{
  "annotation_id": "d8cb88b7-39b3-42e3-b9d8-b817751ab78b",
  "date_created": "2026-03-02T18:00:46.921000Z",
  "date_modified": "2026-03-02T18:00:46.921000Z",
  "file_hash": "1491c41a4d9636c60d38fe958182e3cb7b7219e8a4ba4ec9519c63b7ffcdd44b",
  "private": false,
  "record": {
    "abstract": "The empirical Bath\u0027s law states that the average difference in magnitude\nbetween a mainshock and its largest aftershock is 1.2, regardless of the\nmainshock magnitude. Following Vere-Jones [1969] and Console et al. [2003], we\nshow that the origin of Bath\u0027s law is to be found in the selection procedure\nused to define mainshocks and aftershocks rather than in any difference in the\nmechanisms controlling the magnitude of the mainshock and of the aftershocks.\nWe use the ETAS model of seismicity, which provides a more realistic model of\naftershocks, based on (i) a universal Gutenberg-Richter (GR) law for all\nearthquakes, and on (ii) the increase of the number of aftershocks with the\nmainshock magnitude. Using numerical simulations of the ETAS model, we show\nthat this model is in good agreement with Bath\u0027s law in a certain range of the\nmodel parameters.",
    "arxiv_id": "physics/0307083",
    "authors": [
      "Agnes Helmstetter",
      "Didier Sornette"
    ],
    "categories": [
      "physics.geo-ph"
    ],
    "doi": "10.1029/2003GL018186",
    "journal_ref": "Geophys. Res. Lett., 30, 2069, 10.1029/2003GL018186 (2003)",
    "title": "Bath\u0027s law Derived from the Gutenberg-Richter law and from Aftershock   Properties",
    "url": "https://arxiv.org/abs/physics/0307083"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f8724b2c-c9b0-465d-9c33-a50624f379f8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}