Reflection seismic waveform tomography of physical modelling data

Velocity anisotropy caused by fine layering has a strong effect on the travel paths at large vertical offsets in crosshole seismic data. This effect must be considered in seismic waveform tomography, so that the inversion procedure can match the waveforms in real data. In this paper, we propose to properly take into account this anisotropic effect in two stages. First, we invert for the anisotropy parameter simultaneously with the (horizontal) velocity in travel time tomography. Then we incorporate this estimated anisotropy parameter model in the waveform simulation during waveform tomography, to refine the velocity image. When considering this anisotropic effect, far-offset data are properly used in the inversion, then both travel time and waveform tomography may have a better ray coverage, producing a velocity image with a higher resolution.

Generation of synthetic full-scale burst test data for corroded pipelines using the tabular generative adversarial network

The structure and evolution of the lithosphere and underlying mantle control tectonics, magmatism, and natural resource development and distribution. Seismic tomography offers essential information on mantle temperature, the thickness and strength of the lithosphere, and the convection below it. Here, we report on the completion of a series of continent- and plate-scale waveform tomography studies using the automated multimode inversion of surface and S-wave waveforms. Together, the models cover all of the Earth’s continents and their surroundings and reveal a fascinating diversity of structures, while also indicating common mechanisms of lithospheric dynamics and evolution. Each model used global data coverage that was maximised witin the hemisphere centred at the continent. Structural information was extracted from Rayleigh waves and S and multiple S waves on over a million vertical-component-seismogram waveform fits. The effects of errors were minimised by statistical and targeted outlier analyses and the removal of the least mutually consistent data. The models advance the resolution of the imaging compared to the state of the art at the scale of the continents.Cratonic lithosphere on all continents shows complexities and fragmentation. The lithosphere beneath most diamondiferous kimberlites—originally emplaced on thick cratonic lithosphere—is still thick at present. Relatively low seismic velocities at kimberlite locations are indicative of craton-lithosphere thinning and are detected at multiple locations in all continents with known kimberlites. Cenozoic basalts are found exclusively where the lithosphere is observed to be thin. Beneath some of the volcanic regions, low-velocity anomalies extend deep into the mantle, consistent with deep-mantle upwellings feeding the magmatism. Sediment-hosted metal deposits tend to be located near contrasts in the thickness of the lithosphere, including both craton boundaries and other substantial heterogeneities. Intraplate seismicity is controlled by plate-boundary stresses and by the lateral variations of the lithospheric thickness and strength. Areas with relatively thin lithosphere localise deformation and seismicity, provided that sufficient tectonic stress is transmitted into the plate interior.ReferencesChagas de Melo, B, Lebedev, S, Celli, NL, et al., 2025. The lithosphere of South America from seismic tomography: Structure, evolution, and control on tectonics and magmatism, Gondwana Research, GR Focus - Invited Review, 138, 139–167. doi:10.1016/j.gr.2024.10.012.Chua, EL, Lebedev, S. Waveform tomography of the Antarctic Plate, Geophysical Journal International, submitted.Celli, NL, Lebedev, S, Schaeffer, AJ, Gaina, C, 2021. The tilted Iceland Plume and its effect on the North Atlantic evolution and magmatism, Earth and Planetary Science Letters 569, doi:10.1016/j.epsl.2021.117048.Celli, NL, Lebedev, S, Schaeffer, AJ, et al., 2020. The upper mantle beneath the South Atlantic Ocean, South America and Africa from waveform tomography with massive data sets, Geophysical Journal International 221, 178–204. doi:10.1093/gji/ggz574.de Laat, JI, Lebedev, S, Celli, NL, et al., 2023. Structure and evolution of the Australian plate and underlying upper mantle from waveform tomography with massive data sets, Geophysical Journal International 234, 153–189. doi:10.1093/gji/ggad062Dou, H, Xu, Y, Lebedev, S, et al., 2024. The upper mantle beneath Asia from seismic tomography, with inferences for the mechanisms of tectonics, seismicity, and magmatism, Earth-Science Reviews, 255, doi:10.1016/j.earscirev.2024.10484

