arXiv subjects

Jinghuai Gao

Publications and source records attributed to Jinghuai Gao.

16 recordsLinked to original sources

arXiv2026

Seismic Acoustic Impedance Inversion Framework Based on Conditional Latent Generative Diffusion Model

Seismic acoustic impedance plays a crucial role in lithological identification and subsurface structure interpretation. However, due to the inherently ill-posed nature of the inversion problem, directly estimating impedance from post-stack seismic data remains highly challenging. Recently, diffusion models have shown great potential in addressing such inverse problems due to their strong prior learning and generative capabilities. Nevertheless, most existing methods operate in the pixel domain and require multiple iterations, limiting their applicability to field data. To alleviate these limitations, we propose a novel seismic acoustic impedance inversion framework based on a conditional latent generative diffusion model, where the inversion process is made in latent space. To avoid introducing additional training overhead when embedding conditional inputs, we design a lightweight wavelet-based module into the framework to project seismic data and reuse an encoder trained on impedance to embed low-frequency impedance into the latent space. Furthermore, we propose a model-driven sampling strategy during the inversion process of this framework to enhance accuracy and reduce the number of required diffusion steps. Numerical experiments on a synthetic model demonstrate that the proposed method achieves high inversion accuracy and strong generalization capability within only a few diffusion steps. Moreover, application to field data reveals enhanced geological detail and higher consistency with well-log measurements, validating the effectiveness and practicality of the proposed approach.

cs.LG↗

arXiv2026

Multi-Condition Guided Diffusion Model for Controllable Elastic Parameter Synthesis

Prestack elastic parameter inversion is important for reservoir characterization and quantitative seismic interpretation. Most existing deep-learning-based methods have achieved promising results, but they generally require sufficient labeled training data and have limited flexibility in integrating multi-source conditioning information. To address this issue, we propose a multi-condition guided diffusion model for controllable elastic parameter synthesis. Elastic parameter training datasets are first constructed based on well log statistics and geological characteristics of the target area and are used to train the diffusion model. A unified multi-condition guided diffusion framework is then developed to incorporate both implicit and explicit conditioning information. Specifically, iterative latent variable refinement, Adapter-based conditioning, and a diffusion posterior sampling (DPS)-projection guidance strategy are introduced for implicit model-domain constraints, implicit structural constraints, and explicit conditioning-operator constraints, respectively. Synthetic examples demonstrate that the proposed method can generate elastic parameter samples that are consistent with the prescribed conditions under both single-condition and multi-condition guidance. When seismic data are used as conditioning information, the framework can be further adapted to seismic elastic parameter inversion. Experiments show that the proposed method improves the prediction of representative elastic parameters, including P-wave velocity, S-wave velocity, and density, compared with baseline methods. The synthesized samples can also support downstream deep-learning-based inversion under limited labeled data, achieving competitive performance.

physics.geo-ph↗

arXiv2026

GeoVolDiff: Taming 3D Geological Volumes with Latent Diffusion

Deep learning has become a prevailing paradigm across a wide range of geophysical applications. Yet most existing studies concentrate on methodological refinements -- novel network architectures, physics-informed constraints, or taskspecific loss functions -- while paying comparatively little attention to a more fundamental challenge of any data-driven approach: the availability and representativeness of high-quality training data. This limitation is especially pronounced in geophysics. Unlike computer vision, which benefits from large-scale, well-curated benchmarks such as ImageNet, comparably abundant and reliably labelled geophysical data are prohibitively expensive to acquire and, in most field settings, lack accessible ground-truth supervision. To alleviate this data deficiency, we propose GeoVolDiff, a generative framework for three-dimensional geological volumes. It comprises three coupled stages: (i) constructing a foundational training corpus through physics-based forward simulation; (ii) training a Latent Diffusion Model (LDM) to capture the statistical distribution of 3D geological structures; and (iii) synthesizing diverse, structurally plausible volumes at scale for downstream geophysical tasks. We examine the utility of the synthesized data on a representative downstream task, seismic impedance inversion. Without incorporating any additional physical or geological prior, inversion networks pre-trained exclusively on synthesized data attain competitive performance on both synthetic and field datasets, indicating that data synthesised by the generative model can serve as an effective surrogate for costly field-acquired labels.

physics.geo-ph↗

arXiv2026

A Multi-physics Alternating Coupled Inversion Using Gravity and Full Waveform Data in Salt Dome

