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`](../sfm/compliance.py); the
spectral (FFT) side lives in [`waveform_fft.py`](../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.

---

## 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.

---

## 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.

---

## 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`](../waveform_fft.py) and used for the dominant-frequency
readout and the #10 FFT view — not for this scatter.

---

## 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`.

---

## 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>