L1 ⚛ L1-463 ⊙ Testnet

Seismic Rock Physics (Gassmann)

Petroleum Engineering · Rock physics

⬇ Download bundle 🚀 Submit to mainnet — earn 100 PWM + 5% royalty

Markdown — human-readable source of truth

⚙ auto-generated

⬇ L1-463.md

# ⚛ 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` --- ## 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._

📝 Polish this artifact in your LLM

Download the files on the right.
Paste the Markdown into ChatGPT / Claude / Gemini and edit freely.
Send your edited Markdown back with the prompt below.
Save the regenerated JSON, then submit via /submit.

Prompt to give your LLM

Read the attached Markdown (L1-463.md).
Regenerate L1-463.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

⌥ Hierarchy

Upstream lineage and downstream children

↓ L2 Spec 1 child ▾

L2-463-001 Seismic Rock Physics (Gassmann) — Nominal + Mismatch Specs

⬇ Download bundle

2 files · click to download

📋 JSON metadata

{
  "artifact_id": "L1-463",
  "chain_block": 41555280,
  "chain_hash": "0x1041b6a1a39b244bfc47046352ed96e8ea39fae839bbe3183cebd185ce8f55d5",
  "chain_tx_hash": "0x73645b99894a20b30683099759a9380d5dba1e4fa6faa88b6d3d04e3e767cd0f",
  "domain": "Petroleum Engineering",
  "hardness_fn": {
    "delta": 5,
    "kappa": 2000,
    "metric": "Vp_prediction_RMSE_m_s",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "Vp_prediction_RMSE_m_s",
    "regime": "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.",
    "secondary": "AI_acoustic_impedance_RMSE"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Petroleum Engineering",
    "integration_axis": "pore_fluid",
    "noise_model": "measurement_gaussian",
    "primitives": [
      "D.space",
      "S.hertz_mindlin.dry_frame",
      "O.chi2.elastic_moduli"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "elastic_moduli_fluid_substitution",
    "solution_space": "elastic_moduli_vector",
    "sub_domain": "Rock physics",
    "title": "Seismic Rock Physics (Gassmann)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "elastic_moduli_fluid_substitution"
    ],
    "allowed_omega_dimensions": [
      "porosity_phi",
      "clay_content_Vcl",
      "differential_pressure_MPa",
      "saturation_Sw"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "50 Vp_prediction_RMSE_m_s",
      "forward_operator": "elastic_moduli_fluid_substitution",
      "input_format": "measurement_only",
      "omega": {
        "clay_content_Vcl": 0.1,
        "differential_pressure_MPa": 30,
        "porosity_phi": 0.2,
        "saturation_Sw": 0.8
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "Vp_prediction_RMSE_m_s": [
        10,
        300
      ]
    },
    "omega_bounds": {
      "clay_content_Vcl": [
        0.0,
        0.6
      ],
      "differential_pressure_MPa": [
        5,
        80
      ],
      "porosity_phi": [
        0.05,
        0.4
      ],
      "saturation_Sw": [
        0.0,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Rock physics",
  "title": "Seismic Rock Physics (Gassmann)"
}

🎁

Earn PWM by promoting this to mainnet

• 100 PWM one-time grant on mainnet promotion
• 5% upstream royalty on every downstream L4 mining event, forever
• Your wallet is enrolled the moment the founder accepts

🚀 Submit to mainnet →

How: Download the bundle above → polish the Markdown in ChatGPT / Claude / Gemini → submit your version → founder reviews → mainnet.