FA-71431 / Seismic magnitude estimation / Open access

Teleseismic body-wave magnitude: amplitude over period · case 01

Long-period readings inflate mb.

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

ROOT CAUSE

The amplitude is multiplied by the period instead of divided.

VERIFIED REPAIR

Use log10(A/T).

Unsuccessful approach: Dividing the logarithm by T is not a ground-velocity proxy.

Case contract

P amplitude in micrometres, period in s, epicentral distance in degrees. Valid only for 20 <= delta <= 100 and 0 < period <= 3.0 (else None). Q(delta) is linearly interpolated from [(20,6.0),(30,6.5),(40,6.8),(60,6.9),(80,7.0),(100,7.4)]. mb = log10(A/T) + Q, rounded 0.01.

Why this case matters

mb is the first teleseismic magnitude available for global events.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(amp_um, period_s, delta_deg):
    table = [(20, 6.0), (30, 6.5), (40, 6.8), (60, 6.9), (80, 7.0), (100, 7.4)]
    if not (20 <= delta_deg <= 100):
        return None
    if period_s <= 0 or period_s > 3.0:
        return None
    q = None
    for (d0, q0), (d1, q1) in zip(table, table[1:]):
        if d0 <= delta_deg <= d1:
            q = q0 + (q1 - q0) * (delta_deg - d0) / (d1 - d0)
            break
    return round(math.log10(amp_um * period_s) + q, 2)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['0.05 um 0.5 s at 15 deg', [0.05, 0.5, 15], None], ['0.05 um 0.5 s at 20 deg', [0.05, 0.5, 20], 5.0], ['0.05 um 0.5 s at 25 deg', [0.05, 0.5, 25], 5.25], ['0.05 um 0.5 s at 45 deg', [0.05, 0.5, 45], 5.83], ['0.05 um 0.5 s at 70 deg', [0.05, 0.5, 70], 5.95], ['0.05 um 0.5 s at 99 deg', [0.05, 0.5, 99], 6.38], ['0.05 um 0.5 s at 100 deg', [0.05, 0.5, 100], 6.4], ['0.05 um 0.5 s at 101 deg', [0.05, 0.5, 101], None]], [['0.05 um 0.5 s at 70 deg', [0.05, 0.5, 70], 5.95], ['0.05 um 0.5 s at 101 deg', [0.05, 0.5, 101], None], ['0.05 um 1.0 s at 15 deg', [0.05, 1.0, 15], None], ['0.05 