Inversion Problems in Seismology by Gönenç Onay - DRP Türkiye 2025 Colloquium Talk

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This is a colloquium talk on inversion problems in seismology, given by Prof. Gönenç Onay of Galatasaray University on June 24, 2025. The talk is the first of five colloquia organized as part of DRP Türkiye 2025.

This recording is edited and annotated by https://www.youtube.com/@alpuzman.

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Abstract:

Earthquake analysis presents two fundamental inverse problems that showcase the power of modern computational mathematics. The first—hypocenter location—requires inferring spatial-temporal parameters from arrival time observations across seismic networks. We will expose how Bayesian sampling methods (Octree, MCMC) replace traditional linear approaches by properly characterizing the complete probability distribution of solutions rather than point estimates, addressing the inherent non-linearity of seismic wave propagation.

The second problem involves moment tensor inversion: extracting the source mechanism matrix from seismic waveforms. Traditional approaches require solving expensive PDEs at each evaluation. Neural Operator Networks can fundamentally change this paradigm by learning complex wave propagation relationships directly from data. This can possibly enhance monitoring with particular relevance for the North Anatolian Fault system beneath the Marmara Sea.

The talk will be accessible to undergraduates, with all key mathematical concepts and seismological notions clearly defined.

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Table of Contents:

00:00:00 introduction
00:01:24 beginning of the general overview talk
00:03:20 inverse problems in seismology
00:09:38 p-waves versus s-waves
00:10:14 arrival times
00:12:04 problem 1: locating the earthquake
00:14:41 solution strategies
00:18:17 Metropolis-Hastings algo
00:19:59 problem 2: identifying the source mechanism of the earthquake
00:20:16 moment tensor
00:22:26 key equation; Green's function
00:23:59 neural operator approach
00:25:06 applications of neural ops in seismology
00:27:12 recap
00:28:01 sigma
00:30:05 beginning of the more technical talk
00:30:46 birth of seismic waves
00:30:57 more on p-waves (aka primary waves), s-waves (aka secondary waves)
00:31:05 surface waves
00:31:19 seismometer and seismogram
00:31:48 more on inverse problems
00:32:36 more on problem 1
00:32:45 traditional approach to problem 1
00:33:08 probabilistic approach to problem 1
00:34:16 Markov chain Monte Carlo (MCMC) algo
00:36:58 Oct-Tree method
00:37:48 more on problem 2
00:37:59 more on the moment tensor
00:39:47 moment tensor representation theorem
00:41:50 formal approach to machine learning in seismology
00:43:41 multi-layer perceptron (MLP); universal approximation theorem
00:48:59 traditional approach to problem 2
00:50:15 more on the neural operator approach to problem 2
00:51:33 example: Fourier Neural Operator (FNO)
00:52:29 more on the neural operator approach to problem 2
00:53:45 recap
00:55:11 limitations of the neural op approach

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Links:
Prof. Onay:
https://onayg.com/

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License:

CC BY-NC-SA 4.0
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International Public License
https://creativecommons.org/licenses/by-nc-sa/4.0/

DRP Türkiye 2025
https://sites.google.com/view/drpturkiye/homepage

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