The Skyquake Bench
Fly the paper's SR-71 pass, Mach 3.15 at 21 km, westbound over Edwards: the cone's half-angle is 18.5°, its carpet ends 52.7 km each side of the track and reaches 60 of the 205 stations, the first 265 s before the pass over station EDW and the last 367 s after; the boom under the track is 38 Pa for 0.23 s, 57 to 77 µm/s in the ground. Fit the still-air hyperbola to those arrivals and it reads Mach 3.03. Set the vehicle at Mach 1 relative to the ground's sound speed, the paper's reading of the Lincoln Labs figure, and it sits exactly at the cutoff: the plane of Edwards gets nothing direct, only four stations standing higher catch a grazing boom, and at ground Mach 1.02 a carpet 7.5 km each side appears. D148 reports the 1991 and 1992 booms traced to two F-4s; the paper it cites reads them as indirect booms carried in from offshore by the winds this bench does not model. Both accounts are on the File.
Keep the signal
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Open the interactive ▸ What you're looking at
The Cone is the array from the air in 3D: the 205 CI stations of 9 December 1993 on today’s coastline, station EDW at Edwards at the origin, a vehicle on its track, the Mach cone as a translucent surface, the ground trace drawn live from the refracted rays, and each station lighting the moment the carpet reaches it. Drag to orbit, run the clock, pick a station.
The Array is the map from above with the arrival time of the direct boom as a field, the carpet’s two edges, the trace now, and the read-back: the still-air hyperbola t = (x + √(y² + h²) √(M² − 1))/V fitted to the arrivals for V, M and h, printed beside the truth. With refraction on it reads Mach 3.03 for Mach 3.15; with refraction off it returns the truth.
The Traces stack the stations the carpet reaches in arrival order, each in its own window about its arrival, with the paper’s velocity signature (an inverted U with two downward peaks at the shocks) at Carlson’s strength and the paper’s coupling, and the 0.15 to 0.2 Pa the network’s 1991 amplitudes corresponded to. The Cutoff draws the cutoff Mach against altitude, over sea level and over Edwards, the carpet’s lateral limit against Mach at the dial’s altitude, and Carlson’s ledger. The File holds the record and the paper on cards, and two accounts at equal size.
Why it is here
The record has a briefing on the site, Release 06 Briefing 20, which covers the two 2010 DIRD reference papers as a whole, one of them D148 on detecting and tracking hypersonic vehicles. D148's seismic section is one page, and it puts three things together: a network of 200 seismic stations, three flights it records seismic networks catching (an SR-71 and STS-42 by this one; another Discovery pass by 66 stations in Washington and Oregon), and one sentence: the "mysterious sonic booms" over Southern California in 1991 and 1992 were traced, with TERRAscope array data, to two F-4s near Mach 1 over Edwards Air Force Base. That sentence has a shape, and the shape is one an instrument can take on: a vehicle drags a Mach cone, the boom arrives where the cone meets the ground, and two hundred stations each record the moment they are crossed. The site's craft page also lists five observables, the second of them "hypersonic velocity with no sonic boom"; this bench prices its first half literally.
So the instrument does two things. First it builds the array and the cone: the 205 CI stations the FDSN station service lists as operating on 9 December 1993, each with its place and height; a vehicle in level flight on the dials; every ray off the cone refracted through the standard atmosphere, landing or turning back; each station's arrival time, the N-wave's strength by Carlson's 1978 method, and the ground's motion at the 1.5 to 2 µm/s per pascal of Goforth and McDonald, which the paper cites. Second it reads the paper the record cites. The one reference in D148's seismic section, cited two paragraphs before that sentence for the seismic detection of booms, is Cates and Sturtevant 2002; that paper reports the F-4 attribution as MIT Lincoln Labs's reading, finds it "fails to explain the three events detected", and reads the 1991 and 1992 booms as indirect booms from a source offshore, carried inland by high winds. The bench puts the record's sentence and the paper's finding side by side on the File, each with its author, at equal size; which one the array found is not the bench's to say.
