FA-71556 / Seismic magnitude estimation / Open access

Wood-Anderson amplitude simulation: trapezoid integration · case 01

Displacement amplitudes shift by half a sample of velocity.

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

ROOT CAUSE

Rectangle integration uses only the current sample.

VERIFIED REPAIR

Integrate with the trapezoid rule.

Unsuccessful approach: Omitting dt returns counts-seconds per sample, not metres.

Case contract

Velocity-sensor counts, sensitivity counts per m/s, sample interval s. Remove the mean, convert to m/s, integrate with the trapezoid rule from 0, take the maximum absolute displacement, multiply by the Wood-Anderson gain 2080 and convert to mm. Return mm rounded to 1e-4, None for an empty trace.

Why this case matters

Wood-Anderson amplitudes are the input to local magnitude.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(counts, sens, dt):
    if not counts:
        return None
    mean = sum(counts) / len(counts)
    vel = [(c - mean) / sens for c in counts]
    disp = [0.0]
    for i in range(1, len(vel)):
        disp.append(disp[-1] + vel[i] * dt)
    peak = max(abs(x) for x in disp)
    return round(peak * 2080 * 1000, 4)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['trace 0', [[-399, 158, 716, 1343, 399, -234, 349, 919], 500000000.0, 0.02], 0.0492], ['trace 1', [[-438, -422, -845, 107, -288, 724, -435, -632, 690], 100000000.0, 0.01], 0.1913], ['trace 2', [[8, 47, 118, -519, -421, -54, -238, -121], 100000000.0, 0.01], 0.0842], ['trace 3', [[-701, 88, -234, -70, -529, -1002, 304, -1260, -994, 400], 100000000.0, 0.01], 0.1598], ['trace 4', [[-686, 544, 277, -1046, -766, -1235, 329, -1152, -874, 219], 100000000.0, 0.01], 0.2646], ['trace 5', [[1259, -39, 1475, 880, 416, 768, 982, -232], 1500000000.0, 0.02], 0.0136], ['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 7', [[22, -1189, -875, -394, 216], 500000000.0, 0.02], 0.0764]], [['trace 3', [[-701, 88, -234, -70, -529, -1002, 304, -1260, -994, 400], 100000000.0, 0.01], 0.1598], ['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 7', [[22, -1189, -875, -394, 216], 500000000.0, 0.02], 0.0764], ['trace 8', [[491, -743, 168, -106], 100000000.0, 0.01], 0.0662], ['trace 9', [[1140, 675, -129, 1466, 1180, 1409, 1273, 156], 500000000.0, 0.02], 0.0699], ['trace 10', [[295, -693, -527, -749, -313, 39, 217, -925, 433], 1500000000.0, 0.01], 0.0137], ['trace 