FAILURE MAP
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FA-71406 / Seismic magnitude estimation / Open access

Moment magnitude from fault dimensions: SI moment constant · case 01

Every moment magnitude is 4.7 units low.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The dyne-cm constant 16.1 is applied to a moment already in N*m.

THE FAILURE

The dyne-cm constant 16.1 is applied to a moment already in N*m.

Unsuccessful approach: The constant 10.7 belongs to the 2/3 log10 M0 - 10.7 dyne-cm form, not this bracket.

Case contract

Rigidity in GPa, rupture length and width in km, average slip in m; any non-positive value returns None. M0 = mu * area * slip in N*m (SI), Mw = 2/3 (log10 M0 - 9.1). Return [M0 formatted %.3e, Mw rounded 0.01].

Why this case matters

Scenario ruptures for hazard studies convert fault geometry into moment magnitude.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mu_gpa, length_km, width_km, slip_m):
    if min(mu_gpa, length_km, width_km, slip_m) <= 0:
        return None
    area = (length_km * 1e3) * (width_km * 1e3)
    m0 = mu_gpa * 1e9 * area * slip_m
    mw = (2.0 / 3.0) * (math.log10(m0) - 16.1)
    return ["%.3e" % m0, round(mw, 2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mu 30 GPa L 1 W 1 D 0.05', [30, 1, 1, 0.05], ['1.500e+15', 4.05]], ['mu 30 GPa L 10 W 8 D 0.5', [30, 10, 8, 0.5], ['1.200e+18', 5.99]], ['mu 30 GPa L 50 W 20 D 2.0', [30, 50, 20, 2.0], ['6.000e+19', 7.12]], ['mu 30 GPa L 400 W 100 D 8.0', [30, 400, 100, 8.0], ['9.600e+21', 8.59]], ['mu 30 GPa L 0.5 W 0.3 D 0.01', [30, 0.5, 0.3, 0.01], ['4.500e+13', 3.04]], ['mu 32 GPa L 1 W 1 D 0.05', [32, 1, 1, 0.05], ['1.600e+15', 4.07]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 32 GPa L 50 W 20 D 2.0', [32, 50, 20, 2.0], ['6.400e+19', 7.14]]], [['mu 30 GPa L 400 W 100 D 8.0', [30, 400, 100, 8.0], ['9.600e+21', 8.59]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 32 GPa L 50 W 20 D 2.0', [32, 50, 20, 2.0], ['6.400e+19', 7.14]], ['mu 32 GPa L 400 W 100 D 8.0', [32, 400, 100, 8.0], ['1.024e+22', 8.61]], ['mu 32 GPa L 0.5 W 0.3 D 0.01', [32, 0.5, 0.3, 0.01], ['4.800e+13', 3.05]], ['mu 40 GPa L 1 W 1 D 0.05', [40, 1, 1, 0.05], ['2.000e+15', 4.13]], ['mu 40 GPa L 10 W 8 D 0.5', [40, 