Seismic Full Waveform Inversion Research Articles

Full Waveform Inversion Using a High-Dimensional Local-Coherence Misfit Function

Conventional full-waveform seismic inversion (FWI) tries to estimate a subsurface model that can accurately predict surface records by minimizing an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm misfit between observed and synthetic data. If the initial model is far away from the true model, the cycle-skipping issue might occur and the L2-norm based FWI produces a spurious model. To mitigate this problem, we present a novel FWI scheme using a high-dimensional local coherence misfit function. A 2D/3D window is first used to extract local seismic waveform from the common-shot gathers. Then, we apply a normalized cross-correlation to measure the coherence of local synthetic and observed records, which is used as the misfit to iteratively update subsurface velocity model. The new misfit function enhances the contribution of phase fitting while reducing the amplitude contribution, which helps to increase the tolerance of FWI to an inaccurate initial velocity model. In addition, the computation of local waveform coherence along the temporal and spatial axes can adaptively balance the adjoint source amplitudes for strong near-offset reflections and weak far-offset refractions, which improves the low-wavenumber updates. Numerical experiments for synthetic and field data demonstrate that the proposed FWI scheme has a better tolerance to inaccurate starting models and is less sensitive to cycle-skipping issue compared with conventional FWI method.

Joint FWI of Active Source Data and Passive Virtual Source Data Reconstructed Using an Improved Multidimensional Deconvolution

Traditional full waveform inversion (FWI) highly depends on sufficient low-frequency data or a good initial model. Passive seismic data contain rich low-frequency components, and passive seismic FWI using virtual source data by seismic interferometry (SI) is a promising method. However, the distribution of passive sources in the subsurface is always inhomogeneous, which will lead to artifacts in the reconstruction results by SI using cross-correlation (CC). SI by multidimensional deconvolution (MDD) can counteract the source inhomogeneity but requires the separation of the reference wavefields, which is difficult to achieve for noise source data. To mitigate this problem, we propose an improved SI method by linear Radon transform based multidimensional deconvolution (LRTMDD). The interferometric point-spread function can be extracted more accurately and efficiently in the linear Radon domain, thus improving the reconstruction results. The passive virtual source full waveform inversion (PVSFWI) based on LRTMDD is further proposed, which can effectively use the low-frequency information in the virtual source data to invert the macroscopic velocity structures even in the case of inhomogeneous source distributions, and without the need to estimate the virtual source wavelets. A joint multi-source FWI strategy is proposed to solve the problem of missing low-frequency data suffered by active source FWI. Numerical experiments on the Marmousi model and the SEG/EAGE overthrust model show that the proposed methods can fully combine the respective advantages of multisource seismic data to stably achieve high-accuracy velocity models in the case of inhomogeneous passive source distributions and the lack of low-frequency data in active seismic data.

Weighted-average time-lapse seismic full-waveform inversion

As seismic data can contain information over a large spatial area and are sensitive to changes in the properties of the subsurface, seismic imaging has become the standard geophysical monitoring method for many applications such as carbon capture and storage and reservoir monitoring. The availability of practical tools such as full-waveform inversion (FWI) makes time-lapse seismic FWI a promising method for monitoring subsurface changes. However, FWI is a highly ill-posed problem that can generate artifacts. Because the changes in the earth’s properties are typically small in terms of magnitude and spatial extent, discriminating the true time-lapse signature from noise can be challenging. Different strategies have been proposed to address these difficulties. In this study, we propose a weighted-average (WA) inversion to better control the effects of artifacts and differentiate them from the true 4D changes. We further compare five related strategies with synthetic tests on clean and noisy data. The effects of seawater velocity variation on different strategies also are studied as one of the main sources of nonrepeatability. We tested different strategies of time-lapse FWI (TL-FWI) using the Marmousi and the SEG Advanced Modeling time-lapse models. The results indicate that the WA method can provide the best compromise between accuracy and computation time. This method also provides a range of possible answers of other TL-FWI strategies.

