Low-frequency (LF) data plays a key role in mitigating cycle-skipping in full waveform inversion (FWI). We propose a method to efficiently and accurately reconstruct LF seismic data for a large number of shot gathers based on multi-channel deconvolution (MD) and deep learning (DL). Specifically, we firstly propose a MD method to predict LF data for very limited shot gathers. Then, we use a deep neural network (called ‘acceleration network’) to learn the relation between a shot gather and its corresponding LF data, based on the labels provided by the MD method, enabling efficient prediction for all shot gathers. Next, another deep neural network (called ‘improvement network’) is proposed to improve the accuracy of the LF shot gathers predicted by the ‘acceleration network’. To do so, several horizontal layered velocity models are generated based on the statistical distribution of well logs, and several synthetic shot gathers with and without LF are generated by solving the acoustic wave equation. Based on these synthetic shot gathers, the MD predicted LF data and the corresponding true LF data form a data pair [predicted LF, true LF] for each shot gather, and these data pairs are used to train the ‘improvement network’. Finally, employing a cascade of ‘acceleration network’ and ‘improvement network’, we reconstruct the LF data of all shot gathers. Synthetic and field data examples verify that the proposed method exhibits superior accuracy compared to conventional MD method in LF data reconstruction.

Elastic full waveform inversion (EFWI) is able to simultaneously build multiple subsurface parameters. However, EFWI faces the ill-posed problem and the multi-parameter coupling effects. Building accurate initial P- and S-wave velocity models is crucial for mitigating these issues and ensuring the convergence of EFWI. Yet, limitations of acquisition systems and the different sensitivities of P- and S-waves to wavenumber components pose significant challenges in simultaneously building P- and S-wave velocity models with structural consistency. These issues may result in additional iterations, or in some cases, even non-convergence. Aiming to build accurate long-wavelength velocity models with high structural consistency, a novel structurally consistent elastic frequency controllable envelope inversion (SC-EFCEI) method is proposed in this paper. SC-EFCEI performs multi-scale inversion using elastic frequency-controllable envelope data to build long-wavelength models, and additionally introduces structural constraints between different velocity gradients via automatic differentiation (AD) to enforce consistency between the inverted P- and S-wave velocity models. Numerical experiments on the elastic Overthrust model, modified Marmousi2 model, and Chevron 2014 blind dataset verified the effectiveness of the proposed inversion method. The inverted P- and S-wave velocity models both successfully reveal the large-scale features of the velocity model while exhibiting good structural consistency, which can be used as good initial models for EFWI.

The angle gathers are the data basis of prestack seismic inversion, and their resolution directly determines the resolution of the inverted elastic parameters. Seismic reflectivity inversion (SRI) is a technique that is able to estimate reflectivity from seismic data, and consequently improve the resolution of seismic data. However, the existing SRI method for angle gathers faces two problems: (1) The assumption that the wavelet is known does not align with reality; (2) Compared with the exact Zoeppritz equation, approximation equations will introduce errors in large angles. To overcome these shortcomings, in this paper, we propose a new blind SRI method for enhancing the resolution of angle gathers. This method can simultaneously build the wavelet and reflectivity of angle gathers without the need for a predefined wavelet, and an angle-based regularization term is constructed to ensure the continuity in angle especially in noisy cases. We use both synthetic experiments on a modified Marmousi model and also a field data experiment using a dataset from the Hampson-Russell software to assess the performance of the proposed method and compare its performance with an existing method. The results clearly validate the effectiveness of the proposed method and its superiority over the existing method in producing high-quality reflectivity models for angle gathers.

