FAILURE MAP
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FA-71736 / Seismic magnitude estimation / Open access

Scalar moment from moment tensor: off-diagonal multiplicity · case 01

Strike-slip and oblique mechanisms get Mw too small.

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

ROOT CAUSE

Each off-diagonal element is counted once although the symmetric tensor contains it twice.

THE FAILURE

Each off-diagonal element is counted once although the symmetric tensor contains it twice.

Unsuccessful approach: Doubling the diagonal instead weights the wrong elements.

Case contract

mt = [Mrr, Mtt, Mpp, Mrt, Mrp, Mtp] mantissas; tensor = mantissa * 10^exponent dyne*cm. M0 = sqrt(sum of all nine squared elements / 2) (off-diagonals appear twice), converted to N*m (1e-7). Mw = 2/3 (log10 M0 - 9.1). Flag "non-deviatoric" when |trace| > 0.1 * M0 mantissa norm, else "deviatoric". Return [Mw rounded 0.01, flag].

Why this case matters

Global CMT catalogues report Mw from the scalar moment of the moment tensor.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mt, exponent):
    mrr, mtt, mpp, mrt, mrp, mtp = mt
    s = mrr ** 2 + mtt ** 2 + mpp ** 2 + (mrt ** 2 + mrp ** 2 + mtp ** 2)
    norm = math.sqrt(s / 2)
    m0 = norm * 10 ** exponent * 1e-7
    mw = 2.0 / 3.0 * (math.log10(m0) - 9.1)
    tr = mrr + mtt + mpp
    flag = "non-deviatoric" if abs(tr) > 0.1 * norm else "deviatoric"
    return [round(mw, 2), flag]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['CMT 0', [[1.58, -0.18, -1.4, -0.23, 1.77, 2.88], 24], [5.65, 'deviatoric']], ['CMT 1', [[1.33, 2.91, -4.19, 1.33, -1.96, -1.34], 22], [4.38, 'deviatoric']], ['CMT 2', [[-1.2, 0.01, 1.79, -1.15, 0.15, 2.83], 22], [4.29, 'non-deviatoric']], ['CMT 3', [[1.67, 0.06, -1.73, 1.49, 1.34, -2.67], 22], [4.32, 'deviatoric']], ['CMT 4', [[-1.9, -1.77, 4.27, 0.86, 2.98, 0.36], 22], [4.38, 'non-deviatoric']], ['CMT 5', [[-2.12, 2.5, -0.38, -0.41, -0.33, -2.59], 26], [6.96, 'deviatoric']], ['CMT 6', [[-0.71, 0.51, 0.2, -0.99, 2.74, 2.57], 26], [7.0, 'deviatoric']], ['CMT 7', [[1.65, 1.09, -3.64, 2.79, -1.4, 1.9], 24], [5.71, 'non-deviatoric']]], [['CMT 3', [[1.67, 0.06, -1.73, 1.49, 1.34, -2.67], 22], [4.32, 'deviatoric']], ['CMT 6', [[-0.71, 0.51, 0.2, -0.99, 2.74, 2.57], 26], [7.0, 'deviatoric']], ['CMT 7', [[1.65, 1.09, -3.64, 2.79, -1.4, 1.9], 24], [5.71, 'non-deviatoric']], ['CMT 8', [[1.74, 1.88, -3.62, -0.88, -1.61, -1.39], 22], [4.33, 'deviatoric']], ['CMT 9', [[-0.63, -0.39, 1.02, 1.72, 2.75, -2.36], 24], [5.68, 'deviatoric']], ['CMT 10', [[-2.32, -0.03, 1.45, -0.07, -0.46, -2.98], 26], [6.97, 