{
  "version": 1,
  "topic": "PP06",
  "title": "Sonic porosity and matrix transit time assumptions",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Sonic Porosity Raymer-Hunt-Gardner Method",
    "premise": "Fixed controls: Delta_t = 80 us/ft; C_RHG = 0.67 dimensionless. Delta_t_ma is varied as shown.",
    "formula": "Phi_sonic = C_RHG * (Delta_t - Delta_t_ma) / Delta_t",
    "variables": "Delta_t: Sonic Log Transit Time Reading (us/ft). Delta_t_ma: Matrix Transit Time (us/ft). C_RHG: Raymer-Hunt-Gardner Empirical Constant (dimensionless).",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Matrix Transit Time (us/ft) = 55",
        "explanation": "Fixed controls: Delta_t = 80 us/ft; C_RHG = 0.67 dimensionless. Delta_t_ma is varied as shown."
      },
      {
        "label": "Select the relation",
        "calculation": "Phi_sonic = C_RHG * (Delta_t - Delta_t_ma) / Delta_t",
        "explanation": "Delta_t: Sonic Log Transit Time Reading (us/ft). Delta_t_ma: Matrix Transit Time (us/ft). C_RHG: Raymer-Hunt-Gardner Empirical Constant (dimensionless)."
      },
      {
        "label": "Substitute the values",
        "calculation": "Delta_t = 80; Delta_t_ma = 55; C_RHG = 0.67 → Phi_sonic = 0.209375 fraction",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Phi_sonic (fraction) = 0.209375",
        "explanation": "Matrix transit-time sensitivity uses the documented Raymer–Hunt–Gardner variant. It does not identify lithology."
      }
    ],
    "result": "Phi_sonic (fraction) = 0.209375",
    "interpretation": "Matrix transit-time sensitivity uses the documented Raymer–Hunt–Gardner variant. It does not identify lithology.",
    "control": "Matrix Transit Time (us/ft)",
    "columns": [
      "Matrix Transit Time (us/ft)",
      "Phi_sonic (fraction)"
    ],
    "rows": [
      [
        45,
        0.293125
      ],
      [
        50,
        0.25125000000000003
      ],
      [
        55,
        0.209375
      ],
      [
        60,
        0.1675
      ],
      [
        65,
        0.12562500000000001
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Matrix Transit Time (us/ft) = 45. Phi_sonic (fraction): 0.293125.",
      "Matrix Transit Time (us/ft) = 50. Phi_sonic (fraction): 0.25125.",
      "Matrix Transit Time (us/ft) = 55. Phi_sonic (fraction): 0.209375.",
      "Matrix Transit Time (us/ft) = 60. Phi_sonic (fraction): 0.1675.",
      "Matrix Transit Time (us/ft) = 65. Phi_sonic (fraction): 0.125625."
    ],
    "provenance": "Replayed with the same equation record and calculation engine as /calculators/sonic-porosity-raymer-hunt-gardner-method. Original synthetic inputs; engine outputs are saved in the downloadable record.",
    "questions": [
      {
        "question": "Reproduce the baseline Phi_sonic (fraction) without rounding intermediate values.",
        "answer": "Delta_t = 80; Delta_t_ma = 55; C_RHG = 0.67 → Phi_sonic = 0.209375 fraction. Phi_sonic (fraction) = 0.209375. Matrix transit-time sensitivity uses the documented Raymer–Hunt–Gardner variant. It does not identify lithology."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Matrix Transit Time (us/ft) changes from 45 to 65. Other controls remain as stated in the premise. Phi_sonic (fraction) changes from 0.293125 to 0.125625."
      },
      {
        "question": "What would be needed to apply this example to a different physical system?",
        "answer": "Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Delta_t: Sonic Log Transit Time Reading (us/ft). Delta_t_ma: Matrix Transit Time (us/ft). C_RHG: Raymer-Hunt-Gardner Empirical Constant (dimensionless). Matrix transit-time sensitivity uses the documented Raymer–Hunt–Gardner variant. It does not identify lithology."
      }
    ]
  },
  "recorded": {
    "kind": "scalar",
    "equation": "sonic-porosity-raymer-hunt-gardner-method",
    "parameter": "Delta_t_ma",
    "inputs": {
      "Delta_t": "80",
      "Delta_t_ma": "55",
      "C_RHG": "0.67"
    },
    "values": [
      45,
      50,
      55,
      60,
      65
    ],
    "outputs": [
      {
        "expression": "C_RHG * (Delta_t - Delta_t_ma) / Delta_t",
        "intermediates": {},
        "inputs": {
          "Delta_t": 80,
          "Delta_t_ma": 45,
          "C_RHG": 0.67
        },
        "target": "Phi_sonic",
        "unit": "fraction",
        "value": 0.293125
      },
      {
        "expression": "C_RHG * (Delta_t - Delta_t_ma) / Delta_t",
        "intermediates": {},
        "inputs": {
          "Delta_t": 80,
          "Delta_t_ma": 50,
          "C_RHG": 0.67
        },
        "target": "Phi_sonic",
        "unit": "fraction",
        "value": 0.25125000000000003
      },
      {
        "expression": "C_RHG * (Delta_t - Delta_t_ma) / Delta_t",
        "intermediates": {},
        "inputs": {
          "Delta_t": 80,
          "Delta_t_ma": 55,
          "C_RHG": 0.67
        },
        "target": "Phi_sonic",
        "unit": "fraction",
        "value": 0.209375
      },
      {
        "expression": "C_RHG * (Delta_t - Delta_t_ma) / Delta_t",
        "intermediates": {},
        "inputs": {
          "Delta_t": 80,
          "Delta_t_ma": 60,
          "C_RHG": 0.67
        },
        "target": "Phi_sonic",
        "unit": "fraction",
        "value": 0.1675
      },
      {
        "expression": "C_RHG * (Delta_t - Delta_t_ma) / Delta_t",
        "intermediates": {},
        "inputs": {
          "Delta_t": 80,
          "Delta_t_ma": 65,
          "C_RHG": 0.67
        },
        "target": "Phi_sonic",
        "unit": "fraction",
        "value": 0.12562500000000001
      }
    ]
  }
}