Because of the viscoelastic properties of the Earth, seismic waves experience attenuation during propagation, resulting in decreased amplitude and phase distortion, ultimately reducing resolution. The inverse Q filtering method is an important way to compensate for attenuation and consequently improve the resolution of seismic data. However, the compensatory capability and stability of the existing inverse Q filtering methods present a paradoxical relationship, ensuring compensation ability may diminish stability, and vice versa. In other words, the existing methods can hardly work in scenarios characterized by high levels of noise or significant attenuation (low Q values). In this article, a physics-constrained deep-learning-based attenuation compensation (PCDL-AC) method is proposed. Specifically, we first establish a time-domain attenuation model, which delineates the relation among a stationary seismic trace, the Q model, and the corresponding attenuated seismic trace. Then, we use this model as the physics law and propose a physics-constrained deep learning method for attenuation compensation in a semisupervised or even unsupervised manner. Benefiting from the noise-resistance ability of deep neural networks and the physics law, the proposed method can achieve stable and accurate compensation even when strong noise is present in data. In addition, this method significantly improves the efficiency of attenuation compensation since the application of deep learning is very efficient once it is trained. Both synthetic and field data experiments verify the effectiveness of the proposed method and demonstrate its advantages over common methods.

Migration is the core link in reflection seismic exploration. Seismic images are often extended into angle domain for interpretations. However, affected by limited acquisition aperture and complex overburden, the generated images are far from ideal. The illumination is unbalanced, causing unreliable amplitude variation in angle gathers. Band-limited seismic data and wavelet stretch in large angles, lead to low-resolution angle gathers. Image-domain least-squares migration (IDLSM) implemented by point spread function (PSF) deconvolution is a promising solution. Extending the concept of IDLSM to the angle domain, we develop a new method to construct angle-dependent PSFs and optimize angle gathers. The essential element to construct PSFs is the Green’s function. The proposed method reconstructs Green’s functions using a bidirectional long short-term memory (LSTM) network. We use a ray tracing method to efficiently obtain wave propagation directions (travel-time gradients). And wave-equation forward modeling is used to accurately calculate wavefront amplitudes. The LSTM network is trained by labels composed of travel-time gradients and amplitudes to surrogate the solver of Green’s functions. Angle-dependent PSFs are constructed according to the mathematical model of the angular local Hessian. And inversions with PSFs are performed to optimize angle gathers. Numerical tests on a 3-D synthetic model demonstrate that the proposed method is able to improve the image quality of prestack angle gathers and poststack seismic images. The proposed method compensates illumination and improves the resolution of angle-dependent seismic images. Both vertical and lateral resolution are enhanced. Amplitude versus angle (AVA) responses can be corrected for further analysis and interpretations.

Seismic interpretation and reservoir characterization require the seismic data having faithful amplitudes that relate to subsurface physical parameters. Nowadays, the amplitude fidelity of seismic imaging becomes more important than ever. Although reverse time migration (RTM) adopts the full wave equation as true amplitude seismic wave propagator, it is still not sufficient for true amplitude seismic imaging since migration is only the adjoint operator corresponding to the forward modeling process. The complex overburden and limited migration aperture lead to unbalanced illumination of subsurface structures. Least-squares migration was proposed to correct amplitudes of seismic images, but it is computationally expensive and sometimes unstable. The illumination compensation is an available alternative which only considers the amplitude correction regardless of the resolution issue. In this article, we propose a true amplitude seismic imaging method with illumination compensation performed on both RTM stacked images and angle gathers. We derive the angle-dependent illumination intensity from the Hessian of least-squares migration in which Green’s functions are essential components. We propose a new method to estimate the Green’s function and its corresponding wave propagation direction based on wavefields excitation amplitudes and Poynting vectors at excitation times. Then, the illumination intensity is constructed as a function of dip and reflection angles to correct both angle gathers and stacked images. The proposed method is tested using two synthetic models and a real marine dataset. Numerical results demonstrate that the proposed method can effectively correct amplitudes of seismic images. Deep events beneath complex structures are enhanced with more balance illumination.

