FA-71416 / Seismic magnitude estimation / Open access
Equivalent magnitude of a swarm: energy summation · case 01
A swarm with one large event is reported far smaller than that event alone.
ROOT CAUSE
Energy is computed from the mean magnitude times the event count instead of summing per-event energies.
VERIFIED REPAIR
Sum 10^(1.5M+4.8) over events.
Unsuccessful approach: Keeping only the largest event ignores the rest of the swarm.
Case contract
Surface-wave magnitudes of a swarm; energy per event log10 E = 1.5 Ms + 4.8 (J). Sum energies and invert to the single equivalent magnitude. Return [Meq rounded 0.01, total energy "%.2e"] or None for an empty swarm.
Why this case matters
Swarm summaries compare cumulative energy release with single earthquakes.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mags):
if not mags:
return None
e = len(mags) * 10 ** (1.5 * (sum(mags) / len(mags)) + 4.8)
me = (math.log10(e) - 4.8) / 1.5
return [round(me, 2), "%.2e" % e]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 1', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 2', [[4.5]], [4.5, '3.55e+11']], ['swarm 3', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 4', [[4.2, 4.2]], [4.4, '2.52e+11']], ['swarm 5', [[4.2, 4.2, 4.2, 4.2, 4.2]], [4.67, '6.29e+11']], ['swarm 6', [[6.2, 6.2, 6.2, 6.2, 6.2]], [6.67, '6.29e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 7', [[3.7, 3.7, 3.7]], [4.02, '6.72e+10']], ['swarm 8', [[3.6, 3.6]], [3.8, '3.17e+10']], ['swarm 9', [[2.2, 2.2, 2.2, 2.2]], [2.6, '5.04e+08']], ['swarm 10', [[5.2, 5.2, 5.2, 5.2, 5.2]], [5.67, '1.99e+13']], ['swarm 11', [[2.4, 2.4, 2.4, 2.4]], [2.8, '1.00e+09']], ['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 13', [[6.0, 6.0, 6.0]], [6.32, '1.89e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 14', [[4.7]], [4.7, '7.08e+11']], ['swarm 15', [[6.0, 6.0]], [6.2, '1.26e+14']], ['swarm 16', [[2.7, 2.7, 2.7]], [3.02, '2.12e+09']], ['swarm 17', [[2.6, 2.6, 2.6, 2.6, 2.6]], [3.07, '2.51e+09']], ['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 19', [[3.6, 3.6, 3.6, 3.6, 3.6, 3.6]], [4.12, '9.51e+10']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 21', [[4.6, 4.6]], [4.8, '1.00e+12']], ['swarm 22', [[6.1, 6.1]], [6.3, '1.78e+14']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 24', [[4.9, 4.9, 4.9, 4.9, 4.9, 4.9]], [5.42, '8.48e+12']], ['swarm 25', [[3.2, 3.2, 3.2, 3.2]], [3.6, '1.59e+10']], ['swarm 26', [[4.5, 4.5, 4.5, 4.5, 4.5, 4.5]], [5.02, '2.13e+12']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 28', [[2.9]], [2.9, '1.41e+09']], ['swarm 29', [[2.9, 2.9, 2.9, 2.9, 2.9]], [3.37, '7.06e+09']], ['single event', [[5.0]], [5.0, '2.00e+12']], ['two equal events', [[4.0, 4.0]], [4.2, '1.26e+11']], ['empty', [[]], None], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]]]
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 |
|---|---|---|---|
| swarm 0 | [5.4, '7.98e+12'] | [5.4, '7.98e+12'] | Passed |
| swarm 1 | [2.7, '7.10e+08'] | [2.7, '7.10e+08'] | Passed |
