Geophysical data processing & interpretation, deep learning, image processing, computer vision & computer graphics, geological process modeling, subsurface modeling, geophysical inversion & interpolation, ...

Deep learning for characterizing CO2 migration in time-lapse seismic images

We propose a deep-learning-based method to efficient characterize CO2 plumes in time-lapse seismic data. We train the deep neural network by using synthetic datasets with simulated diffusive CO2 plumes that are various in geometric features (e.g., shapes, sizes, and locations) and physical properties (e.g., densities and velocities). We applied the trained network work to the Sleipner time-lapse seismic data and obtain reasonable CO2 plume predictions that are consistent with human interpretations. To more accurately characterize the CO2 plume migration, we use dynamic image warping to compute relative shifts that register the time-lapse seismic volumes before and after CO2 injection and then apply the same shifts to the predicted CO2 plumes. By doing this, we are able to reduce the inconsistencies that may be introduced by acquisition, processing, push-down effect (velocity decrease by injected CO2), and pull-up effect (wavelet distortion), which is helpful to more accurately characterize the CO2 plume migration.
Sheng, H., X. Wu*, X. Sun, and L. Wu, 2022, Deep learning for characterizing CO2 migration in time-lapse seismic images, submitted.

Stratal surfaces honoring seismic structures and interpreted geologic time surfaces

In basin and regional interpretations, the assumption that seismic horizons represent a stratigraphic surface with constant geologic time may fail, however, when applied to local reservoir scales due to seismic resolution, complex depositional facies transition, and an indented stack of depositional units. To address this limitation, we develop a novel horizon extraction method honoring both seismic structures and time-stratigraphic frameworks, in which seismic reflection structures provide local details and interpreted geologic-time surfaces provide critical constraints in interpreting these reflection events not following geologic surfaces. First, we develop concepts and workflow using a realistic outcrop model. We propose using the improved geology-guided structure tensor by fitting a gradient vector of seismic image and the geological time surfaces. We also consider existing geologic conditions, such as unconformity, and fuse them into calculating accurate slopes and generating reliable relative geologic time (RGT) images at a fine scale, followed by making slices.
Wang, F., X. Wu*, H. Zeng, X. Janson, and C. Kerans, 2022, Stratal surfaces honoring seismic structures and interpreted geologic time surfaces. Geophysics, submitted.

3D Implicit structural modeling with convolutional neural network

Given sparse structural data points, implicit structural modeling computes a scalar field by solving partial differential equations (PDEs) to implicitly represent structural information of the subsurface. However, the PDEs might be insufficient to model highly complex structures in practice and may fail to reasonably fit a global structure trend when the known data are too sparse. In addition, solving the PDEs with iterative optimization solvers could be computationally expensive in 3-D. We propose an efficient deep learning method using a convolution neural network to predict a scalar field from sparse structural data associated with multiple stratigraphic layers and faults. After training with synthetic datasets, our network is able to efficiently predict geologically reasonable and structurally consistent implicit models in field examples, opening new opportunities for improving the efficiency and accuracy of geological modeling.
Bi, Z., X. Wu*, Z. Li, D. Chang, and X. Yong, 2022, 3D Implicit structural modeling with convolutional neural network. Geoscientific Model Development (GMD), in press.

Filling borehole image gaps with partial convolution neural network

Due to the special design of borehole imaging tools, vertical strips of gaps often occur in borehole images. We propose a reasonable way to fill borehole image gaps through a convolutional neural network with partial convolution layers. The partial convolution helps eliminate the affects of the null data during the training by excluding the null-data areas from convolutional computations in the forward and backward propagation of updating the network parameters. To solve the problem of missing training labels, we introduce a self-supervised learning strategy to train the network to fill the image gaps from the image itself. We compare our method with a conventional method (implemented in the CIFLOG software) and two deep-learning based methods (DGP and DIP) by applying them to multiple real borehole images with various pattern features. Quantitative metrics show that our method is superior to the others.
Jiang, L., X. Si, and X. Wu*, 2022, Filling borehole image gaps with partial convolution neural network. Geophysics, submitted.

Automatic velocity analysis with physics-constrained optimal surface picking

We propose a constrained optimal surface picking method to automatically pick a 2D velocity field from a 3D semblance volume with high efficiency and robustness. This method is improved from the 2D dynamic programming algorithm by incorporating both vertically physical constraints in the time direction and laterally smoothness constraints in the common midpoint (CMP) direction. The time-direction physical constraint ensures the picked velocity is positive when converted to interval velocity, which is helpful to avoid picking physically unreasonable velocities along the strong and spatially consistent semblance energy due to consistent noise or multiples (as shown in the left Fig. b). The CMP-direction smoothness constraint ensures the picked 2D velocity field is laterally continuous.
Xue, Z. and X. Wu*, 2022, Automatic velocity analysis with physics-constrained optimal surface picking. Geophysics, submitted.

