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Synthetic Event Alignment Strategies

Problem

The current synthetic event list and INGV catalog share a useful schema: UTC time, latitude, longitude, depth, magnitude, and provenance. They do not yet share the same statistical process. Synthetic events are generated by a simulated avalanche and then assigned earthquake-like metadata; INGV events are an irregular marked point process. Matching individual synthetic events to individual earthquakes would therefore create false precision.

The alignment target should be the distribution and structure of events, not one-to-one event identity.

Candidate Approaches

1. Multi-resolution window targets

Represent each time/spatial cell with several targets:

  • event count above M2.0, M2.5, and M3.0
  • log seismic-energy proxy
  • maximum magnitude
  • time to the next event
  • spatial occupancy or event density

Use the binary occurrence label only as a derived view. Count and energy targets retain information that is discarded by a yes/no target and support zero-inflated or hurdle losses.

2. Marked-process calibration

Calibrate synthetic event marks against the training portion of the real catalog:

  • monotonic quantile mapping for magnitude
  • rate scaling for inter-event times
  • separate calibration for event clusters and quiet periods
  • depth calibration only if the simulation has a defensible depth analogue

All mappings must be fitted on training dates only and frozen before evaluation.

3. Spatial density calibration

Compare and reweight spatial occupancy rather than moving individual events arbitrarily:

  • fixed-cell occupancy at several grid sizes
  • empirical INGV cell-rate weights
  • kernel or nearest-cell density matching
  • optional transport from synthetic cell mass to real cell mass

Persistent localized sandpile sources must remain visible in the uncalibrated signal. Spatial reweighting should be an explicit observation model, not a hidden change to the simulation dynamics.

The first implemented rate-and-magnitude calibration reduces the synthetic-to-real rate ratio from about 2.0 to 1.14 and the magnitude Wasserstein distance from about 2.3 to 0.15 for seed 40. It still covers only 11 of the 63 real occupied cells, so it is not a complete catalog alignment. The next derived catalog also carries per-event cell-rate importance weights; these preserve synthetic coordinates and are intended for weighted training, not for claiming that missing cells have been recovered.

Scope matters: the current simulation profile is labelled central_italy. Against the matching 594-event central-Italy INGV catalog, raw seed 40 is about 16 times too active. A tuned five-event extraction reduces the rate ratio to 0.71, but its sample is too small and its nearest-neighbour distance is much worse. This means a good alignment cannot be declared from a single tuned episode; at least several independent episodes and a joint rate/magnitude/spatial score are required.

The first three-episode combined profile is more useful. After rate and magnitude calibration, it reaches a rate ratio of 0.956, magnitude Wasserstein distance 0.082, and median inter-event time 23.6 hours versus 21.6 hours for central Italy. Spatial quantile transport improves nearest-neighbour Wasserstein distance from 30.939 to 11.212 km and covers 3 of 4 coarse central-Italy cells. This is the first promising intermediate profile, but the remaining spatial clustering error still prevents promotion.

A 40,000-step seed-4500 episode tested whether a longer trajectory would correct the sparse event process. It did not: the default extractor returned five events, and the best tuned profile returned ten. The tuned signal-shape score improved to 0.177394, but rate ratio was 0.606, magnitude Wasserstein distance 2.501, and sample-matched nearest-neighbour distance 91.279 km. Duration is therefore not a sufficient alignment fix; the next useful test is a multi-episode catalog with a minimum event-count gate and held-out validation.

Five default-extraction episodes (40, 41, 42, 4300, and 4500) now provide a larger candidate. Catalog duration must be supplied explicitly because quiet tails are not represented by emitted events. With the known 111.78-day combined coverage, calibration and spatial transport retain 67 events: rate ratio 0.924, magnitude Wasserstein distance 0.046, inter-event Wasserstein distance 22.885 hours, sample-matched nearest-neighbour distance 1.600 km, and 3 of 4 occupied coarse cells. This is the strongest current diagnostic, but it remains subject to held-out validation.

That five-episode result mixed historical high-fill runs with the current source-localized refill profile. A clean rerun of seeds 4600, 4700, and 4800 under the current profile removes that confound. With the q=0.9996, 240-step extractor and explicit 41.89-day coverage, the calibrated and spatially transported catalog reaches rate ratio 0.847, magnitude Wasserstein distance 0.085, inter-event Wasserstein distance 10.415 hours, sample-matched nearest-neighbour distance 7.637 km, and 4 of 4 coarse cells. Use this as the current matched baseline; retain the raw per-seed catalogs for later held-out checks.

Nearest-neighbour comparisons must be sample-size matched. With 594 real events versus 32 calibrated synthetic events, the full-catalog distance is biased upward. Sampling 32 real events repeatedly gives a baseline comparison of 21.570 km; spatial transport reduces the synthetic comparison to 3.469 km. This is a substantial clustering improvement, although cell occupancy and joint spatial structure still need validation on more episodes.

4. Catalog-level distance and simulation calibration

Score each synthetic episode against the real training catalog using a vector of summary statistics:

  • event rate and inter-event-time quantiles
  • Gutenberg-Richter-like magnitude slope and tail counts
  • spatial cell occupancy and nearest-neighbour distances
  • temporal clustering and quiet-period lengths
  • magnitude-energy distribution

Use these scores for approximate Bayesian computation or a bounded parameter sweep over source count, refill, removal, warm-up, and event extraction settings. Select profiles on training data, then evaluate once on held-out real dates.

5. Feature-distribution alignment

After catalog calibration, reweight or select synthetic windows whose observable features resemble real seismic windows. This is a covariate-shift diagnostic, not proof that the modalities share a causal mechanism. The existing embedding and CORAL experiments fit here, but must be compared against random and centroid controls.

6. Event-process or intensity-field models

For a later model, predict a spatial intensity field over the next horizon, with separate heads for count, energy, and magnitude distribution. A point-process model or a cell-wise zero-inflated count model is a better match to the catalog than a single event-list classification head. Keep the Transformer as the multimodal encoder and make the output head replaceable.

  1. Build a catalog comparison report for real INGV and each synthetic episode using the statistics above.
  2. Tune only the observation mapping: time scale, magnitude quantiles, and spatial cell weights. Preserve raw synthetic outputs.
  3. Evaluate multi-resolution count, energy, and occupancy targets with grouped-time and leave-one-episode-out splits.
  4. Add VLF and astronomy as covariates only after seismic-only count/intensity baselines are stable.
  5. Use binary occurrence and weekly event maps as reporting views, not the sole training target.

Evaluation Rules

  • Fit every calibration on training dates only.
  • Keep real dates after synthetic dates in transfer experiments; never mix future real labels into synthetic calibration.
  • Compare against historical-rate, spatial-rate, and shuffled-time controls.
  • Report count error, energy error, spatial distance, calibration, precision, recall, and balanced accuracy together.
  • Do not claim a precursor or prediction result from catalog similarity alone.

Dependencies

The first catalog comparison and calibration pass needs only the existing Python standard library and installed project dependencies. SciPy would be useful later for Wasserstein distances, KDE, and point-process diagnostics, but is not required for the initial implementation.