Low-rank approximation (LRA) is a powerful technique for seismic diffraction separation and imaging, providing higher-resolution images of subsurface discontinuities compared to traditional reflection imaging. However, in complex wavefields where reflections lack distinct low-rank characteristics, diffractions and reflections can overlap within the same eigenimages, making traditional LRA less effective for separation. To address this limitation, we propose a diffraction separation and imaging method based on multi-directional wavefield low-rank approximation (MDWLRA). The MDWLRA method employs multi-directional wavefield decomposition (MDWD) to divide complex wavefields into angular slices with similar dip angles. These slices are classified as either diffraction slices or reflection slices, with the latter containing mostly reflections and some residual diffractions. LRA is then applied to the reflection slices to separate the remaining diffractions from reflections. By reducing wavefield complexity using MDWD, reflections in the reflection slices exhibit clearer low-rank characteristics than those in the full wavefields, allowing for more effective separation using LRA. Numerical tests on synthetic data from the modified Sigsbee2A model and field data demonstrate that the MDWLRA method outperforms traditional methods, achieving more accurate separation with fewer leakages than traditional LRA, while also improving diffraction fidelity compared to the Curvelet-transform-based method.

Blind seismic acoustic-impedance (AI) inversion is a technique for obtaining the AI of the subsurface medium without given a wavelet. An effective way to solve the blind inversion problem is to split the multi-parameter problem into two single-parameter subproblems and solve them in an alternative iteration way. However, this method becomes time-consuming when dealing with large-scale 3D problems and faces challenges in selecting suitable regularization parameters. To overcome these shortcomings, we propose a deep learning accelerated blind seismic AI inversion (DLA-BSAII) method. It mainly has three steps: (1) Only a few 2D profiles are selected from the whole 3D data, and their corresponding AI models and wavelets are inverted using conventional blind seismic AI inversion method. (2) The results of the first step are used to train deep networks to realize the nonlinear mapping from a 2D seismic profile to AI and wavelet. In addition, the trained deep networks are used to generate predictions of AI models and wavelets for the remaining 2D profiles. (3) Benefiting from the predicted AI models and wavelets, a new alternative iteration method with fewer but more effective regularization terms is proposed to obtain the final inverted AI models and wavelets of the remaining 2D profiles. It has the advantages of easier selection of regularization parameters and faster convergence speed. Synthetic and field data examples verify that DLA-BSAII outperforms conventional methods in terms of both efficiency and inversion accuracy.

Seismic facies classification involves assigning geological meaning to seismic amplitudes based on distinct sedimentary facies responses. Various deep learning approaches have been developed for seismic facies classification. Currently, most deep neural networks applied for this task are manually engineered based on domain expertise. However, these human-designed architectures may not be optimal for seismic facies classification. To address this, we introduce differentiable architecture search with partial channel connections (PC-DARTS), enabling automated architecture search instead of manual design. We modify the PC-DARTS search space and propose PC-DARTS for seismic facies classification (PC-DARTS-SFC) to determine architectures tailored for this problem. We apply PC-DARTS-SFC on the Netherlands F3 seismic volume. The results demonstrate the superiority of the architecture discovered by PC-DARTS-SFC over original PC-DARTS, conventional networks, and a previous method. This confirms the potential of leveraging network architecture search (NAS) to find specialized networks surpassing human design for seismic facies classification.

Seismic migration produces the migrated images of subsurface media using seismic data, which is important for geophysical exploration. However, the adjoint-based migration methods may produce a blurry image, convolved by a Hessian matrix. To address this problem, we propose a Hessian-assisted iterative self-training learning (HAISTL) method aimed at approximating the inverse Hessian matrix and deblurring the migrated image. First, we train a long short-term (LSTM) network using labeled images and use it as a teacher network to generate pseudolabels for the unlabeled images. Subsequently, we integrate the demigration and migration operators to identify the pseudolabels with high confidence levels and construct a dataset containing both the true and pseudolabels. The dataset is then used to train a student network with the injection of model noise into the network. Finally, we regard the student network as a new teacher and repeat the process in an iterative STL framework. We demonstrate the effectiveness of our proposed method using two synthetic datasets and field data. Compared with the supervised learning (SL) method, the proposed method exhibits superior generalization capabilities. This advantage stems from the incorporation of the demigration and migration operators, providing a valuable prior for the inverse Hessian matrix in training the model. In contrast to the model-driven least-squares migration (LSM) methods, the proposed method yields high-resolution images with significantly reduced computational costs. However, it may be less effective in recovering small-scale structures when confronted with an extremely limited number of labels.

