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Seismic Imaging and Inversion Techniques
Research Guide
What is Seismic Imaging and Inversion Techniques?
Seismic imaging and inversion techniques are computational methods that estimate subsurface Earth properties by fitting physical wave-propagation models to recorded seismic data and mapping the resulting parameters into interpretable images of the subsurface.
The seismic imaging and inversion literature in this cluster comprises 198,745 works focused on waveform-based inverse problems, including full-waveform tomography, wave-equation migration, and multiparameter estimation of elastic properties and anisotropy. Many workflows combine signal representations for time–frequency localization and denoising with physics-based forward modeling to stabilize inversion and improve resolution; foundational tools include wavelets (Daubechies (1992), "Ten Lectures on Wavelets" (1992)) and wavelet-based practical analysis guidance (Torrence and Compo (1998), "A Practical Guide to Wavelet Analysis" (1998)). Rock and medium physics enter through constitutive models for porous, fluid-saturated rocks (Biot (1956), "Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range" (1956)) and simplified parameterizations of weak elastic anisotropy (Thomsen (1986), "Weak elastic anisotropy" (1986)).
Topic Hierarchy
Research Sub-Topics
Full Waveform Inversion
This sub-topic explores nonlinear optimization techniques for seismic waveform inversion to reconstruct subsurface velocity models. Researchers develop algorithms addressing cycle-skipping and multiparameter inversions in exploration geophysics.
Wavelet Transform Applications
This sub-topic covers wavelet-based methods for seismic signal analysis, denoising, and compression in geophysical data processing. Researchers apply continuous and discrete wavelets for time-frequency analysis of wave propagation.
Elastic Wave Propagation
This sub-topic investigates propagation of elastic waves in fluid-saturated porous media and anisotropic rocks using Biot theory and extensions. Researchers model attenuation, scattering, and velocity dispersion for realistic earth models.
Seismic Anisotropy Characterization
This sub-topic focuses on weak elastic anisotropy, VTI/HTI models, and frequency-dependent effects in seismic data. Researchers quantify azimuthal variations and Thomsen parameters for imaging complex media.
Adjoint State Methods
This sub-topic develops adjoint-based gradient computation for efficient full-physics inversions and migration. Researchers apply it to waveform tomography, least-squares migration, and uncertainty quantification.
Why It Matters
Seismic imaging and inversion techniques directly support subsurface decision-making in exploration geophysics and tectonic hazard studies by turning recorded waveforms into quantitative models of velocity, density, and anisotropy that can be used for interpretation and prediction. In exploration settings, multiparameter inversion targets elastic properties and anisotropy to reduce ambiguity in reservoir characterization; Thomsen (1986) in "Weak elastic anisotropy" (1986) provided a compact parameterization (e.g., δ) that is widely used to connect anisotropic wave behavior to interpretable parameters in imaging and inversion. In rock-physics-informed inversion, Biot (1956) in "Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range" (1956) modeled elastic-wave propagation in fluid-saturated porous solids, enabling inversions to incorporate fluid–solid interactions relevant to water-saturated rocks. For deformation and source-related constraints that complement seismic imaging, Okada (1985) in "Surface deformation due to shear and tensile faults in a half-space" (1985) provided closed-form solutions for surface displacements from faulting that can be used to relate geodetic observations to subsurface fault geometry. In signal processing stages that condition data for inversion, Donoho (1995) in "De-noising by soft-thresholding" (1995) and Donoho and Johnstone (1995) in "Adapting to Unknown Smoothness via Wavelet Shrinkage" (1995) formalized wavelet-thresholding approaches for noise suppression, while Capon (1969) in "High-resolution frequency-wavenumber spectrum analysis" (1969) established array-based f–k spectral estimation used to analyze coherent wavefields and suppress interference.
Reading Guide
Where to Start
Start with Torrence and Compo’s "A Practical Guide to Wavelet Analysis" (1998) because it provides operational choices (wavelet selection, interpretation, and edge effects) that directly translate to seismic time-series conditioning before imaging or inversion.
