seismo-relay/docs/ri8507_compliance_curve.md

USBM RI8507 / OSMRE Blasting Compliance Curve — Reference

Reference for the velocity-vs-frequency blasting compliance chart Blastware draws on its Event Report ("USBM RI8507 And OSMRE"), and how seismo-relay reproduces it. Implemented in sfm/compliance.py; the spectral (FFT) side lives in waveform_fft.py.

Reverse-engineered 2026-09-14 against 7 BE12844 (MiniMate Plus) events, each with a Blastware Event Report + FFT Report as ground truth. Curve values from USBM RI8507 Appendix B and 30 CFR 816.67.

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What it is

Two closely-related sources for the same limit curve:

• USBM RI8507 — Bureau of Mines Report of Investigations 8507 (Siskind et al., 1980), "Structure Response and Damage Produced by Ground Vibration From Surface Mine Blasting." The curve is Figure B-1, Appendix B ("Alternative Blasting Level Criteria"), p.73–74.
• OSMRE / OSM — the Office of Surface Mining Reclamation and Enforcement codified it as 30 CFR 816.67, Figure 1. "CFR" = the U.S. Code of Federal Regulations. Same curve, regulatory force.

The chart plots each geophone channel's significant vibration cycles as (frequency, peak velocity) points against this limit. A point below the line passes; above fails.

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The limit curve

A structure has a resonance band (~4–12 Hz for whole structures) where it is most vulnerable, so the safe velocity is lower at those frequencies and higher away from them. The curve captures this by alternating two kinds of bound:

• Constant-velocity segments — a flat horizontal line at a fixed PPV.
• Constant-displacement segments — a fixed peak displacement d. For simple harmonic motion, peak velocity v = 2πf·d, so on a velocity-vs- frequency log-log plot this is a straight line of slope +1 (velocity rises with frequency). This is why the low- and high-frequency bounds are sloped.

Two lines — structure type

RI8507 gives two lines for two interior-wall constructions (Table 13, p.67):

line	construction	plateau PPV
Drywall (solid)	modern gypsum wallboard	0.75 in/s
Plaster (dashed)	older plaster on wood lath	0.50 in/s

Plaster-on-lath is more damage-prone, hence the lower limit. You apply one line depending on the monitored structure.

The four segments (Figure B-1, p.74)

Going low → high frequency, each line is:

1. Ultimate low-frequency bound — constant displacement 0.030 in (v = 2πf·0.030). Only relevant below ~4 Hz.
2. Plateau — constant velocity 0.75 (Drywall) / 0.50 (plaster) in/s.
3. Rising diagonal — constant displacement 0.008 in (v = 2πf·0.008), climbing from the plateau up to the high-frequency cap.
4. High-frequency cap — constant velocity 2.0 in/s above ~40 Hz.

The segments are drawn continuous: each bound is used over the frequency range where it is the binding (lowest) limit, and consecutive bounds meet where they are equal — so there are no vertical steps. Transition frequencies come straight from the values (f = V / (2π·d)):

transition	formula	Drywall	Plaster
0.030 in → plateau	V_mid / (2π·0.030)	3.98 Hz	2.65 Hz
plateau → 0.008 in	V_mid / (2π·0.008)	14.92 Hz	9.95 Hz
0.008 in → 2.0 in/s	2.0 / (2π·0.008)	39.79 Hz	39.79 Hz

Because both lines share the same 0.008 in rising diagonal, above ~15 Hz they lie on the same line (both reach 2.0 in/s at ~40 Hz) — RI8507's literal construction merges them there. Blastware renders the dashed line as a separate parallel diagonal, but that is cosmetic: above ~15 Hz both structure types carry the identical limit, so compliance is unaffected.

⚠ RI8507's Table 13 is a simpler two-range criterion with a sharp discontinuity at 40 Hz (flat plateau, then a jump to 2.0). Figure B-1 is the smoothed version that adds the 0.008 in transition — that is the one drawn on reports and implemented here.

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The compliance scatter (the points)

The cloud is not the FFT spectrum. It is a per-cycle, time-domain measure by the zero-crossing method (channel_compliance_points):

• Split the channel's waveform at its zero crossings.
• Each half-cycle contributes one point: frequency = 1 / (2 · half-period) (from the samples between the two crossings), velocity = peak |amplitude| in that half-cycle.

This yields ~90–110 points per channel, and — by construction — each channel's highest point equals that channel's PPV. Verified against Blastware: the cloud shape, density, and ceiling all match.

Why not the FFT?

A broadband blast spreads its energy across many FFT bins, so no single bin reaches the time-domain peak — the FFT amplitudes come out ~10× below the compliance-chart velocities. The compliance chart is a per-cycle peak view; the FFT is a separate analysis (Blastware's FFT Report), reproduced by waveform_fft.py and used for the dominant-frequency readout and the #10 FFT view — not for this scatter.

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Implementation

• sfm/compliance.py
  • limit_at(freq, curve) — the limit PPV at a frequency (curve = "Drywall" or "Plaster"); curves are data in _CURVES, so more standards can be added.
  • channel_compliance_points(samples, sps) — the zero-crossing scatter.
  • draw_compliance_chart(ax, channels, sps) — matplotlib rendering (both limit lines + per-channel scatter, Blastware's tick scales and channel markers: Tran + red, Vert × green, Long o blue).
• Tests: tests/test_compliance.py.

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Sources

• USBM RI8507 (Siskind, Stagg, Kopp, Dowding, 1980), Appendix B / Figure B-1, p.73–74; Table 13, p.67. (ref-stuff/usbm-ri8507-ground_vibration.pdf.)
• 30 CFR 816.67, "Use of explosives: Control of adverse effects," Figure 1 — https://www.ecfr.gov/current/title-30/chapter-VII/subchapter-K/part-816/section-816.67