High-precision full waveform inversion imaging and its applications

In modern Earth science research, how to “understand” the Earth’s internal structure and dynamic processes has always been a core issue of concern for scientists. However, due to the inaccessibility of the Earth’s interior, researchers must rely on indirect detection methods such as seismic waves to infer the structure and properties of the Earth’s deep interior. How to use seismic wave data to construct high-resolution subsurface structural models and accurately characterize the dynamic processes within the Earth is a significant challenge currently faced by geophysics and seismology. In recent years, Full Waveform Inversion (FWI) technology, as a high-resolution seismic imaging method constrained by wave equations, has been depicting the complex structures of the Earth’s deep interior with unprecedented precision and resolution, providing new perspectives for a deeper understanding of the Earth’s internal structure and dynamic evolution.

A team led by Professor Dinghui Yang from Tsinghua University, in collaboration with researchers from China Earthquake Administration (the Institute of Geology), University of Electronic Science and Technology of China, Beijing Technology and Business University, and Ministry of Emergency Management of China (the National Institute of Natural Hazards), systematically introduced the basic theory of the high-resolution nonlinear FWI imaging method, reviewed its development history, thoroughly analyzed current technical difficulties and application challenges, and offered perspectives into future development trends and key research directions.

Traditional seismic tomography methods, such as the travel time tomography, primarily rely on ray theory. While these methods can reveal the heterogeneous structure of the Earth’s interior, their resolution limitations make it difficult to effectively resolve small-scale subsurface anomalies. In contrast, FWI imaging methods fully utilize various types of seismic wave information, including amplitude, phase, and waveform, breaking the resolution limitations of traditional methods and enabling high-precision imaging of subsurface structures. FWI not only finely characterizes the complex structures within the Earth’s interior but also provides higher-resolution subsurface models compared to traditional methods, offering significant advantages in revealing deep underground structures and dynamic processes.

In recent years, FWI imaging theories and methods have made significant progress, including:

1. Numerical Methods for Wavefield Simulation

From finite difference methods and spectral element methods to discontinuous Galerkin methods, various efficient algorithms for solving wave equations have provided a more accurate physical modeling foundation for FWI.

1. Construction of New Objective Functions

Traditional objective functions based on the L2 norm are prone to falling into local minima. In contrast, objective functions constructed based on the Wasserstein metric are considered the most ideal approach to address the issue of local minima, significantly improving the reliability of imaging results.

1. Revolutionary Optimization Algorithms

The application of L-BFGS, conjugate gradient, and Gauss-Newton methods has accelerated the convergence speed of FWI. In recent years, new methods combining stochastic optimization, automatic differentiation, and deep learning have further enhanced computational efficiency.

1. Multiscale Imaging

Through multiscale and joint multidata inversion (e.g., combining body waves, surface waves, and converted waves), FWI can provide more comprehensive high-resolution subsurface structural information across different depth ranges.

Currently, FWI technology has been applied to imaging at different scales and in various fields, including:

1. Oil and Gas Exploration

FWI has been successfully applied in the Valhall oil field in the North Sea, Norway, enabling detailed imaging of complex reservoirs and improving the efficiency and resolution of oil and gas resource exploration.

1. Deep Underground Structure Imaging

In regions such as the Tibetan Plateau, the North China Craton, and Southern California, USA, FWI has revealed critical structural information, including subducting slabs, mantle wedges, and crust-mantle interactions, providing new constraints for geodynamic studies.

1. Earthquake Preparation Mechanisms

Through detailed imaging of fault zones and source regions, FWI has provided important insights into the earthquake preparation mechanism. For example, the imaging of the deep structure of the 2022 Luding earthquake highlighted the significant role of melt/fluid migration in the earthquake preparation process.

1. Engineering Geophysics

FWI has been applied in near-surface structure imaging, bridge pile foundation inspection, and railway tunnel inspection, demonstrating its immense potential in the field of engineering geophysics.

1. Medical Imaging

FWI technology has been applied to high-resolution imaging of brain structures, enhancing the precision and reliability of medical imaging.

Despite the advantages of FWI imaging technology, such as its high resolution, and the significant progress made in theoretical and methodological research and applications over the past two decades, it still faces several challenges: (1) High Computational Cost: FWI imaging requires repeatedly solving the wave equation to compute theoretical waveforms and objective function gradients. When performing large-scale and three-dimensional FWI imaging, the computational burden remains a significant challenge. (2) Non-Uniqueness of Solutions: FWI is typically an underdetermined nonlinear optimization problem constrained by the wave equation, leading to non-unique solutions. Additionally, FWI based on the L2-norm objective function suffers from local minima caused by “cycle-skipping”. These issues together contribute to the non-uniqueness of FWI imaging results. (3) Difficulty in the Seismic Phase Extraction and Matching: The simplified assumptions in seismic wave propagation models and the complexity of Earth’s internal geometric structures, lithological properties, and material states create discrepancies between theoretical waveforms and observed seismic phases, making perfect matching challenging.

In the future, the research and application of FWI technology should focus on addressing these challenges to improve the reliability of imaging results and the effectiveness of practical applications. With ongoing advancements, FWI is expected to demonstrate greater potential in fields such as Earth and planetary sciences, engineering, medicine, and disaster prevention and mitigation. In summary, FWI will play an increasingly important role in scientific research and practical applications, becoming a core tool in seismology, geophysics, and multidisciplinary research. It is regarded as a key technology for achieving the goal of a “transparent Earth”.

Yang D, Dong X, Huang J, Fang Z, Huang X, Liu S, Liu M, Meng W. 2025. High-resolution full waveform seismic imaging: Progresses, challenges, and prospects. Science China Earth Sciences, 68(2): 315‒342, https://doi.org/10.1007/s11430-024-1498-0