| swarm 2 | [4.5, '3.55e+11'] | [4.5, '3.55e+11'] | Passed |
| swarm 3 | [2.7, '7.10e+08'] | [2.7, '7.10e+08'] | Passed |
| swarm 4 | [4.4, '2.52e+11'] | [4.4, '2.52e+11'] | Passed |
| swarm 5 | [4.67, '6.29e+11'] | [4.67, '6.29e+11'] | Passed |
| swarm 6 | [6.67, '6.29e+14'] | [6.67, '6.29e+14'] | Passed |
| one big many small | [4.15, '1.06e+11'] | [6.0, '6.31e+13'] | Failed |
SHA-256 / ffede4fc011fdf75e735a3c5449f902777c2f4796138eae0c4e09c83a3e300f8
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mags):
if not mags:
return None
e = 10 ** (1.5 * max(mags) + 4.8)
me = (math.log10(e) - 4.8) / 1.5
return [round(me, 2), "%.2e" % e]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 1', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 2', [[4.5]], [4.5, '3.55e+11']], ['swarm 3', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 4', [[4.2, 4.2]], [4.4, '2.52e+11']], ['swarm 5', [[4.2, 4.2, 4.2, 4.2, 4.2]], [4.67, '6.29e+11']], ['swarm 6', [[6.2, 6.2, 6.2, 6.2, 6.2]], [6.67, '6.29e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 7', [[3.7, 3.7, 3.7]], [4.02, '6.72e+10']], ['swarm 8', [[3.6, 3.6]], [3.8, '3.17e+10']], ['swarm 9', [[2.2, 2.2, 2.2, 2.2]], [2.6, '5.04e+08']], ['swarm 10', [[5.2, 5.2, 5.2, 5.2, 5.2]], [5.67, '1.99e+13']], ['swarm 11', [[2.4, 2.4, 2.4, 2.4]], [2.8, '1.00e+09']], ['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 13', [[6.0, 6.0, 6.0]], [6.32, '1.89e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 14', [[4.7]], [4.7, '7.08e+11']], ['swarm 15', [[6.0, 6.0]], [6.2, '1.26e+14']], ['swarm 16', [[2.7, 2.7, 2.7]], [3.02, '2.12e+09']], ['swarm 17', [[2.6, 2.6, 2.6, 2.6, 2.6]], [3.07, '2.51e+09']], ['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 19', [[3.6, 3.6, 3.6, 3.6, 3.6, 3.6]], [4.12, '9.51e+10']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 21', [[4.6, 4.6]], [4.8, '1.00e+12']], ['swarm 22', [[6.1, 6.1]], [6.3, '1.78e+14']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 24', [[4.9, 4.9, 4.9, 4.9, 4.9, 4.9]], [5.42, '8.48e+12']], ['swarm 25', [[3.2, 3.2, 3.2, 3.2]], [3.6, '1.59e+10']], ['swarm 26', [[4.5, 4.5, 4.5, 4.5, 4.5, 4.5]], [5.02, '2.13e+12']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 28', [[2.9]], [2.9, '1.41e+09']], ['swarm 29', [[2.9, 2.9, 2.9, 2.9, 2.9]], [3.37, '7.06e+09']], ['single event', [[5.0]], [5.0, '2.00e+12']], ['two equal events', [[4.0, 4.0]], [4.2, '1.26e+11']], ['empty', [[]], None], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]]]
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 |
|---|---|---|---|
| swarm 0 | [5.0, '2.00e+12'] | [5.4, '7.98e+12'] | Failed |
| swarm 1 | [2.5, '3.55e+08'] | [2.7, '7.10e+08'] | Failed |
| swarm 2 | [4.5, '3.55e+11'] | [4.5, '3.55e+11'] | Passed |
| swarm 3 | [2.5, '3.55e+08'] | [2.7, '7.10e+08'] | Failed |
| swarm 4 | [4.2, '1.26e+11'] | [4.4, '2.52e+11'] | Failed |
| swarm 5 | [4.2, '1.26e+11'] | [4.67, '6.29e+11'] | Failed |
| swarm 6 | [6.2, '1.26e+14'] | [6.67, '6.29e+14'] | Failed |
