` | L · em dipole source operator |
| `L.diffuse_through_seafloor` | L · diffuse through seafloor operator |
| `L.frequency_domain` | L · frequency domain operator |
| `int.frequency` | Integration over a band of frequencies |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geophysics |
| Sub domain | Marine CSEM for hydrocarbon reservoirs |
| Carrier | em |
| Problem class | nonlinear_inverse |
| Solution space | 3D_resistivity_field |
| Noise model | gaussian |
| Integration axis | frequency |
| Difficulty delta | 5 |
| L dag | 3.3 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | resistivity_rel_error_percent |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `csem` · **Forward operator:** `csem_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 25 |
| N freqs | — | 5 |
| N stations | — | 30 |
| Seawater sigma error | — | 0 |
| Source attitude error | — | 0 |
| Air wave contamination | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N freqs | — | 1 – 30 |
| N stations | — | 5 – 1000 |
| Seawater sigma error | — | 0.0 – 0.1 |
| Source attitude error | — | 0.0 – 0.1 |
| Air wave contamination | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 7.0

| Metric | Range |
|---|---|
| Res rel | 0.5 – 40.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **resistivity_rel_error_percent**, with κ = `600` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xa5d67e05b104284f203944d970e55dcb6f56ec2381d6427ada8eaf70b8ea4e25`
- **Chain tx hash:** `0xe5bb46b459184721f2c4d7e21baae231c46f97e28de60bdaf1562f59d4f8b3b8`
- **Chain block:** `41554064`

---

## File Mapping

This bundle consists of: `L1-282.md`, `L1-282.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-282.md` | Source of truth — edit this | Human or LLM |
| `L1-282.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 `L1-282`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._