Full Waveform Inversion Research Articles

Monitoring underground hydrogen storage migration and distribution using time-lapse acoustic waveform inversion

The ongoing global energy shift from fossil fuels to renewable sources highlights the importance of underground hydrogen storage (UHS) as a sustainable mechanism to counterbalance the seasonal inconsistencies of renewable energy. Comparable to geological CO2 sequestration, UHS necessitates precise subsurface imaging and a thorough understanding of hydrogen behavior within geological formations, including its location and migration patterns. Since direct subsurface measurement is unattainable, there is a pronounced need for robust subsurface characterization and monitoring techniques. This research focuses on UHS feasibility in enduring storage scenarios, employing seismic monitoring strategies adapted from CO2 storage practices. Specifically, we integrate Continuous Active Source Seismic Monitoring (CASSM) and Time-Lapse Full Waveform Inversion (TLFWI) to scrutinize UHS. The study employs synthetic crosshole surveys that initially model the coexistence of hydrogen and water within fractured reservoirs, aiming to pinpoint hydrogen-related velocity alterations in acoustic waveforms. Subsequently, we utilize a time-lapse synthetic model of hydrogen injection to emulate CASSM observations. Utilizing TLFWI in conjunction with White's model, we successfully process the CASSM data to discern and quantify temporal variations in velocity and saturation, which effectively maps the spatial and temporal distribution of mobile hydrogen. The results affirm the capabilities of TLFWI and CASSM as proficient monitoring systems for UHS. This study aspires to offer a dependable methodology for the administration of large-scale and long-term geological hydrogen storage.

Physics‐reliable frugal local uncertainty analysis for full waveform inversion

AbstractFull waveform inversion stands at the forefront of seismic imaging technologies, pivotal in retrieving high‐resolution subsurface velocity models. Its application is especially profound when imaging complex geologies such as salt bodies, which are regions notoriously challenging, yet essential given their hydrocarbon potential. However, with the power of full waveform inversion comes the intrinsic challenge of estimating the associated uncertainties. Such uncertainties are crucial in understanding the reliability of subsurface models, particularly in terrains like subsalt regions. Addressing this, we advocate for a nuanced approach employing the Stein variational gradient descent algorithm. Through a judicious use of a limited number of velocity model particles and the integration of random field‐based perturbations, our methodology provides a local representation of the uncertainties inherent in full waveform inversion. Our evaluations, based on the Marmousi model, showcase the robustness of the proposed technique. Yet, it is our exploration into salt‐intensive terrains, leveraging data from the Sigsbee 2A synthetic model and the Gulf of Mexico, that emphasizes the method's versatility. Findings indicate pronounced uncertainties along salt boundaries and in the deeper subsalt sediments, contrasting the minimal uncertainties in non‐salt terrains. However, anomalies like salt canyons present unique challenges, potentially due to the interplay of multi‐scattering effects. Emphasizing the scalability and cost‐effectiveness of this approach, we highlight its potential for large‐scale industrial applications in full waveform inversion, while also underscoring the necessity for prudence when integrating these uncertainty insights into subsequent seismic‐driven geological and reservoir modelling.

A new highly accurate and efficient pure visco‐acoustic wave equation for tilted transversely isotropic attenuating media

AbstractThe propagation of seismic waves in attenuating anisotropic media exhibits amplitude dissipation and phase dispersion. To describe its effects, the fractional Laplacian pure visco‐acoustic wave equations capable of producing stable and noise‐free wavefields have been derived. However, except for acoustic approximation, previous wave equations utilize the approximations with lower accuracy in simplifying the denominator of the approximate complex‐valued dispersion relation, resulting in reduced accuracy. To address this concern, we use a combination of complex stiffness coefficients to replace the denominator term of the approximate complex‐valued dispersion relation. This approximation effectively reduces the loss of accuracy caused by ignoring the influence of the velocity anisotropy parameter ε and the attenuation anisotropy parameter εQ in the denominator term, leading to a wave equation with high accuracy in media with large anisotropic parameters ε and δ. In addition, the new wave equation only contains two high‐order spatial partial derivatives and has high computational efficiency. Theoretical analysis and numerical examples demonstrate that the proposed pure visco‐acoustic tilted transversely isotropic wave equation outperforms the previous pure visco‐acoustic wave equation in terms of simulation accuracy. The newly developed wave equation is well suited for the application of Q‐compensated reverse time migration and full waveform inversion in attenuating anisotropic media.

