FA-71681 / Seismic magnitude estimation / Open access

Brune source radius and stress drop: angular corner frequency · case 01

Radii are 6.3 times too large and stress drops 250 times too small.

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

ROOT CAUSE

The 2 pi factor of the Brune radius is omitted.

VERIFIED REPAIR

Divide by 2 pi fc.

Unsuccessful approach: Using pi instead of 2 pi doubles the radius.

Case contract

Seismic moment N*m, corner frequency Hz, shear velocity km/s; non-positive input returns None. r = 2.34 beta / (2 pi fc) in m; stress drop = 7/16 M0 / r^3 Pa. Return [r rounded 0.1 m, stress drop in MPa rounded 0.001].

Why this case matters

Stress drop characterises source physics and ground-motion scaling.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(m0_nm, fc_hz, beta_kms):
    if min(m0_nm, fc_hz, beta_kms) <= 0:
        return None
    r = 2.34 * beta_kms * 1000.0 / fc_hz
    ds = 7.0 / 16.0 * m0_nm / r ** 3
    return [round(r, 1), round(ds / 1e6, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['M0 1.0e+12 fc 0.5 beta 3.2', [1000000000000.0, 0.5, 3.2], [2383.5, 0.0]], ['M0 1.0e+12 fc 0.5 beta 3.5', [1000000000000.0, 0.5, 3.5], [2607.0, 0.0]], ['M0 1.0e+12 fc 2.0 beta 3.2', [1000000000000.0, 2.0, 3.2], [595.9, 0.002]], ['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 1.0e+12 fc 10.0 beta 3.2', [1000000000000.0, 10.0, 3.2], [119.2, 0.258]], ['M0 1.0e+12 fc 10.0 beta 3.5', [1000000000000.0, 10.0, 3.5], [130.3, 0.198]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]]], [['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]], ['M0 3.5e+14 fc 2.0 beta 3.2', [350000000000000.0, 2.0, 3.2], [595.9, 0.724]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 3.5e+14 fc 10.0 beta 3.2', [350000000000000.0, 10.0, 3.2], [119.2, 90.467]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 0.5 beta 3.2', [2e+17, 0.5, 3.2], [2383.5, 6.462]]], [['M0 1.0e+12 fc 0.5 beta 3.2', [1000000000000.0, 0.5, 3.2], [2383.5, 0.0]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 2.0 beta 3.2', [2e+17, 2.0, 3.2], [595.9, 413.562]], ['M0 2.0e+17 fc 2.0 beta 3.5', [2e+17, 2.0, 3.5], [651.7, 316.072]], ['M0 2.0e+17 fc 10.0 beta 3.2', [2e+17, 10.0, 3.2], [119.2, 51695.192]], ['M0 2.0e+17 fc 10.0 beta 3.5', [2e+17, 10.0, 3.5], [130.3, 39508.992]], ['zero corner', [100000000000000.0, 0, 3.5], None]], [['M0 1.0e+12 fc 2.0 beta 3.2', [1000000000000.0, 2.0, 3.2], [595.9, 0.002]], ['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 1.0e+12 fc 10.0 beta 3.2', [1000000000000.0, 10.0, 3.2], [119.2, 0.258]], ['M0 1.0e+12 fc 10.0 beta 3.5', [1000000000000.0, 10.0, 3.5], [130.3, 0.198]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 2.0e+17 fc 10.0 beta 3.2', [2e+17, 10.0, 3.2], [119.2, 51695.192]]], [['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 3.5e+14 fc 10.0 beta 3.2', [350000000000000.0, 10.0, 3.2], [119.2, 90.467]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 0.5 beta 3.2', [2e+17, 0.5, 3.2], [2383.5, 6.462]], ['M0 2.0e+17 fc 0.5 beta 3.5', [2e+17, 0.5, 3.5], [2607.0, 4.939]], ['M0 2.0e+17 fc 2.0 beta 3.2', [2e+17, 2.0, 3.2], [595.9, 413.562]], ['M0 2.0e+17 fc 2.0 beta 3.5', [2e+17, 2.0, 3.5], [651.7, 316.072]]]]
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
M0 1.0e+12 fc 0.5 beta 3.2	`[14976.0, 0.0]`	`[2383.5, 0.0]`	Failed
M0 1.0e+12 fc 0.5 beta 3.5	`[16380.0, 0.0]`	`[2607.0, 0.0]`	Failed
M0 1.0e+12 fc 2.0 beta 3.2	`[3744.0, 0.0]`	`[595.9, 0.002]`	Failed
M0 1.0e+12 fc 2.0 beta 3.5	`[4095.0, 0.0]`	`[651.7, 0.002]`	Failed
M0 1.0e+12 fc 10.0 beta 3.2	`[748.8, 0.001]`	`[119.2, 0.258]`	Failed
M0 1.0e+12 fc 10.0 beta 3.5	`[819.0, 0.001]`	`[130.3, 0.198]`	Failed
M0 3.5e+14 fc 0.5 beta 3.2	`[14976.0, 0.0]`	`[2383.5, 0.011]`	Failed
M0 3.5e+14 fc 0.5 beta 3.5	`[16380.0, 0.0]`	`[2607.0, 0.009]`	Failed

