Seismic Inversion Techniques for Wave Propagation Analysis

Seismic inversion constitutes a family of computational methods aimed at recovering subsurface properties by fitting recorded waveforms to numerical models of wave propagation. At its core, forward modelling solves the wave equation for a given velocity or elastic parameter distribution, while inversion iteratively updates the model so that synthetic seismograms match observations. Traditional approaches such as full-waveform inversion employ an adjoint-state method to compute gradients of a misfit function, enabling high-resolution imaging of velocity structures but often encountering cycle-skipping and non-uniqueness. Regularisation strategies—including Tikhonov, total variation and shaping operators—are typically introduced to stabilise the ill-posed problem, preserve geological interfaces and suppress artefacts. More recently, Bayesian frameworks have been adopted to quantify uncertainty by sampling posterior distributions, often leveraging Markov chain Monte Carlo or variational inference. Concurrently, machine-learning techniques have begun to complement physics-driven schemes: custom neural-network layers enforce conservation laws, generative models encode geological priors and adversarial networks accelerate inversion by learning efficient parameter mappings. These advances have broadened the application of seismic inversion from hydrocarbon and geothermal exploration to earthquake hazard assessment, carbon sequestration monitoring and even medical imaging, demonstrating the global significance of accurate subsurface characterisation.

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Research from all publishers

Recent studies have introduced domain-aware deep networks that embed prior geophysical constraints into architectures, improving both interpretability and generalisability by coupling synthetic training datasets with custom non-trainable physical operator layers. A real-time generative adversarial network approach has been developed to reconstruct subsurface velocity images end-to-end, with a transfer-learning strategy to mitigate overfitting and enhance robustness across diverse geological settings. Bayesian inversion guided by deep generative models has been applied to sample Earth models under full-waveform constraints, yielding ensembles that honour both observational data and geological heterogeneity priors while quantifying uncertainty in parameter estimates.

Seismic Inversion Techniques for Wave Propagation Analysis publication trend

The graph below shows the total number of articles in seismic inversion techniques for wave propagation analysis across all publications each year (not limited to Nature Index journals).

Technical terms

Seismic inversion: A computational procedure to infer subsurface elastic or velocity parameters by fitting simulated waveforms to recorded data.

Full-waveform inversion (FWI): An optimisation-based method that uses the complete seismic wavefield and its adjoint to update subsurface models for maximum data fit and resolution.

Regularisation: A stabilisation technique that imposes smoothness, sparsity or structural constraints on an ill-posed inversion to reduce non-uniqueness and artefacts.

Adjoint-state method: A mathematical procedure to compute gradients of a misfit function with respect to model parameters by backpropagating residuals through the wave equation.

Generative adversarial network (GAN): A deep-learning framework comprising a generator and a discriminator, used in seismic inversion to learn complex priors and map recorded data directly to subsurface properties.

References

1. Sensing prior constraints in deep neural networks for solving exploration geophysical problems. Proceedings of the National Academy of Sciences of the United States of America (2023).
2. Stochastic Seismic Waveform Inversion Using Generative Adversarial Networks as a Geological Prior. Mathematical Geosciences (2019).
3. Seismic imaging of incomplete data and simultaneous-source data using least-squares reverse time migration with shaping regularizationLSRTM with shaping regularization. Geophysics (2016).
4. Data-Driven Seismic Waveform Inversion: A Study on the Robustness and Generalization. IEEE Transactions on Geoscience and Remote Sensing (2020).
5. Full-waveform inversion imaging of the human brain. npj Digital Medicine (2020).