Is Earthquake Replenishment Sufficient for Unbiased b-Value Estimation?
Abstract
Short-term aftershock incompleteness biases Gutenberg-Richter b-value estimates because many small earthquakes remain undetected immediately after large events. Two strategies address this problem. Earthquake replenishment reconstructs missing events to restore a more complete catalog, whereas robust positive-difference estimators infer the b-value directly from incomplete observations. Whether these approaches provide equivalent information on the magnitude distribution remains open. We address this issue using synthetic aftershock sequences generated with the Epidemic-Type Aftershock Sequence (ETAS) model and degraded through a time- and magnitude-dependent incompleteness model. Incomplete catalogs are replenished using AutoBETA, and b is estimated using the standard maximum-likelihood, b-more-positive, and b-more-incomplete estimators. Replenishment reconstructs the overall structure of the missing-event population and substantially improves conventional maximum-likelihood estimates, although small residual biases remain. By contrast, both positive-difference estimators recover the imposed b-value directly from incomplete synthetic catalogs. Applications to the Ridgecrest, Landers, and Hector Mine sequences show that b-more-incomplete is less sensitive to replenishment than b-more-positive. Ten independent replenishment seeds indicate that seedto-seed variability is small relative to differences among estimators. Replenishment and robust b-value estimation therefore address different aspects of catalog incompleteness: replenishment provides a more complete aftershock representation, whereas robust estimators are preferable when accurate b-value estimation is the primary objective.
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BibTeX
@misc{prabowo2026earthquake,
title = {{Is Earthquake Replenishment Sufficient for Unbiased b-Value Estimation?}},
author = {Herbian Hokky Prabowo and Giuseppe Petrillo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13380},
eprint = {2610.13380},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13380},
}
RIS
TY - UNPB
TI - Is Earthquake Replenishment Sufficient for Unbiased b-Value Estimation?
AU - Herbian Hokky Prabowo
AU - Giuseppe Petrillo
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13380
UR - https://arxiv.org/abs/2610.13380
AB - Short-term aftershock incompleteness biases Gutenberg-Richter b-value estimates because many small earthquakes remain undetected immediately after large events. Two strategies address this problem. Earthquake replenishment reconstructs missing events to restore a more complete catalog, whereas robust positive-difference estimators infer the b-value directly from incomplete observations. Whether these approaches provide equivalent information on the magnitude distribution remains open. We address this issue using synthetic aftershock sequences generated with the Epidemic-Type Aftershock Sequence (ETAS) model and degraded through a time- and magnitude-dependent incompleteness model. Incomplete catalogs are replenished using AutoBETA, and b is estimated using the standard maximum-likelihood, b-more-positive, and b-more-incomplete estimators. Replenishment reconstructs the overall structure of the missing-event population and substantially improves conventional maximum-likelihood estimates, although small residual biases remain. By contrast, both positive-difference estimators recover the imposed b-value directly from incomplete synthetic catalogs. Applications to the Ridgecrest, Landers, and Hector Mine sequences show that b-more-incomplete is less sensitive to replenishment than b-more-positive. Ten independent replenishment seeds indicate that seedto-seed variability is small relative to differences among estimators. Replenishment and robust b-value estimation therefore address different aspects of catalog incompleteness: replenishment provides a more complete aftershock representation, whereas robust estimators are preferable when accurate b-value estimation is the primary objective.
ER -