Elastic Full Waveform Inversion Research Articles

Onshore model building using elastic full-waveform inversion on surface and body waves: A case study from Sultanate of Oman

We have determined the potential of the elastic full-waveform inversion (FWI) to overcome some difficult challenges in onshore seismic imaging. The approach allows for simultaneous inversion of surface and body waves and, theoretically, is free from the limitations of traditional dispersion curve analysis and traveltime inversion. Indeed, identification and separation of different wavefield types are not required, and all wave types can be treated within a unified inversion scheme. However, FWI requires a reasonably good initial model, and the sensitivity of the misfit function with respect to the different wave types should be appropriately accounted for. This is the most essential step with onshore seismic data because the ground roll is much more energetic in comparison with the body waves. Our approach is based on a time-offset weighting function to balance the contribution of the different wave types in combination with a conventional frequency continuation approach. We first illustrate the feasibility of our approach on a 2D synthetic example representing a complex geology from south Oman. Then, we develop a 3D real data example from south Oman, where the application of our workflow till 8 Hz plays a pivotal role in retrieving a reliable model and in explaining the entire observed wavefields. In this example, the inversion of the ground roll helps improving the recovery of the shallow part of the earth, and hence better constraining the inversion of the body waves.

Influence of shear velocity on elastic full-waveform inversion: Gulf of Mexico case study using multicomponent ocean-bottom node data

Elastic full-waveform inversion (FWI) is superior to acoustic FWI due to its ability to simulate complex mode conversions in fast-varying elastic media. Using elastic FWI may become important when building velocity models in areas of large complex salt bodies that we typically see in the Gulf of Mexico. Accounting for elastic effects in FWI can reduce the artifacts that are caused by using an acoustic approximation. We often rely on petrophysics relations to define an initial shear velocity model, which also could be challenging. We demonstrate how to take advantage of the reflected converted waves from the top of the salt interface recorded in horizontal geophones to improve the estimation of the background shear velocity. Then, we illustrate the impact of the initial background shear velocity in the elastic inversion of the long-offset low-frequency hydrophone data. The workflow is based on a combination of wave-equation traveltime inversion, to cope with the cycle skipping, and FWI, to obtain higher-resolution results.

Elastic full waveform inversion based on equivalent staggered grid FDM and inter-parameter trade-off mitigation

Elastic full waveform inversion based on equivalent staggered grid FDM and inter-parameter trade-off mitigation

Three-dimensional Gauss–Newton constant-Q viscoelastic full-waveform inversion of near-surface seismic wavefields

SUMMARY Full-waveform inversion (FWI) methods rely on accurate numerical simulation of wave propagation in the analysed medium. Acoustic or elastic wave equations are often used to model seismic wave propagation. These types of simulations do not account for intrinsic attenuation effects due to material anelasticity, and thus correction techniques have been utilized in practice to partially compensate the anelasticity. These techniques often only consider the waveform amplitude correction based on averaging of overall amplitude response over the entire data set, and ignore the phase correction. Viscoelastic wave equations account for the anelastic response in both waveform amplitude and phase, and are therefore a more suitable alternative. In this study, we present a novel 3-D Gauss–Newton viscoelastic FWI (3-D GN-VFWI) method. To address the main challenge of the Gauss–Newton optimization, we develop formulas to compute the Jacobian efficiently by the convolution of virtual sources and backward wavefields. The virtual sources are obtained by directly differentiating the viscoelastic wave equations with respect to model parameters. In order to resolve complex 3-D structures with reasonable computational effort, a homogeneous attenuation (Q factor) is used throughout the analysis to model the anelastic effects. Synthetic and field experiments are performed to demonstrate the utility of the method. The synthetic results clearly demonstrate the ability of the method in characterizing a challenging velocity profile, including voids and reverse velocity layers. The field experimental results show that method successfully characterizes the complex substructure with two voids and undulating limestone bedrock, which are confirmed by invasive tests. Compared to 3-D elastic FWI results, the presented viscoelastic method produces more accurate results regarding depths of the voids and bedrock. This study suggests that the improvement of imaging accuracy would warrant the widespread use of viscoelastic wave equations in FWI problems. To our best knowledge, this is the first reported study on 3-D GN-VFWI at any scale. This study provides the new theory and formulation for the use of Gauss–Newton optimization on the 3-D viscoelastic problem.