um 1.0 s at 20 deg', [0.05, 1.0, 20], 4.7], ['0.05 um 1.0 s at 25 deg', [0.05, 1.0, 25], 4.95], ['0.05 um 1.0 s at 45 deg', [0.05, 1.0, 45], 5.52], ['0.05 um 1.0 s at 70 deg', [0.05, 1.0, 70], 5.65], ['0.05 um 2.0 s at 20 deg', [0.05, 2.0, 20], 4.4]], [['0.05 um 1.0 s at 100 deg', [0.05, 1.0, 100], 6.1], ['0.05 um 1.0 s at 101 deg', [0.05, 1.0, 101], None], ['0.05 um 2.0 s at 15 deg', [0.05, 2.0, 15], None], ['0.05 um 2.0 s at 20 deg', [0.05, 2.0, 20], 4.4], ['0.05 um 2.0 s at 25 deg', [0.05, 2.0, 25], 4.65], ['0.05 um 2.0 s at 45 deg', [0.05, 2.0, 45], 5.22], ['0.05 um 2.0 s at 70 deg', [0.05, 2.0, 70], 5.35], ['0.05 um 2.0 s at 100 deg', [0.05, 2.0, 100], 5.8]], [['0.05 um 2.0 s at 70 deg', [0.05, 2.0, 70], 5.35], ['0.05 um 2.0 s at 99 deg', [0.05, 2.0, 99], 5.78], ['0.05 um 2.0 s at 100 deg', [0.05, 2.0, 100], 5.8], ['0.05 um 2.0 s at 101 deg', [0.05, 2.0, 101], None], ['0.05 um 3.0 s at 15 deg', [0.05, 3.0, 15], None], ['0.05 um 3.0 s at 20 deg', [0.05, 3.0, 20], 4.22], ['0.05 um 3.0 s at 25 deg', [0.05, 3.0, 25], 4.47], ['0.05 um 3.0 s at 99 deg', [0.05, 3.0, 99], 5.6]], [['0.05 um 3.0 s at 20 deg', [0.05, 3.0, 20], 4.22], ['0.05 um 3.0 s at 70 deg', [0.05, 3.0, 70], 5.17], ['0.05 um 3.0 s at 99 deg', [0.05, 3.0, 99], 5.6], ['0.05 um 3.0 s at 100 deg', [0.05, 3.0, 100], 5.62], ['0.05 um 3.0 s at 101 deg', [0.05, 3.0, 101], None], ['0.05 um 3.5 s at 15 deg', [0.05, 3.5, 15], None], ['0.05 um 3.5 s at 20 deg', [0.05, 3.5, 20], None], ['0.4 um 0.5 s at 70 deg', [0.4, 0.5, 70], 6.85]]]
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
0.05 um 0.5 s at 15 deg	`None`	`None`	Passed
0.05 um 0.5 s at 20 deg	`4.4`	`5.0`	Failed
0.05 um 0.5 s at 25 deg	`4.65`	`5.25`	Failed
0.05 um 0.5 s at 45 deg	`5.22`	`5.83`	Failed
0.05 um 0.5 s at 70 deg	`5.35`	`5.95`	Failed
0.05 um 0.5 s at 99 deg	`5.78`	`6.38`	Failed
0.05 um 0.5 s at 100 deg	`5.8`	`6.4`	Failed
0.05 um 0.5 s at 101 deg	`None`	`None`	Passed