10, 8, 0.5], ['1.600e+18', 6.07]], ['mu 40 GPa L 50 W 20 D 2.0', [40, 50, 20, 2.0], ['8.000e+19', 7.2]]], [['mu 30 GPa L 1 W 1 D 0.05', [30, 1, 1, 0.05], ['1.500e+15', 4.05]], ['mu 30 GPa L 10 W 8 D 0.5', [30, 10, 8, 0.5], ['1.200e+18', 5.99]], ['mu 30 GPa L 50 W 20 D 2.0', [30, 50, 20, 2.0], ['6.000e+19', 7.12]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 40 GPa L 10 W 8 D 0.5', [40, 10, 8, 0.5], ['1.600e+18', 6.07]], ['mu 40 GPa L 0.5 W 0.3 D 0.01', [40, 0.5, 0.3, 0.01], ['6.000e+13', 3.12]], ['zero slip', [30, 10, 5, 0], None], ['negative width', [30, 10, -5, 1], None]], [['mu 30 GPa L 10 W 8 D 0.5', [30, 10, 8, 0.5], ['1.200e+18', 5.99]], ['mu 30 GPa L 0.5 W 0.3 D 0.01', [30, 0.5, 0.3, 0.01], ['4.500e+13', 3.04]], ['mu 32 GPa L 1 W 1 D 0.05', [32, 1, 1, 0.05], ['1.600e+15', 4.07]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 32 GPa L 50 W 20 D 2.0', [32, 50, 20, 2.0], ['6.400e+19', 7.14]], ['mu 32 GPa L 400 W 100 D 8.0', [32, 400, 100, 8.0], ['1.024e+22', 8.61]], ['mu 32 GPa L 0.5 W 0.3 D 0.01', [32, 0.5, 0.3, 0.01], ['4.800e+13', 3.05]], ['mu 40 GPa L 1 W 1 D 0.05', [40, 1, 1, 0.05], ['2.000e+15', 4.13]]], [['mu 30 GPa L 1 W 1 D 0.05', [30, 1, 1, 0.05], ['1.500e+15', 4.05]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 40 GPa L 10 W 8 D 0.5', [40, 10, 8, 0.5], ['1.600e+18', 6.07]], ['mu 40 GPa L 50 W 20 D 2.0', [40, 50, 20, 2.0], ['8.000e+19', 7.2]], ['mu 40 GPa L 400 W 100 D 8.0', [40, 400, 100, 8.0], ['1.280e+22', 8.67]], ['mu 40 GPa L 0.5 W 0.3 D 0.01', [40, 0.5, 0.3, 0.01], ['6.000e+13', 3.12]], ['zero slip', [30, 10, 5, 0], None], ['negative width', [30, 10, -5, 1], None]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
mu 30 GPa L 1 W 1 D 0.05['1.500e+15', -0.62]['1.500e+15', 4.05]Failed
mu 30 GPa L 10 W 8 D 0.5['1.200e+18', 1.32]['1.200e+18', 5.99]Failed
mu 30 GPa L 50 W 20 D 2.0['6.000e+19', 2.45]['6.000e+19', 7.12]Failed
mu 30 GPa L 400 W 100 D 8.0['9.600e+21', 3.92]['9.600e+21', 8.59]Failed
mu 30 GPa L 0.5 W 0.3 D 0.01['4.500e+13', -1.63]['4.500e+13', 3.04]Failed
mu 32 GPa L 1 W 1 D 0.05['1.600e+15', -0.6]['1.600e+15', 4.07]Failed
mu 32 GPa L 10 W 8 D 0.5['1.280e+18', 1.34]['1.280e+18', 6.0]Failed
mu 32 GPa L 50 W 20 D 2.0['6.400e+19', 2.47]['6.400e+19', 7.14]Failed

