3D Elastic Full Waveform Inversion Research Articles

Redesigning elastic full‐waveform inversion on the new Sunway architecture

AbstractIFOS3D is a three‐dimensional elastic full‐waveform inversion (EFWI) tool designed for high‐resolution estimation of the Earth's material properties within 3D subsurface structures. However, due to the significant computational costs associated with 3D EFWI, leveraging the computing power of a supercomputer for implementation is a logical choice. In this article, we introduce several innovative process‐level and thread‐level optimizations based on heterogeneous many‐core architectures in the new Sunway supercomputer, which is a powerful system globally. These optimizations encompass a process‐level communication overlapping strategy, thread‐level data partitioning and layout approaches, a remote memory access optimized master‐slave communication scheme, and a thread‐level data reuse and overlapping strategy. Through these optimizations, we achieve significant improvements in each iteration, with a kernel function speedup of approximately 59 and an overall program speedup of about 14. Our findings demonstrate the ability of our proposed optimization strategies to overcome the computational challenges associated with 3D EFWI, providing a promising framework for future advancements in the field of subsurface imaging.

Reducing near-surface artifacts from the crossline direction by full-waveform inversion of interferometric surface waves

Seismic incoherent noise and waves scattered from objects in the crossline directions can cause 2D elastic full-waveform inversion (FWI) to produce artifacts in the resulting 2D models. We develop a complete workflow that can determine subsurface S-wave velocity ([Formula: see text]) models inverted from 2D near-surface seismic data more stably. We make use of a combination of supervirtual interferometry and a matched filter to accurately retrieve dominant surface waves from the field data, whereas the incoherent noise and 3D scattering events are significantly suppressed. The subsurface structures obtained from inverting the retrieved data can be interpreted together with the sections resulting from FWI of the original data to mitigate the potential misinterpretation of artifacts. Our results demonstrate that it is possible to invert 2D near-surface seismic data even when the data quality is lowered by the presence of strong noise and 3D scattered events caused by objects located in the crossline direction.

3D elastic multisource full waveform inversion on distributed GPU clusters

Full-waveform inversion (FWI) serves as a useful tool to quantitatively investigate the properties of the media. One of the greatest challenges is its enormous computational cost, especially for the three-dimensional (3D) case. The multisource encoding strategy is a crucial method to speed up FWI. However, current 3D elastic FWI algorithms with the simultaneous sources, such as random time series and random polarity methods, may be subjected to the crosstalk noise, which severely degrades inversion quality. We present a novel 3D elastic crosstalk-free multisource full-waveform inversion method (MFWI). The encoded sources with a series of single-frequency components are excited to perform the seismic wavefield simulation. Extracting the wavefield corresponding to each single-frequency harmonic source by phase-sensitive detection (PSD) algorithm, the multisource wavefield can be decomposed. Therefore, summing the gradients with respect to the model parameters of all decomposed single frequencies can effectively avoid the crosstalk in our MFWI algorithm. Furthermore, to increase the practicability and universality of the algorithm, we adopt the graphic processing unit (GPU) based on the domain decomposition to improve the MFWI algorithm. The multi-scale strategy with a flexible encoding number in each scale helps to enhance the robustness of our algorithm. The numerical examples demonstrate that our method can achieve domain decomposition simulation and obtain 3D crosstalk-free multisource elastic wave inversion results.

Improved imaging of gas hydrate reservoirs and their plumbing system using 2D elastic full-waveform inversion

Gas hydrates are ice-like crystalline materials that form under submarine environments of moderate pressure and low temperature. Another key factor to their formation is the abundance in gas supply from depth in addition to local biogenic gas. Detailed imaging and velocity analysis of the plumbing system of gas hydrates can provide confidence that amplitude anomalies in seismic data are related to gas hydrate accumulations. We have conducted 2D elastic full-waveform inversion (FWI) along a 14 km long segment of a 2D multichannel seismic profile to obtain a high-resolution velocity model of a hydrate system on the southern Hikurangi margin. We compare the FWI velocity model to previously published semblance- and tomography-based velocity models from the same data to explore how much more can be gained from the FWI. The FWI yielded a structurally more accurate velocity model that better delineated the low-velocity zone associated with free gas beneath the bottom simulating reflector (BSR) compared to the semblance- and tomography-based velocity models. Our results also find a lateral velocity inversion, that is, a narrow low-velocity zone surrounded by bands of higher velocities at a seaward-verging protothrust fault, which the two other methodologies failed to resolve. The FWI provides an improved lateral resolution making it an important tool when imaging the “plumbing” systems of gas hydrate reservoirs. In the southeastern limb of the anticline, our results find that the closely spaced landward-vergent protothrusts provide gas-charged fluids for hydrate formation above the BSR. Moreover, at the center of the anticline, our results find that a seaward-vergent protothrust fault appears to be acting as a conduit for gas-rich fluids into strata, although there is no accumulation of any significant hydrate above the BSR at the apex of the anticline. Our finding emphasizes the significance of densely spaced faults and fractures for providing gas for hydrate formation in the hydrate stability zone.