Unsupervised contrastive learning for seismic facies characterization

We propose to leverage a one-stage and end-to-end contrastive learning framework without any manual labels to automatically analyze seismic facies. To improve lateral consistency, we input 3D seismic cubes, instead of traces, into the neural network. Besides, we treat seismic attributes as geologic constraints and feed them into the network along with the seismic cubes. Our contrastive learning method is used to maximize the similarities of the different cubes from the same position, and minimize the similarities of the cubes from different positions. In this way, we are able to enforce the samples with similar features to get close while push the samples with different features to be separated in the space where we make the seismic facies clustering. We apply this method to a field turbidite channel system and obtain a continuous and reasonable facies map.
Li, J., X. Wu*, Y. Ye, C. Yang, Z. Hu, X. Sun, and T. Zhao, 2022, Unsupervised contrastive learning for seismic facies characterization, Geophysics, Vol. 88(1), in press.

Deep learning for realtime detection of submarine cables in sonar images

毕钲发, 刘杨, 伍新明*, 吴丽丽, 2022, 基于声呐图像的海底线缆智能实时探测 (Deep learning for realtime detection of submarine cables in sonar images), 地球物理学报, 已投稿。

Deep learning for efficient microseismic location using source migration-based imaging

Migration-based location methods (e.g., time reversal imaging based on wave equation, Kirchhoff summation and diffraction stacking) are widely used to effectively locate events of low signal to noise ratios by stacking waveforms from many receivers. However, these methods may not produce accurate results if there are polarity reversals in the surface records for a double-couple or even a general moment tensor event. We propose a deep convolutional neural network to predict a better-focused image from a regular migration image that contains a quasi symmetric pattern in both space and time.
Zhang, Q., W. Zhang*, X. Wu*, J. Zhang, W. Kuang, and X. Si, 2021, Deep Learning for efficient microseismic location using source migration-based imaging. JGR, Solid Earth, 127(3), e2021JB022649. [PDF].

Toward accurate seismic flattening

Seismic flattening maps a seismic volume from the original space in depth to the Wheeler domain in geologic time where all the seismic reflections are horizontally aligned. It provides an efficient way to interpret a whole volume of horizons all at once by simply extracting horizontal slices in the flattened space. Conventional flattening methods, based on seismic local slopes, can locally flatten the seismic reflections, however, often fail to flatten the reflections in a global sense and cannot accurately align the reflections across faults. We propose an iterative method to improve the flattening by using both slopes and correlations of seismic traces.
Wu X.*, Y. Li, and P. Sawasdee, 2022, Toward accurate seismic flattening: methods and applications. Geophysics, Geophysics, Vol. 87(5), IM177–IM188. [PDF].

Seismic structural interpretation and modeling

We present a workflow to fully utilize seismic amplitudes, well-log properties, and interpreted seismic structures to build geologically reasonable models. We first automatically interpret structural features (e.g., faults and horizons) from a 3D seismic image. We then use the interpreted structural features to compute an implicit structural model. We further integrate the provided well-logs and the computed implicit structural model to interpolate a subsurface model that conforms to both well-log properties and seismic structural and stratigraphic features. Finally, we predict a final model with deep learning using seismic and well-log data and meanwhile introduce the initial model as low-frequency constraints into the network.
Yan, S., X. Sun, X. Wu*, S. Zhang, and H. Si, 2021, Building subsurface models with horizon-guided interpolation and deep learning: applied to the Volve field. Geophysics, Vol. 87(4), B233–B245. [PDF].

Semi-supervised salt segmentation using mean teacher
Mean teacher 半监督学习与盐丘分割

We propose a semi-supervised framework for salt segmentation, which requires only a small amount of labeled data. We adopt the mean teacher in our semi-supervised method where two models sharing the same network architecture are trained together. The student model is optimized using a combination of supervised loss and unsupervised consistent loss, whereas the teacher model is the exponential moving average (EMA) of the student model. An unsupervised consistent loss is introduced to better extract information from unlabeled data by constraining the network to give consistent predictions for the input data and its perturbed version. We train and validate our novel semi-supervised method on both synthetic and real dataset. Results demonstrate that our proposed semi-supervised salt segmentation method outperforms the supervised method when there is a lack of labeled training data.
Geng, Z., Z. Hu, X. Wu*, and S. Fomel 2021, Semi-supervised salt segmentation using mean teacher. Interpretation, Vol. 10(3), SE21-SE29. [PDF].