Complex salt geometries and strong velocity contrasts pose significant challenges for velocity model building and subsalt imaging. Although full waveform inversion (FWI) provides high-resolution velocity models, its performance strongly depends on the accuracy of initial model. On the other hand, gravity focusing inversion (GFI) can recover compact density distributions and provide reliable long-wavelength structural information for seismic exploration, but it suffers from poor depth resolution and inherent non-uniqueness. To better invert salt structure by leveraging the complementary advantages of full waveform and gravity data, we propose a multi-physics alternating coupled inversion strategy for salt dome model. The proposed strategy mainly includes three parts. First, we perform FWI using a simple layered velocity model to obtain preliminary velocity updates and extract the salt top boundary. Second, this structural information is used as a constraint in GFI to recover a compact salt density distribution beneath the salt top. Third, the resulting salt geometry is used to construct an improved velocity model for the next stage of FWI. Through iterative alternation, FWI provides reliable structural constraints for GFI, while GFI supplies a more reasonable macroscopic salt model for FWI, effectively mitigating the strong dependence on the initial model. In addition, a depth-varying density contrast is introduced in GFI to better represent sediment compaction effects. Compared with unconstrained GFI and conventional FWI using a horizontally layered initial model, the proposed method effectively improves both velocity and density reconstruction in the modified BP salt model and SEG/EAGE salt model.

physics.geo-ph↗

arXiv2026

Unsupervised Posterior Sampling for Seismic Data Recovery via Score-Based Generative Priors

Seismic data restoration is a fundamental task in seismic exploration, yet remains challenging under complex and unknown degradations. Traditional model-driven or task-specific learning methods often require retraining for each degradation type and fail to generalize effectively to unseen field data. In this work, we introduce an unsupervised Posterior Sampling Framework (PSF) built upon Score-based Generative Models (SGMs) for unified seismic data restoration. PSF leverages the pre-trained unconditional SGMs as a seismic-aware generative prior and derives a generalized conditional score function associated with the forward operator of each inverse problem. This enables posterior sampling across different seismic restoration tasks without retraining or supervision. Additionally, an adaptive noise-level estimation mechanism is incorporated to dynamically regulate the noise suppression strength during sampling, enhancing flexibility under varying signal-to-noise ratios and degradation conditions.Extensive experiments on seismic denoising, interpolation, compressed sensing, and deconvolution demonstrate that PSF delivers high-quality samples and exhibits robust generalization to out-of-distribution data. These results highlight the potential of SGMs as a universal prior for seismic inverse problems and establish PSF as a flexible framework for unsupervised posterior inference across diverse degradation scenarios.

physics.geo-ph↗

arXiv2026

Enhanced 3D Gravity Inversion Using ResU-Net with Density Logging Constraints: A Dual-Phase Training Approach

Gravity exploration has become an important geophysical method due to its low cost and high efficiency. With the rise of artificial intelligence, data-driven gravity inversion methods based on deep learning (DL) possess physical property recovery capabilities that conventional regularization methods lack. However, existing DL methods suffer from insufficient prior information constraints, which leads to inversion models with large data fitting errors and unreliable results. Moreover, the inversion results lack constraints and matching from other exploration methods, leading to results that may contradict known geological conditions. In this study, we propose a novel approach that integrates prior density well logging information to address the above issues. First, we introduce a depth weighting function to the neural network (NN) and train it in the weighted density parameter domain. The NN, under the constraint of the weighted forward operator, demonstrates improved inversion performance, with the resulting inversion model exhibiting smaller data fitting errors. Next, we divide the entire network training into two phases: first training a large pre-trained network Net-I, and then using the density logging information as the constraint to get the optimized fine-tuning network Net-II. Through testing and comparison in synthetic models and Bishop Model, the inversion quality of our method has significantly improved compared to the unconstrained data-driven DL inversion method. Additionally, we also conduct a comparison and discussion between our method and both the conventional focusing inversion (FI) method and its well logging constrained variant. Finally, we apply this method to the measured data from the San Nicolas mining area in Mexico, comparing and analyzing it with two recent gravity inversion methods based on DL.

physics.geo-ph↗

arXiv2025

Generative modeling of seismic data using diffusion models and its application to multi-purpose posterior sampling for noisy inverse problems