Seismic lithology interpretation based on seismic data is an important task to delineate oil and gas reservoirs. However, this is an extremely unstable work when only utilizing seismic data, which would result in multiple solutions. We suggest a multiattribute integrated deep learning (MAIDL) workflow for automatic seismic lithology interpretation. To implement the proposed model, we first propose to apply the wavelet scattering transform (WST) to seismic data for multiscale features extraction. Note that the WST has local deformation stability and translation invariance for analyzing seismic data, which would be proven to promote seismic lithology interpretation. Next, the MAIDL model is suggested to combine the multiscale features extracted by the WST and seismic data simultaneously, which can improve the accuracy of automatic seismic lithology prediction. Afterward, the Res-UNet, which incorporates residual blocks into the UNet, is introduced to avoid the over-fitting and the degradation problem of the proposed MAIDL model. Finally, a 2-D synthetic data and a 2-D post-stack field data are adopted to test the effectiveness of the suggested MAIDL model for automatic seismic lithology interpretation.

Amplitude-preserving angle gathers are ideal inputs for seismic prestack inversion. However, due to the limitation of computational efficiency, generating subsurface azimuth–reflection angle gathers from 3-D seismic imaging is still a very difficult task. In this article, we propose a new method to generate azimuth–reflection angle gathers from 3-D reverse time migration (RTM). The proposed method approximately reconstructs the source wavefield using high-dimensional wavelets and the excitation information. After using directional vectors to calculate the subsurface observation angles and applying the cross correlation imaging condition, we can generate azimuth–reflection angle gathers by angle binning. Without storing source wavefields or reconstructing source wavefields using boundary conditions, the proposed method has high computational efficiency. Numerical experiments on a synthetic model and a real marine seismic dataset demonstrate that compared with the excitation amplitude imaging condition, the proposed method can generate azimuth–reflection angle gathers with continuous complete events and high signal-to-noise ratio. The image quality and resolution of angle gathers are significantly improved. At the same time, the computational complexity does not increase much.

Diffraction separation and imaging are important for subsurface discontinuities characterization. However, conventional diffraction separation methods may loss validity when the diffractions and reflections do not have discernible differences in data domain. Moreover, due to limited acquisition geometry and narrow frequency band of seismic data, the diffraction imaging methods that use conventional ray-based or wave-equation-based migration operators may produce images with low resolution. We propose a diffraction separation and least-squares imaging method based on multi-scale and multi-directional wave-field and image decomposition. First, by using the multi-scale and multi-directional properties of the generalized curvelet transform, we reproduce the diffractions from the plane-wave sections according to the differences between the diffractions and reflections in terms of scale and angle. When the diffractions and reflections do not have discernible differences in data domain, their migrated images generally have different dip angles. Therefore, we propose a plane-wave least-squares diffraction imaging method with a curvelet-domain regularization which suppresses the images of residual reflections with small dip angles. Finally, we obtain high-resolution images of the subsurface discontinuities by using a regularized conjugate gradient method. Synthetic and field data examples verify the superiority of the proposed diffraction separation method over the plane-wave destruction filter in terms of better suppression of the reflections and better recovery of the diffractions. Compared with plane-wave reverse time migration, the proposed diffraction imaging method effectively suppresses the residual reflectors and produces images with higher resolution and signal-to-noise ratio.