Deep learning for velocity model building with common-image gathers

The features in the inaccurate common-image gathers (a) migrated from a wrong velocity model (b) are significantly different from those in the accurate gathers (c) migrated from a true velocity model. This means that the residuals of the inaccurate gathers indicate the residuals of the velocity model compared to the true velocity model. We therefore use a deep CNN to analyze the features of inaccurate image gathers to update the initially wrong migration velocity model and obtain a more accurate model (d).
Geng, Z., Z. Zhao, Y. Shi, X. Wu, S. Fomel, and M. Sen, 2022, Deep learning for velocity model building with common-image gathers. GJI, 228, 1054–1070. [PDF].

A comparison of deep learning methods for seismic impedance inversion

We experimentally reveal how network hyperparameters (number of features, kernel sizes, number of layers) and architectures affect the seismic inversion performance, and develop a series of methods which are proven to be effective in reconstructing high-frequency information in the estimated impedance model. Experiments demonstrate that the proposed multi-scale architecture is helpful to reconstruct more high-frequency details than a conventional network. Besides, the reconstruction of high-frequency information can be further promoted by introducing a perceptual loss and a generative adversarial network from the computer vision perspective. More importantly, the experimental results provide valuable references for designing proper network architectures in the seismic inversion problem.
Zhang, S., H. Si, X. Wu*, and S. Yan, 2021, A comparison of deep learning methods for seismic impedance inversion. Petroleum Science, Vol. 19(3), 1019-1030. [PDF].

Deep learning for multi-dimensional seismic impedance inversion

Most methods of deep-learning based impedance inversion are based on a 1D neural network which is straightforward to implement but often yields laterally unreasonable discontinuities in predicting a multi-dimensional impedance model trace-by-trace. We improve the deep learning based impedance prediction by implementing it with a multi-dimensional CNN. Synthetic and field examples show that the proposed multi-dimensional CNN is more robust to noise, better recovers thin layers, and yields a laterally more consistent impedance model than a 1D CNN with the same network architecture and the same training logs.
Wu, X., S. Yan, Z. Bi, S. Zhang, and H. Si, 2021, Deep learning for multi-dimensional seismic impedance inversion. Geophysics, Vol. 86(5), R735–R745. [PDF].

Kernel prediction network for common image gather stacking

In the pre-stack depth migration, obtaining a high-quality seismic image requires an accurate CIG where the diffractions are focused, the reflection events are flat and the depth of the events are correctly migrated. In practice, such an accurate CIG, however, is hard to obtain due to the errors of acquisition, processing, and the migration velocity model. We propose a kernel prediction neural network (KPN) to flatten the events, correct the depth of the improperly migrated events, and remove the noise and unfocused artifacts in CIGs (lower-left image), and further yield an optimally stacked image (lower-right image).

Li, Z., X. Wu*, L. Liang, X. Jia, and W. Jiang, 2020, Kernel prediction network for common image gather stacking . SEG, accepted, Geophysics, in submission.

Deep learning for simultaneous seismic super-resolution and denoising

This work is done by Jintao Li (李金涛), a senior college student at University of Science and Technology of China. He is joining CIG in Fall, 2020.

We propose a deep learning method to simultaneously improve the resolution of an input seismic image (a) and attenuate potential noise in the seismic, which allows us to obtain an output (b) with clearer and more detailed features (e.g., thin layers and sharp faults with small throws).

Li, J., X. Wu* and Z. Hu, 2021, Deep learning for simultaneous seismic super-resolution and denoising. IEEE TGRS, Vol. 60, pp. 1-11, [PDF]. [CODE].

Wavelet estimation and non-stretching NMO correction

This work is done by Hanlin (绳瀚林), a senior college student at University of Science and Technology of China. He is joining CIG in Fall, 2020.

We propose a workflow (left image) for wavelet estimation and non-stretching NMO correction. In this workflow, we first estimate a wavelet based on the waveform stretching in the NMO correction. Secondly, we deconvolve the original CMP gather based on the estimated wavelet. Thirdly, we apply an improved NMO correction to the deconvolved CMP gather and obtain flattened reflectivities. We finally convolve the flattened and deconvolved gather with the estimated wavelet back to obtain a NMO-corrected gather without stretching artifacts.
Sheng, H., X. Wu* and B. Zhang, 2022, Wavelet estimation and NMO correction. Geophysics, Vol. 87(3), V193–V203. [PDF].

Channel simulation and deep learning for channel interpretation in 3D seismic images

This work is done by Hang Gao (高航), a senior college student at China University of Geosciences (Beijing). He is joining CIG in Fall, 2020.

