Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2309.17220

The strongest aftershock in seismic models of epidemic type

George Molchan·Elisa Varini
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider an epidemic-type aftershock model (ETAS($F$)) for a large class of distributions $F$ determining the number of direct aftershocks. This class includes Poisson, Geometric, Negative Binomial distributions and many other. Assuming an exponential form of the productivity and magnitude laws, we find a limiting distribution of the strongest aftershock magnitude $m_a$ when the initial cluster event $m_0$ is large. The regime can be either subcritical or critical; the initial event can be dominant in size or not. In the subcritical regime, the mode of the limiting distribution is determined by the parameters of productivity and the magnitude laws; the shape of this distribution is not universal and is effectively determined by $F$. For example, the Geometric $F$-distribution generates the logistic law, and the Poisson distribution (studied earlier) generates the Gumbel type 1 law. The accuracy of these laws for moderate initial magnitudes is tested numerically. The limit distribution of the Bath's difference $m_0$-$m_a$ is independent of the initial event size only if the regime is critical, and the ratio of exponents in the laws of magnitude and productivity is contained in the interval $(1,2)$. Previous studies of the $m_a$-distribution have dealt with the traditional Poisson $F$ model and with arbitrary (not necessarily dominant) initial magnitude $m_0$.

Explore related subjects

physics.geo-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

George Molchan, Elisa Varini. 2023-11-08. The strongest aftershock in seismic models of epidemic type. https://arxiv.org/abs/2309.17220

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

SPBench: A Multi-Task Evaluation Benchmark for Exploration Seismic Processing

Exploration seismic processing underpins subsurface imaging and resource exploration, but learning-based methods remain difficult to compare across studies. Our survey of 368 papers finds widespread reliance on private or difficult-to-reproduce datasets, with only 25 providing public code. This obscures whether reported gains arise from model design or experimental settings. We introduce the Seismic Processing Benchmark (SPBench), covering six tasks: random noise attenuation, trace interpolation, ground-roll suppression, multiple suppression, deblending, and first-arrival picking. We reproduce 24 supervised methods on 10 datasets under 43 standardized settings and release datasets, implementations, configurations, evaluation scripts, and results. To complement global scores and per-trace pick errors, we introduce signal-component-resolved evaluation (SCoRE) for reconstruction and a reference-free ridge-curvature score (RC_norm) for first-arrival picking. Our analyses show that synthetic rankings do not reliably predict field rankings, with task-dependent agreement when models train within each setting. As degradation strengthens, rankings reorder more under coherent ground roll than under random-like interference. The ridge score agrees with MAE-based model rankings in the evaluated settings, with a mean Kendall correlation of 0.881 across three field surveys, while SCoRE reveals frequency- and energy-dependent differences hidden by global scores. SPBench provides a reproducible basis for comparing learning-based seismic processing methods and characterizes how their relative advantages vary across data settings, degradation strengths, and evaluation criteria.

physics.geo-ph↗
arXiv2026

Bayesian full waveform inversion with learned prior using deep convolutional autoencoder

Full waveform inversion (FWI) can be expressed in a Bayesian framework, where the associated uncertainties are captured by the posterior probability distribution (PPD). In practice, solving Bayesian FWI with sampling-based methods such as Markov chain Monte Carlo (MCMC) is computationally demanding because of the extremely high dimensionality of the model space. To alleviate this difficulty, we develop a deep convolutional autoencoder (CAE) that serves as a learned prior for the inversion. The CAE compresses detailed subsurface velocity models into a low-dimensional latent representation, achieving more effective and geologically consistent model reduction than conventional dimension reduction approaches. The inversion procedure employs an adaptive gradient-based MCMC algorithm enhanced by automatic differentiation-based FWI to compute gradients efficiently in the latent space. In addition, we implement a transfer learning strategy through online fine-tuning during inversion, enabling the framework to adapt to velocity structures not represented in the original training set. Numerical experiments with synthetic data show that the method can reconstruct velocity models and assess uncertainty with improved efficiency compared to traditional MCMC methods.

physics.geo-ph↗
arXiv2026

Assessing foundational atomistic models for iron alloys under Earth's core conditions

We assess the capability of recently developed foundational atomistic models (FAMs) to simulate iron alloys under the extreme pressures and temperatures of Earth's core. Static equations of state for hexagonal close-packed (hcp) and body-centered cubic (bcc) iron, computed using 17 FAMs, are benchmarked against ab initio calculations. Two representative models, MatterSim and MACE, are further evaluated for their ability to reproduce phonon spectra, liquid structure, and melting relations of iron at core conditions. While both models capture several key properties, MACE substantially overestimates the stability of bcc iron and fails to correctly describe the stability of hcp iron. Their performance is also examined for binary liquids, superionic phases, and a seven-component Fe-Ni-Si-S-O-H-C liquid. Although these FAMs were not explicitly trained on data from core conditions, they can reproduce several structural and dynamical properties across a wide range of compositions. However, none of the tested models consistently reproduces all first-principles benchmarks. By analyzing the origins of these discrepancies, we identify several limitations of current FAMs, particularly the lack of an explicit treatment of thermal electronic excitations, which significantly affect phase stability and thermodynamic properties under core conditions. We further discuss directions for improving FAMs to enable predictive simulations of core-forming materials under extreme conditions.

physics.geo-ph↗