Key Papers Explained
A common thread across the most-cited foundations is representing and stabilizing complex wavefields before solving ill-posed inverse problems. Daubechies’ "Ten Lectures on Wavelets" (1992) provides the mathematical basis for multiresolution representations that Torrence and Compo’s "A Practical Guide to Wavelet Analysis" (1998) turns into a workflow for real signals. Donoho’s "De-noising by soft-thresholding" (1995) and Donoho and Johnstone’s "Adapting to Unknown Smoothness via Wavelet Shrinkage" (1995) add principled noise suppression that can be used to prepare seismic traces for inversion. Chen, Donoho, and Saunders’ "Atomic Decomposition by Basis Pursuit" (1998) and "Atomic Decomposition by Basis Pursuit" (2001) connect signal representations to sparse inverse-problem formulations, while Capon’s "High-resolution frequency-wavenumber spectrum analysis" (1969) addresses array-domain characterization of wavefields. Medium-physics constraints enter through Biot’s "Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range" (1956) and Thomsen’s "Weak elastic anisotropy" (1986), which motivate what parameters an inversion should estimate and how they influence waveforms.
Paper Timeline
Most-cited paper highlighted in red. Papers ordered chronologically.
Advanced Directions
Advanced work in this topic typically pushes toward multiparameter, elastic, and anisotropic inversions that remain stable under realistic noise and acquisition limitations, using stronger regularization and better parameterizations. From the provided foundations, a practical frontier is integrating multiscale representations (Daubechies (1992), "Ten Lectures on Wavelets" (1992)) and adaptive denoising (Donoho and Johnstone (1995), "Adapting to Unknown Smoothness via Wavelet Shrinkage" (1995)) with sparse/overcomplete modeling (Chen, Donoho, and Saunders (1998), "Atomic Decomposition by Basis Pursuit" (1998)) while honoring poroelastic and anisotropic physics (Biot (1956); Thomsen (1986)).
Papers at a Glance
| # | Paper | Year | Venue | Citations | Open Access |
|---|---|---|---|---|---|
| 1 | Ten Lectures on Wavelets | 1992 | Computers in Physics | 15.3K | ✕ |
| 2 | A Practical Guide to Wavelet Analysis | 1998 | Bulletin of the Americ... | 14.5K | ✓ |
| 3 | De-noising by soft-thresholding | 1995 | IEEE Transactions on I... | 9.4K | ✕ |
| 4 | Theory of Propagation of Elastic Waves in a Fluid-Saturated Po... | 1956 | The Journal of the Aco... | 7.9K | ✓ |
| 5 | Atomic Decomposition by Basis Pursuit | 1998 | SIAM Journal on Scient... | 6.9K | ✕ |
| 6 | High-resolution frequency-wavenumber spectrum analysis | 1969 | Proceedings of the IEEE | 6.1K | ✕ |
| 7 | Atomic Decomposition by Basis Pursuit | 2001 | SIAM Review | 5.1K | ✕ |
| 8 | Surface deformation due to shear and tensile faults in a half-... | 1985 | Bulletin of the Seismo... | 5.0K | ✕ |
| 9 | Adapting to Unknown Smoothness via Wavelet Shrinkage | 1995 | Journal of the America... | 4.3K | ✕ |
| 10 | Weak elastic anisotropy | 1986 | Geophysics | 4.2K | ✕ |
In the News
Synergizing Deep Learning and Full-Waveform Inversion: Bridging Data-Driven and Theory-Guided Approaches for Enhanced Seismic Imaging
> This review explores the integration of deep learning (DL) with full-waveform inversion (FWI) for enhanced seismic imaging and subsurface characterization. It covers FWI and DL fundamentals, geop...
Elastic MP-FWI imaging: Changing geophysics
ByTom Rayment, James McLeman and Jennifer Badry, DUG Technology Published at:September 17, 2025
Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)
> Full Waveform Inversion (FWI) is an important geophysical technique considered in subsurface property prediction. It solves the inverse problem of predicting high-resolution Earth interior models...
