FA-71711 / Seismic magnitude estimation / Open access

Richter -log A0 table magnitude: interpolation anchor node · case 01

Between table nodes the distance correction moves in the wrong direction; only node distances are right.

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

ROOT CAUSE

The interpolation starts from the upper node value while measuring the fraction from the lower node.

VERIFIED REPAIR

Interpolate c0 + (c1 - c0)*(d - d0)/(d1 - d0).

Unsuccessful approach: Floor-dividing the fraction turns the table into a step function.

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 = c1 - (c1 - c0) * (dist_km - d0) / (d1 - d0)
            break
    logs = [math.log10(a) for a in 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 1.0 mm E 1.0 mm at 150 km', [1.0, 1.0, 150], 3.25], ['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 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 75 km', [0.2, 5.0, 75], 2.8]], [['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 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 150 km', [12.0, 0.0, 150], 4.33]], [['N 12.0 mm E 0.0 mm at 10 km', [12.0, 0.0, 10], 2.58], ['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 30.0 mm E 8.0 mm at 5 km', [30.0, 8.0, 5], 2.64]], [['N 1.0 mm E 1.0 mm at 25 km', [1.0, 1.0, 25], 1.9], ['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 0 km', [0.05, 0.08, 0], 0.2]]]
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	`1.5`	`1.4`	Failed
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	`1.4`	`1.5`	Failed
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	`2.1`	`2.6`	Failed
N 1.0 mm E 1.0 mm at 75 km	`2.8`	`2.8`	Passed
N 1.0 mm E 1.0 mm at 150 km	`3.25`	`3.25`	Passed
N 1.0 mm E 1.0 mm at 600 km	`4.5`	`5.1`	Failed

SHA-256 / f868e9848824ed661552ac4a822ce1d66a4cc9ac28ff222c480004c56e0e95e5

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(a) for a in 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 1.0 mm E 1.0 mm at 150 km', [1.0, 1.0, 150], 3.25], ['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 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 75 km', [0.2, 5.0, 75], 2.8]], [['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 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 150 km', [12.0, 0.0, 150], 4.33]], [['N 12.0 mm E 0.0 mm at 10 km', [12.0, 0.0, 10], 2.58], ['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 30.0 mm E 8.0 mm at 5 km', [30.0, 8.0, 5], 2.64]], [['N 1.0 mm E 1.0 mm at 25 km', [1.0, 1.0, 25], 1.9], ['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 0 km', [0.05, 0.08, 0], 0.2]]]
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	`1.4`	`1.45`	Failed
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	`1.7`	`1.9`	Failed
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	`2.6`	`2.8`	Failed
N 1.0 mm E 1.0 mm at 150 km	`3.0`	`3.25`	Failed
N 1.0 mm E 1.0 mm at 600 km	`5.1`	`5.1`	Passed

SHA-256 / 322ea505450ad1f3824561320d6f5fc94ea8467450505e246e4c1a497877fc7e

3 / The verified repair

Exit 0

"""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(a) for a in 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 1.0 mm E 1.0 mm at 150 km', [1.0, 1.0, 150], 3.25], ['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 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 75 km', [0.2, 5.0, 75], 2.8]], [['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 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 150 km', [12.0, 0.0, 150], 4.33]], [['N 12.0 mm E 0.0 mm at 10 km', [12.0, 0.0, 10], 2.58], ['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 30.0 mm E 8.0 mm at 5 km', [30.0, 8.0, 5], 2.64]], [['N 1.0 mm E 1.0 mm at 25 km', [1.0, 1.0, 25], 1.9], ['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 0 km', [0.05, 0.08, 0], 0.2]]]
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 1.0 mm E 1.0 mm at 150 km	`3.25`	`3.25`	Passed
N 1.0 mm E 1.0 mm at 600 km	`5.1`	`5.1`	Passed

SHA-256 / 985a769e8f8a1e365a6a1d48b141f0bfc5040b17525bea347f51fff3ab0330a1

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 2026-09-29T14:48:32.136518+00:00.

Case digest / b42822d3f265c38fbdb464eb3570a505c4ae5d5f861d31c3946f7ee541612439