FA-71701 / Seismic magnitude estimation / Open access

Richter -log A0 table magnitude: log-domain component average · case 01

Unequal component amplitudes bias ML upward.

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

ROOT CAUSE

Amplitudes are averaged linearly before the logarithm.

THE FAILURE

Amplitudes are averaged linearly before the logarithm.

Unsuccessful approach: Using the larger component alone biases ML upward.

Case contract

Zero-to-peak Wood-Anderson amplitudes on two horizontal components in mm (0 = dead channel, ignored; both dead returns None). -log A0 is linearly interpolated from [(0,1.4),(10,1.5),(20,1.7),(30,2.1),(50,2.6),(100,3.0),(200,3.5),(300,4.0),(400,4.5),(600,5.1)] with 0 <= dist <= 600 inclusive, else None. ML = mean of per-component log10 amplitudes + (-log A0), rounded 0.01.

Why this case matters

Classic ML reproduces Richter tables for historical catalogue homogenisation.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(amp_n_mm, amp_e_mm, dist_km):
    table = [(0, 1.4), (10, 1.5), (20, 1.7), (30, 2.1), (50, 2.6), (100, 3.0), (200, 3.5), (300, 4.0), (400, 4.5), (600, 5.1)]
    if dist_km < 0 or dist_km > 600:
        return None
    comps = [a for a in (amp_n_mm, amp_e_mm) if a > 0]
    if not comps:
        return None
    corr = None
    for (d0, c0), (d1, c1) in zip(table, table[1:]):
        if d0 <= dist_km <= d1:
            corr = c0 + (c1 - c0) * (dist_km - d0) / (d1 - d0)
            break
    logs = [math.log10(sum(comps) / len(comps))]
    return round(sum(logs) / len(logs) + corr, 2)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['N 1.0 mm E 1.0 mm at 0 km', [1.0, 1.0, 0], 1.4], ['N 1.0 mm E 1.0 mm at 5 km', [1.0, 1.0, 5], 1.45], ['N 1.0 mm E 1.0 mm at 10 km', [1.0, 1.0, 10], 1.5], ['N 1.0 mm E 1.0 mm at 25 km', [1.0, 1.0, 25], 1.9], ['N 1.0 mm E 1.0 mm at 50 km', [1.0, 1.0, 50], 2.6], ['N 1.0 mm E 1.0 mm at 75 km', [1.0, 1.0, 75], 2.8], ['N 0.2 mm E 5.0 mm at 0 km', [0.2, 5.0, 0], 1.4], ['N 0.2 mm E 5.0 mm at 5 km', [0.2, 5.0, 5], 1.45]], [['N 1.0 mm E 1.0 mm at 600 km', [1.0, 1.0, 600], 5.1], ['N 1.0 mm E 1.0 mm at 650 km', [1.0, 