We propose a blind nonlinear acoustic impedance inversion method. The seismic wavelet is first extracted through the Euclid deconvolution method from multichannel seismic data. Then, the acoustic impedance is inverted based on the exact nonlinear forward operator. The conventional Euclid deconvolution can theoretically estimate the reflectivity without special prior assumptions, but the method is extremely inefficient and unstable in the case of a large amount of data. We optimize the method and propose a frequency-domain algorithm to improve its efficiency. Conventional impedance inversions are almost implemented based on the linearized approximate formula, but the inversion errors will increase sharply when there is a strong reflection interface. We build the inversion objective function by the accurate nonlinear formula to improve accuracy. The total variation (TV) regularization and low-frequency components of well-logging curves are added to the objective function to make the inversion result have a block structure and converge to the absolute impedance. The nonlinear optimization problem is finally solved by the Levenberg–Marquardt (LM) algorithm. The results of synthetic data and field data verify that our method has high accuracy and good practicability.

The convolutional model, which describes the relation among poststack seismic data, wavelet, and reflectivity, is the foundation of seismic deconvolution (SD). However, this model is only an approximation of the seismic wave equation, and it may not work in complex cases especially when the medium is anelastic, heterogeneous, and anisotropic. In this article, we propose a generalized convolutional model for poststack seismic data. A deep-learning-based data correction term is added to characterize the data ingredients that cannot be characterized by the convolutional model. The data correction term of the new model is realized using the long-short term memory (LSTM)-based deep learning architecture, of which parameters are learned based on the dataset from several well logs. Based on the new model, we propose an SD method and investigate its performance in building reflectivity models using complex numerical examples. The results verified that the new model can accurately characterize complex seismic data, which cannot be characterized by a convolutional model. In addition, the proposed SD method has significant advantages over traditional methods in building high-fidelity reflectivity models in complex cases.

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.

Least-squares reverse time migration (LSRTM) is an amplitude-preserving seismic imaging technique that aims at finding the subsurface reflectivity model. It is often performed iteratively using an inversion algorithm, such as the conjugate gradient method. Such an implementation requires a huge amount of calculation as it may converge slowly. Preconditioning plays a crucial role in seismic inverse problems. In this study, we propose a novel preconditioning method for LSRTM. The proposed method estimates a new guided curvelet-domain deblurring filter for one-step LSRTM and preconditioned LSRTM. Then, the filter is applied to migrated images and gradients in LSRTM. Such a deblurring filter acts as a curvelet-domain local linear approximation of the least-squares functional inverse Hessian, which can improve the image quality and accelerate the convergence. Numerical tests on the synthetic model and a field data example demonstrate that the preconditioning operator can effectively accelerate the convergence of LSRTM. One-step LSRTM can obtain comparable image quality to that of conventional iterative LSRTM with only a single iteration. The comparison of the convergence curves demonstrates that the curvelet-domain preconditioning operators accelerate the convergence of LSRTM. Furthermore, the preconditioned LSRTM achieves better image quality than the conventional LSRTM. We compare preconditioning operators based on diagonal and local linear approximations. The preconditioning operator based on the local linear approximation has more robust performance and more stable convergence curves than the diagonal-based approximation.