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse high-quality stochastic solutions, and limits uncertainty quantification. Addressing this gap, we propose an unsupervised posterior sampling method conditioned on the noisy observations and the inverse problem, eliminating the need to retrain a task-specific conditional diffusion model with paired data for each new application. Specifically, we first propose a diffusion model enhanced with a novel noise schedule for generative modeling of seismic data, and introduce the non-Markov sampling strategy to achieve fast and quality-controllable unconditional sampling. Building upon this, we further present a posterior sampling method for various noisy inverse problems using the trained unconditional diffusion model. Our method requires only a small number of function evaluations to achieve competitive performance, while enabling flexible posterior sampling that interacts adaptively with different noise levels.Experiments on unconditional generation and posterior sampling across different tasks show that our method not only efficiently models the seismic data distribution and posterior conditioned on observations and tasks but also achieves substantially faster sampling and superior out-of-distribution generalization.

physics.geo-ph↗

arXiv2025

Uncertainty-aware Frequency-domain Acoustic Full Waveform Inversion Using Gaussian Random Fields and Ensemble Kalman Inversion

In recent years, uncertainty-aware full waveform inversion (FWI) has received increasing attention, with a growing emphasis on producing informative uncertainty estimates alongside inversion results. Bayesian inference methods--particularly Monte Carlo-based approaches--have been widely employed to quantify uncertainty. However, these techniques often require extensive posterior sampling, resulting in high computational costs. To address this challenge and enable efficient uncertainty quantification in FWI, we introduce an uncertainty-aware FWI framework--EKI-GRFs-FWI--that integrates Gaussian random fields (GRFs) with the ensemble Kalman inversion (EKI) algorithm. This approach jointly infers subsurface velocity fields and provides reliable uncertainty estimates in a computationally efficient manner. The EKI algorithm leverages a derivative-free update mechanism and employs effective stopping criteria to ensure rapid convergence, making it suitable for large-scale inverse problems. Meanwhile, GRFs incorporate prior knowledge of spatial smoothness and correlation length scales, enabling the generation of physically plausible initial ensembles for EKI. Numerical results demonstrate that EKI-GRFs-FWI yields reasonably accurate velocity reconstructions while delivering informative uncertainty estimates.

physics.geo-ph↗

arXiv2022

Bayesian Physics-Informed Neural Networks for the Subsurface Tomography based on the Eikonal Equation

The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty due to the noisy data and data scarcity is less discussed in conventional seismic tomography literature. To mitigate the uncertainty effects and quantify their impacts in the prediction, the so-called Bayesian Physics-Informed Neural Networks (BPINNs) based on the eikonal equation are adopted to infer the velocity field and reconstruct the travel-time field. In BPINNs, two inference algorithms including Stein Variational Gradient Descent (SVGD) and Gaussian variational inference (VI) are investigated for the inference task. The numerical results of several benchmark problems demonstrate that the velocity field can be estimated accurately and the travel-time can be well approximated with reasonable uncertainty estimates by BPINNs. This suggests that the inferred velocity model provided by BPINNs may serve as a valid initial model for seismic inversion and migration.

physics.geo-ph↗

arXiv2020

Posterior contraction for empirical Bayesian approach to inverse problems under non-diagonal assumption

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a hyperparameter that quantifies regularity. By introducing two auxiliary problems, we construct an empirical Bayes method and prove that this method can automatically select the hyperparameter. In addition, we show that this adaptive Bayes procedure provides optimal contraction rates up to a slowly varying term and an arbitrarily small constant, without knowledge about the regularity index. Our method needs not the prior covariance, noise covariance and forward operator have a common basis in their singular value decomposition, enlarging the application range compared with the existing results.

math.ST↗

arXiv2019

Recursive linearization method for inverse medium scattering problems with complex mixture Gaussian error learning

This paper is concerned with the modeling errors appeared in the numerical methods of inverse medium scattering problems (IMSP). Optimization based iterative methods are wildly employed to solve IMSP, which are computationally intensive due to a series of Helmholtz equations need to be solved numerically. Hence, rough approximations of Helmholtz equations can significantly speed up the iterative procedure. However, rough approximations will lead to instability and inaccurate estimations. Using the Bayesian inverse methods, we incorporate the modelling errors brought by the rough approximations. Modelling errors are assumed to be some complex Gaussian mixture (CGM) random variables, and in addition, well-posedness of IMSP in the statistical sense has been established by extending the general theory to involve CGM noise. Then, we generalize the real valued expectation-maximization (EM) algorithm used in the machine learning community to our complex valued case to learn parameters in the CGM distribution. Based on these preparations, we generalize the recursive linearization method (RLM) to a new iterative method named as Gaussian mixture recursive linearization method (GMRLM) which takes modelling errors into account. Finally, we provide two numerical examples to illustrate the effectiveness of the proposed method.