'non-deviatoric']], ['CMT 11', [[-0.92, -0.76, 2.28, 2.62, -2.3, -1.63], 24], [5.69, 'non-deviatoric']], ['CMT 12', [[-2.44, -0.02, 2.51, 1.65, -2.68, -2.39], 24], [5.71, 'deviatoric']]], [['CMT 6', [[-0.71, 0.51, 0.2, -0.99, 2.74, 2.57], 26], [7.0, 'deviatoric']], ['CMT 11', [[-0.92, -0.76, 2.28, 2.62, -2.3, -1.63], 24], [5.69, 'non-deviatoric']], ['CMT 14', [[2.95, -1.69, -0.66, -1.55, 1.63, -1.39], 22], [4.3, 'non-deviatoric']], ['CMT 15', [[-0.88, -0.92, 1.8, 1.6, 2.66, 2.49], 22], [4.35, 'deviatoric']], ['CMT 16', [[0.43, 0.92, -1.3, -1.94, -0.05, -1.89], 24], [5.58, 'deviatoric']], ['CMT 17', [[-1.85, -0.32, 2.22, -2.09, -2.01, 2.89], 26], [7.04, 'deviatoric']], ['CMT 18', [[-0.42, 0.81, -0.39, 1.33, -2.95, 0.45], 22], [4.28, 'deviatoric']], ['CMT 19', [[-1.94, -1.33, 3.27, 1.63, 1.09, 0.68], 26], [6.96, 'deviatoric']]], [['CMT 9', [[-0.63, -0.39, 1.02, 1.72, 2.75, -2.36], 24], [5.68, 'deviatoric']], ['CMT 16', [[0.43, 0.92, -1.3, -1.94, -0.05, -1.89], 24], [5.58, 'deviatoric']], ['CMT 21', [[2.37, -2.79, 0.47, 2.71, 2.28, 2.18], 22], [4.39, 'deviatoric']], ['CMT 22', [[-0.65, -0.33, 0.98, -2.51, 0.29, 0.8], 22], [4.23, 'deviatoric']], ['CMT 23', [[1.22, -0.52, -0.7, -0.46, 0.42, 1.99], 24], [5.51, 'deviatoric']], ['CMT 24', [[-2.95, 2.42, 0.53, -0.96, 2.79, -0.69], 26], [7.01, 'deviatoric']], ['CMT 25', [[-1.12, 1.62, -1.4, -2.67, 2.0, 2.3], 24], [5.7, 'non-deviatoric']], ['CMT 26', [[-1.51, 2.8, -1.24, -0.74, 2.72, 0.61], 26], [6.98, 'deviatoric']]], [['CMT 12', [[-2.44, -0.02, 2.51, 1.65, -2.68, -2.39], 24], [5.71, 'deviatoric']], ['CMT 21', [[2.37, -2.79, 0.47, 2.71, 2.28, 2.18], 22], [4.39, 'deviatoric']], ['CMT 28', [[-2.3, -0.66, 2.96, 1.1, -2.45, 1.63], 22], [4.34, 'deviatoric']], ['CMT 29', [[-2.07, -1.28, 2.45, 2.72, -1.24, 2.82], 26], [7.05, 'non-deviatoric']], ['CMT 30', [[-1.64, -1.22, 2.86, 1.2, 0.73, -0.28], 26], [6.91, 'deviatoric']], ['CMT 31', [[0.79, 1.24, -2.03, 1.61, -0.68, 0.88], 22], [4.21, 'deviatoric']], ['CMT 32', [[-0.32, -2.12, 3.04, 2.57, 2.1, -2.5], 22], [4.39, 'non-deviatoric']], ['CMT 33', [[-2.75, -0.91, 2.76, 1.11, -2.45, 2.96], 26], [7.06, 'non-deviatoric']]]]
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
CMT 0[5.57, 'deviatoric'][5.65, 'deviatoric']Failed
CMT 1[4.35, 'deviatoric'][4.38, 'deviatoric']Failed
CMT 2[4.22, 'non-deviatoric'][4.29, 'non-deviatoric']Failed
CMT 3[4.24, 'deviatoric'][4.32, 'deviatoric']Failed
CMT 4[4.35, 'non-deviatoric'][4.38, 'non-deviatoric']Failed
CMT 5[6.92, 'deviatoric'][6.96, 'deviatoric']Failed
CMT 6[6.9, 'deviatoric'][7.0, 'deviatoric']Failed
CMT 7[5.66, 'non-deviatoric'][5.71, 'non-deviatoric']Failed

