FA-71456 / Seismic magnitude estimation / Open access

Prague surface-wave magnitude: distance term log base · case 01

Ms is about 1.5 units too high.

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

ROOT CAUSE

The distance term uses the natural log.

VERIFIED REPAIR

Use log10 of distance in degrees.

Unsuccessful approach: Converting degrees to km inside the log adds 3.4 units.

Case contract

readings are [amplitude um, period s, distance deg]. Events with depth >= 60 km return None. Use only readings with 18 <= T <= 22, 20 <= delta <= 160 and positive amplitude; Ms_i = log10(A/T) + 1.66 log10(delta) + 3.3; return [mean rounded 0.01, count] or None.

Why this case matters

Ms remains the reference shallow-event magnitude in historical catalogues.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(readings, depth_km):
    if depth_km >= 60:
        return None
    vals = []
    for a, t, d in readings:
        if 18 <= t <= 22 and 20 <= d <= 160 and a > 0:
            vals.append(math.log10(a / t) + 1.66 * math.log(d) + 3.3)
    if not vals:
        return None
    return [round(sum(vals) / len(vals), 2), len(vals)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['Ms event 0', [[[5.0, 20, 10], [300.0, 15, 45], [40.0, 15, 160]], 60], None], ['Ms event 1', [[[40.0, 18, 170], [0, 15, 45], [40.0, 15, 90], [5.0, 15, 160]], 33], None], ['Ms event 2', [[[0, 22, 160], [40.0, 20, 160], [300.0, 17, 170], [0, 22, 90]], 10], [7.26, 1]], ['Ms event 3', [[[5.0, 22, 160], [5.0, 23, 10], [0, 23, 20]], 33], [6.32, 1]], ['Ms event 4', [[[5.0, 22, 10], [40.0, 23, 45], [5.0, 15, 45], [40.0, 18, 170]], 33], None], ['Ms event 5', [[[40.0, 20, 45], [40.0, 20, 160]], 61], None], ['Ms event 6', [[[300.0, 15, 20], [5.0, 20, 160], [0.8, 18, 45], [40.0, 20, 45]], 61], None], ['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]]], [['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]], ['Ms event 8', [[[300.0, 17, 170], [0.8, 23, 170], [0.8, 15, 90], [0.8, 18, 160]], 33], [5.61, 1]], ['Ms event 9', [[[40.0, 23, 45], [0.8, 22, 10], [300.0, 22, 90], [0.8, 23, 45]], 60], None], ['Ms event 10', [[[300.0, 23, 160], [5.0, 15, 160]], 61], None], ['Ms event 11', [[[5.0, 18, 10], [40.0, 15, 20]], 60], None], ['Ms event 12', [[[300.0, 22, 45], [0.8, 22, 170], [0.8, 15, 170], [40.0, 23, 170], [5.0, 22, 10]], 60], None], ['Ms event 13', [[[40.0, 17, 170], [300.0, 18, 45], [5.0, 22, 160], [5.0, 18, 20], [0.8, 20, 20]], 59], [5.64, 4]], ['Ms event 18', [[[40.0, 22, 170], [5.0, 