11', [[415, 520, -255, 348, 660, -938], 500000000.0, 0.02], 0.0541], ['trace 12', [[-597, -489, -301, -271, -999, -558, -230, -970, -1048], 500000000.0, 0.02], 0.0514]], [['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 11', [[415, 520, -255, 348, 660, -938], 500000000.0, 0.02], 0.0541], ['trace 14', [[338, -532, -974, 859, 966, 558], 100000000.0, 0.01], 0.3151], ['trace 15', [[143, 170, -64, 138, 634], 100000000.0, 0.01], 0.0761], ['trace 16', [[1183, 1265, 1030, 749, -390], 500000000.0, 0.02], 0.0798], ['trace 17', [[423, -354, -610, -304, 513, -195, -84, 296], 1500000000.0, 0.02], 0.0218], ['trace 18', [[914, 28, -594, 554, -691, 34, 863, 716, -229, 744], 100000000.0, 0.01], 0.2909], ['trace 19', [[1319, 651, 570, 304, 1072], 1500000000.0, 0.01], 0.0057]], [['trace 9', [[1140, 675, -129, 1466, 1180, 1409, 1273, 156], 500000000.0, 0.02], 0.0699], ['trace 16', [[1183, 1265, 1030, 749, -390], 500000000.0, 0.02], 0.0798], ['trace 21', [[561, 856, 710, 319, 742, 1285, -221, 763], 100000000.0, 0.01], 0.0864], ['trace 22', [[-228, 382, -252, 552, 320, -776], 100000000.0, 0.01], 0.1517], ['trace 23', [[-486, 859, 193, 1092, 1350, -353], 500000000.0, 0.02], 0.0717], ['trace 24', [[-179, 4, 317, 984], 1500000000.0, 0.02], 0.0136], ['trace 25', [[-431, 933, -842, 85, -489, -992, -686, -918], 500000000.0, 0.02], 0.1153], ['trace 26', [[-347, -149, -735, -306, -1255], 1500000000.0, 0.01], 0.0064]], [['trace 0', [[-399, 158, 716, 1343, 399, -234, 349, 919], 500000000.0, 0.02], 0.0492], ['trace 12', [[-597, -489, -301, -271, -999, -558, -230, -970, -1048], 500000000.0, 0.02], 0.0514], ['trace 21', [[561, 856, 710, 319, 742, 1285, -221, 763], 100000000.0, 0.01], 0.0864], ['trace 28', [[-1202, -1275, 528, -292, -12, -129, -528, 349], 100000000.0, 0.01], 0.2021], ['trace 29', [[-178, 10, 1361, 707, 1375, 364, 582, 1449, 423], 1500000000.0, 0.01], 0.0106], ['asymmetric pulse', [[0, 800, 1200, 400, -200, -100], 1000000000.0, 0.01], 0.0239], ['empty', [[], 1000000000.0, 0.01], None], ['offset step', [[1000, 1000, 3000, 1000, 1000], 1000000000.0, 0.01], 0.0166]]]
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
trace 0	`0.083`	`0.0492`	Failed
trace 1	`0.1924`	`0.1913`	Failed
trace 2	`0.0957`	`0.0842`	Failed
trace 3	`0.2045`	`0.1598`	Failed
trace 4	`0.3534`	`0.2646`	Failed
trace 5	`0.0202`	`0.0136`	Failed
trace 6	`0.0161`	`0.0088`	Failed
trace 7	`0.0978`	`0.0764`	Failed