Power-law frequency-dependent Q simulations in viscoacoustic media using decoupled fractional Laplacians

Quantifying the seismic attenuation of wave propagation in the earth’s interior is essential for studying subsurface structures. Previous approaches for attenuation simulations (e.g., the standard linear solid and the fractional derivative model) are mainly based on the frequency-independent quality factor Q assumption. However, seismic attenuation in high-temperature and high-pressure regions usually exhibits power-law frequency-dependent Q characteristics. To simulate this Q effect in attenuative media, we derive a new viscoacoustic wave equation with decoupled fractional Laplacians in the time domain. Unlike the existing methods using relaxation functions to fit the power-law relationship in a specific frequency band, our equation is directly derived from the approximated complex modulus, which explicitly involves the reference quality factor and fractional exponent parameters. Furthermore, this equation contains two fractional Laplacians, which can easily simulate decoupled amplitude dissipation and phase distortion effects, making it amenable to Q-compensated reverse time migration. In the implementation, a Taylor-series expansion and a pseudospectral method are introduced to solve the fractional Laplacians with variable fractional exponents. Numerical experiments demonstrate the effectiveness of our method for power-law frequency-dependent Q simulations. As a forward-modeling engine, our derived viscoacoustic wave equation is a good supplement to the current Q simulation methods and it could be applied in many seismic applications, such as Q-compensated reverse time migration and full-waveform inversion.

Anelastic Tomography of the Arabian Plate

ABSTRACT In this study, we investigate the upper-mantle structure of the Arabian plate based on anelastic full-waveform inversion. The Arabian plate is composed of two main geological provinces—the Arabian Platform in the east and the Arabian Shield in the west. The Shield is dotted with areas of Cenozoic volcanism (harrats) whose precise tectonic and geodynamic origin is still debated. To help shed light on the deep geophysical properties of the Arabia plate and seismic signatures in the Earth’s upper mantle related to the surface volcanism, we use ∼38,400 three-component waveforms filtered between 25 and 100 s from 64 well-distributed regional earthquakes. We fit frequency-dependent travel-time and amplitude information. We follow a hierarchical inversion strategy in which we initially invert for the elastic structure and subsequently for both the elastic and anelastic parameters simultaneously. We assess the resolution and trade-offs between model parameters by conducting point spread function tests. Our model reveals low-wavespeed anomalies associated with mantle material that may originate from the Afar plume. In addition, we identify significant shear attenuation anomalies in the southern and central regions of the western margin of the Arabian plate. We suggest that these anomalies are linked to either the hot asthenosphere from the Afar plume or partial melting triggered by lithospheric thinning along the Red Sea rift.

Accounting for subwavelength heterogeneities in full waveform inversion based on wavefield gradient measurements

SUMMARY Seismic gradient measurements from distributed acoustic sensors and rotational sensors are becoming increasingly available for field surveys. These measurements provide a wealth of information and are currently being considered for many applications such as earthquake detection and subsurface characterizations. In this work, using a simple 2-D numerical approach, we tackle the implications of such wavefield gradient measurements on full waveform inversion (FWI) techniques using a simple 2-D numerical test. In particular, we study the impact of the wavefield gradient measurement sensitivity to heterogeneities that are much smaller than the minimum wavelength. Indeed, as shown through the homogenization theory, small-scale heterogeneities induce an unexpected coupling of the strain components to the wavefield gradient measurement. We further show that this coupling introduces a potential limitation to the FWI results if it is not taken into account. We demonstrate that a gradient measurement-based FWI can only reach the accuracy of a classical displacement field-based FWI if the coupling coefficients are also inverted. Furthermore, there appears to be no specific gain in using gradient measurements instead of conventional displacement (or velocity, acceleration) measurements to image structures. Nevertheless, the inverted correctors contain fine-scale heterogeneities information that could be exploited to reach an unprecedented resolution, particularly if an array of receivers is used.