22, 160], [5.0, 20, 90]], 33], [6.13, 2]]], [['Ms event 14', [[[0, 20, 160], [40.0, 17, 10], [0.8, 22, 10], [300.0, 20, 170]], 10], None], ['Ms event 15', [[[5.0, 20, 170], [0.8, 18, 90], [0, 15, 90], [300.0, 15, 20]], 33], [5.19, 1]], ['Ms event 16', [[[0.8, 23, 10], [0, 15, 90]], 59], None], ['Ms event 17', [[[5.0, 18, 10], [0.8, 22, 90], [0, 17, 160], [0.8, 17, 45], [0, 22, 20]], 61], None], ['Ms event 18', [[[40.0, 22, 170], [5.0, 22, 160], [5.0, 20, 90]], 33], [6.13, 2]], ['Ms event 19', [[[5.0, 20, 10], [40.0, 15, 45], [5.0, 18, 90], [0.8, 15, 90]], 70], None], ['Ms event 20', [[[0.8, 22, 20], [40.0, 15, 170]], 70], None], ['Ms event 36', [[[0, 18, 20], [300.0, 22, 10], [0.8, 22, 160], [0, 22, 10], [0.8, 22, 20]], 59], [4.77, 2]]], [['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]], ['Ms event 21', [[[40.0, 17, 20], [5.0, 17, 90], [0.8, 20, 170], [300.0, 23, 170], [0, 15, 90]], 33], None], ['Ms event 22', [[[5.0, 18, 20], [5.0, 15, 160], [0.8, 17, 90], [0, 15, 160]], 33], [4.9, 1]], ['Ms event 23', [[[40.0, 18, 10], [40.0, 22, 20], [0.8, 18, 170], [5.0, 17, 10]], 59], [5.72, 1]], ['Ms event 24', [[[40.0, 20, 45], [0.8, 18, 20], [5.0, 17, 20], [300.0, 18, 170]], 70], None], ['Ms event 25', [[[0.8, 18, 20], [40.0, 20, 20], [0, 20, 160], [40.0, 15, 160], [40.0, 17, 170]], 60], None], ['Ms event 26', [[[0, 15, 170], [0.8, 17, 90], [300.0, 17, 90], [300.0, 22, 10]], 70], None], ['Ms event 28', [[[300.0, 20, 45], [40.0, 22, 170]], 10], [7.22, 1]]], [['Ms event 22', [[[5.0, 18, 20], [5.0, 15, 160], [0.8, 17, 90], [0, 15, 160]], 33], [4.9, 1]], ['Ms event 28', [[[300.0, 20, 45], [40.0, 22, 170]], 10], [7.22, 1]], ['Ms event 29', [[[40.0, 17, 160], [40.0, 22, 170], [0, 20, 45], [0, 20, 170]], 61], None], ['Ms event 30', [[[0.8, 17, 10], [40.0, 20, 90], [0.8, 17, 45]], 61], None], ['Ms event 31', [[[300.0, 20, 90], [0.8, 22, 45], [40.0, 22, 45], [40.0, 18, 170], [300.0, 22, 170]], 10], [6.21, 3]], ['Ms event 32', [[[40.0, 17, 90]], 10], None], ['Ms event 33', [[[5.0, 23, 10], [0.8, 23, 90], [5.0, 23, 160], [0, 22, 160]], 61], None], ['three stations', [[[10.0, 20, 40], [20.0, 20, 60], [80.0, 18, 30]], 15], [6.1, 3]]]]
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
Ms event 0	`None`	`None`	Passed
Ms event 1	`None`	`None`	Passed
Ms event 2	`[12.03, 1]`	`[7.26, 1]`	Failed
Ms event 3	`[11.08, 1]`	`[6.32, 1]`	Failed
Ms event 4	`None`	`None`	Passed
Ms event 5	`None`	`None`	Passed
Ms event 6	`None`	`None`	Passed
Ms event 7	`[11.02, 2]`	`[6.85, 2]`	Failed

