The concept of neural network (NN)-based seismic resolution enhancement has gained a lot of traction recently. Yet, the majority of works on the topic rely on training NNs on synthetic data via a supervised learning strategy, often encountering generalization issues on real data. To address this problem, we develop a self-supervised learning (SSL) method for seismic resolution enhancement. Specifically, we reinterpret seismic resolution enhancement as a frequency extension task, particularly focusing on the reconstruction of high-frequency components. Initially, we warm up the NN using the original/available band-limited data as pseudolabels, with input data derived from filtering out high-frequency elements from the data. Subsequently, the network undergoes iterative data refinement (IDR), where pseudolabels are predicted from the NN trained in the previous epoch, and input data are obtained by filtering out high-frequency components from these predictions. Based on this strategy, we also present a hybrid framework for simultaneous seismic denoising and resolution enhancement. During the whole training, we used multiloss constraints to enhance the network performance. The efficacy of our method is demonstrated through tests on both synthetic and field data.

Accurate separation of P- and S-waves is essential for multi-component seismic data processing, as it helps eliminate interference between wave modes during imaging or inversion, which leads to high-accuracy results. Traditional methods for separating P- and S-waves rely on the Christoffel equation to compute the polarization direction of the waves in the wavenumber domain, which is computationally expensive. Although machine learning has been employed to improve the computational efficiency of the separation process, most methods still require supervised learning with labeled data, which is often unavailable for field data. To address this limitation, we propose a wavefield separation technique based on Physics-Informed Neural Networks (PINNs), which leverage automatic differentiation to compute partial derivatives. We formulate the P- and S-wave separation equations as loss functions to train a neural network that learns functional solutions to these equations. The network takes spatial coordinates as input and outputs the corresponding separated P- and S-wavefields. Once trained, it enables near-instantaneous evaluation of the separated wavefields at any spatial location. This unsupervised machine learning approach is applicable to unlabeled data. Numerical tests demonstrate that the proposed PINN-based separation method can accurately separate P- and S-waves in both homogeneous and heterogeneous media.

Full waveform inversion (FWI) plays an important role in velocity modeling due to its high-resolution advantages. However, its highly non-linear characteristic leads to numerous local minimums, which is known as the cycle-skipping problem. Therefore, effectively addressing the cycle-skipping issue is crucial to the success of FWI. Well-log data contain rich information about subsurface medium parameters, providing inherent advantages for velocity modeling. Traditional well-log data interpolation methods to build velocity models have limited accuracy and poor adaptability to complex geological structures. We propose a well interpolation algorithm based on a generative diffusion model (GDM) to create initial models for FWI, trying to address the cycle-skipping problem. By integrating well-log data, migration images to encode physics-based geological priors in the velocity-model building process, our approach can provide much more detailed information of the faults and stratigraphic features. Numerical experiments demonstrate that the method produces accurate and reliable initial models. Compared to the conventional purely data-driven methods, our approach significantly enhances FWI performance and effectively mitigates the cycle-skipping issues.

Traditional supervised denoising networks learn network weights through “black box” (pixel-oriented) training, which requires clean training labels. The inability of such denoising networks to interpret their behavior and the requirement for clean data as labels limit their applicability in real-case scenarios. Deep unfolding methods unroll an optimization process into Deep Neural Networks (DNNs), improving the interpretability of networks. Also, modifiable filters in DNNs allow us to embed the prior information of the desired signals to be extracted, in order to remove noise in a self-supervised manner. Thus, we propose a Gabor-based learnable sparse representation network to suppress different noise types in a self-supervised fashion through constraints/bounds applied to the parameters of the Gabor filters of the network during the training stage. The effectiveness of the proposed method is demonstrated on two noise type examples, pseudo-random noise and ground roll, on synthetic and real data.

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions and cannot effectively assess uncertainty, making it hard to evaluate the reliability of their processed results. To address these issues, we propose a new method using a generative diffusion model (GDM). Here, in the training phase, we use the imaging results from sparse data as conditional input, combined with noisy versions of dense data imaging results, for the network to predict the added noise. After training, the network can predict the imaging results for test images from sparse data acquisition, using the generative process with conditional control. This GDM not only improves image quality and removes artifacts caused by sparse data but also naturally evaluates uncertainty by leveraging the probabilistic nature of the GDM. To overcome the decline in generation quality and the memory burden of large-scale images, we develop a patch fusion strategy that effectively addresses these issues. Synthetic and field data examples demonstrate that our method significantly enhances imaging quality and provides effective uncertainty quantification.

The ocean bottom node (OBN) seismic acquisition system is designed to gather high-fidelity, wide-azimuth, and long-offset four-component (4C) data, which includes shear waves and enables the use of the elastic assumption in imaging and inversion. However, deploying geophysical instruments on the seafloor is difficult and costly, leading to the usual adoption of sparse node spacing. This can, however, lead to poor illumination and imaging challenges, especially in the shallow subsurface near the seafloor. To address these issues in the context of 4C elastic imaging, we propose a deep learning-based method using a multi-scale convolutional neural network (Ms-CNN) to improve the imaging quality of OBN surveys with sparse data acquisition. As an alternative to interpolating the sparse seismic data in the data domain, which can be a challenging task due to the limitations attributed to sampling theorem and the often larger amounts of data compared to the image, we train an Ms-CNN in a supervised fashion to map from sparse data images of PP and PS sections produced by 4C Gaussian beam migration to the equivalent dense data images, allowing for the direct processing of sparse data to improve imaging quality. Here, we combine the mean absolute error and multiscale structure similarity index measure in the loss function to optimize the network’s training process, and to help improve the performance. The effectiveness of the method is demonstrated through experiments on synthetic and field data, resulting in improved event continuity and reduced noise in migration results from sparse OBN acquisitions.