Modern global seismic waveform tomography is formulated as a PDE-constrained nonlinear optimization problem, where the optimization variables are Earth's visco-elastic parameters. This particular problem has several defining characteristics. First, the solution to the forward problem, which involves the numerical solution of the elastic wave equation over continental to global scales, is computationally expensive. Second, the determinedness of the inverse problem varies dramatically as a function of data coverage. This is chiefly due to the uneven distribution of earthquake sources and seismometers, which in turn results in an uneven sampling of the parameter space. Third, the seismic wavefield depends nonlinearly on the Earth's structure. Sections of a seismogram which are close in time may be sensitive to structure greatly separated in space.In addition to these theoretical difficulties, the seismic imaging community faces additional issues which are common across HPC applications. These include the storage of massive checkpoint files, the recovery from generic system failures, and the management of complex workflows, among others. While the community has access to solvers which can harness modern heterogeneous computing architectures, the computational bottleneck has fallen to these memory- and manpower-bounded issues.We present a two-tiered solution to the above problems. To deal with the problems relating to computational expense, data coverage, and the increasing nonlinearity of waveform tomography with scale, we present the Collaborative Seismic Earth Model (CSEM). This model, and its associated framework, takes an open-source approach to global-scale seismic inversion. Instead of attempting to monolithically invert all available seismic data, the CSEM approach focuses on the inversion of specific geographic subregions, and then consistently integrates these subregions via a common computational framework. To deal with the workflow and storage issues, we present a suite of workflow management software, along with a custom designed optimization and data compression library. It is the goal of this paper to synthesize these above concepts, originally developed in isolation, into components of an automatic global-scale seismic inversion.

ABSTRACTInterpolation techniques provide an effective method for recovery of missing traces. In recent years, many researchers have applied deep learning methods to seismic data interpolation. Generally, one can choose synthetic data as a training set; however, the features of synthetic data are always inconsistent with those of field data, which may lead to inaccurate interpolation. Meanwhile, U‐Net is a common network structure used in seismic data interpolation; however, the four downsampling and upsampling structures of U‐Net have limited adaptability for different data. In this study, the deep learning method based on U‐Net++ was proposed for seismic data interpolation, which contains U‐Net with different depths. The different depths were connected by skip pathways, and the best depth of the network was chosen for different seismic data by deep supervision. Furthermore, a new strategy for training sets was designed: frequency‐wavenumber (f‐k) bandpass filters were used to convert natural images into a natural seismic training set, which has a stronger generalization capability than synthetic data as the training set. The characteristics of the new training set can effectively improve the accuracy of missing data reconstruction. Compared with the conventional U‐Net and traditional interpolation techniques, for example, the Fourier Bregman method, the proposed method produces more accurate and reasonable interpolation results. Further, it can reconstruct both irregular and regular missing seismic data, even in the presence of strong random noise and aliasing. Synthetic and field data tests showed the effectiveness, robustness and generalization of the proposed method.

This study presents a parameter optimization strategy for generating synthetic seismic data that closely match the characteristics of target field data, aiming to improve deep learning-based fault detection. An analysis in the latent space is conducted to assess the similarities between synthetic data and target field data. Based on the results from this analysis, we optimize the parameters for generating synthetic data. Further refinement of the data generation process is achieved through the application of Explainable Artificial Intelligence (XAI). The fault interpretation results using the U-Net model trained on optimized synthetic data show significant improvements compared to those from the model trained on unoptimized data. The optimization strategy employed allows for the visualization of feature distributions in the latent space, offering a direct understanding of how the distribution of features shifts depending on the desired parameters. This approach not only circumvents the limitations associated with using field data for training, such as the challenge of acquiring accurate fault structure labels and the scarcity of sufficient training data, but also overcomes the potential discrepancies in interpretation results due to significant deviations in the characteristics of synthetic data from the target field data. The proposed optimization framework improves the performance of deep learning models in fault interpretation and establishes an advanced approach for using synthetic data in deep learning–based seismic interpretation.

Deconvolution is an essential step in seismic data processing. Sparse-spike deconvolution often is used to enhance the resolution of the seismic image by adding a model-driven regularization term. However, this method does not consider the features of the data, nor does it exactly describe the relationship between seismic data and the desired attribute (such as seismic reflectivity). We have developed a data and model dual-driven seismic deconvolution method based on error-constrained joint sparse representation (SR) using borehole measurement and surface seismic data. The combined features of the borehole reflectivity and the surface seismic data can be obtained through joint dictionary learning. With the help of the joint dictionary, the relationship between seismic waveforms and reflectivity is captured by the sparse coefficients. We construct the regularization term of deconvolution by alternately decomposing the error of the synthesized data via sparse reconstruction and the observed seismic data. Unlike model-driven methods, the constraint term of the new method can be established by the error-constrained SR. Based on this SR, the initial model of reflectivity is obtained to realize the sparse deconvolution of seismic data under the constraint of borehole data features. In general, this method is a data and model dual-driven deconvolution. Synthetic and field data tests demonstrate that this method can effectively improve the resolution and accuracy of deconvolution.