SHA-256 / c41ba4e2191acf3d158c6e40ff240341fd3f83d29f7e26f8dde336217981bbb0

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(readings, depth_km):
    if depth_km >= 60:
        return None
    vals = []
    for a, t, d in readings:
        if 18 <= t <= 22 and 20 <= d <= 160 and a > 0:
            vals.append(math.log10(a / t) + 1.66 * math.log10(d * 111.19) + 3.3)
    if not vals:
        return None
    return [round(sum(vals) / len(vals), 2), len(vals)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['Ms event 0', [[[5.0, 20, 10], [300.0, 15, 45], [40.0, 15, 160]], 60], None], ['Ms event 1', [[[40.0, 18, 170], [0, 15, 45], [40.0, 15, 90], [5.0, 15, 160]], 33], None], ['Ms event 2', [[[0, 22, 160], [40.0, 20, 160], [300.0, 17, 170], [0, 22, 90]], 10], [7.26, 1]], ['Ms event 3', [[[5.0, 22, 160], [5.0, 23, 10], [0, 23, 20]], 33], [6.32, 1]], ['Ms event 4', [[[5.0, 22, 10], [40.0, 23, 45], [5.0, 15, 45], [40.0, 18, 170]], 33], None], ['Ms event 5', [[[40.0, 20, 45], [40.0, 20, 160]], 61], None], ['Ms event 6', [[[300.0, 15, 20], [5.0, 20, 160], [0.8, 18, 45], [40.0, 20, 45]], 61], None], ['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]]], [['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]], ['Ms event 8', [[[300.0, 17, 170], [0.8, 23, 170], [0.8, 15, 90], [0.8, 18, 160]], 33], [5.61, 1]], ['Ms event 9', [[[40.0, 23, 45], [0.8, 22, 10], [300.0, 22, 90], [0.8, 23, 45]], 60], None], ['Ms event 10', [[[300.0, 23, 160], [5.0, 15, 160]], 61], None], ['Ms event 11', [[[5.0, 18, 10], [40.0, 15, 20]], 60], None], ['Ms event 12', [[[300.0, 22, 45], [0.8, 22, 170], [0.8, 15, 170], [40.0, 23, 170], [5.0, 22, 10]], 60], None], ['Ms event 13', [[[40.0, 17, 170], [300.0, 18, 45], [5.0, 22, 160], [5.0, 18, 20], [0.8, 20, 20]], 59], [5.64, 4]], ['Ms event 18', [[[40.0, 22, 170], [5.0, 22, 160], [5.0, 20, 90]], 33], [6.13, 2]]], [['Ms event 14', [[[0, 20, 160], [40.0, 17, 10], [0.8, 22, 10], [300.0, 20, 170]], 10], None], ['Ms event 15', [[[5.0, 20, 170], [0.8, 18, 90], [0, 15, 90], [300.0, 15, 20]], 33], [5.19, 1]], ['Ms event 16', [[[0.8, 23, 10], [0, 15, 90]], 59], None], ['Ms event 17', [[[5.0, 18, 10], [0.8, 22, 90], [0, 17, 160], [0.8, 17, 45], [0, 22, 20]], 61], None], ['Ms event 18', [[[40.0, 22, 170], [5.0, 22, 160], [5.0, 20, 90]], 33], [6.13, 2]], ['Ms event 19', [[[5.0, 20, 10], [40.0, 15, 45], [5.0, 18, 90], [0.8, 15, 90]], 70], None], ['Ms event 20', [[[0.8, 22, 20], [40.0, 15, 170]], 70], None], ['Ms event 36', [[[0, 18, 20], [300.0, 22, 10], [0.8, 22, 160], [0, 22, 10], [0.8, 22, 20]], 59], [4.77, 2]]], [['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]], ['Ms event 21', [[[40.0, 17, 20], [5.0, 17, 90], [0.8, 20, 170], [300.0, 23, 170], [0, 15, 90]], 33], None], ['Ms event 22', [[[5.0, 18, 20], [5.0, 15, 160], [0.8, 17, 90], [0, 15, 160]], 33], [4.9, 1]], ['Ms event 23', [[[40.0, 18, 10], [40.0, 22, 20], [0.8, 18, 170], [5.0, 17, 10]], 59], [5.72, 1]], ['Ms event 24', [[[40.0, 20, 45], [0.8, 18, 20], [5.0, 17, 20], [300.0, 18, 170]], 70], None], ['Ms event 25', [[[0.8, 18, 20], [40.0, 20, 20], [0, 20, 160], [40.0, 15, 160], [40.0, 17, 170]], 60], None], ['Ms event 26', [[[0, 15, 170], [0.8, 17, 90], [300.0, 17, 90], [300.0, 22, 10]], 70], None], ['Ms event 28', [[[300.0, 20, 45], [40.0, 22, 170]], 10], [7.22, 1]]], [['Ms event 22', [[[5.0, 18, 20], [5.0, 15, 160], [0.8, 17, 90], [0, 15, 160]], 33], [4.9, 1]], ['Ms event 28', [[[300.0, 20, 45], [40.0, 22, 170]], 10], [7.22, 1]], ['Ms event 29', [[[40.0, 17, 160], [40.0, 22, 170], [0, 20, 45], [0, 20, 170]], 61], None], ['Ms event 30', [[[0.8, 17, 10], [40.0, 20, 90], [0.8, 17, 45]], 61], None], ['Ms event 31', [[[300.0, 20, 90], [0.8, 22, 45], [40.0, 22, 45], [40.0, 18, 170], [300.0, 22, 170]], 10], [6.21, 3]], ['Ms event 32', [[[40.0, 17, 90]], 10], None], ['Ms event 33', [[[5.0, 23, 10], [0.8, 23, 90], [5.0, 23, 160], [0, 22, 160]], 61], None], ['three stations', [[[10.0, 20, 40], [20.0, 20, 60], [80.0, 18, 30]], 15], [6.1, 3]]]]
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
Ms event 0	`None`	`None`	Passed
Ms event 1	`None`	`None`	Passed
Ms event 2	`[10.66, 1]`	`[7.26, 1]`	Failed
Ms event 3	`[9.71, 1]`	`[6.32, 1]`	Failed
Ms event 4	`None`	`None`	Passed
Ms event 5	`None`	`None`	Passed
Ms event 6	`None`	`None`	Passed
Ms event 7	`[10.24, 2]`	`[6.85, 2]`	Failed