math.NA↗

arXiv2018

Seismic Wave Equations in Tight Oil/Gas Sandstone Media

The paper is devoted to the derivation of a combined system of motion equations for solid and fluid in isotropic tight oil/gas sandstone media through volume averaging theorems (VAT). Based on the features of the media, four physical assumptions are proposed as the foundation for our derivation. More precisely, volume averaging theorems are applied to the micro-scale motion equations for both the solid and the fluid as well as to the stress-strain relations, resulting in a combined system of macro-scale equations for the tight oil/gas sandstone media. It is worth noting that the four assumptions may not be satisfied in the whole region. Nevertheless, since the characteristic diameter for applying VAT ranges between $10^{-6}$ meters and dozens of meters, we may split the entire domain into several sub-domains such that the four physical assumptions are satisfied in each sub-domain. By choosing a proper characteristic diameter of an averaging volume, we derive a formula for the fluid average pressure in terms of the divergence of the average displacement from the continuity equation of the fluid. As a result, the motion equations derived in this paper are simpler than the Biot equations, and are more suitable for inversion of porous medium parameters. When the fluid is gas and the compressional wave is considered, the derived motion equations can be simplified to the diffusive-viscous wave equation. Moreover, the explicit relationship between the coefficients in this equation and medium parameters is very important for gas detection in tight gas sandstone.

physics.geo-ph↗

arXiv2016

Infinite-dimensional Bayesian approach for inverse scattering problems of a fractional Helmholtz equation

In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named as fractional Helmholtz equation. According to the physical interpretations, this new model could be divided into two separate models: loss-dominated model and dispersion-dominated model. For the loss-dominated model (it is an integer- and fractional-order mixed elliptic equation), a well-posedness theory has been established and the Lipschitz continuity of the scattering field with respect to the scatterer has also been established.Because the complexity of the dispersion-dominated model (it is an integer- and fractional-order mixed elliptic system), we only provide a well-posedness result for sufficiently small wavenumber. In the second part of this paper, we generalize the Bayesian inverse theory in infinite-dimension to allow a part of the noise depends on the target function (the function needs to be estimated). Then, we prove that the estimated function tends to be the true function if both the model reduction error and the white noise vanish. At last, our theory has been applied to the loss-dominated model with absorbing boundary condition.

math.AP↗

arXiv2016

Variable Total Variation Regularization for Backward Time-Space Fractional Diffusion Problem

In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual error in fourier space domain and variable total variation (TV) regularizing term which can protect the edges as TV regularizing term and reduce staircasing effect. The well-posedness of this optimization problem is studied under a very general setting. Actually, we write the time-space fractional diffusion equation as an abstract fractional differential equation and get our results by using fractional semigroup theory, so our results can be applied to other backward problems for more general fractional differential equations. Then a modified Bregman iterative algorithm is proposed to approximate the minimizer. The new features of this algorithm is that the regularizing term changed in each step and we need not to solve the complexed Euler-Lagrange equations of variable TV regularizing term (just need to solve a simpler Euler-Lagrange equations). The convergence of this algorithm and the strategy of choosing parameters are also obtained. Numerical implementations are given to support our analysis to show the flexibility of our minimization model.

math.NA↗

arXiv2015

Bayesian approach to inverse problems for functions with variable index Besov prior

We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant property, so Besov prior has been proposed recently. Different prior measures usually connect to different regularization terms. Variable index TV, variable index Besov regularization terms have been proposed in image analysis, however, there are no such prior measure in Bayesian theory. So in this paper, we propose a variable index Besov prior measure which is a Non-Guassian measure. Based on the variable index Besov prior measure, we build the Bayesian inverse theory. Then applying our theory to integer and fractional order backward diffusion problems. Although there are many researches about fractional order backward diffusion problems, we firstly apply Bayesian inverse theory to this problem which provide an opportunity to quantify the uncertainties for this problem.

math.ST↗

arXiv2015

Well-posedness for compressible MHD system with highly oscillating initial data

In this paper, we transform compressible MHD system written in Euler coordinate to Lagrange coordinate in critical Besov space. Then we construct unique local solutions for compressible MHD system. Our results improve the range of Lebesgue exponent in Besov space from $[2, N)$ to $[2, 2N)$ with $N$ stands for dimension. In addition, we give a lower bound for the maximal existence time which is important for our construction of global solutions. Based on the local solution, we obtain a unique global solution with high oscillating initial velocity and density by using effective viscous flux and Hoff's energy methods to explore the structure of compressible MHD system.

math.AP↗