In this work, we propose a workflow to first numerically simulate meandering channel systems which are then integrated with folding structures to build realistic structural models. With such models, we are able to automatically generate numerous training seismic images and the corresponding channel labels. We consider the channel characterization in 3D seismic images as an image segmentation problem and design a 3D convolutional neural network (CNN) for the channel segmentation. We train the CNN by using synthetic datasets that are generated by using the proposed simulation workflow. The trained CNN works well to detect the meandering channel systems in field seismic images.
Gao, H., X. Wu* and G. Liu, 2021, ChannelSeg3D: channel simulation and deep learning for channel interpretation in 3D seismic images. Geophysics, Vol. 86(4), IM73–IM83. [PDF]. [CODE].

Deep learning for paleokarst delineation

This is a great collaboration with international researchers including Dr. Jie Qi from University of Oklahoma and Dr. Hongliu Zeng from the Bureau of Economic Geology.
In this work, we propose a workflow to simulate realistic structural features of folding and paleokarst systems in 3D seismic images. We consider the paleokarst delineation in 3D seismic images as an image segmentation problem and design a deep convolutional neural network (CNN) for the paleokarst segmentation. We train the CNN by using synthetic datasets that are generated by using the proposed simulation workflow. The trained CNN works well to detect the paleokarst features in field seismic images (a) by computing a probability image (b), from which we are able to automatically extract the 3D paleokarst systems (c).
Wu, X., S. Yan, J. Qi, and H. Zeng, 2020, Seismic simulation of paleokarst systems and deep learning for characterizing paleokarst features in 3D seismic images. JGR, Solid Earth, Vol. 125(9), 1-23, e2020JB019685. [PDF]

Numerical modeling of channels

In order to understand the development of the channel systems, we have been working on the numerical simulation of meandering and delta channels. The cartoons on the left are Hang Gao's research with CIG. Hang Gao is currently a senior at China University of Geosciences (Beijing). He is joining CIG as a graduate student in the Fall of 2020.
updated on Dec. 8th, 2019...

Multi-task learning for seismic image processing

We design a single convolutional neural network to simultaneously perform three image processing tasks:
  • compute a clean and sharp fault image
  • estimate a seismic normal vector field
  • compute a smoothed seismic image with enhanced reflections and sharpened faults while noise removed
  • Wu, X., L. Liang, Y. Shi, Z. Geng and S. Fomel, 2019, Multi-task learning for local seismic image processing: fault detection, structure-oriented smoothing with edge-preserving, and seismic normal estimation by using a single CNN. GJI, Vol. 210(3), 2097-2109. [PDF]

    Building realistic structure models

    We propose a workflow to automatically build diverse structure models with realistic folding and faulting features. In this workflow, with some assumptions about typical folding and faulting patterns, we simulate structural features in a 3D model by using a set of parameters. By randomly choosing the parameters from some predefined ranges, we are able to automatically generate numerous structure models with realistic and diverse structural features. Based on these structure models with known structural information, we further automatically create numerous synthetic seismic images and the corresponding ground truth of structural labels to train CNNs for structural interpretation in field seismic images. Accurate results of structural interpretation in multiple field seismic images show that the proposed workflow simulates realistic and generalized structure models from which the CNNs effectively learn to recognize real structures in field images.
    Wu, X., Z. Geng, Y. Shi, N. Pham, S. Fomel, and G. Caumon, 2019, Building realistic structure models to train convolutional neural networks for seismic structural interpretation. Geophysics, Vol. 85(4), WA27-WA39. [PDF]

    Deep learning flood-filling network

    We design a deep learning workflow to interactively track seismic geobodies, such as salt bodies and faults. The algorithm is based on a flood-filling network, which performs iterative segmentation and moving the field of view (FoV). Instead of an end-to-end segmentation from the image to the classification mask, the proposed network takes the previous mask output, together with the seismic image in a new FoV, as a combined input to predict the mask at this FoV. The movement of the FoV is guided by the flood-filling algorithm in order to visit and segment the full extent of a geobody. Unlike the conventional seismic image segmentation methods that can only output attribute volumes, the proposed workflow can not only detect geobodies but also track individual geobody instances.
    Shi, Y. and X. Wu*, 2019, Interactive tracking of seismic geobodies using deep learning flood-filling network. Geophysics, Vol. 86(1), A1-A5. [PDF]

    Forward simulation of geologic process

    We have been working on forward numerical simulation of various geologic processes, which would be helpful for our geologic understanding or interpretation of geophysical datasets. This cartoon shows a simple implementation of 2D stratigraphic modeling.