Target-oriented high-resolution elastic full-waveform inversion with an elastic redatuming method

Characterizing the elastic properties in deep-buried reservoirs beneath complex overburden structures remains challenging for seismic inversion. Elastic full-waveform inversion (FWI) is capable of quantitatively estimating the subsurface elastic properties with a reasonably high resolution. However, elastic FWI using high frequencies is computationally expensive because fine discretization is required to stabilize the wavefield simulation. In addition, it is challenging for elastic FWI to obtain the high-resolution inversion results of the deep targets due to complex overburden structures and limited energy illumination of the target of interest. To overcome these limitations, we propose a target-oriented high-resolution elastic FWI scheme by using the estimated elastic data for a virtual survey deployed only above a zone of interest. Specifically, we have developed an elastic redatuming approach to retrieve virtual elastic data by solving an iterative least-squares data-fitting problem. In addition to the elastic multicomponent data recorded at the acquisition surface, an estimate of the overburden model is required. A synthetic data example indicates that an overburden model estimated by elastic FWI with a low-frequency band enables our elastic redatuming approach to reconstruct the virtual elastic data representing the seismic reflection response from the target zone. We then perform regularized elastic FWI by using the redatumed elastic data to estimate the elastic properties in the target zone with reduced computational cost. In the numerical examples, the Marmousi2 synthetic data and 2D Volve field data are used to demonstrate the feasibility and practicality of the proposed method.

Elastic full waveform inversion based on decoupled wave equations

Elastic full waveform inversion (FWI) attempts to deduce accurate subsurface elastic parameters from multi-component seismic data. However, the inversion accuracy of elastic FWI degrades due to the crosstalk effect caused by coupled elastic wavefields. Decomposing coupled elastic wavefields into pure P- and S-waves is an effective method to suppress the crosstalk noises. Wavefields decomposition method plays a crucial role in wave mode decomposition-based elastic FWI method. Considering trade-off between calculation accuracy and efficiency, we have developed a new elastic FWI method based on decoupled wave equations to improve the inversion accuracy of elastic FWI. New decoupled adjoint state wave equations are proposed to obtain adjoint P- and S-waves. The wave mode decomposition-based gradient equations are further used to update the P- and S-wave velocity models. The synthetic examples reveal that our new elastic FWI method can obtain higher resolution models than conventional elastic FWI method. In addition, our new elastic FWI based on decoupled wave equations does not significantly increase the calculation amount but can speed up the convergence of the elastic FWI.

Elastic full waveform inversion in VTI media using logging data constraints and gradient precondition

Elastic full waveform inversion in VTI media using logging data constraints and gradient precondition

Using convolutional neural networks to develop starting models for near-surface 2-D full waveform inversion

SUMMARY Non-invasive subsurface imaging using full waveform inversion (FWI) has the potential to fundamentally change near-surface (<30 m) site characterization by enabling the recovery of high-resolution (metre-scale) 2-D/3-D maps of subsurface elastic material properties. Yet, FWI results are quite sensitive to their starting model due to their dependence on local-search optimization techniques and inversion non-uniqueness. Starting model dependence is particularly problematic for near-surface FWI due to the complexity of the recorded seismic wavefield (e.g. dominant surface waves intermixed with body waves) and the potential for significant spatial variability over short distances. In response, convolutional neural networks (CNNs) are investigated as a potential tool for developing starting models for near-surface 2-D elastic FWI. Specifically, 100 000 subsurface models were generated to be representative of a classic near-surface geophysics problem; namely, imaging a two-layer, undulating, soil-over-bedrock interface. A CNN has been developed from these synthetic models that is capable of transforming an experimental wavefield acquired using a seismic source located at the centre of a linear array of 24 closely spaced surface sensors directly into a robust starting model for FWI. The CNN approach was able to produce 2-D starting models with seismic image misfits that were significantly less than the misfits from other common starting model approaches, and in many cases even less than the misfits obtained by FWI with inferior starting models. The ability of the CNN to generalize outside its two-layered training set was assessed using a more complex, three-layered, soil-over-bedrock formation. While the predictive ability of the CNN was slightly reduced for this more complex case, it was still able to achieve seismic image and waveform misfits that were comparable to other commonly used starting models, despite not being trained on any three-layered models. As such, CNNs show great potential as tools for rapidly developing robust, site-specific starting models for near-surface elastic FWI.