SHA-256 / 71e808589b63c80675ae4f9ce8e8b4384cf458f5ab25b69731dde3d995da9295

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(m0_nm, fc_hz, beta_kms):
    if min(m0_nm, fc_hz, beta_kms) <= 0:
        return None
    r = 2.34 * beta_kms * 1000.0 / (math.pi * fc_hz)
    ds = 7.0 / 16.0 * m0_nm / r ** 3
    return [round(r, 1), round(ds / 1e6, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['M0 1.0e+12 fc 0.5 beta 3.2', [1000000000000.0, 0.5, 3.2], [2383.5, 0.0]], ['M0 1.0e+12 fc 0.5 beta 3.5', [1000000000000.0, 0.5, 3.5], [2607.0, 0.0]], ['M0 1.0e+12 fc 2.0 beta 3.2', [1000000000000.0, 2.0, 3.2], [595.9, 0.002]], ['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 1.0e+12 fc 10.0 beta 3.2', [1000000000000.0, 10.0, 3.2], [119.2, 0.258]], ['M0 1.0e+12 fc 10.0 beta 3.5', [1000000000000.0, 10.0, 3.5], [130.3, 0.198]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]]], [['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]], ['M0 3.5e+14 fc 2.0 beta 3.2', [350000000000000.0, 2.0, 3.2], [595.9, 0.724]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 3.5e+14 fc 10.0 beta 3.2', [350000000000000.0, 10.0, 3.2], [119.2, 90.467]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 0.5 beta 3.2', [2e+17, 0.5, 3.2], [2383.5, 6.462]]], [['M0 1.0e+12 fc 0.5 beta 3.2', [1000000000000.0, 0.5, 3.2], [2383.5, 0.0]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 2.0 beta 3.2', [2e+17, 2.0, 3.2], [595.9, 413.562]], ['M0 2.0e+17 fc 2.0 beta 3.5', [2e+17, 2.0, 3.5], [651.7, 316.072]], ['M0 2.0e+17 fc 10.0 beta 3.2', [2e+17, 10.0, 3.2], [119.2, 51695.192]], ['M0 2.0e+17 fc 10.0 beta 3.5', [2e+17, 10.0, 3.5], [130.3, 39508.992]], ['zero corner', [100000000000000.0, 0, 3.5], None]], [['M0 1.0e+12 fc 2.0 beta 3.2', [1000000000000.0, 2.0, 3.2], [595.9, 0.002]], ['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 1.0e+12 fc 10.0 beta 3.2', [1000000000000.0, 10.0, 3.2], [119.2, 0.258]], ['M0 1.0e+12 fc 10.0 beta 3.5', [1000000000000.0, 10.0, 3.5], [130.3, 0.198]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 2.0e+17 fc 10.0 beta 3.2', [2e+17, 10.0, 3.2], [119.2, 51695.192]]], [['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 3.5e+14 fc 10.0 beta 3.2', [350000000000000.0, 10.0, 3.2], [119.2, 90.467]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 0.5 beta 3.2', [2e+17, 0.5, 3.2], [2383.5, 6.462]], ['M0 2.0e+17 fc 0.5 beta 3.5', [2e+17, 0.5, 3.5], [2607.0, 4.939]], ['M0 2.0e+17 fc 2.0 beta 3.2', [2e+17, 2.0, 3.2], [595.9, 413.562]], ['M0 2.0e+17 fc 2.0 beta 3.5', [2e+17, 2.0, 3.5], [651.7, 316.072]]]]
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
M0 1.0e+12 fc 0.5 beta 3.2	`[4767.0, 0.0]`	`[2383.5, 0.0]`	Failed
M0 1.0e+12 fc 0.5 beta 3.5	`[5213.9, 0.0]`	`[2607.0, 0.0]`	Failed
M0 1.0e+12 fc 2.0 beta 3.2	`[1191.8, 0.0]`	`[595.9, 0.002]`	Failed
M0 1.0e+12 fc 2.0 beta 3.5	`[1303.5, 0.0]`	`[651.7, 0.002]`	Failed
M0 1.0e+12 fc 10.0 beta 3.2	`[238.4, 0.032]`	`[119.2, 0.258]`	Failed
M0 1.0e+12 fc 10.0 beta 3.5	`[260.7, 0.025]`	`[130.3, 0.198]`	Failed
M0 3.5e+14 fc 0.5 beta 3.2	`[4767.0, 0.001]`	`[2383.5, 0.011]`	Failed
M0 3.5e+14 fc 0.5 beta 3.5	`[5213.9, 0.001]`	`[2607.0, 0.009]`	Failed