    Deep learning for estimating RGT and horizons

    Constructing a Relative Geologic Time (RGT) image from a seismic image is crucial for seismic structural and stratigraphic interpretation. In conventional methods, automatic RGT estimation from a seismic image is typically based on only local image features, which makes discontinuous structures (e.g., faults and unconformities) challenging to cope with. We consider the estimation of 2D RGT images as a regression problem, where we design a deep convolutional neural network (CNN) to directly and automatically compute an RGT image from a 2D seismic image. This CNN consists of three parts: an encoder, a decoder and a refinement module. We train this CNN by using 2080 pairs of synthetic input seismic images and target RGT images and then test it on 960 testing seismic images. Although trained with only synthetic images, the network can generate accurate results on real seismic images. Multiple field examples show that our CNN-based method is significantly superior to conventional methods, especially in dealing with complex structures such as crossing faults and complicatedly folded horizons, without the need of any manual picking.
    Geng, Z., X. Wu*, Y. Shi, S. Fomel, 2019, Deep learning for relative geologic time and seismic horizons. Geophysics, Vol. 85(4), WA87–WA100. [PDF].

    Waveform embedding with unsupervised deep learning

    We propose an unsupervised approach, Waveform Embedding, based on a deep convolutional autoencoder network to learn to transform seismic waveform samples to a latent space in which any waveform can be represented as an embedded vector. The regularizing mechanism of the autoencoder ensures that similar waveform patterns are mapped to embedded vectors with shorter distance in the latent space. Within a search region, we transform all the waveform samples to latent space and compute their corresponding distance to the embedded vector of a control point that is set to the target horizon; we then convert the distance to a horizon probability map that highlights where the horizon is likely to be located. labels.
    Shi, Y., X. Wu*, and S. Fomel, 2020, Waveform embedding: automatic horizon picking with unsupervised deep learning. Geophysics, Vol. 85(4), WA67–WA76. [PDF].

    Convolutional long short-term memory network

    We propose a method to estimate missing well logs by using a bidirectional convolutional long short-term memory (bidirectional ConvLSTM) cascaded with fully connected neural networks (FCNNs). We train the model on 177 wells from mature areas of the UK continental shelf (UKCS). We test the trained model on one blind well from UKCS, three wells from the Volve field in the Norwegian continental shelf (NCS), and one well from the Penobscot field in the Scotian shelf offshore Canada. The method takes into account the depth trend and the local shape of logs by using LSTM and convolutional architecture. The method is examined on sonic log prediction and can produce an accurate prediction of sonic logs from gamma-ray and density logs. The advantages of our method are that it is not applied on an interval by interval basis like rock physics based methods and it also outputs the uncertainties facilitated by a dropout layer and Monte-Carlo sampling at inference time.
    Pham, N., X. Wu*, and E. Naeini, 2020, Missing well log prediction using convolutional long short-term memory network. Geophysics, Vol. 85(4), WA159–WA171. [PDF].

    FaultSeg3D: Using synthetic data sets to train a CNN for 3D seismic fault segmentation

    We consider fault detection as a binary image segmentation problem of labeling a 3D seismic image with ones on faults and zeros else- where. We have performed an efficient image-to-image fault segmentation using a supervised fully convolutional neural network. To train the network, we automatically create 200 3D synthetic seismic images and corresponding binary fault labeling images, which are shown to be sufficient to train a good fault segmentation network. After training with only the synthetic data sets, the network automatically learns to calculate rich and proper features that are important for fault detection. Multiple field examples indicate that the neural network (trained by only synthetic data sets) can predict faults from 3D seismic images much more accurately and efficiently than conventional methods.
    Wu, X., L. Liang, Y. Shi and S. Fomel, 2019, FaultSeg3D: using synthetic datasets to train an end-to-end convolutional neural network for 3D seismic fault segmentation. Geophysics, Vol. 84(3), IM35-IM45. [PDF] [CODE].

    FaultNet3D: predicting fault probabilities, strikes, and dips with a single CNN

    We simultaneously estimate fault probabilities, strikes, and dips directly from a seismic image by using a single convolutional neural network (CNN). In this method, we assume a local 3-D fault is a plane defined by a single combination of strike and dip angles. We assume the fault strikes and dips, respectively, are in the ranges of [0°, 360°) and [64°, 85°], which are divided into 577 classes corresponding to the situation of no fault and 576 different combinations of strikes and dips. We construct a 7-layer CNN to classify the fault strike and dip in a local seismic cube and obtain the classification probability at the same time. With the fault probability, strike and dip estimated at some seismic pixel, we further compute a fault cube (centered at the pixel) with fault features elongated along the fault plane. By sliding the classification window within a full seismic image, we are able to obtain a lot of overlapping fault cubes which are stacked to compute three full images of enhanced and continuous fault probabilities, strikes, and dips.
    Wu, X., Y. Shi, S. Fomel, L. Liang, Q. Zhang and A. Yusifov, 2019, FaultNet3D: predicting fault probabilities, strikes and dips with a single convolutional neural network. IEEE TGRS, Vol. 57(11), 9138-9155. [PDF]