1.0, 650], None], ['N 0.2 mm E 5.0 mm at 0 km', [0.2, 5.0, 0], 1.4], ['N 0.2 mm E 5.0 mm at 5 km', [0.2, 5.0, 5], 1.45], ['N 0.2 mm E 5.0 mm at 10 km', [0.2, 5.0, 10], 1.5], ['N 0.2 mm E 5.0 mm at 25 km', [0.2, 5.0, 25], 1.9], ['N 0.2 mm E 5.0 mm at 50 km', [0.2, 5.0, 50], 2.6], ['N 0.2 mm E 5.0 mm at 150 km', [0.2, 5.0, 150], 3.25]], [['N 0.2 mm E 5.0 mm at 75 km', [0.2, 5.0, 75], 2.8], ['N 0.2 mm E 5.0 mm at 150 km', [0.2, 5.0, 150], 3.25], ['N 0.2 mm E 5.0 mm at 600 km', [0.2, 5.0, 600], 5.1], ['N 0.2 mm E 5.0 mm at 650 km', [0.2, 5.0, 650], None], ['N 12.0 mm E 0.0 mm at 0 km', [12.0, 0.0, 0], 2.48], ['N 12.0 mm E 0.0 mm at 5 km', [12.0, 0.0, 5], 2.53], ['N 12.0 mm E 0.0 mm at 10 km', [12.0, 0.0, 10], 2.58], ['N 0.05 mm E 0.08 mm at 25 km', [0.05, 0.08, 25], 0.7]], [['N 12.0 mm E 0.0 mm at 25 km', [12.0, 0.0, 25], 2.98], ['N 12.0 mm E 0.0 mm at 50 km', [12.0, 0.0, 50], 3.68], ['N 12.0 mm E 0.0 mm at 75 km', [12.0, 0.0, 75], 3.88], ['N 12.0 mm E 0.0 mm at 150 km', [12.0, 0.0, 150], 4.33], ['N 12.0 mm E 0.0 mm at 600 km', [12.0, 0.0, 600], 6.18], ['N 12.0 mm E 0.0 mm at 650 km', [12.0, 0.0, 650], None], ['N 0.05 mm E 0.08 mm at 5 km', [0.05, 0.08, 5], 0.25], ['N 30.0 mm E 8.0 mm at 0 km', [30.0, 8.0, 0], 2.59]], [['N 0.0 mm E 0.0 mm at 5 km', [0.0, 0.0, 5], None], ['N 0.0 mm E 0.0 mm at 10 km', [0.0, 0.0, 10], None], ['N 0.0 mm E 0.0 mm at 25 km', [0.0, 0.0, 25], None], ['N 0.0 mm E 0.0 mm at 50 km', [0.0, 0.0, 50], None], ['N 0.0 mm E 0.0 mm at 75 km', [0.0, 0.0, 75], None], ['N 0.0 mm E 0.0 mm at 150 km', [0.0, 0.0, 150], None], ['N 0.05 mm E 0.08 mm at 50 km', [0.05, 0.08, 50], 1.4], ['N 30.0 mm E 8.0 mm at 75 km', [30.0, 8.0, 75], 3.99]]]
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 fixture	Actual	Expected	Outcome
N 1.0 mm E 1.0 mm at 0 km	`1.4`	`1.4`	Passed
N 1.0 mm E 1.0 mm at 5 km	`1.45`	`1.45`	Passed
N 1.0 mm E 1.0 mm at 10 km	`1.5`	`1.5`	Passed
N 1.0 mm E 1.0 mm at 25 km	`1.9`	`1.9`	Passed
N 1.0 mm E 1.0 mm at 50 km	`2.6`	`2.6`	Passed
N 1.0 mm E 1.0 mm at 75 km	`2.8`	`2.8`	Passed
N 0.2 mm E 5.0 mm at 0 km	`1.81`	`1.4`	Failed
N 0.2 mm E 5.0 mm at 5 km	`1.86`	`1.45`	Failed