How it works
Everything on the bench is arithmetic on the standard atmosphere, one ray-tracing rule, one published boom method and the coupling the paper cites; the vehicle, its track and the atmosphere’s temperature offset are dials. The script that ships with the site re-derives every displayed number before the build is allowed to pass.
β = arcsin(1/M) · n_h(z) = a(z) n_h(h_v)/a(h_v) · Mc = a(z_g)/a(h_v) · sin²φ_c = (1/Mc² − 1/M²)/(1 − 1/M²) · t = (x − D_x)/V + τ · Δp = K_p K_R √(p_v p_g) (M² − 1)^(1/8) h_e^(−3/4) l^(3/4) K_S
The cone and the trace. The record’s own equation gives the Mach angle, β = arcsin(1/M). A ray leaves the cone at azimuth φ (0 straight down) with direction (sin β along the track, cos β sin φ across, cos β cos φ down) and keeps its horizontal slowness through a still, stratified ISA (1976, seven layers to 86 km, a = √(γ R T)); it turns where its horizontal direction cosine reaches 1, and lands otherwise after a run D and a time τ integrated in 50 m steps. A station at along-track x and cross-track y is reached by the ray whose lateral run is y, at t = (x − D_x)/V + τ; in still air that reduces to the hyperbola, which the tune checks: the closed forms to 10⁻⁹, the arrivals to 10⁻⁴.
The cutoff. The ray straight down turns where a(z) equals the vehicle’s speed (the paper’s eq. 5), so no direct boom reaches the ground below Mc = a(ground)/a(altitude): 1.153 from 11 km at sea level, 1.143 over Edwards’ 789 m, 1.140 from 21 km. The lateral edge is the ray that just grazes the ground, sin²φ_c = (1/Mc² − 1/M²)/(1 − 1/M²): 59.5° for the SR-71 pass, and a carpet 52.7 km each side, where h √(M² − 1) is 60.4 km: the distance behind the vehicle at which the cone meets the ground. In still air the carpet has no edge, the boom only weakens. A surface-temperature dial adds an offset that fades to zero at 11 km; a warmer ground raises the bar.
The boom and the ground. Carlson’s simplified method (NASA TP-1122, 1978): Δp = K_p K_R √(p_v p_g) (M² − 1)^(1/8) h_e^(−3/4) l^(3/4) K_S and Δt = K_t (3.42/a_v) M (M² − 1)^(−3/8) h_e^(1/4) l^(3/4) K_S, with K_R = 2 (the report’s assumption), K_p = K_t = 1 (its reference case, a uniform atmosphere at the geometric-mean pressure; its charts raise K_p toward cutoff), h_e the cross-track slant as its sample problem 2 builds it, and the shape factor and length as dials defaulting to its sample problem 1 (0.087, 32.7 m). The bench reproduces two of the report’s three sample problems (74 Pa and 0.17 s; 36.1 Pa and 0.19 s) with the report’s own factors. Ground velocity follows at 1.5 µm/s per pascal on high-density rock and 2 on low-density, the Goforth and McDonald figures the paper cites.
No constant is fitted to the record; the one fit on the bench is the read-back, which fits the model’s own arrivals. The only choices are the dials: the vehicle’s altitude, Mach, heading and track point, refraction on or off, the ground’s temperature offset, the shape factor, the length, the coupling and the clock; every finding is quoted at the presets and across them.
The dials that decide the result
Five presets from the record and the paper, a free vehicle, and the atmosphere. Together they draw the cones the record, the paper and the craft page name, and the dials reach any other.
- SR-71, 9 December 1993. The paper’s Mach 3.15 at 21 km, westbound over station EDW (the record says Mach 3.2). The default: 60 stations, 52.7 km each side, −265 to +367 s.
- Discovery, 9 December 1992. Mach 14 at 55 km, the paper’s read of the Washington and Oregon hyperbolae, flown southbound over this array as a staging: a carpet 155 km each side and 152 stations.
- Two F-4s. Mach 1 relative to the ground’s sound speed at the altitude dial, the paper’s reading of the Lincoln Labs account: exactly at cutoff: the plane of Edwards gets nothing direct and only the stations standing higher catch a grazing boom (4 of 205 from 10 km); at ground Mach 1.02 from 10 km the carpet is 7.5 km each side.
