# ⚛  L1 Principle — Seismic Reflection — post-stack migration and imaging

**ID:** `L1-276` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geophysics — *Reverse-time migration (RTM) of reflection seismology*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D reflectivity image
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554051

---

## 🧠 1. Introduction

**Seismic Reflection — post-stack migration and imaging** is a **linear inverse problem** whose unknown lives in **3D reflectivity image** space, within the **Reverse-time migration (RTM) of reflection seismology** sub-domain of **Geophysics**.

Measurements consist of acoustic pressure waves recorded by transducers via a **hydrophone geophone array** sensing mechanism.

The forward operator applies, in order: isotropic point-source emission model; L · wave propagate operator; L · reverse time migrate operator; pixel-level spatial averaging on the detector.

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

## ⚙ 2. Forward Model

Physical chain: **x** → Source emission → L · wave propagate → L · reverse time migrate → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.reverse_time_migrate` `L.wave_propagate` δ_source x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.source_emit` | Isotropic point-source emission model |
| `L.wave_propagate` | L · wave propagate operator |
| `L.reverse_time_migrate` | L · reverse time migrate operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geophysics |
| Sub domain | Reverse-time migration (RTM) of reflection seismology |
| Carrier | acoustic |
| Problem class | linear_inverse |
| Solution space | 3D_reflectivity_image |
| Noise model | gaussian |
| Integration axis | spatial |
| 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:** `reflection_migration` · **Forward operator:** `reflection_migration_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 1024 |
| W | px | 1024 |
| Z | — | 512 |
| Snr db | dB | 30 |
| N shots | — | 256 |
| N receivers | — | 512 |
| Source pos error | — | 0 |
| Topography error | — | 0 |
| Velocity model error | — | 0 |
| Dipole sensitivity error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 128 – 8192 |
| W | px | 128 – 8192 |
| Z | — | 64 – 4096 |
| Snr db | dB | 0 – 40 |
| N shots | — | 16 – 100000 |
| N receivers | — | 64 – 100000 |
| Source pos error | — | 0.0 – 0.05 |
| Topography error | — | 0.0 – 0.1 |
| Velocity model error | — | 0.0 – 0.2 |
| Dipole sensitivity error | — | 0.0 – 0.2 |

## 🎯 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 = `700` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xe004e27864f2cacd8a95c758f293a705a1be930683fdbbeed1a5d87e7d6fb90e`
- **Chain tx hash:** `0xbe9febbf008ee252420c5ceb9e96fb94f021c3d838becf47fee7602c3bedf139`
- **Chain block:** `41554051`

---

## File Mapping

This bundle consists of: `L1-276.md`, `L1-276.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-276.md` | Source of truth — edit this | Human or LLM |
| `L1-276.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 `L1-276`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._