SHA-256 / c09d4e450eba19d9513e6a80c8497b7fc2268b57cfaf775fa8129bdf79a760cb

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(amp_n_mm, amp_e_mm, dist_km):
    table = [(0, 1.4), (10, 1.5), (20, 1.7), (30, 2.1), (50, 2.6), (100, 3.0), (200, 3.5), (300, 4.0), (400, 4.5), (600, 5.1)]
    if dist_km < 0 or dist_km > 600:
        return None
    comps = [a for a in (amp_n_mm, amp_e_mm) if a > 0]
    if not comps:
        return None
    corr = None
    for (d0, c0), (d1, c1) in zip(table, table[1:]):
        if d0 <= dist_km <= d1:
            corr = c0 + (c1 - c0) * (dist_km - d0) / (d1 - d0)
            break
    logs = [math.log10(max(comps))]
    return round(sum(logs) / len(logs) + corr, 2)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['N 1.0 mm E 1.0 mm at 0 km', [1.0, 1.0, 0], 1.4], ['N 1.0 mm E 1.0 mm at 5 km', [1.0, 1.0, 5], 1.45], ['N 1.0 mm E 1.0 mm at 10 km', [1.0, 1.0, 10], 1.5], ['N 1.0 mm E 1.0 mm at 25 km', [1.0, 1.0, 25], 1.9], ['N 1.0 mm E 1.0 mm at 50 km', [1.0, 1.0, 50], 2.6], ['N 1.0 mm E 1.0 mm at 75 km', [1.0, 1.0, 75], 2.8], ['N 0.2 mm E 5.0 mm at 0 km', [0.2, 5.0, 0], 1.4], ['N 0.2 mm E 5.0 mm at 5 km', [0.2, 5.0, 5], 1.45]], [['N 1.0 mm E 1.0 mm at 600 km', [1.0, 1.0, 600], 5.1], ['N 1.0 mm E 1.0 mm at 650 km', [1.0, 1.0, 650], None], ['N 0.2 mm E 5.0 mm at 0 km', [0.2, 5.0, 0], 1.4], ['N 0.2 mm E 5.0 mm at 5 km', [0.2, 5.0, 5], 1.45], ['N 0.2 mm E 5.0 mm at 10 km', [0.2, 5.0, 10], 1.5], ['N 0.2 mm E 5.0 mm at 25 km', [0.2, 5.0, 25], 1.9], ['N 0.2 mm E 5.0 mm at 50 km', [0.2, 5.0, 50], 2.6], ['N 0.2 mm E 5.0 mm at 150 km', [0.2, 5.0, 150], 3.25]], [['N 0.2 mm E 5.0 mm at 75 km', [0.2, 5.0, 75], 2.8], ['N 0.2 mm E 5.0 mm at 150 km', [0.2, 5.0, 150], 3.25], ['N 0.2 mm E 5.0 mm at 600 km', [0.2, 5.0, 600], 5.1], ['N 0.2 mm E 5.0 mm at 650 km', [0.2, 5.0, 650], None], ['N 12.0 mm E 0.0 mm at 0 km', [12.0, 0.0, 0], 2.48], ['N 12.0 mm E 0.0 mm at 5 km', [12.0, 0.0, 5], 2.53], ['N 12.0 mm E 0.0 mm at 10 km', [12.0, 0.0, 10], 2.58], ['N 0.05 mm E 0.08 mm at 25 km', [0.05, 0.08, 25], 0.7]], [['N 12.0 mm E 0.0 mm at 25 km', [12.0, 0.0, 25], 2.98], ['N 12.0 mm E 0.0 mm at 50 km', [12.0, 0.0, 50], 3.68], ['N 12.0 mm E 0.0 mm at 75 km', [12.0, 0.0, 75], 3.88], ['N 12.0 mm E 0.0 mm at 150 km', [12.0, 0.0, 150], 4.33], ['N 12.0 mm E 0.0 mm at 600 km', [12.0, 0.0, 600], 6.18], ['N 12.0 mm E 0.0 mm at 650 km', [12.0, 0.0, 650], None], ['N 0.05 mm E 0.08 mm at 5 km', [0.05, 0.08, 5], 0.25], ['N 30.0 mm E 8.0 mm at 0 km', [30.0, 8.0, 0], 2.59]], [['N 0.0 mm E 0.0 mm at 5 km', [0.0, 0.0, 5], None], ['N 0.0 mm E 0.0 mm at 10 km', [0.0, 0.0, 10], None], ['N 0.0 mm E 0.0 mm at 25 km', [0.0, 0.0, 25], None], ['N 0.0 mm E 0.0 mm at 50 km', [0.0, 0.0, 50], None], ['N 0.0 mm E 0.0 mm at 75 km', [0.0, 0.0, 75], None], ['N 0.0 mm E 0.0 mm at 150 km', [0.0, 0.0, 150], None], ['N 0.05 mm E 0.08 mm at 50 km', [0.05, 0.08, 50], 1.4], ['N 30.0 mm E 8.0 mm at 75 km', [30.0, 8.0, 75], 3.99]]]
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 fixture	Actual	Expected	Outcome
N 1.0 mm E 1.0 mm at 0 km	`1.4`	`1.4`	Passed
N 1.0 mm E 1.0 mm at 5 km	`1.45`	`1.45`	Passed
N 1.0 mm E 1.0 mm at 10 km	`1.5`	`1.5`	Passed
N 1.0 mm E 1.0 mm at 25 km	`1.9`	`1.9`	Passed
N 1.0 mm E 1.0 mm at 50 km	`2.6`	`2.6`	Passed
N 1.0 mm E 1.0 mm at 75 km	`2.8`	`2.8`	Passed
N 0.2 mm E 5.0 mm at 0 km	`2.1`	`1.4`	Failed
N 0.2 mm E 5.0 mm at 5 km	`2.15`	`1.45`	Failed

SHA-256 / 3707fb5ce4ae61fa2f8b2cfd42f4e49a4e36cf77a5d3e9ddb2008d240ca80680

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 2026-09-29T14:48:31.982540+00:00.

Case digest / 5caf2938030b4e7544828472aa55596f227996d4bf6561a261c4abd758c95933