SHA-256 / 0527a9117da73ba674e2da78cc09d784498b367098feab9f85e4b8b659883a5d

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(readings, depth_km):
    if depth_km >= 60:
        return None
    vals = []
    for a, t, d in readings:
        if 18 <= t <= 22 and 20 <= d <= 160 and a > 0:
            vals.append(math.log10(a / t) + 1.66 * math.log10(d) + 3.3)
    if not vals:
        return None
    return [round(sum(vals) / len(vals), 2), len(vals)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['Ms event 0', [[[5.0, 20, 10], [300.0, 15, 45], [40.0, 15, 160]], 60], None], ['Ms event 1', [[[40.0, 18, 170], [0, 15, 45], [40.0, 15, 90], [5.0, 15, 160]], 33], None], ['Ms event 2', [[[0, 22, 160], [40.0, 20, 160], [300.0, 17, 170], [0, 22, 90]], 10], [7.26, 1]], ['Ms event 3', [[[5.0, 22, 160], [5.0, 23, 10], [0, 23, 20]], 33], [6.32, 1]], ['Ms event 4', [[[5.0, 22, 10], [40.0, 23, 45], [5.0, 15, 45], [40.0, 18, 170]], 33], None], ['Ms event 5', [[[40.0, 20, 45], [40.0, 20, 160]], 61], None], ['Ms event 6', [[[300.0, 15, 20], [5.0, 20, 160], [0.8, 18, 45], [40.0, 20, 45]], 61], None], ['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]]], [['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]], ['Ms event 8', [[[300.0, 17, 170], [0.8, 23, 170], [0.8, 15, 90], [0.8, 18, 160]], 33], [5.61, 1]], ['Ms event 9', [[[40.0, 23, 45], [0.8, 22, 10], [300.0, 22, 90], [0.8, 23, 45]], 60], None], ['Ms event 10', [[[300.0, 23, 160], [5.0, 15, 160]], 61], None], ['Ms event 11', [[[5.0, 18, 10], [40.0, 15, 20]], 60], None], ['Ms event 12', [[[300.0, 22, 45], [0.8, 22, 170], [0.8, 15, 170], [40.0, 23, 170], [5.0, 22, 10]], 60], None], ['Ms event 13', [[[40.0, 17, 170], [300.0, 18, 45], [5.0, 22, 160], [5.0, 18, 20], [0.8, 20, 20]], 59], [5.64, 4]], ['Ms event 18', [[[40.0, 22, 170], [5.0, 22, 160], [5.0, 20, 90]], 33], [6.13, 2]]], [['Ms event 14', [[[0, 20, 160], [40.0, 17, 10], [0.8, 22, 10], [300.0, 20, 170]], 10], None], ['Ms event 15', [[[5.0, 20, 170], [0.8, 18, 90], [0, 15, 90], [300.0, 15, 20]], 33], [5.19, 1]], ['Ms event 16', [[[0.8, 23, 10], [0, 15, 90]], 59], None], ['Ms event 17', [[[5.0, 18, 10], [0.8, 22, 90], [0, 17, 160], [0.8, 17, 45], [0, 22, 20]], 61], None], ['Ms event 18', [[[40.0, 22, 170], [5.0, 22, 160], [5.0, 20, 90]], 33], [6.13, 2]], ['Ms event 