Least-squares reverse time migration (LSRTM) can estimate high-quality reflectivity of subsurface medium from seismic data. However, the subsurface reflectivity depends on reflection angles, and its variations over reflection angles are extremely important because they can be used to estimate sub-surface physical properties for seismic interpretation. We present a new formulation of the LSRTM method that can estimate reflection-angle-dependent reflectivity from seismic data. We derive a forward modeling operator which predicts the reflection data without calculating the reflection angles, and verify that it approximately equals to the reflection-angle-dependent wave-equation-based Kirchhoff modeling operator under the assumption that the velocity perturbation is small and the reflection angle is smaller than the critical angle. Based on the proposed modeling operator associated with the adjoint of the angle-dependent wave-equation-based Kirchhoff modeling operator, we reformulate LSRTM as an inverse problem to invert for reflection-angle-dependent reflectivity using a preconditioned conjugate gradient algorithm. The algorithm uses a low-rank filter as the preconditioner to attenuate migration artifacts. Imaging tests on synthetic and field seismic data are used to verify validity and superiority of the proposed method. The tests illustrate that the proposed method can produce the reflection-angle-dependent reflectivity with much higher signal-to-noise ratio, resolution and amplitude fidelity than reverse time migration. Compared with conventional LSRTM, it can produce more focused stacked image when the migration velocity contains errors. Moreover, conventional LSRTM only produces the angle-independent reflectivity, whereas the proposed method has the feasibility to produce the reflection-angle-dependent reflectivity.

Building reflectivity and quality factor (Q) using nonstationary post-stack seismic data is important for vertical resolution enhancement of seismic data and reservoir identification. However, it is well-known that both reflectivity and Q affect the waveform of seismic data, leading to the fact that simultaneously estimating them is a strong ill-posed multi-parameter inverse problem which faces the crosstalk problem. In this paper, we propose a new method for simultaneous inversion of reflectivity and Q. A deep-learning-based data decoupling operator is proposed to decouple the effects of the two parameters on nonstationary seismic data. Based on the decoupled data, we transform the original multi-parameter inverse problem into two independent singe-parameter inverse problems that are immune to crosstalk and can build reasonable initial models for reflectivity and Q. Then alternative iteration is conducted to update the two built initial models to obtain the final models. A few well-logs are used to train the deep learning architecture and specific regularization terms are constructed for the inverse problem to ensure physically reasonable results. Synthetic and field data examples verify the effectiveness of the proposed method and its advantages over a conventional model-driven joint inversion method.

In this letter, we propose a new global optimization method for nonlinear seismic inversion problems. The proposed method is a development of the existing method MMDE-Net by introducing a learnable strategy for choosing problem-dependent basis vectors and regularization parameters that are considered to be fixed in MMDE-Net. We name the proposed method as the optimized MMDE-Net (OMMDE-Net) and investigate its performance in seismic inversion through both synthetic and field data examples. The experimental results demonstrate that OMMDE-Net has advantages over MMDE-Net in effectiveness and efficiency.

Seismic inversion problems often involve strong nonlinear relationships between model and data so that their misfit functions usually have many local minima. Global optimization methods are well known to be able to find the global minimum without requiring an accurate initial model. However, when the dimensionality of model space becomes large, global optimization methods will converge slow, which seriously hinders their applications in large-dimensional seismic inversion problems. In this article, we propose a new method for large-dimensional seismic inversion based on global optimization and a machine learning technique called autoencoder. Benefiting from the dimensionality reduction characteristics of autoencoder, the proposed method converts the original large-dimensional seismic inversion problem into a low-dimensional one that can be effectively and efficiently solved by global optimization. We apply the proposed method to seismic impedance inversion problems to test its performance. We use a trace-by-trace inversion strategy, and regularization is used to guarantee the lateral continuity of the inverted model. Well-log data with accurate velocity and density are the prerequisite of the inversion strategy to work effectively. Numerical results of both synthetic and field data examples clearly demonstrate that the proposed method can converge faster and yield better inversion results compared with common methods.

