# ⚛  L1 Principle — Earthquake Source Inversion — finite-fault slip

**ID:** `L1-278` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geophysics — *Finite-fault slip from teleseismic + strong-motion*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D slip distribution
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554052

---

## 🧠 1. Introduction

**Earthquake Source Inversion — finite-fault slip** is a **linear inverse problem** whose unknown lives in **2D slip distribution** space, within the **Finite-fault slip from teleseismic + strong-motion** sub-domain of **Geophysics**.

Measurements consist of acoustic pressure waves recorded by transducers via a **teleseismic strong motion gps** sensing mechanism.

The forward operator applies, in order: L · green function operator; L · source time operator; L · linearize operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Ill-posed for finite-fault; regularization essential.

## ⚙ 2. Forward Model

Physical chain: **x** → L · green function → L · source time → L · linearize → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.linearize` `L.source_time` `L.green_function` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.green_function` | L · green function operator |
| `L.source_time` | L · source time operator |
| `L.linearize` | L · linearize operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geophysics |
| Sub domain | Finite-fault slip from teleseismic + strong-motion |
| Carrier | acoustic |
| Problem class | linear_inverse |
| Solution space | 2D_slip_distribution |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 10 |
| L dag | 3.7 |

## 📡 4. Measurement Model

Ill-posed for finite-fault; regularization essential.

| Metric | Value |
|---|---|
| Metric | slip_correlation_percent |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `finite_fault` · **Forward operator:** `finite_fault_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 25 |
| N samples | — | 2048 |
| N stations | — | 50 |
| N subfaults | — | 200 |
| Fault geometry error | — | 0 |
| Green function error | — | 0.1 |
| Rupture velocity error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N samples | — | 100 – 65536 |
| N stations | — | 5 – 1000 |
| N subfaults | — | 10 – 10000 |
| Fault geometry error | — | 0.0 – 0.3 |
| Green function error | — | 0.0 – 0.3 |
| Rupture velocity error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 25.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **slip_correlation_percent**, with κ = `800` and δ = `10`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x55689a911261e3aeeaffd3e2690ae9308a5d7eb6f9a6c2eb1d34d8e9350a8e86`
- **Chain tx hash:** `0xe5f82a61a0e02220a4d679fff313c81226ad9c7dc6e391fad773b37c4826c2eb`
- **Chain block:** `41554052`

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## File Mapping

This bundle consists of: `L1-278.md`, `L1-278.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-278.md` | Source of truth — edit this | Human or LLM |
| `L1-278.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 `L1-278`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._