    SaltSeg: automatic 3D salt segmentation using a deep CNN

    We have formulated the problem as 3D image segmentation and evaluated an efficient approach based on deep convolutional neural networks (CNNs) with an encoder-decoder architecture. To train the model, we design a data generator that extracts randomly positioned sub-volumes from large-scale 3D training data set followed by data augmentation, then feed a large number of sub-volumes into the network while using salt/nonsalt binary labels generated by thresholding the velocity model as ground truth labels. We test the model on validation data sets and compare the blind test predictions with the ground truth. Our results indicate that our method is capable of automatically capturing subtle salt features from the 3D seismic image with less or no need for manual input. We further test the model on a field example to indicate the generalization of this deep CNN method across different data sets.
    Shi, Y., X. Wu* and S. Fomel, 2019, SaltSeg: Automatic 3D salt body segmentation using a deep convolutional neural network. Interpretation, SE113-SE122. [PDF]

    Normal fault populations in the Costa Rica Margin

    From the 3D seismic image (right above) acquired in Costa Rica subduction area (left above), we automatically compute more than 10 thousands 3D fault surfaces and their strikes, dips, and slips. With these computed high-resolution fault positions and strikes, we are able to make the “blooming roses” (the cartoon below) to visualize the fault-strike variations with depth (or geologic time) and space.

    Optimal surface voting

    We proposed a method to automatically pick optimal surfaces from an input fault attribute image (a) and use the surfaces to vote for an enhanced fault image (b), from which we further automatically construct fault surfaces (c). Our parallel implementation of this method takes only seconds for this example.

    The corresponding software package has been widely used in industry. One of xinming's favorite work

    Wu, X. and S. Fomel, 2018, Automatic fault interpretation with optimal surface voting. Geophysics, Vol. 83(5), O67-O82. [PDF] [CODE]

    Least-squares horizons

    We have developed a novel method to compute horizons that globally fit the local slopes and multigrid correlations of seismic traces. In this method, we first estimate local reflection slopes by using structure tensors and compute laterally multigrid slopes by using dynamic time warping (DTW) to correlate seismic traces within multiple laterally coarse grids. These coarse-grid slopes can correctly correlate reflections that may be significantly dislocated by faults or other discontinuous structures. Then, we compute a horizon by fitting, in the least-squares sense, the slopes of the horizon with the local reflection slopes and multigrid slopes or correlations computed by DTW.

    Wu, X. and S. Fomel, 2018, Least-squares horizons with local slopes and multi-grid correlations, Geophysics, Vol. 83(4), IM29–IM40. [PDF] [CODE]
    Best Paper, Honorable Mention, 2018

    Interactive salt boundary picking

    In this method, we first pick a few points to interpolate an initial curve that is close to the true salt boundary. These points are picked near the salt boundary but are not required to be exactly on the boundary, which makes human interactions convenient and efficient. We then resample the envelope image in a band area centered at the initial curve to obtain a new image where the true salt boundary is an open curve extending from left to right. We then extract the salt boundary in the new image using an optimal-path picking algorithm, which is robust to track a highly discontinuous salt boundary by picking the optimal path with globally maximum envelope values. We finally map the picked path back to the original image to obtain a final salt boundary.
    Wu, X., S. Fomel, and M. Hudec, 2018, Fast salt boundary interpretation with optimal path picking. Geophysics, Vol. 83(3), O45–O53. [PDF] [CODE]

    Incremental correlation of well logs

    In this method, we first automatically compute an optimal path that starts with longer logs and follows geologically more continuous structures. We then use the dynamic warping technique to sequentially correlate the logs following the path. To avoid potential error propagation with the path, we modify the dynamic warping algorithm to use all the previously correlated logs as references to correlate the current log in the path. During the sequential correlations, we compute geologic distances between the current log and all the reference logs. Such distances are proportional to Euclidean distances but increase dramatically across discontinuous structures such as faults and unconformities that separate the current log from the reference logs. We also compute correlation confidences to provide quantitatively quality control of the correlation results. We use both the geologic distances and correlation confidences to weight the references in correlating the current log.
    Wu, X., Y. Shi, S. Fomel, and F. Li, 2018, Incremental correlation of multiple well logs following geologically optimal neighbors. Interpretation, Vol. 6(3), T713–T722. [PDF]