Truncated Gauss-Newton full-waveform inversion of pure quasi-P waves in vertical transverse isotropic media

Full-waveform inversion (FWI) uses the full information of seismic data to obtain a quantitative estimation of subsurface physical parameters. Anisotropic FWI has the potential to recover high-resolution velocity and anisotropy parameter models, which are critical for imaging the long-offset and wide-azimuth data. We develop an acoustic anisotropic FWI method based on a simplified pure quasi P-wave (qP-wave) equation, which can be solved efficiently and is beneficial for the subsequent inversion. Using the inverse Hessian operator to precondition the functional gradients helps to reduce the parameter tradeoff in the multi-parameter inversion. To balance the accuracy and efficiency, we extend the truncated Gauss-Newton (TGN) method into FWI of pure qP-waves in vertical transverse isotropic (VTI) media. The inversion is performed in a nested way: a linear inner loop and a nonlinear outer loop. We derive the formulation of Hessian-vector products for pure qP-waves in VTI media based on the Lagrange multiplier method and compute the model update by solving a Gauss-Newton linear system via a matrix-free conjugate gradient method. A suitable preconditioner and the Eisenstat and Walker stopping criterion for the inner iterations are used to accelerate the convergence and avoid prohibitive computational cost. We test the proposed FWI method on several synthetic data sets. Inversion results reveal that the pure acoustic VTI FWI exhibits greater accuracy than the conventional pseudoacoustic VTI FWI. Additionally, the TGN method proves effective in mitigating the parameter crosstalk and increasing the accuracy of anisotropy parameters.

Wave propagation across fluid-solid interfaces with LBM-LSM coupling schemes

Seismic wave propagation in fluid-solid coupled media is currently a popular topic. However, traditional wave equation-based simulation methods have to consider complex boundary conditions at the fluid-solid interface. To address this challenge, we propose a novel numerical scheme that integrates the lattice Boltzmann method (LBM) and lattice spring model (LSM). In this scheme, LBM simulates viscoacoustic wave propagation in the fluid area and LSM simulates elastic wave propagation in the solid area. We also introduce three different LBM-LSM coupling strategies, a standard bounce back scheme, a specular reflection scheme, and a hybrid scheme, to describe wave propagation across fluid-solid boundaries. To demonstrate the accuracy of these LBM-LSM coupling schemes, we simulate wave propagation in a two-layer model containing a fluid-solid interface. We place excitation sources in the fluid layer and the solid layer respectively, to observe the wave phenomena when seismic waves propagate to interface from different sides. The simulated results by LBM-LSM are compared with the reference wavefields obtained by the finite difference method (FDM) and the analytical solution (ANA). Our LBM-LSM coupling scheme was verified effective, as the relative errors between the LBM-LSM solutions and reference solutions were within an acceptable range, sometimes around 1.00%. The coupled LBM-LSM scheme is further used to model seismic wavefields across a more realistic rugged seabed, which reveals the potential applications of the coupled LBM-LSM scheme in marine seismic imaging techniques, such as reverse-time migration and full-waveform inversion. The method also has potential applications in simulating wave propagation in complex two- and multi-phase media.