SHA-256 / 7166bfa1efd0090a9e08cdefcf36ec1268a5d00514933be0c93b312a2f2c46cd

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(amp_um, period_s, delta_deg):
    table = [(20, 6.0), (30, 6.5), (40, 6.8), (60, 6.9), (80, 7.0), (100, 7.4)]
    if not (20 <= delta_deg <= 100):
        return None
    if period_s <= 0 or period_s > 3.0:
        return None
    q = None
    for (d0, q0), (d1, q1) in zip(table, table[1:]):
        if d0 <= delta_deg <= d1:
            q = q0 + (q1 - q0) * (delta_deg - d0) / (d1 - d0)
            break
    return round(math.log10(amp_um) / period_s + q, 2)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['0.05 um 0.5 s at 15 deg', [0.05, 0.5, 15], None], ['0.05 um 0.5 s at 20 deg', [0.05, 0.5, 20], 5.0], ['0.05 um 0.5 s at 25 deg', [0.05, 0.5, 25], 5.25], ['0.05 um 0.5 s at 45 deg', [0.05, 0.5, 45], 5.83], ['0.05 um 0.5 s at 70 deg', [0.05, 0.5, 70], 5.95], ['0.05 um 0.5 s at 99 deg', [0.05, 0.5, 99], 6.38], ['0.05 um 0.5 s at 100 deg', [0.05, 0.5, 100], 6.4], ['0.05 um 0.5 s at 101 deg', [0.05, 0.5, 101], None]], [['0.05 um 0.5 s at 70 deg', [0.05, 0.5, 70], 5.95], ['0.05 um 0.5 s at 101 deg', [0.05, 0.5, 101], None], ['0.05 um 1.0 s at 15 deg', [0.05, 1.0, 15], None], ['0.05 um 1.0 s at 20 deg', [0.05, 1.0, 20], 4.7], ['0.05 um 1.0 s at 25 deg', [0.05, 1.0, 25], 4.95], ['0.05 um 1.0 s at 45 deg', [0.05, 1.0, 45], 5.52], ['0.05 um 1.0 s at 70 deg', [0.05, 1.0, 70], 5.65], ['0.05 um 2.0 s at 20 deg', [0.05, 2.0, 20], 4.4]], [['0.05 um 1.0 s at 100 deg', [0.05, 1.0, 100], 6.1], ['0.05 um 1.0 s at 101 deg', [0.05, 1.0, 101], None], ['0.05 um 2.0 s at 15 deg', [0.05, 2.0, 15], None], ['0.05 um 2.0 s at 20 deg', [0.05, 2.0, 20], 4.4], ['0.05 um 2.0 s at 25 deg', [0.05, 2.0, 25], 4.65], ['0.05 um 2.0 s at 45 deg', [0.05, 2.0, 45], 5.22], ['0.05 um 2.0 s at 70 deg', [0.05, 2.0, 70], 5.35], ['0.05 um 2.0 s at 100 deg', [0.05, 2.0, 100], 5.8]], [['0.05 um 2.0 s at 70 deg', [0.05, 2.0, 70], 5.35], ['0.05 um 2.0 s at 99 deg', [0.05, 2.0, 99], 5.78], ['0.05 um 2.0 s at 100 deg', [0.05, 2.0, 100], 5.8], ['0.05 um 2.0 s at 101 deg', [0.05, 2.0, 101], None], ['0.05 um 3.0 s at 15 deg', [0.05, 3.0, 15], None], ['0.05 um 3.0 s at 20 deg', [0.05, 3.0, 20], 4.22], ['0.05 um 3.0 s at 25 deg', [0.05, 3.0, 25], 4.47], ['0.05 um 3.0 s at 99 deg', [0.05, 3.0, 99], 5.6]], [['0.05 um 3.0 s at 20 deg', [0.05, 3.0, 20], 4.22], ['0.05 um 3.0 s at 70 deg', [0.05, 3.0, 70], 5.17], ['0.05 um 3.0 s at 99 deg', [0.05, 3.0, 99], 5.6], ['0.05 um 3.0 s at 100 deg', [0.05, 3.0, 100], 5.62], ['0.05 um 3.0 s at 101 deg', [0.05, 3.0, 101], None], ['0.05 um 3.5 s at 15 deg', [0.05, 3.5, 15], None], ['0.05 um 3.5 s at 20 deg', [0.05, 3.5, 20], None], ['0.4 um 0.5 s at 70 deg', [0.4, 0.5, 70], 6.85]]]
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
0.05 um 0.5 s at 15 deg	`None`	`None`	Passed
0.05 um 0.5 s at 20 deg	`3.4`	`5.0`	Failed
0.05 um 0.5 s at 25 deg	`3.65`	`5.25`	Failed
0.05 um 0.5 s at 45 deg	`4.22`	`5.83`	Failed
0.05 um 0.5 s at 70 deg	`4.35`	`5.95`	Failed
0.05 um 0.5 s at 99 deg	`4.78`	`6.38`	Failed
0.05 um 0.5 s at 100 deg	`4.8`	`6.4`	Failed
0.05 um 0.5 s at 101 deg	`None`	`None`	Passed

