L1 ⚛ L1-104 ⊙ Testnet

Ground Penetrating Radar (GPR)

Remote Sensing · Subsurface EM sounding

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⬇ L1-104.md

# ⚛ L1 Principle — Ground Penetrating Radar (GPR) **ID:** `L1-104` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Remote Sensing — *Subsurface EM sounding* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D subsurface dielectric > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554197 --- ## 🧠 1. Introduction **Ground Penetrating Radar (GPR)** is a **nonlinear inverse problem** whose unknown lives in **2D subsurface dielectric** space, within the **Subsurface EM sounding** sub-domain of **Remote Sensing**. Measurements consist of radio-frequency electromagnetic waves via a **subsurface em radar** sensing mechanism. The forward operator applies, in order: L · emit · em pulse operator; L · subsurface reflect operator; L · migration operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D subsurface dielectric is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); soil_permittivity_variation dominates the stability cliff; clutter and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → L · emit · em pulse → L · subsurface reflect → L · migration → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.migration` `L.subsurface_reflect` `L.emit.em_pulse` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.em_pulse` | L · emit · em pulse operator | | `L.subsurface_reflect` | L · subsurface reflect operator | | `L.migration` | L · migration operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Remote Sensing | | Sub domain | Subsurface EM sounding | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 2D_subsurface_dielectric | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 2D subsurface dielectric is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); soil_permittivity_variation dominates the stability cliff; clutter and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `gpr_radar` · **Forward operator:** `gpr_radar_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | F mhz | MHz | 250 | | Snr db | dB | 15 | | Clutter | — | 0 | | N traces | — | 256 | | N samples | — | 512 | | Depth range m | m | 10 | | Attenuation depth | — | 0.5 | | Soil permittivity variation | — | 0.05 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | F mhz | MHz | 25 – 2000 | | Snr db | dB | 0.0 – 30.0 | | Clutter | — | 0.0 – 0.5 | | N traces | — | 64 – 1024 | | N samples | — | 128 – 2048 | | Depth range m | m | 0.1 – 100 | | Antenna coupling | — | 0.0 – 0.3 | | Attenuation depth | — | 0.1 – 2.0 | | Soil permittivity variation | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 18.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xe335faa007a1b51c7dae3113128ba8b9ed064a55ca7ec2e4b6ead8503a044dd8` - **Chain tx hash:** `0xd5ea017b8daf6fafc1a1bbdb65927e673fc968ff918d9351812068929bf1e802` - **Chain block:** `41554197` --- ## File Mapping This bundle consists of: `L1-104.md`, `L1-104.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-104.md` | Source of truth — edit this | Human or LLM | | `L1-104.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 `L1-104`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-104.md).
Regenerate L1-104.json so every field matches the Markdown.
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L2-104-001 Ground Penetrating Radar (GPR) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554197,
  "chain_hash": "0xe335faa007a1b51c7dae3113128ba8b9ed064a55ca7ec2e4b6ead8503a044dd8",
  "chain_tx_hash": "0xd5ea017b8daf6fafc1a1bbdb65927e673fc968ff918d9351812068929bf1e802",
  "domain": "Remote Sensing",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D subsurface dielectric is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); soil_permittivity_variation dominates the stability cliff; clutter and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "radio_wave",
    "difficulty_delta": 5,
    "domain": "Remote Sensing",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.emit.em_pulse",
      "L.subsurface_reflect",
      "L.migration",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "subsurface_em_radar",
    "solution_space": "2D_subsurface_dielectric",
    "sub_domain": "Subsurface EM sounding",
    "title": "Ground Penetrating Radar (GPR)"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "N_traces",
      "f_MHz",
      "depth_range_m",
      "SNR_dB",
      "soil_permittivity_variation",
      "clutter",
      "attenuation_depth",
      "soil_permittivity_variation",
      "clutter",
      "attenuation_depth",
      "antenna_coupling"
    ],
    "allowed_problem_classes": [
      "gpr_radar"
    ],
    "center_spec": {
      "epsilon_fn_center": "18.0",
      "forward_operator": "gpr_radar_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_samples": 512,
        "N_traces": 256,
        "SNR_dB": 15.0,
        "attenuation_depth": 0.5,
        "clutter": 0.0,
        "depth_range_m": 10,
        "f_MHz": 250,
        "soil_permittivity_variation": 0.05
      },
      "problem_class": "gpr_radar"
    },
    "epsilon_bounds": {
      "psnr_db": [
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        40.0
      ]
    },
    "omega_bounds": {
      "N_samples": [
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        2048
      ],
      "N_traces": [
        64,
        1024
      ],
      "SNR_dB": [
        0.0,
        30.0
      ],
      "antenna_coupling": [
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        0.3
      ],
      "attenuation_depth": [
        0.1,
        2.0
      ],
      "clutter": [
        0.0,
        0.5
      ],
      "depth_range_m": [
        0.1,
        100
      ],
      "f_MHz": [
        25,
        2000
      ],
      "soil_permittivity_variation": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Subsurface EM sounding",
  "title": "Ground Penetrating Radar (GPR)"
}

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