Generalizable data driven full waveform inversion for complex structures and severe topographies

Traditionally, simplification has been used in scientific modeling practices. However, recent advancements in deep learning techniques have provided a means to represent complex models. As a result, deep neural networks should be able to approximate the complex models, with a high degree of generalization. To achieve generalization, it is necessary to have a diverse range of examples in the training of the neural network, for example in data-driven FWI, training data should cover the expected subsurface models. To meet this requirement, we porposed a method to creat geologically meaningful velocity models with complex structures and severe topography. However, it is important to note that generalization comes with its own set of challenges.Because of significant variation in topography of the generated velocity models, we need to include this information as an additional input data in training of the network. Therefore, we have transformed the seismic data to a fixed datum to incorporate geometric information. Additionally, we have enhanced the network's performance by introducing a term in the network loss function. Multiple metrics have been employed to evaluate the performance of the network. The results indicate that by providing the necessary information to the network and employing computational techniques to refine the model's accuracy, deep neural networks are capable of accurately estimating velocity models in complex environments characterized by extreme topography.

When Data Driven Reduced Order Modeling Meets Full Waveform Inversion

When Data Driven Reduced Order Modeling Meets Full Waveform Inversion

Iterative PDE-Constrained Optimization for Seismic Full-Waveform Inversion

Iterative PDE-Constrained Optimization for Seismic Full-Waveform Inversion

Machine learning-based time-lapse 1D seismic full-waveform inversion with efficient training data generation in a carbon capture and storage monitoring

Machine learning (ML)-based time-lapse and seismic full-waveform inversion has recently gained attention in carbon capture and storage (CCS) research because of its potential to overcome the limitations of theory-based inversion and its excellent imaging performance for CO2 plumes. We propose a ML-based time-lapse 1D inversion method with efficient training data generation. The proposed method exploits time-lapse seismic data to infer time-lapse velocity changes and uses a 1D inversion strategy to enable the UNet3+ model to learn the general characteristics of velocity changes between baseline and monitoring phases. Our proposed method quickly generates various 1D velocity models and rapidly provides numerous near-offset data by using 1D ray-based modeling method. This allows us to overcome a challenge in constructing of 2D velocity models based on limited geological assumptions and forward modeling to generate seismic gathers, which requires massive computational resources. However, because 2D effects such as diffraction caused by the CO2 plume only affect the monitoring data, inaccurate predictions in the 1D inversion occurred near the plume, following the diffraction trajectory. We corrected this effect using a diffraction removal process for 2D target data, thereby improving the prediction accuracy of the ML model. The ML model was trained with a large amount of training data generated using the proposed method and validated on 2D target data with three different CO2 injection plume shapes obtained from a modified Marmousi2 velocity model. As a result, information about the CO2 plume was reasonably delineated, although the magnitude of the time-lapse velocity change near the plume boundary was reduced by small amplitude losses during the diffraction removal process. Our results suggest that the proposed method is a powerful tool for CCS monitoring, which requires forward modeling for each iterative survey.

Scale-Aware Edge-Preserving Full Waveform Inversion with Diffusion Filter for Crosshole Sensor Arrays.

Full waveform inversion (FWI) is recognized as a leading data-fitting methodology, leveraging the detailed information contained in physical waveform data to construct accurate, high-resolution velocity models essential for crosshole surveys. Despite its effectiveness, FWI is often challenged by its sensitivity to data quality and inherent nonlinearity, which can lead to instability and the inadvertent incorporation of noise and extraneous data into inversion models. To address these challenges, we introduce the scale-aware edge-preserving FWI (SAEP-FWI) technique, which integrates a cutting-edge nonlinear anisotropic hybrid diffusion (NAHD) filter within the gradient computation process. This innovative filter effectively reduces noise while simultaneously enhancing critical small-scale structures and edges, significantly improving the fidelity and convergence of the FWI inversion results. The application of SAEP-FWI across a variety of experimental and authentic crosshole datasets clearly demonstrates its effectiveness in suppressing noise and preserving key scale-aware and edge-delineating features, ultimately leading to clear inversion outcomes. Comparative analyses with other FWI methods highlight the performance of our technique, showcasing its ability to produce images of notably higher quality. This improvement offers a robust solution that enhances the accuracy of subsurface imaging.