Challenges in shallow target reconstruction by 3D elastic full-waveform inversion — Which initial model?

Elastic full-waveform inversion (FWI) is a powerful tool for high-resolution subsurface multiparameter characterization. However, 3D FWI applied to land data for near-surface applications is particularly challenging because the seismograms are dominated by highly energetic, dispersive, and complex-scattered surface waves (SWs). In these conditions, a successful deterministic FWI scheme requires an accurate initial model. Our study, primarily focused on field data analysis for 3D applications, aims at enhancing the resolution in the imaging of complex shallow targets, by integrating devoted SW analysis techniques with a 3D spectral-element-based elastic FWI. From dispersion curves, extracted from seismic data recorded over a sharp-interface shallow target, we build different initial S-wave ([Formula: see text]) and P-wave ([Formula: see text]) velocity models (laterally homogeneous and laterally variable), using a specific data transform. Starting from these models, we carry out 3D FWI tests on synthetic and field data, using a relatively straightforward inversion scheme. The field data processing before FWI consists of band-pass filtering and muting of noisy traces. During FWI, a weighting function is applied to the far-offset traces. We test 2D and 3D acquisition layouts, with different positions of the sources and variable offsets. The 3D FWI workflow enriches the overall content of the initial models, allowing a reliable reconstruction of the shallow target, especially when using laterally variable initial models. Moreover, a 3D acquisition layout guarantees a better reconstruction of the target’s shape and lateral extension. In addition, the integration of model-oriented (preliminary monoparametric FWI) and data-oriented (time windowing) strategies into the main optimization scheme has produced further improvement of the FWI results.

Assessing the performances of recent global search algorithms using analytic objective functions and seismic optimization problems

We have compared the performances of six recently developed global optimization algorithms: imperialist competitive algorithm, firefly algorithm (FA), water cycle algorithm (WCA), whale optimization algorithm (WOA), fireworks algorithm (FWA), and quantum particle swarm optimization (QPSO). These methods have been introduced in the past few years and have found very limited or no applications to geophysical exploration problems thus far. We benchmark the algorithms’ results against the particle swarm optimization (PSO), which is a popular and well-established global search method. In particular, we are interested in assessing the exploration and exploitation capabilities of each method as the dimension of the model space increases. First, we test the different algorithms on two multiminima and two convex analytic objective functions. Then, we compare them using the residual statics corrections and 1D elastic full-waveform inversion, which are highly nonlinear geophysical optimization problems. Our results demonstrate that FA, FWA, and WOA are characterized by optimal exploration capabilities because they outperform the other approaches in the case of optimization problems with multiminima objective functions. Differently, QPSO and PSO have good exploitation capabilities because they easily solve ill-conditioned optimizations characterized by a nearly flat valley in the objective function. QPSO, PSO, and WCA offer a good compromise between exploitation and exploration.