Integrating physics and machine learning for unified ...
In petroleum exploration and production, accurate reservoir characterization and seismic modeling depend on linking macroscale seismic data with microscale reservoir properties. Prior research has ...
The future of seismic imaging and technology
elastic Full Wavefield Inversion (eFWI) technology will allow us to increase resource recovery with less capital.
Code & Tools
JUDI is a framework for large-scale seismic modeling and inversion and is designed to enable rapid translations of algorithms to fast and efficient...
ADSeismic is built for general seismic inversion problems, such as estimating velocity model, source location and time function. The package implem...
**ADFWI**is an open-source framework for high-resolution subsurface parameter estimation by minimizing discrepancies between observed and simulated...
applications. While traditional techniques for solving forward and inverse problems are computationally prohibitive, there is a growing interest to...
SeisLib is a Python package that allows for obtaining seismic images of the sub-surface from the local to the global scale. It is the result of a l...
Recent Preprints
Multiscale full waveform inversion
We develop and apply a full waveform inversion method that incorporates seismic data on a wide range of spatio-temporal scales, thereby constraining the details of both crustal and uppermantle str...
A consistent multiparameter Bayesian full waveform inversion scheme for imaging heterogeneous isotropic elastic media
A consistent multiparameter Bayesian full waveform inversion scheme for imaging heterogeneous isotropic elastic media Li-Yu Kan, Sébastien Chevrot, Vadim Monteiller To cite this version: Li-Yu Kan,...
Seismic Full‐Waveform Inversion of the Crust‐Mantle Structure Beneath China and Adjacent Regions
Abstract We present the first-generation full-waveform tomographic model (SinoScope 1.0) for the crust-mantle structure beneath China and adjacent regions. The three-component seismograms from 410...
High-resolution multiparameter characterization of the subsurface using full waveform inversion on broad-band data: application to the oceanic crust in the North Sea using a dense ocean bottom cable data set
This study focuses on the hydrophone component of a dense ocean bottom cable data set from the North Sea. This data had already been used in the past to illustrate the high resolution power of full...
Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures
Key words: Full Waveform, Theory, Computing aspects, Numerical study, Imaging 1 INTRODUCTION Full Waveform Inversion (FWI) is a powerful seismic imaging tool, dedicated to quantitative estimations...
Latest Developments
Recent research as of February 2026 indicates that seismic imaging and inversion techniques are being significantly advanced through the integration of artificial intelligence and physics-based models, with studies demonstrating major improvements in speed, accuracy, and scalability (EurekAlert!). Notably, developments include AI-embedded workflows for surface-wave analysis, full-waveform inversion (FWI) methodologies such as dynamic matching, elastic FWI, and multi-parameter FWI, as well as innovative imaging methods like Reverse Time Migration FWI, which provide clearer subsurface images and better resolution in complex geological settings (Viridien, Chevron, Nature Communications). Additionally, recent advances include the application of deep learning to enhance seismic modeling and inversion, bridging data-driven and theory-guided approaches for high-resolution imaging (arXiv, Springer).
Sources
Frequently Asked Questions
What are seismic imaging and inversion techniques in practical terms?
Seismic imaging and inversion techniques estimate subsurface parameters by comparing recorded seismic data with predictions from wave-propagation models and updating the model to reduce the mismatch. In practice, this includes modeling choices for the medium (e.g., poroelasticity in Biot (1956), "Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range" (1956)) and parameterizations for anisotropy (Thomsen (1986), "Weak elastic anisotropy" (1986)).
How do wavelets enter seismic data processing for imaging and inversion?
Wavelets provide localized time–scale representations that are useful for analyzing nonstationary seismic signals and for multiresolution processing prior to inversion. Daubechies (1992) in "Ten Lectures on Wavelets" (1992) formalized wavelet constructions, and Torrence and Compo (1998) in "A Practical Guide to Wavelet Analysis" (1998) described step-by-step wavelet analysis decisions such as wavelet choice and edge-effect handling.
