Find the hidden source.: sources & model

Watch waves emerge from a buried source, pick synthetic arrivals and reveal the location one clue at a time. Test the clocks, depth and velocity assumptions—and compare the model with real recorded evidence.

What supports the explanation?

What this model assumes

1. Flat homogeneous direct-arrival teaching model. No layered/spherical travel paths, reflections, surface waves, attenuation, actual ground-motion amplitudes or finite-rupture dynamics.
2. Source generation is fictional. Default coordinates and clock values are authored and not a real earthquake record. The source speeds are chosen from a documented model, not universal rock constants.
3. Fault poses and local wave displacements are illustrations. They do not calculate stress thresholds, fault failure, displacement magnitude or future-event probability.
4. Central gaps, depth consistency and station geometry are checked. Materially inconsistent or collinear cases are retained as unresolved; numerical roundoff is not used to repair data.
5. Known-depth map constraints and three-pair depth recovery are distinct experiments. Reading annuli exclude uncertainty in depth and material speeds.
6. RMS is a conditional timing fit, not a location confidence level, magnitude estimate or safety forecast.
7. Source GIFs are historic annotated displays, not raw calibrated waveform data. No sample rate, amplitude calibration, channel response or pixel-derived measurement has been fabricated.
8. Paper cards are rounded calculated examples. Compass precision is not graded against unrounded machine values, and the physical worksheet has not been learner-trialed.
9. A homogeneous direct-arrival model: This lesson uses a flat zero-elevation surface and one isotropic solid with vP=6.2 km/s and vS=3.57 km/s. Those chosen speeds are traceable to the Canadian EPB location model described in USGS OFR82-777. Our fictional event is not a reconstruction of its New Brunswick aftershocks. The original study included elevation corrections; this model does not.
10. Coordinates and propagation: Coordinates are local kilometres: x east, y north and h positive downward. R²=(x−xᵢ)²+(y−yᵢ)²+h². A source at origin time t₀ gives P=t₀+R/vP and S=t₀+R/vS. The 3D map uses [x,−h,−y] with one common scale.
11. The gap removes common origin time: S−P=R(1/vS−1/vP). With the stated speeds, the coefficient is approximately0.118821722 s/km and R≈8.415969582 times the gap in seconds. A5.00 s gap gives42.07984791 km. It supplies a source distance, not a direction.
12. Source distance is not the map radius: At known depth h, the map radius is ρ=√(R²−h²). The default source is(30,40,12) km, origin20 s; stationA is at(0,0,0). Its source distance is51.419841 km but its horizontal radius is50 km. If R<h, no exact circle exists at that depth.
13. The surface front has an emergence time: After elapsed time τ, a direct spherical front has radius vτ. Its surface intersection exists only for τ≥h/v and has radius√((vτ)²−h²). At12 km, P emerges at1.935484 s and S at3.361345 s. The initial apparent ring speed is a geometric intersection effect, not a faster material wave.
14. Three complete pairs versus three P arrivals: With three non-collinear surface stations and exact P/S gaps, squared-range differences solve x and y; R²−ρ² gives h². Selecting h≥0 chooses the below-plane branch. Three P times alone leave four unknowns(x,y,h,t₀), and the reference examples give distinct depth/origin combinations with the same P arrivals.
15. Fit a common origin, then inspect residuals: For a candidate source, t₀*=Σwⱼ(tⱼ−Tⱼ)/Σwⱼ. RMS=√[Σwⱼ(tⱼ−t₀*−Tⱼ)²/Σwⱼ]. The examples use equal positive weights on six arrivals. RMS is in seconds; it depends on the model and picks. Small residuals do not prove spatial accuracy or predict another event.
16. Reading bounds make bands: Authored P and S reading bounds of±0.05 and±0.10 s give a worst-case gap bound±0.15 s and source-range bound±1.262395437 km. At a fixed depth these become annuli. The continuous overlap is not a rectangle or a statistical confidence interval. Separate coordinate extrema are computed from boundary intersections and circle extrema.
17. Sampling and rounding are different: The map’s filled cells sample the band overlap at1 km cell centers; absence of a sampled cell is not proof that a smaller overlap is absent. Rounded0.01 s paper times instead have±0.005 s time-rounding bounds and±0.01 s worst-case gap rounding. That is different from the larger reading-bound exercise.
18. A fixed observation set for each assumption test: Generation controls recompute synthetic records after moving the fictional source or station geometry. The reference audit freezes its original observations before changing a pick, clock or assumed speed. The proposed fourth station compares two fixed P-only source candidates; it does not create a new earthquake or forecast.
19. What ideal P and S motion leave out: The local marker illustration uses a chosen sinusoid and envelope. Its direction respects the inclined ray, but its frequency, amplitude, repeated timing and display length are authored. Real paths include refraction, reflection, conversions, surface waves, attenuation, radiation patterns and finite rupture. Propagating shear S waves do not traverse a liquid; no interface solver is implemented here.
20. Magnitude and local intensity: Magnitude estimates event size using a specified method. Shaking intensity varies with location. Propagation, local geology, radiation and instruments affect recordings. A gain control on an arbitrary synthetic pulse cannot establish a real magnitude or damage level.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

USGS Public Domain Loma Prieta site-response composite, preserving the map, damage photograph and recorded shaking displays. The original GIF is unchanged. The cover is a resized format derivative without cropping. This is qualitative observed context with no calibrated amplitude extraction or damage ratio claim.