Angle-domain common image gathers (ADCIGs) describe the reflectivity variation over reflection angles which are important for seismic exploration. The ADCIGs could be obtained using reverse time migration (RTM). However, because of the limitation of seismic frequency band and acquisition geometry, RTM produces the ADCIGs with low fidelity. We propose a reflection angle-domain pseudoextended least-squares RTM method to improve the quality of the ADCIGs in which the Poynting vector is used to efficiently calculate the angles. We first extend the inverted model in the reflection angle domain and derive a feasible pseudoextended Born modeling operator which can map the reflection angle-domain extended model to seismic data. The modeling operator, associated with an adjoint operator, are then used to build a pseudoextended linearized inversion framework for inverting the angle-dependent reflectivity. Taking advantage of the simplicity and coherency of the ADCIGs, we impose a series of low-rank constraints on the extended angle dimension and a sparse constraint on the whole dimension to ensure the production of high-quality ADCIGs. The proposed method is finally solved by a regularized conjugate gradient algorithm. We conduct several numerical examples on a flat layer model, the Marmousi model, and the Sigsbee2A salt model to test the validity and superiority of the proposed method. The results demonstrate that the proposed method could produce the ADCIGs and the stacked image with higher fidelity than RTM, which provides a reliable input for migration velocity analysis, anisotropic model building, and amplitude versus angle analysis.

Seismic full-waveform inversion (FWI) aims to build high-resolution images of the physical properties of the subsurface. However, the ill-posedness and nonlinear problems pose a great challenge to the high-resolution reconstruction. Although the nonlinear problem can be mitigated by matching a subset of observation data, the resulting images are generally low-resolution background structures. Regularization-based techniques can mitigate the ill-posedness of FWI, but the iterative method suffers from the cycle-skipping and computational burden problems. To overcome these problems, we develop an adjoint-driven deep-learning FWI (AD-DLFWI) approach which utilizes the fully convolutional network (FCN) to invert subsurface velocity from reflection seismic data. Specifically, AD-DLFWI is implemented in a two-step iterative scheme, in which an optimal update result at each step is learned via a FCN-based learned updating operator. The proposed approach uses the seismic image of applying the adjoint operator of the scattering wave equation, which is equivalent to the gradient of classical FWI, as the data engine of FCN. Inspired by the wave-equation migration velocity analysis approach, we propose to unfold the gradient of FWI into the common-source domain to keep the information about the measure of velocity error. To ensure the interpretability of each network’s role, we design a two-step training scheme to successively reconstruct the low and high wavenumber components of subsurface velocity. Using synthetic experiments with reflection-dominant seismic data, we have confirmed that the proposed FWI approach not only can provide a reliable velocity estimation but also is not sensitive to the cycle-skipping problem.

Subsurface scatters are sometimes masked by reflectors in seismic migration images, because the diffractions are much weaker in energy than the reflections. We propose a novel imaging method, named reflection-damped plane-wave least-squares reverse time migration (RD_PLSRTM), to enhance the scatters in the migration image. We formulate seismic imaging as an inverse problem that minimizes a weighted residual between the modeled and observed seismic data. In the proposed approach, we use the plane-wave destruction filter to separate the diffractions from the reflections in the data residual. A reflection-damped weighting matrix is then used to govern the fitting of the diffractions and the reflections, and therefore emphasize the updates of the scatters. The inverse problem is finally solved by using an iteratively reweighted least-squares (IRLS) algorithm. The proposed method provides a generalized formulation that could be reduced to conventional PLSRTM and PLSRTM of diffractions (PLSRTM_D) by using specific damping factors. We conduct imaging tests on synthetic and field data that prove the superiority of the proposed method over PLSRTM in imaging deep scatters and subsalt scatters. Compared with PLSRTM_D, it could produce high-quality images of not only the scatters but also the reflectors.

Full-waveform inversion (FWI) attempts to find optimal models of subsurface by using full information of the observed data. One difficulty in conventional FWI is that the misfit function has many local minima because of cycle skipping. Envelope inversion (EI), which uses the envelope operator (EO)-based misfit function, has been proven to be effective in mitigating cycle skipping and recovering long-wavelength velocity model. However, EI ignores the fact that the information within different frequency bands plays different roles in inversion. In this paper, a frequency controllable EO, which can control the frequency components being used to construct envelope, is proposed. We propose a new misfit function and a multiscale FWI method. Using synthetic experiments based on the Marmousi model, we demonstrate that the proposed method is better than EI in mitigating cycle skipping and in building an accurate initial model for conventional FWI to significantly improve its final result. In addition, this method can tolerate a wide range of noise levels. Its effectiveness has also been successfully demonstrated using a field data set.