SHA-256 / 945845446ed239b19532b95e29619ce29ae7e0b3b85e45dd0931e255dfca4b87

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mt, exponent):
    mrr, mtt, mpp, mrt, mrp, mtp = mt
    s = 2 * (mrr ** 2 + mtt ** 2 + mpp ** 2) + mrt ** 2 + mrp ** 2 + mtp ** 2
    norm = math.sqrt(s / 2)
    m0 = norm * 10 ** exponent * 1e-7
    mw = 2.0 / 3.0 * (math.log10(m0) - 9.1)
    tr = mrr + mtt + mpp
    flag = "non-deviatoric" if abs(tr) > 0.1 * norm else "deviatoric"
    return [round(mw, 2), flag]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['CMT 0', [[1.58, -0.18, -1.4, -0.23, 1.77, 2.88], 24], [5.65, 'deviatoric']], ['CMT 1', [[1.33, 2.91, -4.19, 1.33, -1.96, -1.34], 22], [4.38, 'deviatoric']], ['CMT 2', [[-1.2, 0.01, 1.79, -1.15, 0.15, 2.83], 22], [4.29, 'non-deviatoric']], ['CMT 3', [[1.67, 0.06, -1.73, 1.49, 1.34, -2.67], 22], [4.32, 'deviatoric']], ['CMT 4', [[-1.9, -1.77, 4.27, 0.86, 2.98, 0.36], 22], [4.38, 'non-deviatoric']], ['CMT 5', [[-2.12, 2.5, -0.38, -0.41, -0.33, -2.59], 26], [6.96, 'deviatoric']], ['CMT 6', [[-0.71, 0.51, 0.2, -0.99, 2.74, 2.57], 26], [7.0, 'deviatoric']], ['CMT 7', [[1.65, 1.09, -3.64, 2.79, -1.4, 1.9], 24], [5.71, 'non-deviatoric']]], [['CMT 3', [[1.67, 0.06, -1.73, 1.49, 1.34, -2.67], 22], [4.32, 'deviatoric']], ['CMT 6', [[-0.71, 0.51, 0.2, -0.99, 2.74, 2.57], 26], [7.0, 'deviatoric']], ['CMT 7', [[1.65, 1.09, -3.64, 2.79, -1.4, 1.9], 24], [5.71, 'non-deviatoric']], ['CMT 8', [[1.74, 1.88, -3.62, -0.88, -1.61, -1.39], 22], [4.33, 'deviatoric']], ['CMT 9', [[-0.63, -0.39, 1.02, 1.72, 2.75, -2.36], 24], [5.68, 'deviatoric']], ['CMT 10', [[-2.32, -0.03, 1.45, -0.07, -0.46, -2.98], 26], [6.97, 'non-deviatoric']], ['CMT 11', [[-0.92, -0.76, 2.28, 2.62, -2.3, -1.63], 24], [5.69, 'non-deviatoric']], ['CMT 12', [[-2.44, -0.02, 2.51, 1.65, -2.68, -2.39], 24], [5.71, 'deviatoric']]], [['CMT 6', [[-0.71, 0.51, 0.2, -0.99, 2.74, 2.57], 26], [7.0, 'deviatoric']], ['CMT 11', [[-0.92, -0.76, 2.28, 2.62, -2.3, -1.63], 24], [5.69, 'non-deviatoric']], ['CMT 14', [[2.95, -1.69, -0.66, -1.55, 1.63, -1.39], 22], [4.3, 'non-deviatoric']], ['CMT 15', [[-0.88, -0.92, 1.8, 1.6, 2.66, 2.49], 22], [4.35, 'deviatoric']], ['CMT 16', [[0.43, 0.92, -1.3, -1.94, -0.05, -1.89], 24], [5.58, 'deviatoric']], ['CMT 