L1 ⚛ L1-272 ⊙ Testnet

Seismic Travel-Time Tomography — ray-based velocity imaging

Geophysics · First-arrival travel-time tomography

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⬇ L1-272.md

# ⚛ L1 Principle — Seismic Travel-Time Tomography — ray-based velocity imaging **ID:** `L1-272` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *First-arrival travel-time tomography* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D velocity field > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554050 --- ## 🧠 1. Introduction **Seismic Travel-Time Tomography — ray-based velocity imaging** is a **linear inverse problem** whose unknown lives in **3D velocity field** space, within the **First-arrival travel-time tomography** sub-domain of **Geophysics**. Measurements consist of acoustic pressure waves recorded by transducers via a **geophones** sensing mechanism. The forward operator applies, in order: L · eikonal operator; L · ray trace operator; L · linearize operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Ill-posed; null space for regions with no ray coverage. ## ⚙ 2. Forward Model Physical chain: **x** → L · eikonal → L · ray trace → L · linearize → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.linearize` `L.ray_trace` `L.eikonal` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.eikonal` | L · eikonal operator | | `L.ray_trace` | L · ray trace operator | | `L.linearize` | L · linearize operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | First-arrival travel-time tomography | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | 3D_velocity_field | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Ill-posed; null space for regions with no ray coverage. | Metric | Value | |---|---| | Metric | velocity_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `traveltime_tomo` · **Forward operator:** `traveltime_tomo_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Snr db | dB | 30 | | N sources | — | 32 | | N receivers | — | 128 | | Picker error | — | 0 | | Source error | — | 0 | | Ray coverage gaps | — | 0 | | Velocity prior error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 1024 | | W | px | 32 – 1024 | | Z | — | 16 – 512 | | Snr db | dB | 0 – 40 | | N sources | — | 4 – 1024 | | N receivers | — | 16 – 8192 | | Picker error | — | 0.0 – 0.05 | | Source error | — | 0.0 – 0.05 | | Ray coverage gaps | — | 0.0 – 0.5 | | Velocity prior error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 5.0 | Metric | Range | |---|---| | Velocity rel error | 0.5 – 50.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **velocity_rel_error_percent**, with κ = `600` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe50bd37c5b909a13a9270fb9c8572b77fc01a9306d0fb047238a19c66b51b67c` - **Chain tx hash:** `0xedefd71993f70361daf8861ff945586658ec8565c58c64dd87ef7787796a526a` - **Chain block:** `41554050` --- ## File Mapping This bundle consists of: `L1-272.md`, `L1-272.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-272.md` | Source of truth — edit this | Human or LLM | | `L1-272.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 `L1-272`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-272.md).
Regenerate L1-272.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-272-001 Seismic Travel-Time Tomography — ray-based velocity imaging Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-272",
  "chain_block": 41554050,
  "chain_hash": "0xe50bd37c5b909a13a9270fb9c8572b77fc01a9306d0fb047238a19c66b51b67c",
  "chain_tx_hash": "0xedefd71993f70361daf8861ff945586658ec8565c58c64dd87ef7787796a526a",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 600,
    "metric": "velocity_rel_error_percent",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "velocity_rel_error_percent",
    "regime": "Ill-posed; null space for regions with no ray coverage.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Geophysics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.eikonal",
      "L.ray_trace",
      "L.linearize",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "geophones",
    "solution_space": "3D_velocity_field",
    "sub_domain": "First-arrival travel-time tomography",
    "title": "Seismic Travel-Time Tomography \u2014 ray-based velocity imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "traveltime_tomo_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_sources",
      "N_receivers",
      "SNR_dB",
      "velocity_prior_error",
      "source_error",
      "picker_error",
      "ray_coverage_gaps",
      "velocity_prior_error",
      "source_error",
      "picker_error",
      "ray_coverage_gaps"
    ],
    "allowed_problem_classes": [
      "traveltime_tomo"
    ],
    "center_spec": {
      "epsilon_fn_center": "5.0",
      "forward_operator": "traveltime_tomo_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 256,
        "N_receivers": 128,
        "N_sources": 32,
        "SNR_dB": 30,
        "W": 256,
        "Z": 128,
        "picker_error": 0.0,
        "ray_coverage_gaps": 0.0,
        "source_error": 0.0,
        "velocity_prior_error": 0.0
      },
      "problem_class": "traveltime_tomo"
    },
    "epsilon_bounds": {
      "velocity_rel_error": [
        0.5,
        50.0
      ]
    },
    "omega_bounds": {
      "H": [
        32,
        1024
      ],
      "N_receivers": [
        16,
        8192
      ],
      "N_sources": [
        4,
        1024
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        1024
      ],
      "Z": [
        16,
        512
      ],
      "picker_error": [
        0.0,
        0.05
      ],
      "ray_coverage_gaps": [
        0.0,
        0.5
      ],
      "source_error": [
        0.0,
        0.05
      ],
      "velocity_prior_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "First-arrival travel-time tomography",
  "title": "Seismic Travel-Time Tomography \u2014 ray-based velocity imaging"
}

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