SHA-256 / 85d6bed8f5efc5fa7508cc39be32ebd07b31bab8ac75fadb9df6dd05d3c56328

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(m0_nm, fc_hz, beta_kms):
    if min(m0_nm, fc_hz, beta_kms) <= 0:
        return None
    r = 2.34 * beta_kms * 1000.0 / (2 * math.pi * fc_hz)
    ds = 7.0 / 16.0 * m0_nm / r ** 3
    return [round(r, 1), round(ds / 1e6, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['M0 1.0e+12 fc 0.5 beta 3.2', [1000000000000.0, 0.5, 3.2], [2383.5, 0.0]], ['M0 1.0e+12 fc 0.5 beta 3.5', [1000000000000.0, 0.5, 3.5], [2607.0, 0.0]], ['M0 1.0e+12 fc 2.0 beta 3.2', [1000000000000.0, 2.0, 3.2], [595.9, 0.002]], ['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 1.0e+12 fc 10.0 beta 3.2', [1000000000000.0, 10.0, 3.2], [119.2, 0.258]], ['M0 1.0e+12 fc 10.0 beta 3.5', [1000000000000.0, 10.0, 3.5], [130.3, 0.198]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]]], [['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]], ['M0 3.5e+14 fc 2.0 beta 3.2', [350000000000000.0, 2.0, 3.2], [595.9, 0.724]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 3.5e+14 fc 10.0 beta 3.2', [350000000000000.0, 10.0, 3.2], [119.2, 90.467]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 0.5 beta 3.2', [2e+17, 0.5, 3.2], [2383.5, 6.462]]], [['M0 1.0e+12 fc 0.5 beta 3.2', [1000000000000.0, 0.5, 3.2], [2383.5, 0.0]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 2.0 beta 3.2', [2e+17, 2.0, 3.2], [595.9, 413.562]], ['M0 2.0e+17 fc 2.0 beta 3.5', [2e+17, 2.0, 3.5], [651.7, 316.072]], ['M0 2.0e+17 fc 10.0 beta 3.2', [2e+17, 10.0, 3.2], [119.2, 51695.192]], ['M0 2.0e+17 fc 10.0 beta 3.5', [2e+17, 10.0, 3.5], [130.3, 39508.992]], ['zero corner', [100000000000000.0, 0, 3.5], None]], [['M0 1.0e+12 fc 2.0 beta 3.2', [1000000000000.0, 2.0, 3.2], [595.9, 0.002]], ['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 1.0e+12 fc 