3D viscoelastic full waveform inversion of seismic waves for geotechnical site investigation

Full waveform inversion (FWI) methods are becoming efficient geophysical tools for geotechnical site investigation. They rely on a mathematical description of wave propagation phenomena to generate synthetic wave-fields, which are then matched with measured wave-fields for extraction of material properties. Due to the inherent computational challenges in implementing a viscoelastic treatment of the wave propagation phenomena, most of the existing 3D FWI algorithms are based on an elastic treatment, and hence ignore the anelastic behavior of materials. The focus of this study is to account for the anelastic effect of materials in the inversion analysis to improve inverted results. Therefore, a 3D viscoelastic FWI method is developed and tested on synthetic and field datasets. The method is based on an existing solution of 3D viscoelastic wave equations (finite-difference solver SOFI3D) and the adjoint-state inversion approach. The results show that the viscoelastic waveform analysis was able to characterize low- and high-velocity synthetic layers, and real variable soil layers. The S-wave velocity (Vs) profiles from field experiment generally agree with invasive standard penetration test (SPT) N-values, including identification of a low-velocity zone. Vs profiles obtained from a 3D elastic FWI are also included for comparison, and results from the viscoelastic inversion are more consistent with the SPT N-values in both trend and magnitudes.

Tunnel detection at Yuma Proving Ground, Arizona, USA — Part 2: 3D full-waveform inversion experiments

We have applied time-domain 3D elastic full-waveform inversion (FWI) to a known tunnel constructed 10 m below the surface with no distinguishing surface expressions. Multicomponent inversion experiments that use an initial model estimated from surface wave methods suggest that the vertical sources and the combination of vertical and longitudinal receivers result in the clearest image of the tunnel. We obtain an approximate 3D image of the tunnel using 24 vertical sources and 720 vertical and 720 longitudinal receivers. We find that increasing the number of vertical sources to 216 does not significantly improve the details of the tunnel. Further experimentation indicates that we can detect the tunnel using a reduced data set of 6–10 vertical sources and 216 vertical sensors. In addition, calculating the [Formula: see text] ratio helps remove artifacts from the inverted model and highlights the location of the tunnel. We compare the 3D inversion results with the 2D FWI results for the same tunnel that we previously evaluated. The variety of successful inversion experiments suggest that FWI is capable of imaging shallow tunnels in desert geologies.

A numerical study of 3D frequency-domain elastic full-waveform inversion

We have developed a 3D elastic full-waveform inversion (FWI) algorithm with forward modeling and inversion performed in the frequency domain. The Helmholtz equation is solved with a second-order finite-difference method using an iterative solver equipped with an efficient complex-shifted incomplete LU-based preconditioner. The inversion is based on the minimization of the data misfit functional and a total variation regularization for the unknown model parameters. We implement the Gauss-Newton method as the optimization engine for the inversions. The codes are parallelized with a message passing interface based on the number of shots and receivers. We examine the performance of this elastic FWI algorithm and workflow on synthetic examples including surface seismic and vertical seismic profile configurations. With various initial models, we manage to obtain high-quality velocity images for 3D earth models.

Site characterization with 3D elastic full-waveform tomography

We have developed a 3D elastic full-waveform inversion (FWI) method for geotechnical site characterization. The method is based on a solution of 3D elastic-wave equations for forward modeling to simulate wave propagation and a local optimization approach based on the adjoint-state method to update the model parameters. The staggered-grid finite-difference technique is used to solve the wave equations together with implementation of the perfectly matched layer condition for boundary truncation. Seismic wavefields are acquired from geophysical testing using sensors and sources located in uniform 2D grids on the ground surface, and they are then inverted for the extraction of 3D subsurface wave velocity structures. The capability of the presented FWI method is tested on synthetic and field data sets. The inversion results from synthetic data indicate the ability of characterizing laterally variable low- and high-velocity layers. Field experimental data were collected using 96 receivers and a propelled energy generator to induce seismic wave energy. The field data result indicates that the waveform analysis was able to delineate variable subsurface soil layers. The seismic inversion results are generally consistent with invasive standard penetration test [Formula: see text]-values, including identification of a low-velocity zone.

3D elastic full-waveform inversion of surface waves in the presence of irregular topography using an envelope-based misfit function

Full-waveform inversion (FWI) is a powerful method for estimating the earth’s material properties. We demonstrate that surface-wave-driven FWI is well-suited to recovering near-surface structures and effective at providing S-wave speed starting models for use in conventional body-wave FWI. Using a synthetic example based on the SEG Advanced Modeling phase II foothills model, we started with an envelope-based objective function to invert for shallow large-scale heterogeneities. Then we used a waveform-difference objective function to obtain a higher-resolution model. To accurately model surface waves in the presence of complex tomography, we used a spectral-element wave-propagation solver. Envelope misfit functions are found to be effective at minimizing cycle-skipping issues in surface-wave inversions, and surface waves themselves are found to be useful for constraining complex near-surface features.