SHA-256 / 11fe8369dab40646068964cbb31f91653c3543279bad516f4bb4470417272e76

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(counts, sens, dt):
    if not counts:
        return None
    mean = sum(counts) / len(counts)
    vel = [(c - mean) / sens for c in counts]
    disp = [0.0]
    for i in range(1, len(vel)):
        disp.append(disp[-1] + 0.5 * (vel[i - 1] + vel[i]))
    peak = max(abs(x) for x in disp)
    return round(peak * 2080 * 1000, 4)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['trace 0', [[-399, 158, 716, 1343, 399, -234, 349, 919], 500000000.0, 0.02], 0.0492], ['trace 1', [[-438, -422, -845, 107, -288, 724, -435, -632, 690], 100000000.0, 0.01], 0.1913], ['trace 2', [[8, 47, 118, -519, -421, -54, -238, -121], 100000000.0, 0.01], 0.0842], ['trace 3', [[-701, 88, -234, -70, -529, -1002, 304, -1260, -994, 400], 100000000.0, 0.01], 0.1598], ['trace 4', [[-686, 544, 277, -1046, -766, -1235, 329, -1152, -874, 219], 100000000.0, 0.01], 0.2646], ['trace 5', [[1259, -39, 1475, 880, 416, 768, 982, -232], 1500000000.0, 0.02], 0.0136], ['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 7', [[22, -1189, -875, -394, 216], 500000000.0, 0.02], 0.0764]], [['trace 3', [[-701, 88, -234, -70, -529, -1002, 304, -1260, -994, 400], 100000000.0, 0.01], 0.1598], ['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 7', [[22, -1189, -875, -394, 216], 500000000.0, 0.02], 0.0764], ['trace 8', [[491, -743, 168, -106], 100000000.0, 0.01], 0.0662], ['trace 9', [[1140, 675, -129, 1466, 1180, 1409, 1273, 156], 500000000.0, 0.02], 0.0699], ['trace 10', [[295, -693, -527, -749, -313, 39, 217, -925, 433], 1500000000.0, 0.01], 0.0137], ['trace 11', [[415, 520, -255, 348, 660, -938], 500000000.0, 0.02], 0.0541], ['trace 12', [[-597, -489, -301, -271, -999, -558, -230, -970, -1048], 500000000.0, 0.02], 0.0514]], [['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 11', [[415, 520, -255, 348, 660, -938], 500000000.0, 0.02], 0.0541], ['trace 14', [[338, -532, -974, 859, 966, 558], 100000000.0, 0.01], 0.3151], ['trace 15', [[143, 170, -64, 138, 634], 100000000.0, 0.01], 0.0761], ['trace 16', [[1183, 1265, 1030, 749, -390], 500000000.0, 0.02], 0.0798], ['trace 17', [[423, -354, -610, -304, 513, -195, -84, 296], 1500000000.0, 0.02], 0.0218], ['trace 18', [[914, 28, -594, 554, -691, 34, 863, 716, -229, 744], 100000000.0, 0.01], 0.2909], ['trace 19', [[1319, 651, 570, 304, 1072], 1500000000.0, 0.01], 0.0057]], [['trace 9', [[1140, 675, -129, 1466, 1180, 1409, 1273, 156], 500000000.0, 0.02], 0.0699], ['trace 16', [[1183, 1265, 1030, 749, -390], 500000000.0, 0.02], 0.0798], ['trace 21', [[561, 856, 710, 319, 742, 1285, -221, 763], 100000000.0, 0.01], 0.0864], ['trace 22', [[-228, 382, -252, 552, 320, -776], 100000000.0, 0.01], 0.1517], ['trace 23', [[-486, 859, 193, 1092, 1350, -353], 500000000.0, 0.02], 0.0717], ['trace 24', [[-179, 4, 317, 984], 1500000000.0, 0.02], 0.0136], ['trace 25', [[-431, 933, -842, 85, -489, -992, -686, -918], 500000000.0, 0.02], 0.1153], ['trace 26', [[-347, -149, -735, -306, -1255], 1500000000.0, 0.01], 0.0064]], [['trace 0', [[-399, 158, 716, 1343, 399, -234, 349, 919], 500000000.0, 0.02], 0.0492], ['trace 12', [[-597, -489, -301, -271, -999, -558, -230, -970, -1048], 500000000.0, 0.02], 0.0514], ['trace 21', [[561, 856, 710, 319, 742, 1285, -221, 763], 100000000.0, 0.01], 0.0864], ['trace 28', [[-1202, -1275, 528, -292, -12, -129, -528, 349], 100000000.0, 0.01], 0.2021], ['trace 29', [[-178, 10, 1361, 707, 1375, 364, 582, 1449, 423], 1500000000.0, 0.01], 0.0106], ['asymmetric pulse', [[0, 800, 1200, 400, -200, -100], 1000000000.0, 0.01], 0.0239], ['empty', [[], 1000000000.0, 0.01], None], ['offset step', [[1000, 1000, 3000, 1000, 1000], 1000000000.0, 0.01], 0.0166]]]
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
trace 0	`2.4606`	`0.0492`	Failed
trace 1	`19.1256`	`0.1913`	Failed
trace 2	`8.424`	`0.0842`	Failed
trace 3	`15.9786`	`0.1598`	Failed
trace 4	`26.4576`	`0.2646`	Failed
trace 5	`0.6777`	`0.0136`	Failed
trace 6	`0.8776`	`0.0088`	Failed
trace 7	`3.8189`	`0.0764`	Failed