Adaptive structure-based full-waveform inversion

In simultaneous-shot full-waveform inversion (FWI), the re-started limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm can be used to suppress crosstalk, but crosstalk cannot be completely eliminated from the inversion results. To further solve the crosstalk problem caused by the interference among individual shots in simultaneous-shot FWI, adaptive structure-based smoothing is applied to the FWI with the restarted L-BFGS algorithm. Structure-based smoothing can mitigate the crosstalk by highlighting structure boundaries. To perform structure-based smoothing, an implicit anisotropic diffusion equation is solved. We carry out a multiscale inversion strategy. Because the FWI results in the low-frequency band contain less structural information and more crosstalk, structure-based smoothing is applied to the frequency band at frequencies higher than the peak frequency to prevent negative effects from the model structure in the low-frequency band. The estimated structural information is iteratively updated during the inversion process. Furthermore, structure-based smoothing is only added to the iterations with invariant encoding to reduce oversmoothing. The invariant encoding means that the shot encoding remains unchanged between iterations. Numerical experiments with an overthrust model indicate that the proposed adaptive structure-based FWI method can effectively suppress artifacts and provide a high-resolution inversion result, even when the encoded data are contaminated with strong noise. Another advantage of the adaptive structure-based FWI method is that no seismic migration needs to be performed, which makes it more efficient for real data.

Pseudo-Helmholtz decomposition for an elastic VTI wavefield based on wavefront phase direction

P and S waves are coupled when propagating in anisotropic elastic media. The separation of P and S waves helps to study the characteristics of different types of seismic waves as well as mitigating crosstalk artifacts in elastic reverse time migration and elastic full-waveform inversion. At present, the methods of seismic wave mode separation in anisotropic media are mainly built on divergence- and curl-like operations, pseudo-Helmholtz decomposition, and low-rank approximation. We develop a new pseudo-Helmholtz decomposition operator based on eigenform analysis and the wavefront phase direction to decompose vertically transversely isotropic elastic wavefields. The corresponding P-/S-wave decoupling formulas are also derived in detail. Compared with the divergence- and curl-like methods, the new method does not change the phase of P and S waves. Compared with existing pseudo-Helmholtz decomposition methods based on eigenform analysis, our method achieves more accurate wavefield separation than the zero-order pseudo-Helmholtz decomposition operator. Our method requires solving one vector Poisson equation only, resulting in much less computational cost than the existing first-order pseudo-Helmholtz decomposition methods. In addition, the accuracy of our method is analyzed by providing homogeneous media with different parameter settings. Finally, the numerical examples demonstrate that the new pseudo-Helmholtz decomposition method is effective, efficient, and robust against random noise.

Robust elastic full-waveform inversion using an alternating direction method of multipliers with reconstructed wavefields

Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem with two sets of constraints: partial-differential equation (PDE) constraints governing elastic wave propagation and physical model constraints implementing prior information. The alternating direction method of multipliers is used to solve the problem, resulting in an iterative algorithm with well-conditioned subproblems. Although wavefield reconstruction is the most challenging part of the iteration, sparse linear algebra techniques can be used for moderate-sized problems and frequency domain formulations. The Hessian matrix is blocky with diagonal blocks, making model updates fast. Gradient ascent is used to update Lagrange multipliers by summing PDE violations. Various numerical examples are used to investigate algorithmic components, including model parameterizations, physical model constraints, the role of the Hessian matrix in suppressing interparameter cross-talk, computational efficiency with the source sketching method, and the effect of noise and near-surface effects.