| one big many small | [6.0, '6.31e+13'] | [6.0, '6.31e+13'] | Passed |
SHA-256 / 687a872412c88ba2b69b9f9da288bc9da003b71827be2006c9bc4a6aa9855ee5
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(mags):
if not mags:
return None
e = sum(10 ** (1.5 * m + 4.8) for m in mags)
me = (math.log10(e) - 4.8) / 1.5
return [round(me, 2), "%.2e" % e]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 1', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 2', [[4.5]], [4.5, '3.55e+11']], ['swarm 3', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 4', [[4.2, 4.2]], [4.4, '2.52e+11']], ['swarm 5', [[4.2, 4.2, 4.2, 4.2, 4.2]], [4.67, '6.29e+11']], ['swarm 6', [[6.2, 6.2, 6.2, 6.2, 6.2]], [6.67, '6.29e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 7', [[3.7, 3.7, 3.7]], [4.02, '6.72e+10']], ['swarm 8', [[3.6, 3.6]], [3.8, '3.17e+10']], ['swarm 9', [[2.2, 2.2, 2.2, 2.2]], [2.6, '5.04e+08']], ['swarm 10', [[5.2, 5.2, 5.2, 5.2, 5.2]], [5.67, '1.99e+13']], ['swarm 11', [[2.4, 2.4, 2.4, 2.4]], [2.8, '1.00e+09']], ['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 13', [[6.0, 6.0, 6.0]], [6.32, '1.89e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 14', [[4.7]], [4.7, '7.08e+11']], ['swarm 15', [[6.0, 6.0]], [6.2, '1.26e+14']], ['swarm 16', [[2.7, 2.7, 2.7]], [3.02, '2.12e+09']], ['swarm 17', [[2.6, 2.6, 2.6, 2.6, 2.6]], [3.07, '2.51e+09']], ['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 19', [[3.6, 3.6, 3.6, 3.6, 3.6, 3.6]], [4.12, '9.51e+10']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 21', [[4.6, 4.6]], [4.8, '1.00e+12']], ['swarm 22', [[6.1, 6.1]], [6.3, '1.78e+14']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 24', [[4.9, 4.9, 4.9, 4.9, 4.9, 4.9]], [5.42, '8.48e+12']], ['swarm 25', [[3.2, 3.2, 3.2, 3.2]], [3.6, '1.59e+10']], ['swarm 26', [[4.5, 4.5, 4.5, 4.5, 4.5, 4.5]], [5.02, '2.13e+12']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 28', [[2.9]], [2.9, '1.41e+09']], ['swarm 29', [[2.9, 2.9, 2.9, 2.9, 2.9]], [3.37, '7.06e+09']], ['single event', [[5.0]], [5.0, '2.00e+12']], ['two equal events', [[4.0, 4.0]], [4.2, '1.26e+11']], ['empty', [[]], None], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]]]
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 |
|---|---|---|---|
| swarm 0 | [5.4, '7.98e+12'] | [5.4, '7.98e+12'] | Passed |
| swarm 1 | [2.7, '7.10e+08'] | [2.7, '7.10e+08'] | Passed |
| swarm 2 | [4.5, '3.55e+11'] | [4.5, '3.55e+11'] | Passed |
| swarm 3 | [2.7, '7.10e+08'] | [2.7, '7.10e+08'] | Passed |
| swarm 4 | [4.4, '2.52e+11'] | [4.4, '2.52e+11'] | Passed |
| swarm 5 | [4.67, '6.29e+11'] | [4.67, '6.29e+11'] | Passed |
| swarm 6 | [6.67, '6.29e+14'] | [6.67, '6.29e+14'] | Passed |
| one big many small | [6.0, '6.31e+13'] | [6.0, '6.31e+13'] | Passed |
SHA-256 / fc2bf381e28075dae1de0b0b6e2b99c171c74b51989c9cfe78f30ff6d98dd6ea
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 2026-09-29T14:48:29.421882+00:00.
Case digest / 812a23b123e54af7456cc58ec3449c28aee8b11c02d5328f2380d179227baae0