    Regularization in geophysical inversion

    Geophysical inversion is often ill-posed because of inaccurate and insufficient data. Regularization is often applied to the inversion problem to obtain a stable solution by imposing additional constraints on the model. Common regularization schemes impose isotropic smoothness on solutions and may have difficulties in obtaining geologically reasonable models that are often supposed to be anisotropic and conform to subsurface structural and stratigraphic features. Xinming introduces a general method to incorporate constraints of seismic structural and stratigraphic orientations and fault slips into geophysical inversion problems. He first uses a migrated seismic image to estimate structural and stratigraphic orientations and fault slip vectors that correlate fault blocks on opposite sides of a fault. He then uses the estimated orientations and fault slips to construct simple and convenient anisotropic regularization operators in inversion problems to spread information along structural and stratigraphic orientations and across faults. In this way, we are able to compute inverted models that conform to seismic reflectors, faults, and stratigraphic features such as channels. The regularization is also helpful to integrate well-log properties into the inversion by spreading the measured rock properties away from the well-log positions into the whole inverted model across faults and along structural and stratigraphic orientations.
    Wu, X., 2017, Structure-, stratigraphy-, and fault-guided regularization in geophysical inversion. Geophysical Journal International, Vol. 210(1), 184-195. [PDF]

    Simultaneous multiple well-seismic ties

    Most methods tie multiple wells to seismic data one-by-one, hence do not guarantee lateral consistency among multiple well ties. We propose to simultaneously tie multiple wells by first flattening synthetic and real seismograms so that all seismic reflectors are horizontally aligned. By doing this, we turn multiple well-seismic tying into a 1D correlation problem. We then simply compute only vertically-variant but laterally-constant shifts to correlate these horizontally aligned (flattened) synthetic and real seismograms. This two-step correlation method maintains lateral consistency among multiple well ties by computing a laterally and vertically optimized correlation of all synthetic and real seismograms.
    Wu, X. and G. Caumon, 2017, Simultaneous multiple well-seismic ties with flattened synthetic and real seismograms. Geophysics, Vol. 82(1), IM13-IM20. [PDF]

    Subsurface modeling

    Xinming proposed an automatic method to fully use both seismic and borehole data to build subsurface models that honor borehole measurements and conform to seismic horizons, faults, unconformities, and stratigraphic features such as channels. In this method, he first automatically removes the faulting and folding in both seismic and borehole data and map them into a flattened space, in which seismic reflectors and borehole measurements corresponding to the same geologic layers are horizontally aligned. He then builds a subsurface model in this flattened space by computing a sequence of 2D horizontal interpolations of well logs. Each horizontal interpolation is guided by the stratigraphic features apparent in the corresponding horizontal seismic slice, so that the interpolant conforms to the seismic stratigraphic features. He finally maps the interpolated model back into the input space and obtain a subsurface model that honors both the seismic and borehole data.
    Wu, X., 2017, Building 3D subsurface models conforming to seismic structural and stratigraphic features. Geophysics, Vol.82(3), IM21-IM30. [PDF]

    Structure- and stratigraphy-oriented smoothing

    We proposed a method to efficiently enhance seismic reflections, faults, and channels in a 3D seismic image while at the same time computing a mapping of faults and channels.

    Wu, X. and Z. Guo, 2019, Detecting faults and channels while enhancing seismic structural and stratigraphic features. Interpretation, Vol. 7(1), T155–T166. [PDF] [CODE]

    Estimating seismic structural and stratigraphic orientations

    Conventional structure-tensor method often generates significant errors in estimating orientations of the reflections with steep and rapidly varying slopes. To better estimate reflection orientations, we propose to construct structure tensors in a new space, where the reflections are mostly flat or only slightly dipping and the variation of reflection slopes is reduced. We use these constructed structure tensors to compute reflection normals in this new space and then transform the normals back to obtain a better estimation of reflection orientations in the original space. Seismic stratigraphic features such as channels are often aligned within dipping reflections. It is not discussed previously by others to estimate orientations of such features directly from a seismic image. An ideal way to estimate stratigraphic orientations is to first extract a horizon surface with stratigraphic features, and then construct structure tensors with gradients on the surface to estimate the orientations of the features. However, extracting horizon surfaces can be a difficult and time-consuming task in practice. Fortunately, computing gradients on a horizon surface is only a local operation and is equivalent to directly compute directional derivatives along reflection slopes without picking horizons. Based on this observation, we propose to use an equivalent but more efficient way to estimate seismic stratigraphic orientations by using structure tensors constructed with the directional derivatives along reflections.
    Wu, X. and X., Janson, 2017, Directional structure tensors in estimating seismic structural and stratigraphic orientations. Geophysical Journal International, Vol. 210(1), 534-548. [PDF]

