Application of machine learning for the extrapolation of seismic data - Master’s Thesis

Aug 4, 2026

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Low frequencies in seismic data are often difficult to acquire, which can cause full-waveform inversion to fail due to cycle-skipping. This thesis studies whether neural networks can extrapolate missing low frequencies. The workflow requires suitable training/testing data, conditioning for machine learning, and a designed extrapolation procedure followed by comparison with reference synthetic data. Synthetic Asse II-based models generate shot gathers for a U-Net reconstruction.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages100

Reading Time4 h 12 min

AccessFree to download

Contents

1. Introduction

2. Theoretical background

3. Data generation and preparation

4. Application of deep learning for low-frequency extrapolation

5. Conclusions

Acknowledgements

Appendix

| | DEPARTMENT OF PHYSICS Geophysical Institute | | --- | --- | | Application of machine learning for the extrapolation of seismic data
Master’s Thesis
of
Amelie Cathrine Nüsse
at the Geophysical Institute
Reviewer: Prof. Dr. Thomas Bohlen
Second Reviewer: Prof. Dr. Dirk Gajewski
Date of submission: 22 .11.2022 | | Erklärung zur Selbstständigkeit Ich versichere, dass ich diese Arbeit selbstständig verfasst habe und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe, die wörtlich oder inhaltlich übernommenen Stellen als solche kenntlich gemacht und die Satzung des KIT zur Sicherung guter wissenschaftlicher Praxis in der jeweils gültigen Fassung beachtet habe. Karlsruhe, den 22.11.2022, Amelie Cathrine Nüsse Abstract Low frequencies in seismic data are often challenging to acquire. Without low frequencies, though, a method like full-waveform inversion might fail due to cycle-skipping. This thesis aims to investigate the potential of neural networks for the task of low-frequency extrapolation to overcome aforementioned problem. Several steps are needed to achieve this goal: First, suitable data for training and testing the network must be found. Second, the data must be pre-processed to condition them for machine learning and e􀀞cient application. Third, a speci􀀜c work􀀝ow for the task of low-frequency extrapolation must be designed. Finally, the trained network can be applied to data it has not seen before and compared to reference data. In this work, synthetic data are used for training and evaluation because in such a controlled experiment the target for the network is known. For this purpose, 30 random but geologically plausible subsurface models were generated based on a simpli􀀜ed geology around the Asse II salt mine, and used for 􀀜nite-di􀀛erence simulations of seismograms. The corresponding shot gathers were pre-processed by, among others, normalizing them and splitting them up into patches, and fed into a convolutional neural network (U-Net) to assess the network’s performance and its ability to reconstruct the data. Two di􀀛erent approaches were investigated for the task of low-frequency extrapolation. The 􀀜rst approach is based on using only low frequencies as the network’s target, while the second approach has the full bandwidth as target. The latter yielded superior results and was therefore chosen for subsequent applications. Further tests of the network design led to the introduction of ResNet blocks instead of simple convolutions in the U-Net layers, and the use of the mean-absolute-error instead of the mean-squared-error loss function. The 􀀜nal network designed in this way was then applied to the synthetic data originally reserved for testing. It turned out that the chosen method is able to successfully extrapolate low frequencies by more than half an octave (from about 8 to 5 Hz) given the experimental setup at hand. Although the results start to deteriorate in the low-frequency band for larger o􀀛sets, full-waveform inversion will overall bene􀀜t from the application of the presented machine learning approach. Contents 1. Introduction 1 1.1. Related work ................................... 2 1.2. Thesis outline ................................... 3 2. Theoretical background 5 2.1. Deep learning ................................... 5 2.1.1. Neurons and neural networks ...................... 5 2.1.2. Activation functions ........................... 6 2.1.3. Training neural networks ........................ 7 2.1.4. Convolutional neural networks ..................... 10 2.1.5. Autoencoders ............................... 12 2.1.5.1. U-Net .............................. 12 2.1.5.2. Residual U-Net ......................... 13 2.2. Seismic modeling ................................. 15 2.2.1. Seismic wave propagation in acoustic media .............. 15 2.2.2. Finite-di􀀛erence method ......................... 16 2.2.2.1. Numerical dispers

FAQs

Why is low-frequency seismic data important for full-waveform inversion?

Low frequencies are often required for full-waveform inversion to avoid cycle-skipping. Without them, the inversion method can fail to converge to the correct solution.

How is the training data for the neural network prepared?

Geologically plausible subsurface models around the Asse II salt mine are generated and used in finite-difference simulations to create shot gathers. The data are normalized, split into patches, and prepared for machine learning input.

Which neural network approaches are compared for low-frequency extrapolation?

Two target strategies are investigated: using only low frequencies as the network target, and using the full bandwidth as the target. The full-bandwidth approach produces superior results and is used for subsequent applications.

Aug 4, 2026

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