# ⚛  L1 Principle — Ambient-Noise Tomography — Green-function retrieval

**ID:** `L1-277` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geophysics — *Cross-correlation of ambient seismic noise*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D phase velocity map
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554051

---

## 🧠 1. Introduction

**Ambient-Noise Tomography — Green-function retrieval** is a **linear inverse problem** whose unknown lives in **2D phase velocity map** space, within the **Cross-correlation of ambient seismic noise** sub-domain of **Geophysics**.

Measurements consist of acoustic pressure waves recorded by transducers via a **continuous seismometer** sensing mechanism.

The forward operator applies, in order: L · cross correlate operator; L · green retrieve operator; L · tomographic invert 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 · cross correlate → L · green retrieve → L · tomographic invert → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.tomographic_invert` `L.green_retrieve` `L.cross_correlate` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.cross_correlate` | L · cross correlate operator |
| `L.green_retrieve` | L · green retrieve operator |
| `L.tomographic_invert` | L · tomographic invert operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geophysics |
| Sub domain | Cross-correlation of ambient seismic noise |
| Carrier | acoustic |
| Problem class | linear_inverse |
| Solution space | 2D_phase_velocity_map |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.3 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | c_rel_error_percent |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `ant` · **Forward operator:** `ant_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N days | — | 365 |
| Snr db | dB | 25 |
| N freqs | — | 10 |
| N stations | — | 50 |
| Scattering unmodelled | — | 0 |
| Station pair imbalance | — | 0 |
| Source distribution nonuniform | — | 0.1 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N days | — | 7 – 3650 |
| Snr db | dB | 0 – 40 |
| N freqs | — | 1 – 50 |
| N stations | — | 5 – 5000 |
| Scattering unmodelled | — | 0.0 – 0.3 |
| Station pair imbalance | — | 0.0 – 0.3 |
| Source distribution nonuniform | — | 0.0 – 0.5 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 5.0

| Metric | Range |
|---|---|
| C rel | 0.5 – 30.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **c_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:** `0xc80cca227b15a29210429b8b75e41e2590f9197ec7f4b025e3a6faf56b373a4e`
- **Chain tx hash:** `0x6cc7c9773073bbe621b89e52d95244aed1f1cfc377e8f9b81db2d99ad3e10db2`
- **Chain block:** `41554051`

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## File Mapping

This bundle consists of: `L1-277.md`, `L1-277.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-277.md` | Source of truth — edit this | Human or LLM |
| `L1-277.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 `L1-277`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._