Full-waveform inversion method for tunnel seismic forward prospecting

SUMMARY During tunnel construction, accurately ascertaining the adverse geological condition in front of the tunnel face is essential to ensure construction safety and decrease economic loss. As an accurate wave velocity modelling method, seismic full-waveform inversion (FWI) still faces many difficulties when applied in a tunnel observation environment because of fewer observation data and smaller offset than ground seismic detection. This paper analysed the FWI for tunnel active seismic forward prospecting with a single shot. We adopted the N-order time integral wavefield and normalized integration objective function method to improve the stability and reduce the dependence of FWI on the initial model. Based on two assumptions on the wave velocity distribution in the tunnel, we proposed a 1-D velocity structure correction method to reduce the multiplicity of inversion. Then the improved tunnel FWI method based on these two inversion strategies was applied to a synthetic model with a rectangular anomaly and a lithology interface, verifying the method's effectiveness. Based on typical adverse geological bodies during tunnelling, three additional adverse geological models were built and verified the reliability of the methods in tunnel detection environments. There are still some false anomalies interference in the inversion results of the synthetic models from the inversion results. However, these problems are acceptable in limited tunnel observation space. Then the method was applied in a field example in the Yinsong water supply project in Jilin Province, China, and verified the effect on field data. Finally, the influence of the shot number on the inversion effect and the method's robustness are discussed.

Data-driven seismic prestack velocity inversion via combining residual network with convolutional autoencoder

Seismic full-waveform inversion (FWI) is a powerful imaging approach in exploration geophysics, to estimate high-resolution subsurface geophysical properties via fitting synthetic data to observed seismic records. Nevertheless, there exist several intractable issues, e.g., solution non-uniqueness, cycle-skipping phenomenon, weak robustness and high computational burden. Recently, more attention has been paid to data-driven FWI techniques based on deep neural networks. However, their success greatly depends on an ocean of training instances, which is not available in oil exploration conveniently. To cope with this situation, an effective strategy is to reduce the dimensionality of input and output spaces for given training instances. By exploiting 2D velocity profile nonlinear compressibility, we train a residual convolutional autoencoder under an unsupervised mode using velocity data, where its encoder acts as a velocity dimensionality reduction operator to transform 2D velocity profiles into low-dimensional 1D pseudo-velocity curves. Then, a residual network is trained to build a nonlinear mapping from multi-shot seismic records to 1D pseudo-velocity curves. In the inference stage, the trained decoder converts those predicted 1D curves back to 2D velocity profiles. Therefore, we propose a novel two-stage data-driven seismic inversion technique combining a residual network with a residual convolutional autoencoder. The detailed experiments on four synthetic data sets (salt body, layered, faulted and salt dome models) illustrate that our proposed method with three different residual network architectures outperforms other approaches including FCNVMB, VelocityGAN and pure residual network, according to four objective evaluation metrics and subjective visualization.

Enhancement of In-Plane Seismic Full Waveform Inversion with CPU and GPU Parallelization

Full waveform inversion is a widely used technique to estimate the subsurface parameters with the help of seismic measurements on the surface. Due to the amount of data, model size and non-linear iterative procedures, the numerical computation of Full Waveform Inversion are computationally intensive and time-consuming. This paper addresses the parallel computation of seismic full waveform inversion with Graphical Processing Units. Seismic full-waveform inversion of in-plane wave propagation in the finite difference method is presented here. The stress velocity formulation of the wave equation in the time domain is used. A four nodded staggered grid finite-difference method is applied to solve the equation, and the perfectly matched layers are considered to satisfy Sommerfeld’s radiation condition at infinity. The gradient descent method with conjugate gradient method is used for adjoined modelling in full-waveform inversion. The host code is written in C++, and parallel computation codes are written in CUDA C. The computational time and performance gained from CUDA C and OpenMP parallel computation in different hardware are compared to the serial code. The performance improvement is enhanced with increased model dimensions and remains almost constant after a certain threshold. A GPU performance gain of up to 90 times is obtained compared to the serial code.

Potential of Phase-Amplitude-Based Multi-Scale Full Waveform Inversion with Total-Variation Regularization for Seismic Imaging of Deep-Seated Ores

As the demand for ore resources increases, the target for mineral exploration gradually shifts from shallow to deep parts of the Earth (&gt;1 km). However, for the ore-hosting strata, it is difficult to obtain high-resolution images by using the electromagnetic method. Seismic full waveform inversion (FWI) is an optimization algorithm which aims at minimizing the prestack seismic data residual between synthetic and observed data. In this case, FWI provides an effective way to achieve high-resolution imaging of subsurface structures. However, acquired seismic data usually lack low frequencies, resulting in severe cycle skipping of FWI, when the initial velocity model is far away from the true one. Phase information in the seismic data provides the kinematic characteristics of waves and has a quasi-linearly relationship with subsurface structures. In this article, we propose to use a phase-amplitude-based full waveform inversion with total-variation regularization (TV-PAFWI) to invert the deep-seated ores. The ore-hosting velocity model test results demonstrate that the TV-PAFWI is suitable for high-resolution velocity model building, especially for deep-seated ores.

