# ⚛  L1 Principle — Tsunami Propagation — shallow-water wave simulation

**ID:** `L1-289` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geophysics — *Nonlinear shallow-water tsunami*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** tsunami wave height field
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554065

---

## 🧠 1. Introduction

**Tsunami Propagation — shallow-water wave simulation** is a **linear inverse problem** whose unknown lives in **tsunami wave height field** space, within the **Nonlinear shallow-water tsunami** sub-domain of **Geophysics**.

Measurements consist of acoustic pressure waves recorded by transducers via a **tide gauges dart** sensing mechanism.

The forward operator applies, in order: L · initial conditions operator; L · shallow water operator; L · runup 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 · initial conditions → L · shallow water → L · runup → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.runup` `L.shallow_water` `L.initial_conditions` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.initial_conditions` | L · initial conditions operator |
| `L.shallow_water` | L · shallow water operator |
| `L.runup` | L · runup operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geophysics |
| Sub domain | Nonlinear shallow-water tsunami |
| Carrier | acoustic |
| Problem class | linear_inverse |
| Solution space | tsunami_wave_height_field |
| 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 | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `tsunami_swe` · **Forward operator:** `tsunami_swe_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 1024 |
| W | px | 1024 |
| Snr db | dB | 25 |
| N times | — | 1000 |
| Source error | — | 0 |
| Bathymetry error | — | 0 |
| Runup friction error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 8192 |
| W | px | 128 – 8192 |
| Snr db | dB | 0 – 40 |
| N times | — | 100 – 100000 |
| Source error | — | 0.0 – 0.3 |
| Bathymetry error | — | 0.0 – 0.1 |
| Runup friction error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 22.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x68f55924d032c6e8c633d8542b242217ffe3c7b4771a7acceb84b6fcc4d41e3b`
- **Chain tx hash:** `0x8c03d5263b1ab58e94e367b0d6a669b7441e4ed4675c37df769fff8787c0555b`
- **Chain block:** `41554065`

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## File Mapping

This bundle consists of: `L1-289.md`, `L1-289.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-289.md` | Source of truth — edit this | Human or LLM |
| `L1-289.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 `L1-289`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._