Multi-scale ground penetrating radar full waveform inversion with hybrid Tikhonov and total-variation regularization for different geometric structure

Abstract Full waveform inversion (FWI) is a high-resolution technique to estimate the parameters of dielectric permittivity (ϵ) and electrical conductivity (σ) and identify the structure of the subsurface for Ground Penetrating Radar (GPR) application. However, permittivity and conductivity parameters can be coupled in bi-parameter GPR inversion. This coupling effect leads to the crosstalk in the FWI result. To solve this problem, we propose a novel approach to use the multi-scale FWI with the hybrid regularization method, which combines Tikhonov and total-variation (TV) regularizers that simultaneously invert the ϵ and the σ parameters, which improve the inversion accuracy and reduce the crosstalk effect. The multi-scale strategy uses the Wiener filtering to process the GPR data in different frequency ranges. Then, the low frequencies signal updates the bottom part and subsequently increases the frequencies to invert for the shallow areas. The Tikhonov regularization stabilizes the reconstruction of the smoothly varying background part. In contrast, Total Variation (TV) regularization can recover the large contrasts associated with the LNAPL model. The new Tikhonov-TV (TT) regularization can mitigate the crosstalk caused by the parameter coupling effect. Numerical tests with typical GPR models demonstrate that the proposed multi-scale TT-FWI strategy can effectively eliminate the crosstalk and improve the reconstruction accuracy when the model parameters have a different structure.

Feasibility Study of Anisotropic Full-Waveform Inversion with DAS Data in a Vertical Seismic Profile Configuration at the Newell County Facility, Alberta, Canada

Feasibility Study of Anisotropic Full-Waveform Inversion with DAS Data in a Vertical Seismic Profile Configuration at the Newell County Facility, Alberta, Canada

3D Full-Waveform Tomography of Standard Penetration Test-Seismic Wavefields in Karst Florida Limestone

The shallow subsurface across large parts of Florida consists of weathered karst limestone, a spatially variable porous stratigraphy with significant influence in the design and load capacity of deep foundations. For reliable load transfer of the super structure into the bearing soil/rock, detection of voids and weak zones is crucial. This study investigated the capabilities of a recently developed standard penetration test (SPT)-seismic testing method for characterizing a large volume of soil/rock properties with a single SPT. The method utilizes a three-dimensional full-waveform inversion (3D FWI) of wavefields induced by SPT blows at depths (in-depth source) to characterize the subsurface around the SPT borehole. A site in Florida that presents shallow, surface karst limestone, was the location of a field experiment that consisted of two 36- × 18-m areas, each with an SPT at the area center. Seismic wavefields induced by SPT blows at depth were recorded by 72 vertical geophones on the ground surface and analyzed by the 3D FWI. The results revealed that subsurface soil/rock properties were characterized in submeter pixels over a large 3D domain of 24 × 36 × 18 m (depth × length × width). Multiple voids at various depths from 5 to 17 m were successfully detected at the site and confirmed by SPT data. The results suggested that the SPT-seismic method is an efficient tool for site investigation, as a bridge pier or pile group could be designed with only one SPT.

Acoustic 2-D Full-Waveform Inversion with Non-Balanced Finite differences and Adaptive Weight Decay Methods

Full waveform inversion (FWI) is a powerful seismic imaging technique that aims to achieve high-resolution subsurface models by iteratively comparing recorded seismic waveforms with modeled waveforms. The success of FWI relies on the precision of forward modeling algorithms and the effectiveness of optimization strategies. In this study, we propose a FWI methodology that leverages non-balanced staggered-grid finite differences schemes (NBFD) in the forward modeling process. By employing operators with spatial differencing of varying lengths, these schemes enhance the efficiency of forward modeling.For the optimization process, we employ adaptive gradient-based optimization with weight decay, a widely-used approach in machine learning and deep learning algorithms for model training. These methods demonstrate efficient optimization processing for large data volumes with high precision. The objective of adaptive gradient-based optimization is to dynamically adjust the update rate model parameters during the iterative process. This facilitates improved convergence speed, enhances stability, and overcomes challenges associated with traditional fixed-rate adjustment methods.To ensure accurate inversion results and avoid local minima in the cost function minimization, we implement a Multiscaling inversion strategy within the workflow. The obtained results are compared with those achieved through conventional FWI using standard staggered finite differences and various optimization methods. Our findings demonstrate that employing non-balanced staggered-grid finite differences scheme leads to significant improvements compared to the previously reported results in the literature.