SHA-256 / ac27b0a7551e9fe24bd1b08fad245dd9cc835965e7c5d1452a49ee4276e9c17f

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(counts, sens, dt):
    if not counts:
        return None
    mean = sum(counts) / len(counts)
    vel = [(c - mean) / sens for c in counts]
    disp = [0.0]
    for i in range(1, len(vel)):
        disp.append(disp[-1] + 0.5 * (vel[i - 1] + vel[i]) * dt)
    peak = max(abs(x) for x in disp)
    return round(peak * 2080 * 1000, 4)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['trace 0', [[-399, 158, 716, 1343, 399, -234, 349, 919], 500000000.0, 0.02], 0.0492], ['trace 1', [[-438, -422, -845, 107, -288, 724, -435, -632, 690], 100000000.0, 0.01], 0.1913], ['trace 2', [[8, 47, 118, -519, -421, -54, -238, -121], 100000000.0, 0.01], 0.0842], ['trace 3', [[-701, 88, -234, -70, -529, -1002, 304, -1260, -994, 400], 100000000.0, 0.01], 0.1598], ['trace 4', [[-686, 544, 277, -1046, -766, -1235, 329, -1152, -874, 219], 100000000.0, 0.01], 0.2646], ['trace 5', [[1259, -39, 1475, 880, 416, 768, 982, -232], 1500000000.0, 0.02], 0.0136], ['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 7', [[22, -1189, -875, -394, 216], 500000000.0, 0.02], 0.0764]], [['trace 3', [[-701, 88, -234, -70, -529, -1002, 304, -1260, -994, 400], 100000000.0, 0.01], 0.1598], ['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 7', [[22, -1189, -875, -394, 216], 500000000.0, 0.02], 0.0764], ['trace 8', [[491, -743, 168, -106], 100000000.0, 0.01], 0.0662], ['trace 9', [[1140, 675, -129, 1466, 1180, 1409, 1273, 156], 500000000.0, 0.02], 0.0699], ['trace 10', [[295, -693, -527, -749, -313, 39, 217, -925, 433], 1500000000.0, 0.01], 0.0137], ['trace 11', [[415, 520, -255, 348, 660, -938], 500000000.0, 0.02], 0.0541], ['trace 12', [[-597, -489, -301, -271, -999, -558, -230, -970, -1048], 500000000.0, 0.02], 0.0514]], [['trace 6', [[967, -475, -512, 255, 516, 486, -840, 288], 1500000000.0, 0.01], 0.0088], ['trace 11', [[415, 520, -255, 348, 660, -938], 500000000.0, 0.02], 0.0541], ['trace 14', [[338, -532, -974, 859, 966, 558], 100000000.0, 0.01], 0.3151], ['trace 15', [[143, 170, -64, 138, 634], 100000000.0, 0.01], 0.0761], ['trace 16', [[1183, 1265, 1030, 749, -390], 500000000.0, 0.02], 0.0798], ['trace 17', [[423, -354, -610, -304, 513, -195, -84, 296], 1500000000.0, 0.02], 0.0218], ['trace 18', [[914, 28, -594, 554, -691, 34, 863, 716, -229, 744], 100000000.0, 0.01], 0.2909], ['trace 19', [[1319, 651, 570, 304, 1072], 1500000000.0, 0.01], 0.0057]], [['trace 9', [[1140, 675, -129, 1466, 1180, 1409, 1273, 156], 500000000.0, 0.02], 0.0699], ['trace 16', [[1183, 1265, 1030, 749, -390], 500000000.0, 0.02], 0.0798], ['trace 21', [[561, 856, 710, 319, 742, 1285, -221, 763], 100000000.0, 0.01], 0.0864], ['trace 22', [[-228, 382, -252, 552, 320, -776], 100000000.0, 0.01], 0.1517], ['trace 23', [[-486, 859, 193, 1092, 1350, -353], 500000000.0, 0.02], 0.0717], ['trace 24', [[-179, 4, 317, 984], 1500000000.0, 0.02], 0.0136], ['trace 25', [[-431, 933, -842, 85, -489, -992, -686, -918], 500000000.0, 0.02], 0.1153], ['trace 26', [[-347, -149, -735, -306, -1255], 1500000000.0, 0.01], 0.0064]], [['trace 0', [[-399, 158, 716, 1343, 399, -234, 349, 919], 500000000.0, 0.02], 0.0492], ['trace 12', [[-597, -489, -301, -271, -999, -558, -230, -970, -1048], 500000000.0, 0.02], 0.0514], ['trace 21', [[561, 856, 710, 319, 742, 1285, -221, 763], 100000000.0, 0.01], 0.0864], ['trace 28', [[-1202, -1275, 528, -292, -12, -129, -528, 349], 100000000.0, 0.01], 0.2021], ['trace 29', [[-178, 10, 1361, 707, 1375, 364, 582, 1449, 423], 1500000000.0, 0.01], 0.0106], ['asymmetric pulse', [[0, 800, 1200, 400, -200, -100], 1000000000.0, 0.01], 0.0239], ['empty', [[], 1000000000.0, 0.01], None], ['offset step', [[1000, 1000, 3000, 1000, 1000], 1000000000.0, 0.01], 0.0166]]]
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
trace 0	`0.0492`	`0.0492`	Passed
trace 1	`0.1913`	`0.1913`	Passed
trace 2	`0.0842`	`0.0842`	Passed
trace 3	`0.1598`	`0.1598`	Passed
trace 4	`0.2646`	`0.2646`	Passed
trace 5	`0.0136`	`0.0136`	Passed
trace 6	`0.0088`	`0.0088`	Passed
trace 7	`0.0764`	`0.0764`	Passed

SHA-256 / bc9e803c11cdb4b389cecbca58750cafdd04371a7d3dcfff6bfe5a2f0570fc3c

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 2026-09-29T14:48:30.664974+00:00.

Case digest / 4ebe052b5a690847fc36142819ecfb6395807c3fa14db4991896b1ace0628d6c