<p>Southeast Asia is one of the most complex tectonic regions on Earth. This is mainly a result of its location within the triple junction of the Australian, Eurasian and Philippine Sea plates which has created a complicated configuration of active plate tectonic boundaries. Adjoint waveform tomography is especially suitable for imaging such complex regions. By simulating the 3D wavefield, it is possible to directly compare observed and simulated seismograms, thereby taking into account both body and surface waves. The method can account for the effects of anisotropy, anelasticity, wavefront healing, interference and (de)focusing that can hamper other seismological methods.</p><p>To date, sparse instrument coverage in the region has contributed to a heterogeneous path coverage. In this project, we make use of publicly available data as well as our recently deployed networks of broadband seismometers on Borneo and Sulawesi. This, in addition to access to national permanent networks, provides data from over 300 stations which promises a significant improvement in data coverage around the Banda Arc, Borneo and Sulawesi. We employ a geographical weighting scheme to minimise the effect of dense regional arrays and compile a catalogue of 118 well-constrained earthquakes, optimising for coverage, signal-to-noise ratio and data availability. An optimised window selection algorithm allows us to balance amplitude differences and include as much signal as possible while avoiding noisy data.</p><p>Here, we present a seismic waveform tomography for upper mantle structure in Southeast Asia, imaging radially anisotropic S velocity, P velocity and density. We use a gradient-based optimisation scheme (L-BFGS) and adjoint methods to obtain sensitivity kernels as the corresponding gradients. In the first part of the inversion, periods down to 50 s are used to update a 1D initial model, adapting a multi-scale approach in which long periods are inverted for first to avoid cycle skipping. In our long-period results, we observe a strong regional low S-velocity structure with an underlying high-velocity anomaly. The results are consistent with the global <em>S40RTS</em> model. </p>

Conventional migration uses the seismic data set recorded at a given depth as one initial condition from which to implement wavefield extrapolation in the depth domain. In using only one initial condition to solve the second-order acoustic wave equation, some approximations are used, resulting in the limitation of imaging angles and inaccurate imaging amplitudes. We use an over/under bilayer sensor seismic data acquisition system that can provide the two initial conditions required to make the second-order acoustic wave equation solvable in the depth domain, and we develop a two-way wave equation depth migration algorithm by adopting concepts from one-way propagators, called bilayer sensor migration. In this new migration method, two-way wave depth extrapolation can be achieved with two one-way propagators by combining the wavefields at two different depths. It makes it possible to integrate the advantages of one-way migration methods into the bilayer sensor system. More detailed bilayer sensor migration methods are proposed to demonstrate the feasibility. In the impulse response tests, the propagating angle of the bilayer sensor migration method can reach up to 90°, which is superior to those of the corresponding one-way propagators. To test the performance, several migration methods are used to image the salt model, including the one-way generalized screen propagator, reverse time migration (RTM), and our bilayer sensor migration methods. Bilayer sensor migration methods are capable of imaging steeply dipping structures, unlike one-way propagators; meanwhile, bilayer sensor migration methods can greatly reduce the numbers of artifacts generated by salt multiples in RTM.

We describe the waveform tomographic inversion of seismic crosshole data from the Nimr field in Oman. Our initial ray-theoretical inversions of the traveltimes suggest a low level of P-wave anisotropy, as do our initial, longwavelength waveform inversion results. Higher resolution, 2-D waveform inversions that include this low level of background anisotropy are successful in predicting the observed data, but the velocity models are smoother than expected. Surprisingly, similar waveform inversions that do not include any anisotropy are also successful in modelling the observed data. These latter inversions yield velocity models with far stronger velocity contrasts in the thin layers recovered during the 2-D inversions. We conclude that the anisotropy is primarily layer-induced, and that when an isotropic approach is used a long-wavelength anisotropy is “created” during the inversion.

The resolution of seismic data determines the ability to characterize individual geological structures in a seismic image. Sparse spike inversion (SSI) is an effective approach for improving the resolution of seismic data. However, the basic assumption of SSI is that the strong reflectivity of the formation is sparse, which may not be a reasonable fit for weak thin-layer reflections. In this study, we propose a deep learning-based method to reconstruct high-resolution seismic data by combining information from the longitudinal reflectivity distribution and lateral geological structure features in the field data. A U-shaped network that fuses residual block and attention mechanism is used to learn the relationship between low resolution and high resolution. In addition, we use a hybrid loss function that combines <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\ell _{1}}$ </tex-math></inline-formula> loss and structural similarity (SSIM) loss to optimize the network parameters for better distinguishing the geometrical features characterized by structural amplitude changes. To train the network, we adopt a workflow to automatically generate numerous 2-D low-resolution data and their corresponding high-resolution data. In this workflow, the prior information, such as statistical reflectivity distribution of well logs and structural features of the data are considered. The synthetic data and field data tests show that our method can work well compared to the traditional method even though only a few well logs are available. Especially in the field data example, our method recovers thin layers better and yields laterally more consistent high-resolution results.

