Hypocenter Inversion Eval

---
name: hypocenter-inversion-eval
description: Evaluates the accuracy and uncertainty quantification of a physics-informed neural network for locating earthquake hypocenters using synthetic seismic arrival times. Use when the user wants to benchmark on Synthetic Seismic Array, or asks about evaluating this task. Reports location uncertainty.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2101.03271
  bibtex_key: smith2021hyposvi
  confidence: high
---

# hypocenter-inversion-eval

> HypoSVI: Hypocenter inversion with Stein variational inference and Physics Informed Neural Networks — Smith et al. (2021) (arXiv:2101.03271, 2021)

## What this evaluates

Evaluates the accuracy and uncertainty quantification of a physics-informed neural network for locating earthquake hypocenters using synthetic seismic arrival times.

## Datasets

- **Synthetic Seismic Array** — total ?; splits: test (-1); repo https://github.com/Ulvetanna/HypoSVI

## Metrics

- `location uncertainty` **(primary)** — range: km | percent
  - Distance between the recovered hypocenter and the true hypocenter, assessed alongside whether the true location falls within the predicted 95% posterior uncertainty contour.

## Input / output format

**Input**: Synthetic phase arrival times at fixed elevation (0 km) with 0.01s picking uncertainty, paired with station coordinates.

**Output**: Predicted hypocenter coordinates (latitude, longitude, depth) and a posterior distribution representing location uncertainty.

## Scoring recipe

```python
def score(predictions, gold):
    pred_loc = predictions['hypocenter']
    true_loc = gold['true_hypocenter']
    dist = euclidean_distance(pred_loc, true_loc)
    contour = predictions['95pct_contour']
    coverage = true_loc in contour
    return {'distance_error_km': dist, 'coverage_rate': coverage}
```

## Common pitfalls

- Synthetic tests use regularly spaced stations and a simplified velocity model, which may overestimate performance on real, clustered seismic networks.
- The evaluation relies on visual/contour comparison rather than a standardized numerical metric like RMSE, making cross-study comparison difficult.

## Evidence (verbatim from paper)

> The recovered optimal hypocentre and location uncertainty are then compared with the true earthquake locations and an expected 95 percentile contour from a the solution of a grid-search inversion.

## Citation

```bibtex
@misc{smith2021hyposvi,
  title={HypoSVI: Hypocenter inversion with Stein variational inference and Physics Informed Neural Networks},
  author={Smith et al. (2021)},
  year={2021},
  note={arXiv:2101.03271}
}
```

- arXiv: 2101.03271