SHA-256 / 746337d00042c08b806153fd81c5b8e9044130eafb5ee11432e5ab29e21ba690

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(amp_um, period_s, delta_deg):
    table = [(20, 6.0), (30, 6.5), (40, 6.8), (60, 6.9), (80, 7.0), (100, 7.4)]
    if not (20 <= delta_deg <= 100):
        return None
    if period_s <= 0 or period_s > 3.0:
        return None
    q = None
    for (d0, q0), (d1, q1) in zip(table, table[1:]):
        if d0 <= delta_deg <= d1:
            q = q0 + (q1 - q0) * (delta_deg - d0) / (d1 - d0)
            break
    return round(math.log10(amp_um / period_s) + q, 2)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['0.05 um 0.5 s at 15 deg', [0.05, 0.5, 15], None], ['0.05 um 0.5 s at 20 deg', [0.05, 0.5, 20], 5.0], ['0.05 um 0.5 s at 25 deg', [0.05, 0.5, 25], 5.25], ['0.05 um 0.5 s at 45 deg', [0.05, 0.5, 45], 5.83], ['0.05 um 0.5 s at 70 deg', [0.05, 0.5, 70], 5.95], ['0.05 um 0.5 s at 99 deg', [0.05, 0.5, 99], 6.38], ['0.05 um 0.5 s at 100 deg', [0.05, 0.5, 100], 6.4], ['0.05 um 0.5 s at 101 deg', [0.05, 0.5, 101], None]], [['0.05 um 0.5 s at 70 deg', [0.05, 0.5, 70], 5.95], ['0.05 um 0.5 s at 101 deg', [0.05, 0.5, 101], None], ['0.05 um 1.0 s at 15 deg', [0.05, 1.0, 15], None], ['0.05 um 1.0 s at 20 deg', [0.05, 1.0, 20], 4.7], ['0.05 um 1.0 s at 25 deg', [0.05, 1.0, 25], 4.95], ['0.05 um 1.0 s at 45 deg', [0.05, 1.0, 45], 5.52], ['0.05 um 1.0 s at 70 deg', [0.05, 1.0, 70], 5.65], ['0.05 um 2.0 s at 20 deg', [0.05, 2.0, 20], 4.4]], [['0.05 um 1.0 s at 100 deg', [0.05, 1.0, 100], 6.1], ['0.05 um 1.0 s at 101 deg', [0.05, 1.0, 101], None], ['0.05 um 2.0 s at 15 deg', [0.05, 2.0, 15], None], ['0.05 um 2.0 s at 20 deg', [0.05, 2.0, 20], 4.4], ['0.05 um 2.0 s at 25 deg', [0.05, 2.0, 25], 4.65], ['0.05 um 2.0 s at 45 deg', [0.05, 2.0, 45], 5.22], ['0.05 um 2.0 s at 70 deg', [0.05, 2.0, 70], 5.35], ['0.05 um 2.0 s at 100 deg', [0.05, 2.0, 100], 5.8]], [['0.05 um 2.0 s at 70 deg', [0.05, 2.0, 70], 5.35], ['0.05 um 2.0 s at 99 deg', [0.05, 2.0, 99], 5.78], ['0.05 um 2.0 s at 100 deg', [0.05, 2.0, 100], 5.8], ['0.05 um 2.0 s at 101 deg', [0.05, 2.0, 101], None], ['0.05 um 3.0 s at 15 deg', [0.05, 3.0, 15], None], ['0.05 um 3.0 s at 20 deg', [0.05, 3.0, 20], 4.22], ['0.05 um 3.0 s at 25 deg', [0.05, 3.0, 25], 4.47], ['0.05 um 3.0 s at 99 deg', [0.05, 3.0, 99], 5.6]], [['0.05 um 3.0 s at 20 deg', [0.05, 3.0, 20], 4.22], ['0.05 um 3.0 s at 70 deg', [0.05, 3.0, 70], 5.17], ['0.05 um 3.0 s at 99 deg', [0.05, 3.0, 99], 5.6], ['0.05 um 3.0 s at 100 deg', [0.05, 3.0, 100], 5.62], ['0.05 um 3.0 s at 101 deg', [0.05, 3.0, 101], None], ['0.05 um 3.5 s at 15 deg', [0.05, 3.5, 15], None], ['0.05 um 3.5 s at 20 deg', [0.05, 3.5, 20], None], ['0.4 um 0.5 s at 70 deg', [0.4, 0.5, 70], 6.85]]]
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
0.05 um 0.5 s at 15 deg	`None`	`None`	Passed
0.05 um 0.5 s at 20 deg	`5.0`	`5.0`	Passed
0.05 um 0.5 s at 25 deg	`5.25`	`5.25`	Passed
0.05 um 0.5 s at 45 deg	`5.83`	`5.83`	Passed
0.05 um 0.5 s at 70 deg	`5.95`	`5.95`	Passed
0.05 um 0.5 s at 99 deg	`6.38`	`6.38`	Passed
0.05 um 0.5 s at 100 deg	`6.4`	`6.4`	Passed
0.05 um 0.5 s at 101 deg	`None`	`None`	Passed

SHA-256 / 7558bc3c2e9ceec053cc45f0875d7601be49d942b54b1cfe3fd8eb14b724c12b

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 2026-09-29T14:48:29.631232+00:00.

Case digest / 3ae9bfab84d85c56185a075db1b575527cd3fc33904d1b200ed2cbfd65a493b9