Deep learning (DL) applications of seismic reservoir characterization often require the generation of synthetic data to augment available sparse labeled data. An approach for generating synthetic training data consists of specifying probability distributions modeling prior geologic uncertainty on reservoir properties and forward modeling the seismic data. A prior falsification approach is critical to establish the consistency of the synthetic training data distribution with real seismic data. With the help of a real case study of facies classification with convolutional neural networks (CNNs) from an offshore deltaic reservoir, we have highlighted several practical nuances associated with training DL models on synthetic seismic data. We highlight the issue of overfitting of CNNs to the synthetic training data distribution and propose regularization strategies to address it. We demonstrate the efficacy of our proposed strategies by training the CNN on synthetic data and making robust predictions with real 3D partial stack seismic data.

Summary Deep learning have led to a certain extent breakthrough in seismic facies analysis(SFA). The greatest challenge in the SFA domain is how to cope with large seismic datasets and the limited amount of annotated samples, especially when employing supervised machine learning algorithms that require labelled data and larger training sample. we develop a supervised seismic facies analysis via an improved Auxiliary Classifier Generative Adversarial Network(ACGAN).To solve the problem of imbalanced seismic facies class distribution, and limited training data with labels, we used an improved ACGAN to generate synthetic seismic data sets, and then train Convolutional Neural Networks(CNN) using theses generated synthetic data. Fault data and seismic facies data test demonstrated that generated seismic data via the improved ACGAN can be used for synthetic data augmentation as for increased the performance of CNN and avoided overfitting compared to original seismic data training set. Therefore, we believe that the proposed method can effectively alleviate the problems of insufficient and imbalanced seismic data in SFA, and also can generalize to other seismic data classification applications.

Summary The seismic data spectral inversion method, arisen in recent years, can improve the resolution of seismic data for obtaining reservoir characteristics. It does not rely on prior information such as well-logging data. By using partial spectrum information from the input seismic trace data, a sparse reflectivity series can be inverted. The inverted reflectivity series can be used to improve the resolution and impedance inversion for thin layer reservoir prediction. In this paper, we implement seismic spectral inversion based on a compressed sensing algorithm, which can solve the ill-posed problem of the inversion process. In the process of inversion, we introduce a quadratic spectrum method to calculate the spectrum of seismic wavelet in the frequency domain, which can stabilize the inversion and handle real field data. Synthetic and real field seismic data examples show that the proposed spectral inversion based on compressed sensing algorithm is stable and effective. Moreover, the real field data inversion results show a good signal-to-noise ratio (SNR) and lateral continuity.

Historically, machine learning techniques and particularly neural networks have been applied in the domain of Geophysics to discern rock properties through a quantitative approach from seismic data and associated seismic attributes. However, the success or failure of neural network is dependent on amount of available data. In general, more labelled data during training of the neural network results in accurate predictions. Therefore, seismic based rock property prediction models and their calibration needs to be fed with labelled data coming from well logs in adequate amount. The fact that the number of wells are often limited can be a huge challenge in adopting neural networks predictions. Downton and Hampson (2019) developed a Hybrid Theory-guided Data Science (TGDS) technique to improve the training of the network by augmenting the amount of data used for training. This technique aims at overcoming the issue of scarcity of the well log data. By using the outputs of theory based components like Rock Physics theory as input to the data science component of augmenting the amount of the data. In this method, Rock Physics is applied to model the elastic response due to the changes in rock and fluid properties of the available well control to create a huge dataset of pseudo wells. Then, synthetic seismic gathers are modeled at the pseudo well locations to train a Deep Feed-Forwards Neural Network (DFNN). The parameters estimated during DFNN training with synthetic seismic gathers are then applied on a real seismic dataset. The final predicted P-impedance from this formerly described method was compared to conventional inverted Pre-Stack Elastic Inversion. This paper shows the application of the method of TGDS based synthetic seismic catalog generation followed by DFNN applied on real seismic dataset for a commercially oil producing field in North Sea. The reservoirs are injectite sands which are difficult to image but can be key pay zones with quite high porosity and permeability. Well log curves e.g. P-Impedance, Porosity and Water Saturation serve as guidelines to create the synthetic seismic data. Additionally, with the added advantage of increased synthetic data, pseudo wells were broken into training and validation datasets. So, the DFNN training is carried out on a portion of the training data subset. During the process of training the DFNN, the seismic data remains blind. The estimated DFNN non-linear operator is applied to the seismic data, however, it needs to be scaled to the real data as the training was performed on the synthetic seismic data. The final result of the data science and machine learning approach driven derived P-impedance showed higher frequency and better lateral continuity than the conventional theory based approach of Pre-Stack Elastic Inversion. Augmenting the amount of training data by generating synthetic data based on the statistics of from nearby well control and rock physics relationships is prime differentiator of this workflow. By using rock physics theory a large number of pseudo wells can be generated that gives a range of expected geologic scenarios. Key wells from nearby fields, that do not necessarily tie the seismic under consideration, can be incorporated into the analysis and also, if required additional wells could be incorporated into the analysis as drilled.