L1 ⚛ L1-275 ⊙ Testnet

Receiver Function — teleseismic crust imaging

Geophysics · P-to-S converted phase receiver function

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Markdown — human-readable source of truth

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⬇ L1-275.md

# ⚛ L1 Principle — Receiver Function — teleseismic crust imaging **ID:** `L1-275` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Geophysics — *P-to-S converted phase receiver function* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** crust velocity discontinuities > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554051 --- ## 🧠 1. Introduction **Receiver Function — teleseismic crust imaging** is a **linear inverse problem** whose unknown lives in **crust velocity discontinuities** space, within the **P-to-S converted phase receiver function** sub-domain of **Geophysics**. Measurements consist of acoustic pressure waves recorded by transducers via a **broadband seismometer** sensing mechanism. The forward operator applies, in order: L · deconvolve operator; L · stack back azimuth operator; L · invert layers operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · deconvolve → L · stack back azimuth → L · invert layers → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.invert_layers` `L.stack_back_azimuth` `L.deconvolve` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.deconvolve` | L · deconvolve operator | | `L.stack_back_azimuth` | L · stack back azimuth operator | | `L.invert_layers` | L · invert layers operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Geophysics | | Sub domain | P-to-S converted phase receiver function | | Carrier | acoustic | | Problem class | linear_inverse | | Solution space | crust_velocity_discontinuities | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.3 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `receiver_function` · **Forward operator:** `receiver_function_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | N events | — | 50 | | Bg noise | — | 0 | | N samples | — | 1024 | | Bandwidth error | — | 0 | | P slowness error | — | 0 | | Multiples contamination | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N events | — | 5 – 1000 | | Bg noise | — | 0.0 – 0.5 | | N samples | — | 128 – 65536 | | Bandwidth error | — | 0.0 – 0.3 | | P slowness error | — | 0.0 – 0.05 | | Multiples contamination | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb878ba8807d15203e611d9d9423e3ce60b4ab50a422e3c521f13f33121f401c0` - **Chain tx hash:** `0x846f79c3fa40ae9dcbba180ee7064d2a0d86fc2f85aec26d3c2d9792920dca0a` - **Chain block:** `41554051` --- ## File Mapping This bundle consists of: `L1-275.md`, `L1-275.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-275.md` | Source of truth — edit this | Human or LLM | | `L1-275.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 `L1-275`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-275.md).
Regenerate L1-275.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.

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L2-275-001 Receiver Function — teleseismic crust imaging Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-275",
  "chain_block": 41554051,
  "chain_hash": "0xb878ba8807d15203e611d9d9423e3ce60b4ab50a422e3c521f13f33121f401c0",
  "chain_tx_hash": "0x846f79c3fa40ae9dcbba180ee7064d2a0d86fc2f85aec26d3c2d9792920dca0a",
  "domain": "Geophysics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.3,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Geophysics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.deconvolve",
      "L.stack_back_azimuth",
      "L.invert_layers",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "broadband_seismometer",
    "solution_space": "crust_velocity_discontinuities",
    "sub_domain": "P-to-S converted phase receiver function",
    "title": "Receiver Function \u2014 teleseismic crust imaging"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "receiver_function_forward"
    ],
    "allowed_omega_dimensions": [
      "N_events",
      "N_samples",
      "SNR_dB",
      "p_slowness_error",
      "bandwidth_error",
      "bg_noise",
      "multiples_contamination",
      "p_slowness_error",
      "bandwidth_error",
      "bg_noise",
      "multiples_contamination"
    ],
    "allowed_problem_classes": [
      "receiver_function"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "receiver_function_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_events": 50,
        "N_samples": 1024,
        "SNR_dB": 25,
        "bandwidth_error": 0.0,
        "bg_noise": 0.0,
        "multiples_contamination": 0.0,
        "p_slowness_error": 0.0
      },
      "problem_class": "receiver_function"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "N_events": [
        5,
        1000
      ],
      "N_samples": [
        128,
        65536
      ],
      "SNR_dB": [
        0,
        40
      ],
      "bandwidth_error": [
        0.0,
        0.3
      ],
      "bg_noise": [
        0.0,
        0.5
      ],
      "multiples_contamination": [
        0.0,
        0.3
      ],
      "p_slowness_error": [
        0.0,
        0.05
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "P-to-S converted phase receiver function",
  "title": "Receiver Function \u2014 teleseismic crust imaging"
}

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