Love wave full-waveform inversion for archaeogeophysics: From synthesis tests to a field case

High precision detection of the shallow-surface structure is of great significance to geotechnical engineering and archaeological geophysical research. Surface wave Full waveform inversion (FWI) is attracting more and more attention in shallow seismic exploration. The FWI of Love waves is more straightforward and has a higher precision and resolution compared with Rayleigh waves. In the classic gradient-based FWI algorithm, the gradient amplitude does not scale with increasing depth due to the coupling effect and double scattering; thus, the inversion image cannot represent the significant small-scale characteristic structures in archaeogeophysics. To overcome the above limitations, a pre-conditioned FWI approach was presented, and a complete elastic Love waves FWI workflow was developed for archaeogeophysics. The superior performance of the developed method was verified through synthesis tests and a field experiment. The synthetic tests on a tomb model show that the pre-conditioned approach has a better parameter reconstruction capability, can characterize small-scale anomalies, improves the convergence rate, and has a strong anti-noise ability. In the field experiment, the pre-conditioned approach-based Love waves FWI workflow was adopted to invert the recorded Love waves datasets gathered in Xianyang City, China. The target of the survey was to determine the location and approximate size of a buried ancient tomb to provide reliable guidance for further excavation. The obtained FWI image revealed an underground profile with a depth of 9.5 m, and a low-velocity anomaly with a height of about 1.6 m and a length of about 4.7 m was delineated, which we identified as the tomb. The subsequent excavation confirmed this conclusion. The above results show that the complete Love wave FWI workflow developed has the ability to perform accurate imaging under the condition of few shots.

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.

Critical Zone Structure by Elastic Full Waveform Inversion of Seismic Refractions in a Sandstone Catchment, Central Pennsylvania, USA

AbstractSeismic imaging provides key information for revealing structures within Earth's critical zone (CZ) and quantifying subsurface fluid properties. The P‐wave velocity (Vp) models estimated by seismic refraction tomography or acoustic full waveform inversion (FWI) are useful to delineate the thicknesses of weathered bedrock but ambiguously map fluid properties in CZ. Considering the complementary sensitivity of S‐wave to subsurface fluid saturation, we explore advanced elastic full waveform inversion (EFWI) to estimate both Vp and S‐wave velocity (Vs) models simultaneously. Several strategies are proposed for robust EFWI implementation of noisy single (vertical) component refraction data: (a) we window seismic data to preserve early arrivals mainly including P‐wave, converted waves, and S‐wave refractions; (b) we use a correlative misfit rather than the classic L2 misfit to alleviate the interference of unreliable data amplitudes; and (c) we perform inversion using a multiscale frequency strategy with the iterative constraint with the rule of Vp/Vs > 1. We validate that the EFWI approach reliably reconstructs Vp and Vs models using synthetic data. Then, we apply our EFWI approach to seismic refraction data acquired at the Garner Run site of the Susquehanna Shale Hills Critical Zone Observatory. The inverted Vp and Vs models indicate three distinguished layers and with significant lateral and depth heterogeneities (e.g., low Vp and Vs zones). Joint analyses of Vp, Vs, and Vp/Vs with rock‐physics knowledge reveal potential gas or water gathering zones.

Elastic wave full-waveform inversion in the time domain by the trust region method

In this paper, we investigate the elastic wave full-waveform inversion (FWI) by the trust region method. FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually the gradient-based search methods such as the steepest descent method or quasi-Newton's methods are applied to update the model parameters iteratively. And the L-BFGS method with approximated Hessian information is preferred for its high computational efficiency and accuracy. At each iteration, a line search method computes a search direction and then finds a suitable step length or how far to move along the direction. The trust region method is an effective alternative to solve nonlinear optimization problems. In this paper, we investigate the performance of the trust region method in elastic time-domain FWI. In the trust region method, a trial step length called the trust-region radius is forced within a certain neighborhood of the current iterate point and a trust-region subproblem requires to solve. In order to solve the trust-region subproblem, the dogleg method and the two dimensional subspace method are adopted in this paper. In the trust region method, as long as the trust-region radius is well updated, the model updating can be performed for every iteration with the fixed trial step and there is no more extra computation for forward problem like the line search method. Numerical computations for the benchmark Marmousi model are given. The inversion results and comparisons show that the trust region method is very efficient and behaves better than the line search method such as the well-known L-BFGS method.