Application of a complete workflow for 2D elastic full-waveform inversion to recorded shallow-seismic Rayleigh waves

The S-wave velocity of the shallow subsurface can be inferred from shallow-seismic Rayleigh waves. Traditionally, the dispersion curves of the Rayleigh waves are inverted to obtain the (local) S-wave velocity as a function of depth. Two-dimensional elastic full-waveform inversion (FWI) has the potential to also infer lateral variations. We have developed a novel workflow for the application of 2D elastic FWI to recorded surface waves. During the preprocessing, we apply a line-source simulation (spreading correction) and perform an a priori estimation of the attenuation of waves. The iterative multiscale 2D elastic FWI workflow consists of the preconditioning of the gradients in the vicinity of the sources and a source-wavelet correction. The misfit is defined by the least-squares norm of normalized wavefields. We apply our workflow to a field data set that has been acquired on a predominantly depth-dependent velocity structure, and we compare the reconstructed S-wave velocity model with the result obtained by a 1D inversion based on wavefield spectra (Fourier-Bessel expansion coefficients). The 2D S-wave velocity model obtained by FWI shows an overall depth dependency that agrees well with the 1D inversion result. Both models can explain the main characteristics of the recorded seismograms. The small lateral variations in S-wave velocity introduced by FWI additionally explain the lateral changes of the recorded Rayleigh waves. The comparison thus verifies the applicability of our 2D FWI workflow and confirms the potential of FWI to reconstruct shallow small-scale lateral changes of S-wave velocity.

Acceleration strategies for elastic full waveform inversion workflows in 2D and 3D

Full waveform inversion (FWI) is one of the most challenging procedures to obtain quantitative information of the subsurface. For elastic inversions, when both compressional and shear velocities have to be inverted, the algorithmic issue becomes also a computational challenge due to the high cost related to modelling elastic rather than acoustic waves. This shortcoming has been moderately mitigated by using high-performance computing to accelerate 3D elastic FWI kernels. Nevertheless, there is room in the FWI workflows for obtaining large speedups at the cost of proper grid pre-processing and data decimation techniques. In the present work, we show how by making full use of frequency-adapted grids, composite shot lists and a novel dynamic offset control strategy, we can reduce by several orders of magnitude the compute time while improving the convergence of the method in the studied cases, regardless of the forward and adjoint compute kernels used.

Efficient 3D elastic full-waveform inversion using wavefield reconstruction methods

In reverse time migration (RTM) or full-waveform inversion (FWI), forward and reverse time propagating wavefields are crosscorrelated in time to form either the image condition in RTM or the misfit gradient in FWI. The crosscorrelation condition requires both fields to be available at the same time instants. For large-scale 3D problems, it is not possible, in practice, to store snapshots of the wavefields during forward modeling due to extreme storage requirements. We have developed an approximate wavefield reconstruction method that uses particle velocity field recordings on the boundaries to reconstruct the forward wavefields during the computation of the reverse time wavefields. The method is computationally effective and requires less storage than similar methods. We have compared the reconstruction method to a boundary reconstruction method that uses particle velocity and stress fields at the boundaries and to the optimal checkpointing method. We have tested the methods on a 2D vertical transversely isotropic model and a large-scale 3D elastic FWI problem. Our results revealed that there are small differences in the results for the three methods.

Laplace-domain wave-equation modeling and full waveform inversion in 3D isotropic elastic media