- Offshore, hypersonic. The first read, Mach 5.5 (the middle of the paper’s "Mach 5 – 6") at 30 km, heading 340° along the coast and clear of it, on a track 230 km west and 150 km south of Edwards; the track and altitude are staging, because the paper gives neither.
- The observable. Mach 5 at 10 km westbound over Edwards: 40 stations, a carpet 35.6 km each side.
- The atmosphere and the boom. Refraction on (the ISA) or off (still air at the vehicle’s sound speed: no edge); a ground offset of −20 to +30 K; Carlson’s shape factor 0.05 to 0.15 and length 10 to 60 m; high- or low-density rock.
The claims, as they stand
The record’s sentences and the paper’s one by one, and where each lands when the array is built and the cone is flown.
| 'Caltech and the U.S.G.S. operate 200 seismographic stations throughout Southern California as part of the TERRAscope seismic network', sensing 'between 1 and 20 Hz' stated by D148, p. 31 | REPORTED | The paper: over 200 stations (TERRAscope, the SCSN and the UCLA basin network) at 100 samples a second over 50,000 km², and 209 sites analysed for the 1991 and 1992 events. The FDSN station service lists 205 CI stations operating on 9 December 1993 and 200 on 30 January 1992. The bench draws the 205. |
| 'On 9 December 1993, the network successfully detected the flight of an SR-71 flying over Edwards Air Force Base at a maximum speed of Mach 3.2' stated by D148, p. 31 | REPORTED | The paper: Mach 3.15 at 21 km, east to west, ray tracing that compares well with the arrivals and a primary carpet wider than the tracing gives. Flown on the bench through a still ISA: 60 stations, 52.7 km each side, −265 to +367 s, 38 Pa under the track. |
| 'The angle of the Mach cone showed that the shuttle was traveling at Mach 14, corresponding to an altitude of 55 km' stated by D148, p. 31, of another Discovery landing | REPORTED | The paper, of the 9 December 1992 pass over Washington and Oregon: Mach 14 from the hyperbola contours, 55 km from a typical reentry profile, 66 sites over 500 km. The bench fits the same hyperbola to its own arrivals: on refracted data it reads Mach 3.03 for a truth of 3.15; on still air it returns the truth. |
| 'By using data from the TERRAscope array, the source of these disturbances was traced to two F-4 Phantom aircraft flying over Edwards Air Force Base at speeds near Mach 1' stated by D148, p. 31; the section’s one reference, two paragraphs earlier, is Cates and Sturtevant 2002 | REPORTED | Basis: the record's own, the array's data; the paper reports the analysis behind it as MIT Lincoln Labs's, on 41 sites, with an attempt made to include deceleration and refraction. On the bench a vehicle at Mach 1 relative to the ground's sound speed sits exactly at the cutoff for its altitude (nothing direct to the plane of Edwards; a carpet 7.5 km each side at ground Mach 1.02 from 10 km). Caveat: the paper finds the read 'fails to explain the three events detected'. Account A on the File. |
| 'all the observed booms appear to be indirect booms from a source offshore propagated inland by high winds' stated by Cates and Sturtevant 2002, section 5 | REPORTED | Basis: the paper's own analysis of all 209 sites: three booms on 31 October 1991 (90, 104 and 30 sites, an average of 83 and 84 s apart), the same pattern on 30 January 1992, nothing on the north-western sites, no N-wave signatures. Caveat: the record, eight years later, gives the F-4 read as the outcome; the paper's word is 'appear to be' and its search for a source came back empty; the bench cannot draw this account, having no winds. Account B on the File. |
