Richter/Moment Magnitude ↔ Seismic Energy mechanism

Model scope

The numerical relation is standard under the stated joule convention, but the instrument needs an explicit magnitude-scale scope, the reverse formula, a TNT conversion constant, a clear label such as 'estimated seismic-wave energy,' input validation for positive reverse-energy inputs, and the missing reference data before it can receive an unqualified PASS.

• log10(E[J]) = 4.8 + 1.5M is a standard empirical estimate for radiated seismic-wave energy, but the spec ambiguously presents it as universally valid for both Mw and ML; these magnitude scales are not interchangeable and ML can saturate for larger earthquakes.
• The reverse computation is claimed but its formula is not explicitly specified; it should be M = (log10(E[J]) - 4.8) / 1.5.
• The phrase 'energy released' is potentially misleading because this relation estimates seismic-wave energy, not the earthquake's total physical energy budget.
• TNT-equivalent output is specified without providing the required conversion constant.

Units and conventions

• E is seismic energy in joules.
• log10 is base-10 logarithm.
• M is treated as a dimensionless magnitude value and the same empirical relation is applied to the declared magnitude scale.
• For TNT conversion, 1 tonne of TNT = 4.184e9 J and 1 kilotonne of TNT = 4.184e12 J.
• Negative or zero magnitudes are mathematically permitted by the relation, although zero magnitude is an edge case rather than a typical damaging earthquake.
• The requested historical-earthquake comparisons require a reference table that is not included in the supplied spec.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "magnitude": 5,
    "magnitude_type": "Mw"
  },
  "expected_outputs": {
    "energy_j": 1995262314968.879,
    "tnt_tonnes": 476.8791,
    "tnt_kilotonnnes": 0.4768791
  },
  "working": "log10(E) = 4.8 + 1.5*5.0 = 4.8 + 7.5 = 12.3. Therefore E = 10^12.3 = 1.9952623149688788e12 J. TNT tonnes = 1.9952623149688788e12 / 4.184e9 = 476.8791 tonnes. TNT kilotonnes = 476.8791 / 1000 = 0.4768791 kt."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Zero joules is a valid-looking numeric input but makes the inverse logarithm undefined. The instrument must reject E = 0; returning a finite magnitude would be a failure.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json