Elastic Full-Waveform Inversion Using Both the Multiparametric Approximate Hessian and the Discrete Cosine Transform

We propose seismic elastic full-waveform inversion (EFWI) using both the multiparametric approximate Hessian and the discrete cosine transform (DCT). EFWI is a promising technology for obtaining physical parameters. EFWI using the multiparametric approximate Hessian can suppress crosstalk artifacts for each physical parameter, but the computational burden increases as the number of physical parameters considered increases. In this study, to reduce the computational burden, DCT was used to compress the model parameters and accelerate EFWI in the truncated DCT domain. EFWI using DCT is possible to increase the calculation efficiency by reducing the total number of unknown variables. We implemented EFWI using monoparametric Hessian and multiparametric Hessian, which reduced the computational burden using DCT and conducted tests through numerical experiments using each Hessian. In numerical result, despite using a small number of DCT coefficients, we confirmed that contamination due to crosstalk artifacts was suppressed when EFWI was performed using the multiparametric approximate Hessian.

Deep Learning for Low-Frequency Extrapolation of Multicomponent Data in Elastic FWI

Full waveform inversion (FWI) strongly depends on an accurate starting model to succeed. This is particularly true in the elastic regime: The cycle-skipping phenomenon is more severe in elastic FWI compared to acoustic FWI, due to the short S-wave wavelength. In this paper, we extend our work on extrapolated FWI (EFWI) by proposing to synthesize the low frequencies of multi-component elastic seismic records, and use those "artificial" low frequencies to seed the frequency sweep of elastic FWI. Our solution involves deep learning: we separately train the same convolutional neural network (CNN) on two training datasets, one with vertical components and one with horizontal components of particle velocities, to extrapolate the low frequencies of elastic data. The architecture of this CNN is designed with a large receptive field, by either large convolutional kernels or dilated convolution. Numerical examples on the Marmousi2 model show that the 2-4Hz low frequency data extrapolated from band-limited data above 4Hz provide good starting models for elastic FWI of P-wave and S-wave velocities. Additionally, we study the generalization ability of the proposed neural network over different physical models. For elastic test data, collecting the training dataset by elastic simulation shows better extrapolation accuracy than acoustic simulation, i.e., a smaller generalization gap.

Elastic Full Waveform Inversion Based on Full-Band Seismic Data Reconstructed by Dual Deconvolution

Affected by the low-frequency seismic data missing and multiple parameters coupling, elastic full waveform inversion is easy to fall into local minima. This paper attempts to solve the local minima problem from two aspects: low-frequency seismic data reconstruction and wave mode decomposition. First, by introducing the envelope into sparse constrained deconvolution, an envelope-based sparse constrained deconvolution method is proposed to overcome the problem caused by the phase shift and side lobes. However, the resolution of the envelope is insufficient to identify overlapping seismic events, which are generated by velocity models rich in thin layers. Therefore, sparse constrained deconvolution and envelope-based sparse constrained deconvolution are combined, and a dual deconvolution method is proposed: sparse constrained deconvolution is used to improve the resolution of the original seismic data, then envelope-based sparse constrained deconvolution is used to reconstruct high-precision reflection sequence. Convolve the reconstructed reflection sequence with the full-band source wavelet to obtain the full-band seismic data. Secondly, for the multi-parameter coupling problem, we use wave mode decomposition to obtain separated P- and S-wave. Finally, a multi-scale elastic full waveform inversion method based on dual deconvolution and wave mode decomposition is proposed. Numerical experiment results demonstrate the algorithm proposed in the article.

Three-Dimensional Elastic Full-Waveform Inversion Using Temporal Fourth-Order Finite-Difference Approximation

Full-waveform inversion (FWI) serves as a useful tool to quantitatively investigate the properties of the subsurface. Presently, 3-D elastic FWI uses a finite-difference time-domain (FDTD) approach in numerical simulation. However, such an FDTD scheme often includes only second-order temporal approximations, causing errors in temporal dispersion in the case of a large time-stepping size. Such temporal dispersion will affect the inversion results and reduce the inversion quality. We introduce a unique 3-D elastic FWI using a temporal fourth-order finite-difference (FD) approximation. A new quasi-stress–velocity elastic equation is solved by the temporal fourth-order and spatial arbitrary even-order FDTD method, and a novel inversion procedure for the convolutional objective function based on this equation is derived. The multiscale strategy is used to enhance the robustness of our algorithm. The forward modeling and FWI examples presented here demonstrate that our method can achieve modeling and inversion with a high degree of accuracy.