| 'For an aircraft flying at below the ambient sound speed at the ground, all rays will be turned and none will reach the ground' stated by Cates and Sturtevant 2002, section 2, eq. 5 | EXACT | Mc = a(ground)/a(altitude): 1.153 from 11 km at sea level, 1.143 over Edwards, 1.140 from 21 km, 1.126 from 10 km. The lateral edge follows from the same rule: 59.5° off straight down for the SR-71 pass. |
| Δp = K_p K_R √(p_v p_g) (M² − 1)^(1/8) h_e^(−3/4) l^(3/4) K_S stated by Carlson, NASA TP-1122, eq. 1 | MODELLED | Reproduced on two of the report’s three sample problems (74 Pa, 0.17 s; 36.1 Pa, 0.19 s) with its own factors; run on the bench with K_p = K_t = 1 and the report’s sample shape factor and length: 38.3 Pa and 0.227 s under the SR-71’s track. |
| 'approximately 1.5 µm/sec per Pascal of overpressure' on high-density rock, 'approximately 2 µm/sec per Pascal for low-density rock' stated by Cates and Sturtevant 2002, citing Goforth and McDonald 1968 | MODELLED | 57 to 77 µm/s under the SR-71’s track; the 0.15 to 0.2 Pa the paper matches its 1991 amplitudes to is 0.23 to 0.4 µm/s, two hundred times less. |
| The pitch: "STS-42 read as Mach 14 at 55 km over 500 km of track and 66 stations" stated by the bench’s pitch on the backlog board | REPORTED | Two flights run together: the record gives Mach 14, 55 km, 500 km and 66 stations for another Discovery landing, which the paper dates 9 December 1992 over Washington and Oregon; STS-42 is the 30 January 1992 landing at Edwards, on which the paper reports four booms and nearly the whole network detecting at least one. The bench carries both as the sources give them. |
| 'Hypersonic velocity with no sonic boom' stated by the site’s craft page, the second of the five observables Elizondo describes | READING | Priced literally: a vehicle above cutoff over land lays a carpet the stations record; at Mach 5 from 10 km the model reaches 40 stations on a carpet 35.6 km each side. Winds, secondary carpets and the thermal half are not on the bench. Priced, not judged. |
| What the bench amounts to stated by this bench | READING | One array, one cone, one sentence and its footnote. The record says the array found two F-4s near Mach 1; the paper it cites says it found indirect booms from offshore. The bench builds the array, flies the cone, shows what each reading asks of it, and chooses neither. |
Try this
- Start in the air. Run the clock on the SR-71 pass and watch the trace, a hyperbola bent by refraction, cross the array from the east: 60 stations light, the basin south of the track stays dark.
- Read the hyperbola. Open the Array. The still-air formula fitted to refracted arrivals reads Mach 3.03 and 20.3 km for Mach 3.15 and 20.2 km above the ground; switch refraction off and it reads 3.15.
- Find the edge. On the Cutoff, slide the altitude from 1 km to 80 km and watch the cutoff Mach fall to 1.03 near 50 km and climb again; then warm the ground by 20 K.
- Put the F-4s on the edge. Pick the two-F-4 preset at 10 km: ground Mach 1, no carpet over the plane of Edwards, four high stations grazed. Nudge the Mach dial up a few hundredths: the carpet appears across the basin.
- Hear the ground. On the Traces, compare the 57 to 77 µm/s the SR-71 leaves under its track with the 0.23 to 0.4 µm/s that the 0.15 to 0.2 Pa the paper matched its 1991 amplitudes to come to.
- Finish in the file. The seven Thursdays, the three reads, the sentence and its footnote, then the two accounts.