10.0 beta 3.2', [1000000000000.0, 10.0, 3.2], [119.2, 0.258]], ['M0 1.0e+12 fc 10.0 beta 3.5', [1000000000000.0, 10.0, 3.5], [130.3, 0.198]], ['M0 3.5e+14 fc 0.5 beta 3.2', [350000000000000.0, 0.5, 3.2], [2383.5, 0.011]], ['M0 3.5e+14 fc 0.5 beta 3.5', [350000000000000.0, 0.5, 3.5], [2607.0, 0.009]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 2.0e+17 fc 10.0 beta 3.2', [2e+17, 10.0, 3.2], [119.2, 51695.192]]], [['M0 1.0e+12 fc 2.0 beta 3.5', [1000000000000.0, 2.0, 3.5], [651.7, 0.002]], ['M0 3.5e+14 fc 2.0 beta 3.5', [350000000000000.0, 2.0, 3.5], [651.7, 0.553]], ['M0 3.5e+14 fc 10.0 beta 3.2', [350000000000000.0, 10.0, 3.2], [119.2, 90.467]], ['M0 3.5e+14 fc 10.0 beta 3.5', [350000000000000.0, 10.0, 3.5], [130.3, 69.141]], ['M0 2.0e+17 fc 0.5 beta 3.2', [2e+17, 0.5, 3.2], [2383.5, 6.462]], ['M0 2.0e+17 fc 0.5 beta 3.5', [2e+17, 0.5, 3.5], [2607.0, 4.939]], ['M0 2.0e+17 fc 2.0 beta 3.2', [2e+17, 2.0, 3.2], [595.9, 413.562]], ['M0 2.0e+17 fc 2.0 beta 3.5', [2e+17, 2.0, 3.5], [651.7, 316.072]]]]
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
M0 1.0e+12 fc 0.5 beta 3.2	`[2383.5, 0.0]`	`[2383.5, 0.0]`	Passed
M0 1.0e+12 fc 0.5 beta 3.5	`[2607.0, 0.0]`	`[2607.0, 0.0]`	Passed
M0 1.0e+12 fc 2.0 beta 3.2	`[595.9, 0.002]`	`[595.9, 0.002]`	Passed
M0 1.0e+12 fc 2.0 beta 3.5	`[651.7, 0.002]`	`[651.7, 0.002]`	Passed
M0 1.0e+12 fc 10.0 beta 3.2	`[119.2, 0.258]`	`[119.2, 0.258]`	Passed
M0 1.0e+12 fc 10.0 beta 3.5	`[130.3, 0.198]`	`[130.3, 0.198]`	Passed
M0 3.5e+14 fc 0.5 beta 3.2	`[2383.5, 0.011]`	`[2383.5, 0.011]`	Passed
M0 3.5e+14 fc 0.5 beta 3.5	`[2607.0, 0.009]`	`[2607.0, 0.009]`	Passed

SHA-256 / 416f0f0e52813226c913d6e56937a4827f39f26b1aea9f982c702a85e813937a

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 2026-09-29T14:48:31.758473+00:00.

Case digest / 51be0caa7d4d6aff68c28e10287ce3fdf1a144f2a6b0cdfd73c1c2b75af9f911