Abstract The 3D elastic problem has not been widely studied because of the computational burden. Over the past few years, 3D elastic full waveform inversion (FWI) techniques in the time and frequency domains have been proposed by some researchers based on developments in computer science. However, these techniques still have the non-uniqueness and high nonlinearity problems. In this paper, we propose a 3D elastic FWI algorithm in the Laplace domain that can mitigate these problems. To efficiently solve the impedance matrix, we adopt a first-order absorbing boundary condition that results in a symmetric system. A conjugate gradient (CG) solver can be used because the Laplace-domain wave equation is naturally positive definite. We apply the Jacobi preconditioner to increase the convergence speed. We identify the permissible range of Laplace damping constants through dispersion analysis and accuracy tests. We perform the Laplace-domain FWI based on a logarithmic objective function, and the inversion examples are designed for a land setting, which means that the source is vertically excited and multi-component data are considered. The inversion results indicate that the inversion that uses only the vertical component performs slightly better than the multi-component inversion. This unexpected result is obtained partly because we use a vertically polarized source. We analyze the residuals and Frechet derivatives for each component to examine the characteristics of the Laplace-domain multi-component FWI. The results indicate that the residuals and Frechet derivatives for the horizontal component have a singularity problem. The numerical examples demonstrate that the singularity problem is related to the directivity of the displacement and to taking the logarithm of Laplace-domain wave fields. To avoid this singularity problem, we use a simple method that excludes the data near the singular region. Although we can use either simultaneous or sequential strategies to invert the Laplace-domain data, we apply a simultaneous inversion strategy in this paper. Nonetheless, the numerical examples demonstrate that our inversion algorithm yields reasonable long-wavelength velocity structures.

Shallow-structure characterization by 2D elastic full-waveform inversion

Assessing the effectiveness of elastic full-waveform-inversion (FWI) algorithms when applied to shallow 2D structures in the presence of a complex topography is critically important. By using FWI, we overcome inherent limitations of conventional seismic methods used for near-surface prospecting (acoustic tomography and multichannel spectral analysis of surface waves). The elastic forward problem, formulated in the frequency domain, is based on a mixed finite-element P0-P1 discontinuous Galerkin method to ensure accurate modeling of complex topography effects at a reasonable computing cost. The inversion problem uses an FWI algorithm to minimize the misfit between observed and calculated data. Based on results from a numerical experiment performed on a realistic landslide model inspired from the morphostructure of the Super-Sauze earthflow, we analyzed the effect of using a hierarchical preconditioning strategy, based on a simultaneous multifrequency inversion of damped data, to mitigate the strong nonlinearities coming from the surface waves. This strategy is a key point in alleviating the strong near-surface effects and avoiding convergence toward a local minimum. Using a limited-memory quasi-Newton method improved the convergence level. These findings are analogous to recent applications on large-scale domains, although limited source-receiver offset ranges, low-frequency content of the source, and domination of surface waves on the signal led to some difficulties. Regarding the impact of data decimation on the inversion results, we have learned that an inversion restricted to the vertical data component can be successful without significant loss in terms of parameter imagery resolution. In our investigations of the effect of increased source spacing, we found that a sampling of 4 m (less than three times the theoretical maximum of one half-wavelength) led to severe aliasing.

An overview of full-waveform inversion in exploration geophysics

Full-waveform inversion (FWI) is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of thewave-physics complexity. Different hierarchical multiscale strategies are designed to mitigate the nonlinearity and ill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from [Formula: see text] and [Formula: see text] velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as (1) building accurate starting models with automatic procedures and/or recording low frequencies, (2) defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and (3) improving computational efficiency by data-compression techniques to make 3D elastic FWI feasible.

Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion

Quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil- and gas-reservoir characterization. A realistic synthetic example provides for an assessment of the potential and limits of 2D elastic full-waveform inversion (FWI) of wide-aperture seismic data for recovering high-resolution P- and S-wave velocity models of complex onshore structures. FWI of land data is challenging because of the increased nonlinearity introduced by free-surface effects such as the propagation of surface waves in the heterogeneous near-surface. Moreover, the short wavelengths of the shear wavefield require an accurate S-wave velocity starting model if low frequencies are unavailable in the data. We evaluated different multiscale strategies with the aim of mitigating the nonlinearities. Massively parallel full-waveform inversion was implemented in the frequency domain. The numerical optimization relies on a limited-memory quasi-Newton algorithm thatoutperforms the more classic preconditioned conjugate-gradient algorithm. The forward problem is based upon a discontinuous Galerkin (DG) method on triangular mesh, which allows accurate modeling of free-surface effects. Sequential inversions of increasing frequencies define the most natural level of hierarchy in multiscale imaging. In the case of land data involving surface waves, the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion. A second level of hierarchy implemented with complex-valued frequencies is necessary and provides convergence of the inversion toward acceptable P- and S-wave velocity models. Among the possible strategies for sampling frequencies in the inversion, successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies. This suggests that simultaneous inversion of multiple frequencies is critical when considering complex wave phenomena.