# ⚛  L1 Principle — Seismic Rock Physics (Gassmann)

**ID:** `L1-463` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Petroleum Engineering — *Rock physics*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** elastic moduli vector
> **📡 Carrier:** acoustic · **🌫 Noise:** measurement gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555280

---

## 🧠 1. Introduction

**Seismic Rock Physics (Gassmann)** is a **parameter-estimation problem** whose unknown lives in **elastic moduli vector** space, within the **Rock physics** sub-domain of **Petroleum Engineering**.

Measurements consist of acoustic pressure waves recorded by transducers via a **elastic moduli fluid substitution** sensing mechanism.

The forward operator applies, in order: gradient / divergence with respect to position; S · hertz mindlin · dry frame operator; O · chi2 · elastic moduli operator.

Observations are corrupted by measurement gaussian. Existence of the recovered elastic_moduli_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); clay_mineral_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → Spatial derivative → S · hertz mindlin · dry frame → O · chi2 · elastic moduli → **y** (detector).

```
y = `O.chi2.elastic_moduli` `S.hertz_mindlin.dry_frame` ∇ x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `D.space` | Gradient / divergence with respect to position |
| `S.hertz_mindlin.dry_frame` | S · hertz mindlin · dry frame operator |
| `O.chi2.elastic_moduli` | O · chi2 · elastic moduli operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Petroleum Engineering |
| Sub domain | Rock physics |
| Carrier | acoustic |
| Problem class | parameter_estimation |
| Solution space | elastic_moduli_vector |
| Noise model | measurement_gaussian |
| Integration axis | pore_fluid |
| Difficulty delta | 5 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered elastic_moduli_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 100); clay_mineral_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | Vp_prediction_RMSE_m_s |
| Secondary | AI_acoustic_impedance_RMSE |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `elastic_moduli_fluid_substitution`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Porosity phi | — | 0.2 |
| Saturation sw | — | 0.8 |
| Clay content vcl | — | 0.1 |
| Differential pressure mpa | — | 30 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Porosity phi | — | 0.05 – 0.4 |
| Saturation sw | — | 0.0 – 1.0 |
| Clay content vcl | — | 0.0 – 0.6 |
| Differential pressure mpa | — | 5 – 80 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 50 Vp_prediction_RMSE_m_s

| Metric | Range |
|---|---|
| Vp prediction rmse m s | 10 – 300 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **Vp_prediction_RMSE_m_s**, with κ = `2000` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x1041b6a1a39b244bfc47046352ed96e8ea39fae839bbe3183cebd185ce8f55d5`
- **Chain tx hash:** `0x73645b99894a20b30683099759a9380d5dba1e4fa6faa88b6d3d04e3e767cd0f`
- **Chain block:** `41555280`

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## File Mapping

This bundle consists of: `L1-463.md`, `L1-463.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-463.md` | Source of truth — edit this | Human or LLM |
| `L1-463.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 `L1-463`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._