17', [[-1.85, -0.32, 2.22, -2.09, -2.01, 2.89], 26], [7.04, 'deviatoric']], ['CMT 18', [[-0.42, 0.81, -0.39, 1.33, -2.95, 0.45], 22], [4.28, 'deviatoric']], ['CMT 19', [[-1.94, -1.33, 3.27, 1.63, 1.09, 0.68], 26], [6.96, 'deviatoric']]], [['CMT 9', [[-0.63, -0.39, 1.02, 1.72, 2.75, -2.36], 24], [5.68, 'deviatoric']], ['CMT 16', [[0.43, 0.92, -1.3, -1.94, -0.05, -1.89], 24], [5.58, 'deviatoric']], ['CMT 21', [[2.37, -2.79, 0.47, 2.71, 2.28, 2.18], 22], [4.39, 'deviatoric']], ['CMT 22', [[-0.65, -0.33, 0.98, -2.51, 0.29, 0.8], 22], [4.23, 'deviatoric']], ['CMT 23', [[1.22, -0.52, -0.7, -0.46, 0.42, 1.99], 24], [5.51, 'deviatoric']], ['CMT 24', [[-2.95, 2.42, 0.53, -0.96, 2.79, -0.69], 26], [7.01, 'deviatoric']], ['CMT 25', [[-1.12, 1.62, -1.4, -2.67, 2.0, 2.3], 24], [5.7, 'non-deviatoric']], ['CMT 26', [[-1.51, 2.8, -1.24, -0.74, 2.72, 0.61], 26], [6.98, 'deviatoric']]], [['CMT 12', [[-2.44, -0.02, 2.51, 1.65, -2.68, -2.39], 24], [5.71, 'deviatoric']], ['CMT 21', [[2.37, -2.79, 0.47, 2.71, 2.28, 2.18], 22], [4.39, 'deviatoric']], ['CMT 28', [[-2.3, -0.66, 2.96, 1.1, -2.45, 1.63], 22], [4.34, 'deviatoric']], ['CMT 29', [[-2.07, -1.28, 2.45, 2.72, -1.24, 2.82], 26], [7.05, 'non-deviatoric']], ['CMT 30', [[-1.64, -1.22, 2.86, 1.2, 0.73, -0.28], 26], [6.91, 'deviatoric']], ['CMT 31', [[0.79, 1.24, -2.03, 1.61, -0.68, 0.88], 22], [4.21, 'deviatoric']], ['CMT 32', [[-0.32, -2.12, 3.04, 2.57, 2.1, -2.5], 22], [4.39, 'non-deviatoric']], ['CMT 33', [[-2.75, -0.91, 2.76, 1.11, -2.45, 2.96], 26], [7.06, 'non-deviatoric']]]]
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
CMT 0[5.6, 'deviatoric'][5.65, 'deviatoric']Failed
CMT 1[4.43, 'deviatoric'][4.38, 'deviatoric']Failed
CMT 2[4.26, 'non-deviatoric'][4.29, 'non-deviatoric']Failed
CMT 3[4.29, 'deviatoric'][4.32, 'deviatoric']Failed
CMT 4[4.42, 'non-deviatoric'][4.38, 'non-deviatoric']Failed
CMT 5[6.99, 'deviatoric'][6.96, 'deviatoric']Failed
CMT 6[6.91, 'deviatoric'][7.0, 'deviatoric']Failed
CMT 7[5.73, 'non-deviatoric'][5.71, 'non-deviatoric']Failed

SHA-256 / 408a8f09ec6c38c275da9db1686b1c2b6b90dc81de935284bbf394d8777ab2c5

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 2026-09-29T14:48:32.369084+00:00.

Case digest / d970ee7fcddffb1067cdd7526f5fa60692f4182f216442adb4017b9ee8cbeb4e