Supplementary material "Seismic full-waveform inversion of the crust-mantle structure beneath China and adjacent regions" --- Part 1

Supplementary material "Seismic full-waveform inversion of the crust-mantle structure beneath China and adjacent regions" --- Part 1

Seismic full-waveform inversion of the crust-mantle structure beneath China and adjacent regions

Seismic full-waveform inversion of the crust-mantle structure beneath China and adjacent regions

Supplementary material "Seismic full-waveform inversion of the crust-mantle structure beneath China and adjacent regions" --- Part 3

Supplementary material "Seismic full-waveform inversion of the crust-mantle structure beneath China and adjacent regions" --- Part 3

Supplementary material "Seismic full-waveform inversion of the crust-mantle structure beneath China and adjacent regions" --- Part 2

Supplementary material "Seismic full-waveform inversion of the crust-mantle structure beneath China and adjacent regions" --- Part 2

Wave-equation migration velocity analysis via the optimal-transport-based objective function

Wave-equation migration velocity analysis builds a kinematically accurate macrovelocity model containing the large-scale structures of the model for seismic imaging or full-waveform inversion (FWI). Differential semblance optimization formulates the misfit function in the subsurface domain by applying a penalty to the unfocused subsurface-offset gathers or the nonflattened angle gathers. Such a penalty leads to gradients with strong artifacts and spurious oscillations, which then leads to slow convergence. We formulate the misfit function using the optimal transport (OT) among neighboring traces in angle-domain common-image gathers (CIGs). Specifically, we measure the unflatness of the gathers by comparing the Wasserstein distance of adjacent traces. Because CIGs are ideal to form a probability distribution, which is required by OT, it is natural to use OT to measure the time shifts between two distributions. Our objective function exhibits well-behaved convex and unimodal properties in a simple model with a single interface, and it is expected to be minimum for the correct velocity when the angle gathers are flat. A synthetic data set example on the Marmousi model indicates the ability of our method to provide an initial model for FWI that allows FWI to converge. We also apply the approach on a marine field data set to further demonstrate its effectiveness in estimating the macrovelocity model.

Generalized Effective Biot Theory and Seismic Wave Propagation in Anisotropic, Poroviscoelastic Media

AbstractThe interior of the Earth is quite complex due to the actual geometrical structure and the presence of complex rheological materials, including viscoelastic rocks, porous sediments and the presence of anisotropy. Seismic wavefield forward modeling in such media forms the basis of most wave equation‐based methods for investigating the structure of the Earth and processing and imaging of seismic data, e.g., seismic full waveform inversion. Numerical modeling using Biot's equations that describe the physics of poroelasticity provides a useful framework to investigate wave attenuation and dispersion. Poroelasticity describes the interaction between the deformation of an elastic porous solid and the fluid flow in the porous structure. We present a time‐domain finite‐difference method for seismic wavefield modeling, taking into account both attenuation and anisotropy of poroviscoelastic Earth structure. The mathematical formulations and modeling methods are based on (a) the linear Biot's poroelastic theory and double porosity models in anisotropic media and (b) a relaxation function that uses the generalized standard linear solid model with anisotropic τ parameter for magnitude of attenuation and nearly constant Q model. Using a modified relaxation function that is suggested to describe the anisotropy attenuation, we develop a generalized anisotropic Biot model in the anisotropic, viscoelastic media. In addition to the anisotropic poroelasticity based on Biot theory, we implement the generalized anisotropic Biot model with complex moduli for an effective Biot's model in which the attenuative anisotropic viscoelastic model with the generalized standard linear solid model is used to approximate the attenuation factor function. The method generalizes the linear poroviscoelastic model based on effective Biot theory for seismic wave modeling to the attenuative, anisotropic case. In the anisotropic, poroviscoelastic model, we represent the bulk modulus and shear modulus of the solid frame by the modified relaxation function. We present time‐domain finite‐difference modeling for seismic wavefields in anisotropic, viscoelastic porous media including transversely isotropic media with a vertical, tilted or horizontal symmetry axis (VTI, TTI, and HTI). We also consider the extension of the two new models to nearly constant Q viscoelastic anisotropy.