19', [[[5.0, 20, 10], [40.0, 15, 45], [5.0, 18, 90], [0.8, 15, 90]], 70], None], ['Ms event 20', [[[0.8, 22, 20], [40.0, 15, 170]], 70], None], ['Ms event 36', [[[0, 18, 20], [300.0, 22, 10], [0.8, 22, 160], [0, 22, 10], [0.8, 22, 20]], 59], [4.77, 2]]], [['Ms event 7', [[[0.8, 23, 160], [40.0, 18, 45], [40.0, 20, 170], [0, 18, 170], [40.0, 18, 160]], 59], [6.85, 2]], ['Ms event 21', [[[40.0, 17, 20], [5.0, 17, 90], [0.8, 20, 170], [300.0, 23, 170], [0, 15, 90]], 33], None], ['Ms event 22', [[[5.0, 18, 20], [5.0, 15, 160], [0.8, 17, 90], [0, 15, 160]], 33], [4.9, 1]], ['Ms event 23', [[[40.0, 18, 10], [40.0, 22, 20], [0.8, 18, 170], [5.0, 17, 10]], 59], [5.72, 1]], ['Ms event 24', [[[40.0, 20, 45], [0.8, 18, 20], [5.0, 17, 20], [300.0, 18, 170]], 70], None], ['Ms event 25', [[[0.8, 18, 20], [40.0, 20, 20], [0, 20, 160], [40.0, 15, 160], [40.0, 17, 170]], 60], None], ['Ms event 26', [[[0, 15, 170], [0.8, 17, 90], [300.0, 17, 90], [300.0, 22, 10]], 70], None], ['Ms event 28', [[[300.0, 20, 45], [40.0, 22, 170]], 10], [7.22, 1]]], [['Ms event 22', [[[5.0, 18, 20], [5.0, 15, 160], [0.8, 17, 90], [0, 15, 160]], 33], [4.9, 1]], ['Ms event 28', [[[300.0, 20, 45], [40.0, 22, 170]], 10], [7.22, 1]], ['Ms event 29', [[[40.0, 17, 160], [40.0, 22, 170], [0, 20, 45], [0, 20, 170]], 61], None], ['Ms event 30', [[[0.8, 17, 10], [40.0, 20, 90], [0.8, 17, 45]], 61], None], ['Ms event 31', [[[300.0, 20, 90], [0.8, 22, 45], [40.0, 22, 45], [40.0, 18, 170], [300.0, 22, 170]], 10], [6.21, 3]], ['Ms event 32', [[[40.0, 17, 90]], 10], None], ['Ms event 33', [[[5.0, 23, 10], [0.8, 23, 90], [5.0, 23, 160], [0, 22, 160]], 61], None], ['three stations', [[[10.0, 20, 40], [20.0, 20, 60], [80.0, 18, 30]], 15], [6.1, 3]]]]
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
Ms event 0	`None`	`None`	Passed
Ms event 1	`None`	`None`	Passed
Ms event 2	`[7.26, 1]`	`[7.26, 1]`	Passed
Ms event 3	`[6.32, 1]`	`[6.32, 1]`	Passed
Ms event 4	`None`	`None`	Passed
Ms event 5	`None`	`None`	Passed
Ms event 6	`None`	`None`	Passed
Ms event 7	`[6.85, 2]`	`[6.85, 2]`	Passed

SHA-256 / 77d84f24f7dcf43d6aa5305988994080905176db346889c2424b5b044ca97426

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 2026-09-29T14:48:29.794305+00:00.

Case digest / 615a2aeb933567330b2b4e5f3d934283aa2e29548184a545cfe3e56bb2c57817