How is noise reduced before or during inversion, and what guarantees exist?
Wavelet-thresholding denoising suppresses noise by shrinking small wavelet coefficients while preserving larger, signal-dominated coefficients. Donoho (1995) in "De-noising by soft-thresholding" (1995) presented soft-thresholding for reconstruction from noisy samples, and Donoho and Johnstone (1995) in "Adapting to Unknown Smoothness via Wavelet Shrinkage" (1995) introduced adaptive threshold selection (SureShrink) to handle unknown smoothness.
Which methods help separate coherent wave energy from interference in seismic arrays?
Frequency–wavenumber (f–k) spectrum estimation characterizes wavefields recorded on arrays as superpositions of traveling waves and can be used to identify coherent energy and suppress unwanted components. Capon (1969) in "High-resolution frequency-wavenumber spectrum analysis" (1969) developed a high-resolution f–k approach for array data modeled as a homogeneous random field.
Which papers are central for sparse representations relevant to seismic inversion?
Sparse and overcomplete representations support inverse problems by favoring compact explanations of data in large waveform dictionaries. Chen, Donoho, and Saunders (1998) in "Atomic Decomposition by Basis Pursuit" (1998) framed decomposition in overcomplete dictionaries, and Chen, Donoho, and Saunders (2001) in "Atomic Decomposition by Basis Pursuit" (2001) presented a closely related treatment in a review venue.
How are elastic anisotropy and poroelastic effects represented in inversion-oriented modeling?
Weak anisotropy can be expressed with simplified parameters that control key wave-propagation effects, enabling tractable inversion updates. Thomsen (1986) in "Weak elastic anisotropy" (1986) provided simplified weak-anisotropy equations highlighting parameters such as δ, while Biot (1956) in "Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range" (1956) modeled wave propagation in porous elastic solids containing viscous fluid, supporting inversions in fluid-saturated rock settings.
Open Research Questions
- ? How can inversion algorithms jointly enforce physical wave-propagation constraints and sparse or multiscale structure (as in wavelet and basis-pursuit formulations) without introducing bias in recovered elastic parameters?
- ? Which anisotropy parameterizations beyond weak-anisotropy approximations preserve interpretability while remaining identifiable from realistic acquisition geometries, given the simplified framework in Thomsen (1986), "Weak elastic anisotropy" (1986)?
- ? How should poroelastic effects described by Biot (1956), "Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range" (1956) be incorporated into waveform inversion so that fluid–solid coupling is separable from purely elastic heterogeneity in the recovered model?
- ? What is the best way to combine array-domain f–k characterization (Capon (1969), "High-resolution frequency-wavenumber spectrum analysis" (1969)) with waveform-domain inversion objectives so that coherent noise suppression does not remove inversion-relevant signal?
- ? How can adaptive denoising rules (Donoho and Johnstone (1995), "Adapting to Unknown Smoothness via Wavelet Shrinkage" (1995)) be integrated into end-to-end inversion workflows while preserving uncertainty quantification of the final model?
Recent Trends
Within the provided data, the most visible continuity is the sustained reliance on multiresolution and sparse representations (Daubechies , "Ten Lectures on Wavelets" (1992); Chen, Donoho, and Saunders (1998), "Atomic Decomposition by Basis Pursuit" (1998)) and on principled denoising (Donoho (1995), "De-noising by soft-thresholding" (1995)) as enabling components for ill-posed seismic inverse problems.
1992The topic cluster itself is large, comprising 198,745 works, reflecting broad use across waveform inversion, migration, anisotropy, and rock-physics-informed modeling.
Across these foundations, a consistent trend is moving from purely signal-domain characterization (Capon , "High-resolution frequency-wavenumber spectrum analysis" (1969)) toward representations and priors (wavelets and basis pursuit) that can be coupled to physics-based inversion objectives while retaining interpretability through medium models such as Biot poroelasticity (Biot (1956)) and Thomsen-style weak anisotropy (Thomsen (1986)).
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