Optimization of seismic-guided 3-D marine magnetotelluric imaging in a complex fold-thrust belt setting in NW Borneo, Malaysia

SUMMARY The use of seismic-derived structure tensor to guide the inversion of non-seismic data has been gaining increasing attention because of its ability to constrain the inversion result to honour structural information from seismic reflectivity. While the cross-gradient method has been recently adapted to this problem, there is a need to further examine how the choice of the various regularization weighting factors and the design of the starting model impact the image-guided results. In this paper focused on marine magnetotellurics (MT), we study several practical aspects of seismic-guided electromagnetic (EM) inversion to see on what can be improved from the current practice. We then show practical examples of how the cross-gradient method can be applied to get a more geologically pleasing model that fits the data. We also show that there are subjective choices in how to effectively apply the method. First, using a field-realistic synthetic model, we established what would be the suitable regularization weights in the vertical and horizontal directions. Secondly, for the actual 3-D survey data, we compared the use of structure tensors derived from anisotropic pre-stack depth migration (APSDM) reflectivity, high-fidelity full-waveform inversion (FWI) velocity and acoustic impedance inversion volumes to guide cross-gradient anisotropic resistivity inversion with initial half-space resistivity starting models. We determined post-facto the optimum structure tensor weights using well logs as the ground truth. We found that the initial model built using horizon-based interpolated resistivity logs from multiple wells in the anisotropic inversion guided with seismic FWI velocity gave the best match to well logs as compared to the other options. However, given that resistivity logs from multiple wells may not always be available for a robust initial model construction in frontier exploration, we suggest that the structure tensor from APSDM reflectivity data is still preferred since the APSDM reflectivity data have well-defined structural information.

Building a full-waveform inversion starting model from wells with dynamic time warping and convolutional neural networks

Seismic full-waveform inversion (FWI) needs a feasible starting model because otherwise it might converge to a local minimum and the inversion result might suffer from detrimental artifacts. We have built a feasible starting model from wells by applying dynamic time warping (DTW) localized rewarp and convolutional neural network (CNN) methods alternatively. We use the DTW localized rewarp method to extrapolate the velocities at well locations to the nonwell locations in the model space. Rewarping is conducted based on the local structural coherence, which is extracted from a migration image of an initial infeasible model. The extraction uses the DTW method. The purpose of velocity extrapolation is to provide sufficient training samples to train a CNN, which maps local spatial features on the migration image into the velocity quantities of each layer. Furthermore, we design an interactive workflow to reject inaccurate network predictions and to improve CNN prediction accuracy by incorporating the Monte Carlo dropout method. We have determined that our method is robust against kinematic incorrectness in the migration velocity model, and it is capable of producing a feasible FWI starting model.

Self-Supervised Deep Learning for Nonlinear Seismic Full Waveform Inversion

Seismic full waveform inversion (FWI) is able to build high-resolution velocity model based on the full information carried by seismic wave. However, FWI requires an accurate enough initial model to ensure convergence. In this paper, we propose a new nonlinear FWI method to mitigate the initial model dependence problem. Specifically, we firstly propose a nonlinear operator within the hybrid model- and data-driven framework based on the frequency controllable envelope operator (FCEO) and a deep learning architecture U-Net. FCEO is used to obtain the envelope of a band-limited data and U-Net realizes the mapping from this envelope to that corresponding to a lower frequency band. The U-Net is trained in a self-supervised manner that avoids the reliance on labeled data and benefits the generalization ability. Based on the nonlinear operator, a nonlinear FWI method is proposed by defining a new misfit function. In addition, the calculation of gradient is derived using the adjoint-state method. Using numerical examples, we investigate the performance of the proposed nonlinear operator and the new nonlinear FWI method. The results clearly demonstrate that the proposed nonlinear operator is effective in obtaining low-frequency envelope data, and the new nonlinear FWI method has advantages over common method in mitigating cycle-skipping and building an initial model for conventional FWI.