Salt Structure Elastic Full Waveform Inversion Based on the Multiscale Signed Envelope

Building high-fidelity velocity models for salt structures is a valuable and difficult problem in seismic exploration. Acoustic-based full-waveform inversion (FWI) methods usually produce velocity artifacts around high-contrast interfaces due to the generation of converted waves. Therefore, elastic FWI (EFWI) should be used in salt model velocity building. Two problems that restrict EFWI are: lack of low-frequency seismic data and multiparameter coupling. For the first problem, envelope is a good choice because of its ability to reconstruct low-frequency components independent of the frequency range of seismic data. However, envelope is instantaneous energy flow and lacks polarity information, while the elastic waves are vectors. Thus, the direct use of envelope to reconstruct the low-frequency components of elastic waves causes serious artificial artifacts in envelope inversion. Therefore, we introduce signed demodulation and window average function to obtain the multiscale (MS) envelope with polarity, defined as the MS signed envelope to reconstruct low-frequency elastic data. The reconstructed low-frequency data are then used in EFWI, and an elastic MS signed direct envelope inversion algorithm is proposed. For the second problem, wave mode decomposition and hierarchical inversion strategies are integrated into the inversion to eliminate the multiparameter coupling effect. A salt layer model and BP model are used to verify the effectiveness of the algorithm. Finally, the deficiencies in the research of this article and further improvement plans are also discussed.

Well-Guided Multisource Elastic Full-Waveform Inversion

Full waveform inversion (FWI) has been considered one of the most promising approaches to estimating the high-resolution subsurface parameters, which takes advantage of the kinematics and dynamics information of seismic data. However, FWI is greatly dependent on the accuracy of the initial model and vulnerable to the issue of local minimum. Moreover, the multi-source and multi-parameter crosstalk artifacts make multi-source elastic FWI (MS-EFWI) more likely to trap into a suboptimal inversion result. To remedy this defect, this study proposes an efficient elastic FWI (EFWI) paradigm that combines the crosstalk-free MS-EFWI method and a well-guided initial model-building algorithm. Specifically, we apply a harmonic wavelet encoding technology to MS-EFWI, by which the multi-source wavefields can be completely deblended without crosstalk noise. The well-guided structure-oriented interpolation, with the aid of the dip information derived from the initial migration images, is designed to build a satisfactory initial model and therefore reduce the risk of cycle skipping. Numerical examples based on the 2D Overthrust model and Marmousi model further demonstrate the feasibility and robustness of the proposed method with a relatively little number of iterations.

Subsurface Elastic Parameter Reconstruction Based on Seismic Data From the High-Speed Trains Using Full Waveform Inversion

In this study, we attempt to use the high-speed train (HST)-induced seismic data for subsurface elastic parameter reconstruction by the full waveform inversion (FWI) method. The HSTs provide a new kind of seismic source as the superposition of a series of moving subsources. We consider the situation of HST running on the viaduct and use a finite difference method to simulate the seismic wave excitation. The result shows that the HST-induced seismic data are highly complex in the time domain but appear as a series of discrete peaks in the frequency domain. Elastic FWI is used to retrieve the P- and S-wave velocities of the subsurface based on this new kind of seismic data. The alternative iteration strategy and multiscale inversion are used to improve the inversion results. Numerical examples with the Marmousi2 model show the feasibility and the great potential of using this new kind of seismic data in seismic imaging.

Target-Oriented Time-Lapse Elastic Full-Waveform Inversion Constrained by Deep Learning-Based Prior Model

Time-lapse (TL) seismic monitoring plays a vital role in reservoir characterization and management. Elastic full-waveform inversion (EFWI) has been applied to time-lapse seismic data to allow for a quantitative estimation of time-varying elastic properties. However, the high-resolution inversion can be computationally intense and ill-posed. To estimate the high-resolution time-lapse changes at a reasonable cost, we utilize two key techniques for the inversion: 1) we develop an elastic redatuming approach to retrieve the virtual elastic data for both base and monitor data at the target level using mainly a kinematically accurate velocity, thus, reducing the computational cost by focusing the high-resolution inversion on the target zone; 2) We integrate high-resolution well information and seismic data in the target-oriented inversion, where a high-resolution prior model is predicted by deep learning to regularize the inversion. A deep neural network (DNN) is capable of learning the mappings between the time-lapse seismic estimation and the facies interpreted from well information after the training process. Thus, we can derive a prior model for time-lapse changes by mapping the facies characterized by the property changes to the target inversion domain. We then implement the target-oriented TLEFWI regularized by the prior model, where the redatumed time-lapse elastic data and the prior model jointly contributes to the inversion result. The numerical examples validate that the proposed approach enables us to retrieve the time-lapse changes of elastic property in the target zone with improved resolution and well consistency.