Accuracy
The honest line between what is reported, what is documented, what is arithmetic on them, and what is a reading:
| Feature | Status | What that means |
|---|---|---|
| The record and the paper it cites | Reported | D148 p. 31: the network, its band, the SR-71 at Mach 3.2, STS-42, the Discovery pass read as Mach 14 at 55 km, and the sentence tracing the 1991 and 1992 booms to two F-4s near Mach 1. Cates and Sturtevant 2002: over 200 stations, the coupling, the SR-71 at Mach 3.15 and 21 km, the seven Thursdays, the three reads and its own finding. Each quoted as printed, with its author. |
| The array and the map | Documented | The 205 CI stations the FDSN station service at Caltech lists as operating on 9 December 1993, with their places and heights (200 on 30 January 1992); the coastline and borders from Natural Earth, today’s lines. |
| The arithmetic | Exact | The ISA to 86 km; β = arcsin(1/M); the ray trace and its cutoff; the arrival times; the still-air hyperbola and its fit. Checked against the ISA tables, the still-air closed forms and two of Carlson’s three sample problems. No constant is fitted to the record; the hyperbola read-back is the one fit, on the model’s own arrivals. |
| The dials, and what is left out | Modelled | The vehicle and its staging (the paper gives no track for the offshore read and no altitude); no wind, which the paper found carries booms in from offshore; the ground’s temperature offset; Carlson’s factors at 1, the shape factor, the length; the coupling; the drawn trace shape; a flat ground. |
| What it amounts to | Reading | Whether the array found two F-4s, as the record says, or indirect booms from offshore, as the paper the record cites says, is a reading, and the bench declines to make it for you; the pitch’s figures are quoted as the board’s, never as the bench’s. |
In one line: Every sentence of the record and of the paper it cites is quoted as printed and attributed; the array is a public station list; the cone, the trace, the cutoff and the fit are arithmetic; the vehicle, the winds it lacks and Carlson’s factors are named as choices; and which account of the 1991 and 1992 booms fits is left where the record and the paper left it, with the reader.
Sources
- DOW-UAP-D148, "AAWSAP DIRD Detection and High Resolution Tracking of Vehicles at Hypersonic Velocities November 20 2010", U.S. Department of War, PURSUE Release 06 (war.gov/ufo, 18 September 2026): p. 29 (the Mach angle) and p. 30 (Figure 18), p. 31 (the "Seismic" section: the network, the SR-71, STS-42, the Discovery pass, the 1991 and 1992 booms), p. 46 (reference 27).
- Cates, J. E. & Sturtevant, B. (2002) "Seismic detection of sonic booms" Journal of the Acoustical Society of America 111(1), 614 to 628, doi 10.1121/1.1413754: sections 2 (geometrical acoustics, eq. 5, the carpets), 3 (the network, the ground’s response, the coupling), 4 (the SR-71 pass, STS-42, the Discovery pass), 5 (the mystery booms, Table 1, the three reads) and 6.
- Carlson, H. W. (1978) Simplified Sonic-Boom Prediction, NASA Technical Paper 1122, Langley Research Center: eqs. (1) and (2), the atmospheric-factor definition, the reflection factor, the shape-factor charts’ guidance, and sample problems 1 and 2 of the three in Appendix B.
- Caltech Seismological Laboratory, SCEDC FDSN station web service (service.scedc.caltech.edu/fdsnws/station/1), network CI, level station, text format, with startbefore 1993-12-09 and endafter 1993-12-10 (205 stations) and with startbefore 1992-01-30 and endafter 1992-01-31 (200 stations); retrieved 30 September 2026. Station EDW, "Edwards Air Force Base", 34.88303°N 117.99106°W, 789 m, is the scene’s origin; names on the map are the service’s own.
- Natural Earth, 10 m cultural and physical vectors (public domain): ne_10m_coastline, ne_10m_admin_1_states_provinces_lines and ne_10m_admin_0_boundary_lines_land, as GeoJSON from the nvkelso/natural-earth-vector repository, clipped to 32.0 to 37.8°N and 121.5 to 114.0°W and simplified to 0.4 km; retrieved 30 September 2026. Today’s lines stand in for the 1990s’.
- U.S. Standard Atmosphere, 1976 (NOAA, NASA, USAF): the seven-layer temperature profile to 86 km and its base pressures, checked in the bench’s script against the table’s values at 11, 20, 32, 47 and 71 km; the same constants INST-53 and INST-54 use.
- Goforth, T. & McDonald, J. (1968) Seismic Effects of Sonic Booms, NASA CR-1137, and Rickley, E. & Pierce, A. (1980) Detection and Assessment of Secondary Sonic Booms in New England, FAA-AEE-80-22, both as Cates and Sturtevant 2002 cite them (the coupling; the 0.15 to 0.2 Pa of Concorde’s indirect booms); not read directly.
- Signals from the Periphery, Release 06 Briefing 20, the briefing on D137 and D148; the craft topic page and the Elizondo dossier for the five observables; The Belgian Wave (INST-54), the site’s other sonic-boom bench.