Randomized Source Sketching for Full Waveform Inversion

Partial differential equation (PDE) constrained optimization problems such as seismic full waveform inversion (FWI) frequently arise in the geoscience and related fields. For such problems, many observations are usually gathered by multiple sources, which form the right-hand-sides of the PDE constraint. Solving the inverse problem with such massive data sets is computationally demanding, in particular when dealing with large number of model parameters. This paper proposes a novel randomized source sketching method for the efficient resolution of multisource PDE constrained optimization problems. We first formulate the different source-encoding strategies used in seismic imaging into a unified framework based on a randomized sketching. To this end, the source dimension of the problem is projected in a smaller domain by a suitably defined projection matrix that gathers the physical sources in super-sources through a weighted summation. This reduction in the number of physical sources decreases significantly the number of PDE solves while suitable sparsity-promoting regularization can efficiently mitigate the footprint of the cross-talk noise to maintain the convergence speed of the algorithm. We implement the randomized sketching method in an extended search-space formulation of frequency-domain FWI, which relies on the alternating direction method of multipliers (ADMM). Numerical examples carried out with a series of well documented 2D benchmarks demonstrate that the randomized sketching algorithm reduces the cost of large-scale problems by at least one order of magnitude compared to the original deterministic algorithm.

Physics-Consistent Data-Driven Waveform Inversion With Adaptive Data Augmentation

Seismic full-waveform inversion (FWI) is a nonlinear computational imaging technique that can provide detailed estimates of subsurface geophysical properties. Solving the FWI problem can be challenging due to its ill-posedness and high computational cost. In this work, we develop a new hybrid computational approach to solve FWI that combines physics-based models with data-driven methodologies. In particular, we develop a data augmentation strategy that can not only improve the representativity of the training set but also incorporate important governing physics into the training process and therefore improve the inversion accuracy. To validate the performance, we apply our method to synthetic elastic seismic waveform data generated from a subsurface geologic model built on a carbon sequestration site at Kimberlina, California. We compare our physics-consistent data-driven inversion method to both purely physics-based and purely data-driven approaches and observe that our method yields higher accuracy and greater generalization ability.

Multiscale Data-Driven Seismic Full-Waveform Inversion With Field Data Study

Seismic full-waveform inversion (FWI), which uses iterative methods to estimate high-resolution subsurface models from seismograms, is a powerful imaging technique in exploration geophysics. In recent years, the computational cost of FWI has grown exponentially due to the increasing size and resolution of seismic data. Moreover, it is a non-convex problem and can encounter local minima due to the limited accuracy of the initial velocity models or the absence of low frequencies in the measurements. To overcome these computational issues, we develop a multiscale data-driven FWI method based on fully convolutional networks (FCN). In preparing the training data, we first develop a real-time style transform method to create a large set of synthetic subsurface velocity models from natural images. We then develop two convolutional neural networks with encoder-decoder structure to reconstruct the low- and high-frequency components of the subsurface velocity models, separately. To validate the performance of our data-driven inversion method and the effectiveness of the synthesized training set, we compare it with conventional physics-based waveform inversion approaches using both synthetic and field data. These numerical results demonstrate that, once our model is fully trained, it can significantly reduce the computation time, and yield more accurate subsurface velocity models in comparison with conventional FWI.

InversionNet3D: Efficient and Scalable Learning for 3-D Full-Waveform Inversion

Seismic full-waveform inversion (FWI) techniques aim to find a high-resolution subsurface geophysical model provided with waveform data. Some recent effort in data-driven FWI has shown some encouraging results in obtaining 2-D velocity maps. However, due to high computational complexity and large memory consumption, the reconstruction of 3-D high-resolution velocity maps via deep networks is still a great challenge. In this article, we present InversionNet3D (InvNet3D), an efficient and scalable encoder&#x2013;decoder network for 3-D FWI. The proposed method employs group convolution in the encoder to establish an effective hierarchy for learning information from multiple sources while cutting down unnecessary parameters and operations at the same time. The introduction of invertible layers further reduces the memory consumption of intermediate features during training and, thus, enables the development of deeper networks with more layers and higher capacity as required by different application scenarios. Experiments on the 3-D Kimberlina dataset demonstrate that InvNet3D achieves state-of-the-art reconstruction performance with lower computational cost and lower memory footprint compared to the baseline.