# Improving moment tensor solutions under Earth structure uncertainty with simulation-based inference

arXiv: https://arxiv.org/abs/2603.18925 · HTML: https://mlsanity.com/paper/2603.18925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 131 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 23 of 23)

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- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
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- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks](https://mlsanity.com/paper/2112.08866/) (2021)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation](https://mlsanity.com/paper/2208.13624/) (2022)
- [Earthquake Phase Association with Graph Neural Networks](https://mlsanity.com/paper/2209.07086/) (2022)
- [SeisCLIP: A seismology foundation model pre-trained by multi-modal data for multi-purpose seismic feature extraction](https://mlsanity.com/paper/2309.02320/) (2023)
- [Hybrid Summary Statistics](https://mlsanity.com/paper/2410.07548/) (2024)
- [Full-waveform earthquake source inversion using simulation-based inference](https://mlsanity.com/paper/2410.23238/) (2024)

## Abstract (arXiv)

Bayesian inference represents a principled way to incorporate Earth structure uncertainty in full-waveform moment tensor inversions, but traditional approaches generally require significant approximations that risk biasing the resulting solutions. We introduce a robust method for handling theory errors using simulation-based inference (SBI), a machine learning approach that empirically models their impact on the observations. This framework retains the rigour of Bayesian inference while avoiding restrictive assumptions about the functional form of the uncertainties. We begin by demonstrating that the common Gaussian parametrisation of theory errors breaks down under minor (1-3 %) 1-D Earth model uncertainty. To address this issue, we develop two formalisms for utilising SBI to improve the quality of the moment tensor solutions: one using physics-based insights into the theory errors, and another utilising an end-to-end deep learning algorithm. We then compare the results of moment tensor inversion with the standard Gaussian approach and SBI, and demonstrate that Gaussian assumptions induce bias and significantly under-report moment tensor uncertainties. We also show that these effects are particularly problematic when inverting short period data and for shallow, isotropic events. On the other hand, SBI produces more reliable, better calibrated posteriors of the earthquake source mechanism. Finally, we successfully apply our methodology to two well studied moderate magnitude earthquakes: one from the 1997 Long Valley Caldera volcanic earthquake sequence, and the 2020 Zagreb earthquake.