L1 ⚛ L1-273 ⊙ Testnet

Full Waveform Inversion (FWI) — subsurface velocity imaging

Geophysics · Seismic FWI (crown jewel of PDE inverse problems)

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⬇ L1-273.md

# ⚛ L1 Principle — Full Waveform Inversion (FWI) — subsurface velocity imaging **ID:** `L1-273` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *Seismic FWI (crown jewel of PDE inverse problems)* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D elastic velocity density > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 50 · **⛓ Block:** 41554051 --- ## 🧠 1. Introduction **Full Waveform Inversion (FWI) — subsurface velocity imaging** is a **nonlinear inverse problem** whose unknown lives in **3D elastic velocity density** space, within the **Seismic FWI (crown jewel of PDE inverse problems)** sub-domain of **Geophysics**. Measurements consist of acoustic pressure waves recorded by transducers via a **geophones hydrophones** sensing mechanism. The forward operator applies, in order: L · wave propagate operator; L · adjoint wave operator; L · gradient integrate operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Highly non-convex; cycle-skipping from poor initial model; frontier-level inverse problem. ## ⚙ 2. Forward Model Physical chain: **x** → L · wave propagate → L · adjoint wave → L · gradient integrate → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.gradient_integrate` `L.adjoint_wave` `L.wave_propagate` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.wave_propagate` | L · wave propagate operator | | `L.adjoint_wave` | L · adjoint wave operator | | `L.gradient_integrate` | L · gradient integrate operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | Seismic FWI (crown jewel of PDE inverse problems) | | Carrier | acoustic | | Problem class | nonlinear_inverse | | Solution space | 3D_elastic_velocity_density | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 50 | | L dag | 4.5 | ## 📡 4. Measurement Model Highly non-convex; cycle-skipping from poor initial model; frontier-level inverse problem. | Metric | Value | |---|---| | Metric | velocity_rel_error_percent | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `fwi` · **Forward operator:** `fwi_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | N rec | — | 256 | | Snr db | dB | 25 | | N shots | — | 64 | | Bc error | — | 0 | | N samples | — | 2000 | | Cycle skipping | — | 0 | | Initial model error | — | 0.1 | | Source wavelet error | — | 0 | | Anisotropy unmodelled | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 4096 | | W | px | 32 – 4096 | | Z | — | 16 – 2048 | | N rec | — | 16 – 100000 | | Snr db | dB | -5 – 40 | | N shots | — | 4 – 10000 | | Bc error | — | 0.0 – 0.3 | | N samples | — | 100 – 100000 | | Cycle skipping | — | 0.0 – 0.5 | | Initial model error | — | 0.0 – 0.3 | | Source wavelet error | — | 0.0 – 0.3 | | Anisotropy unmodelled | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 10.0 | Metric | Range | |---|---| | Velocity rel error | 1.0 – 60.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **velocity_rel_error_percent**, with κ = `2400` and δ = `50`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xea54bb76f6b95cd294440f9119311e25a3c3dfb348156fe7e689b2205a078b32` - **Chain tx hash:** `0x525bb4e5374ba0f9c49a57fd90395835a1494eafbe838368bcdac1a9b2dc2942` - **Chain block:** `41554051` --- ## File Mapping This bundle consists of: `L1-273.md`, `L1-273.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-273.md` | Source of truth — edit this | Human or LLM | | `L1-273.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 `L1-273`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-273.md).
Regenerate L1-273.json so every field matches the Markdown.
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L2-273-001 Full Waveform Inversion (FWI) — subsurface velocity imaging Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Geophysics",
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    "title": "Full Waveform Inversion (FWI) \u2014 subsurface velocity imaging"
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  "status": "testnet",
  "sub_domain": "Seismic FWI (crown jewel of PDE inverse problems)",
  "title": "Full Waveform Inversion (FWI) \u2014 subsurface velocity imaging"
}

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