The development of reliable operational earthquake forecasts is
dependent upon managing uncertainty and bias in the parameter
estimations obtained from models like the Epidemic-Type Aftershock
Sequence (ETAS) model. Given the intrinsic complexity of the ETAS model,
this paper is motivated by the questions: “What constitutes a
representative sample for fitting the ETAS model?” and “What biases
should we be aware of during survey design?”. In this regard, our
primary focus is on enhancing the ETAS model’s performance when dealing
with short-term temporally transient incompleteness, a common phenomenon
observed within early aftershock sequences due to waveform overlaps
following significant earthquakes. We introduce a methodological
modification to the inversion algorithm of the ETAS model, enabling the
model to effectively operate on incomplete data and produce accurate
estimates of the ETAS parameters. We build on a Bayesian approach known
as inlabru, which is based on the Integrated Nested Laplace
Approximation (INLA) method. This approach provides posterior
distributions of model parameters instead of point estimates, thereby
incorporating uncertainties. Through a series of synthetic experiments,
we compare the performance of our modified version of the ETAS model
with the original (standard) version when applied to incomplete
datasets. We demonstrate that the modified ETAS model effectively
retrieves posterior distributions across a wide range of mainshock
magnitudes and can adapt to various forms of data incompleteness,
whereas the original model exhibits bias. In order to put the scale of
bias into context, we compare and contrast further biases arising from
different scenarios using simulated datasets. We consider: (1)
sensitivity analysis of the modified ETAS model to a time binning
strategy; (2) the impact of including and conditioning on the historic
run-in period; (3) the impact of combination of magnitudes and trade-off
between the two productivity parameters K
and α; and (4) the sensitivity to incompleteness
parameter choices. Finally, we explore the utility of our modified
approach on three real earthquake sequences including the 2016 Amatrice
earthquake in Italy, the 2017 Kermanshah earthquake in Iran, and the
2019 Ridgecrest earthquake in the US. The outcomes suggest a significant
reduction in biases, underlining a marked improvement in parameter
estimation accuracy for the modified ETAS model, substantiating its
potential as a robust tool in seismicity analysis.