SHA-256 / df206f6fde06654d724183255e012a6d4fb627f647e02da624f3ac98f83aefcb

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mu_gpa, length_km, width_km, slip_m):
    if min(mu_gpa, length_km, width_km, slip_m) <= 0:
        return None
    area = (length_km * 1e3) * (width_km * 1e3)
    m0 = mu_gpa * 1e9 * area * slip_m
    mw = (2.0 / 3.0) * (math.log10(m0) - 10.7)
    return ["%.3e" % m0, round(mw, 2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['mu 30 GPa L 1 W 1 D 0.05', [30, 1, 1, 0.05], ['1.500e+15', 4.05]], ['mu 30 GPa L 10 W 8 D 0.5', [30, 10, 8, 0.5], ['1.200e+18', 5.99]], ['mu 30 GPa L 50 W 20 D 2.0', [30, 50, 20, 2.0], ['6.000e+19', 7.12]], ['mu 30 GPa L 400 W 100 D 8.0', [30, 400, 100, 8.0], ['9.600e+21', 8.59]], ['mu 30 GPa L 0.5 W 0.3 D 0.01', [30, 0.5, 0.3, 0.01], ['4.500e+13', 3.04]], ['mu 32 GPa L 1 W 1 D 0.05', [32, 1, 1, 0.05], ['1.600e+15', 4.07]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 32 GPa L 50 W 20 D 2.0', [32, 50, 20, 2.0], ['6.400e+19', 7.14]]], [['mu 30 GPa L 400 W 100 D 8.0', [30, 400, 100, 8.0], ['9.600e+21', 8.59]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 32 GPa L 50 W 20 D 2.0', [32, 50, 20, 2.0], ['6.400e+19', 7.14]], ['mu 32 GPa L 400 W 100 D 8.0', [32, 400, 100, 8.0], ['1.024e+22', 8.61]], ['mu 32 GPa L 0.5 W 0.3 D 0.01', [32, 0.5, 0.3, 0.01], ['4.800e+13', 3.05]], ['mu 40 GPa L 1 W 1 D 0.05', [40, 1, 1, 0.05], ['2.000e+15', 4.13]], ['mu 40 GPa L 10 W 8 D 0.5', [40, 10, 8, 0.5], ['1.600e+18', 6.07]], ['mu 40 GPa L 50 W 20 D 2.0', [40, 50, 20, 2.0], ['8.000e+19', 7.2]]], [['mu 30 GPa L 1 W 1 D 0.05', [30, 1, 1, 0.05], ['1.500e+15', 4.05]], ['mu 30 GPa L 10 W 8 D 0.5', [30, 10, 8, 0.5], ['1.200e+18', 5.99]], ['mu 30 GPa L 50 W 20 D 2.0', [30, 50, 20, 2.0], ['6.000e+19', 7.12]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 40 GPa L 10 W 8 D 0.5', [40, 10, 8, 0.5], ['1.600e+18', 6.07]], ['mu 40 GPa L 0.5 W 0.3 D 0.01', [40, 0.5, 0.3, 0.01], ['6.000e+13', 3.12]], ['zero slip', [30, 10, 5, 0], None], ['negative width', [30, 10, -5, 1], None]], [['mu 30 GPa L 10 W 8 D 0.5', [30, 10, 8, 0.5], ['1.200e+18', 5.99]], ['mu 30 GPa L 0.5 W 0.3 D 0.01', [30, 0.5, 0.3, 0.01], ['4.500e+13', 3.04]], ['mu 32 GPa L 1 W 1 D 0.05', [32, 1, 1, 0.05], ['1.600e+15', 4.07]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 32 GPa L 50 W 20 D 2.0', [32, 50, 20, 2.0], ['6.400e+19', 7.14]], ['mu 32 GPa L 400 W 100 D 8.0', [32, 400, 100, 8.0], ['1.024e+22', 8.61]], ['mu 32 GPa L 0.5 W 0.3 D 0.01', [32, 0.5, 0.3, 0.01], ['4.800e+13', 3.05]], ['mu 40 GPa L 1 W 1 D 0.05', [40, 1, 1, 0.05], ['2.000e+15', 4.13]]], [['mu 30 GPa L 1 W 1 D 0.05', [30, 1, 1, 0.05], ['1.500e+15', 4.05]], ['mu 32 GPa L 10 W 8 D 0.5', [32, 10, 8, 0.5], ['1.280e+18', 6.0]], ['mu 40 GPa L 10 W 8 D 0.5', [40, 10, 8, 0.5], ['1.600e+18', 6.07]], ['mu 40 GPa L 50 W 20 D 2.0', [40, 50, 20, 2.0], ['8.000e+19', 7.2]], ['mu 40 GPa L 400 W 100 D 8.0', [40, 400, 100, 8.0], ['1.280e+22', 8.67]], ['mu 40 GPa L 0.5 W 0.3 D 0.01', [40, 0.5, 0.3, 0.01], ['6.000e+13', 3.12]], ['zero slip', [30, 10, 5, 0], None], ['negative width', [30, 10, -5, 1], None]]]
for label, args, expected in fixtures[N - 1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
mu 30 GPa L 1 W 1 D 0.05['1.500e+15', 2.98]['1.500e+15', 4.05]Failed
mu 30 GPa L 10 W 8 D 0.5['1.200e+18', 4.92]['1.200e+18', 5.99]Failed
mu 30 GPa L 50 W 20 D 2.0['6.000e+19', 6.05]['6.000e+19', 7.12]Failed
mu 30 GPa L 400 W 100 D 8.0['9.600e+21', 7.52]['9.600e+21', 8.59]Failed
mu 30 GPa L 0.5 W 0.3 D 0.01['4.500e+13', 1.97]['4.500e+13', 3.04]Failed
mu 32 GPa L 1 W 1 D 0.05['1.600e+15', 3.0]['1.600e+15', 4.07]Failed
mu 32 GPa L 10 W 8 D 0.5['1.280e+18', 4.94]['1.280e+18', 6.0]Failed
mu 32 GPa L 50 W 20 D 2.0['6.400e+19', 6.07]['6.400e+19', 7.14]Failed

SHA-256 / 8a400b04421b32f827282df2a10fa1d13d9d2a5c58c845a1046f816d6a4f7ee0

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

Stipulated deterministic teaching model of a seismological magnitude procedure; constants and tables are fixed by the contract and no claim of agency or standards conformance is made. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:29.378921+00:00.

Case digest / 82c63aa14138034397af106558522c9ba7c4a9b49904e0e1abc8df3fdec93961