Seismic inversion problems are well-known to be nonlinear and their misfit functions often involve many local minima. Global optimization methods are capable of converging to the global minimum of a misfit function, thus, they are promising in seismic inversion. As a global optimization method, multimutation differential evolution (MMDE) has been proven to be effective in solving high-dimensional seismic inversion problems. However, it is challenging to choose the optimal parameters for MMDE to achieve the best performance in seismic inversion. In this paper, we propose a new deep network based on MMDE and name it as MMDE-Net, which enables us to learn the optimal parameters by using a network training procedure rather than empirically choosing them. Benefiting from the learned parameters, MMDE-Net has advantages over MMDE in applications. Numerical examples based on synthetic and field data set clearly indicate that MMDE-Net can provide faster convergence speed and better inversion result than conventional methods in seismic inversion.

Seismic inversion problems often involve nonlinear relationships between data and model and usually have many local minima. Linearized inversion methods have been widely used to solve such problems. However, these kinds of methods often strongly depend on the initial model and are easily trapped in a local minimum. Global optimization methods, on the other hand, do not require a very good initial model and can approach a global minimum. However, global optimization methods are exhaustive search techniques that can be very time consuming. When the model dimension or the search space becomes large, these methods can be very slow to converge. In this paper, we propose a new global optimization algorithm by incorporating a new multimutation scheme into a differential evolution algorithm. Because mutation operation with the new multimutation scheme can generate better mutant vectors, the new global optimization algorithm has a very good ability of exploring the search space and can converge very fast. We apply the proposed algorithm to both synthetic and field data to test its performance. The results have clearly indicated that the new global optimization algorithm provides faster convergence and yields better results compared with the conventional global optimization methods in seismic inversion.

In this letter, a new adaptive differential evolution (DE) for high-dimensional waveform inversion is proposed. In conventional DE algorithms, individuals are treated as a whole and share the same fitness function and parameters. However, conventional DE algorithms have ignored the huge difference among the subcomponents in an individual and are not effective for high-dimensional problems. Therefore, for high-dimensional problems, we expand the unit of crossover rate from the whole individual to its subcomponents and propose a new adaption algorithm by adjusting the crossover rate of each subcomponent. In our algorithm, both kinds of crossover rate, including individual crossover rate and subcomponent crossover rate, play important roles in crossover operation. Based on local fitness function, the subcomponent crossover rate is adaptively obtained to improve the efficiency of crossover operation. On the other hand, the individual crossover rate is used to prevent the population diversity from decreasing in crossover operation. We embed the adaption algorithm into cooperative coevolutionary DE (CCDE) and propose a new adaptive DE by adjusting the subcomponent crossover rate named CRsADE. We have conducted experiments on waveform inversion to test the performance of the proposed algorithm. The results show that CRsADE performs better than CCDE significantly both on convergence speed and accuracy. In order to estimate the validity of CRsADE, we have also applied it to real seismic data.

In this letter, a new differential evolution (DE) algorithm is proposed and applied to waveform inversion. The traditional evolution strategy of this algorithm is not efficient because it treats the individuals in a population equally and evolves all of them in each generation. In order to overcome this shortcoming, we propose a new population evolution strategy (PES) to decrease the population size based on the differences among individuals during an evolution process. We embed the new strategy into the cooperative coevolutionary DE (CCDE) and obtain a new highly efficient DE (HEDE). We apply this new algorithm to waveform inversion experiments of both synthetic and real seismic data to test its performance and demonstrate its validity. The results have clearly shown that, under the same inversion precision, the HEDE can reduce the runtime by about 50% compared with the CCDE.