The pseudoacoustic approximations are commonly used for migration and inversion in transversely isotropic (TI) media, as they accurately characterize the P-wave propagation and are simpler than their elastic counterparts, resulting in computational savings. This article is devoted to presenting an approach for generalized Radon transform (GRT) migration and inversion in acoustic TI media with a tilted symmetry axis (TTI). In parameterizing an acoustic TTI medium with the P-wave normal move-out (NMO) velocity$v_{n}$, Thomsen’s parameter$\delta $, and anelliptic parameter$\eta $, a concise single-scattering integral for NMO pressure is obtained by perturbing the TTI medium from a background nonelliptically anisotropic medium. It results in explicitly representing the perturbation scattering patterns of each parameter ($v_{n}$,$\delta $, and$\eta $), helping us understand the scattering angular influence of the perturbed parameters. The application of GRT on this scattering integral allows a direct construction of the acoustic TTI inversion operator. Numerical examples verify the effectiveness of the proposed acoustic TTI GRT inversion method and show its considerably good performance in the presence of steeply dipping anisotropic layering.

Current data-driven inversion methods based on deep learning (DL) use an end-to-end learning to obtain a mapping relationship from seismic data to the velocity model. This method requires truncating the feature maps in the output layer of the network to build the velocity model with a specified size. Therefore, it lacks the flexibility of handling output velocity models of different sizes, as the network needs to be retrained to achieve reliable results when changing the desired size of the velocity model. Here, to solve the problem of data-driven velocity inversion with variable size output, a novel sampling matrix is proposed to compress the seismic data to the same size as the model to avoid clipping the feature maps. The compressed seismic data is fed into the designed deep convolutional neural network (CNN) model for training. Here, the network has a multi-scale encoder-decoder structure and is composed of several residual blocks. Also, the multi-objective loss functions balance strategy is used to optimize the training process. Utilizing the trained network to test compressed synthetic seismic data of various sizes, the effectiveness of the proposed method for inversion of variable-size elastic wave velocity models is verified.

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.

Although the pseudoacoustic wave equation has good accuracy in characterizing anisotropic wave propagation and obtaining interpretable seismic images, a high-precision multiparameter inversion accounting for anisotropy from compressional wavefields is still confronted with challenges, even in the simple transversely isotropic (TI) case, due to the complicated relationship between anisotropic properties and pressure data. To reduce difficulty in correctly inverting surface compressional data in anisotropic media, an appropriate parameterization for inversion is necessary. For acoustic TI media with a tilted symmetry axis (TTI), we describe the pseudoacoustic TTI equations with the P-wave normal moveout velocity$v_{n}$and anisotropic parameters$\eta $and$\delta $, and aim to invert this parameterization by the scattering integral method. Using the perturbation theory in formulating the integral solution of the singly scattered pressure wavefield allows to acquire a scattering radiation pattern that explicitly illustrates the angular effect (including migration dip and scattering angles) of the TTI perturbation parameters, in which perturbations, whether in the wavefield or anisotropic parameters, are from the elliptical anisotropic background medium. Taking advantage of a ray-theoretical approximation to the background Green’s function, we can establish a relationship between the scattering integral and a form of TTI generalized Radon transform (GRT). As a result, we develop an acoustic TTI pseudoinverse GRT operator for estimating the corresponding perturbation parameters. Numerical tests on two simple models and a part of the BP 2007 anisotropic benchmark model verify the effectiveness of the presented acoustic TTI GRT inversion/migration method and show its evident advantages over the conventional acoustic isotropic and TI with a vertical symmetry axis (VTI) approaches.

In anisotropic media, the compressional wave scattering phenomena is governed by several parameters and can be simulated using a good kinematic approximation. How to retrieve anisotropic properties from recorded seismic data free of shear waves for exploration geophysics is interesting and challenging. We present an approach to infer the material properties in acoustic transversely isotropic (TI) media with a vertical axis of symmetry (VTI) described by a combination of the normal-moveout velocity$v_{n}$and anisotropic parameters$\eta $and$\delta $. The method we consider is based on the true-amplitude generalized Radon transform (GRT) inversion strategy. Because the scattering integral is at the kernel of the inversion engine, we start our investigation from a fourth-order pseudo-acoustic VTI equation instead of the conventionally coupled system of second-order wave equations. With the single-scattering approximation and high-frequency asymptotic analysis, the integral representation of P-wave scattered wavefield is incorporated into a weighted GRT operator that contains VTI scattering patterns of each parameter perturbation, which leads the way in constructing an acoustic VTI amplitude-preserving GRT pseudo-inverse operator. We describe an appropriate survey design by shooting a fan of rays from the target area toward the acquisition system, which is necessary when calculating the pseudo-inverse operator. Numerical test results from 2-D synthetic data verify the effectiveness of our method.