    Enhanced coherence

    A coherence image can be computed from the eigenvalues of conventional structure tenors, which are outer products of gradients of a seismic image. Xinming proposes a simple but effective method to improve such a coherence image by using directional structure tensors, which are different from the conventional structure tensors in only two aspects. Firstly, instead of using image gradients with vertical and horizontal derivatives, he uses directional derivatives, computed in directions perpendicular and parallel to seismic structures (reflectors), to construct directional structure tensors. With these directional derivatives, lateral seismic discontinuities, especially those subtle stratigraphic features aligned within dipping structures, can be better captured in the structure tensors. Secondly, instead of applying Gaussian smoothing to each element of the constructed structure tensors, He applies approximately fault- and stratigraphy-oriented smoothing to enhance the lateral discontinuities corresponding to faults and stratigraphic features in the structure tensors.
    Wu, X., 2017, Directional structure-tensor based coherence to detect seismic channels and faults. Geophysics, Vol. 82(2), A13-A17. [PDF]
    This paper was recognized as “Geophysics Bright Spots” by The Leading Edge

    Salt likelihood and salt boundary surface

    From a 3D seismic image, Xinming first efficiently computes a salt likelihood image, in which the ridges of likelihood values indicate locations of salt boundaries. He then extracts salt samples on the ridges. These samples can be directly connected to construct salt boundaries in cases when salt structures are simple and the boundaries are clean. In more complicated cases, these samples may be noisy and incomplete, and some of the samples can be outliers unrelated to salt boundaries. Therefore, he finally develops a method to accurately fit noisy salt samples, reasonably fill gaps, and handle outliers to simultaneously construct multiple salt boundaries. In this step of constructing salt boundaries, he also proposes a convenient way to incorporate human interactions to obtain more accurate salt boundaries in especially complicated cases.
    Wu, X., 2016, Methods to compute salt likelihoods and extract salt boundaries from 3D seismic images. Geophysics, 81(6), IM119-IM126. [PDF]

    Unfaulting and flattening

    We developed two methods to compute vector shifts that simultaneously move fault blocks and the faults themselves to obtain an unfaulted image with minimal distortions. For both methods, we use estimated fault positions and slip vectors to construct unfaulting equations for image samples alongside faults, and we construct simple partial differential equations for samples away from faults. We solve these two different kinds of equations simultaneously to compute unfaulting vector shifts that are continuous everywhere except at faults.
    Wu, X., S. Luo, and D. Hale, 2016, Moving faults while unfaulting 3D seismic images. Geophysics, 81(2), IM25-IM33. [PDF]
    Technical talk:
    Recognized as “Geophysics Bright Spots” by The Leading Edge

    Fault scanning and fault surface construction

    Numerous methods have been proposed to automatically extract fault surfaces from 3D seismic images, and those surfaces are often represented by meshes of triangles or quadrilaterals. Such mesh data structures are more complex than the arrays used to represent seismic images, and are more complex than necessary for subsequent processing tasks, such as that of automatically estimating fault slip vectors. To facilitate image processing for faults, we propose a simpler linked data structure in which each sample of a fault corresponds to exactly one image sample. Using this linked data structure, we extracted multiple intersecting fault surfaces from 3D seismic images. We then used the same structure in subsequent processing to estimate fault slip vectors, and to assess the accuracy of estimated slips by unfaulting the seismic images.
    Wu, X. and D. Hale, 2016, 3D seismic image processing for faults. Geophysics, 81(2), IM1–IM11. [PDF] [CODE]
    Technical talk:
    2016 Best Paper Award in Geophysics

    3D seismic image processing for unconformities

    We propose a 3D seismic unconformity attribute to detect complete unconformities, highlighting both their termination areas and correlative conformities. We then extract unconformity surfaces on the ridges of the unconformity attribute image. These detected unconformities are further used as constraints to more accurately estimate seismic normal vectors at unconformities. Then, using seismic normal vectors and detected unconformities as constraints, we can better flatten seismic images containing unconformities.
    Wu, X. and D. Hale, 2015, 3D seismic image processing for unconformities. Geophysics, 80 (2), IM35-IM44. [PDF]
    Technical talk:
    This paper was recognized as “Geophysics Bright Spots” by The Leading Edge

    Seismic horizon volumes

    We propose two methods for constructing seismic horizons aligned with reflectors in a 3D seismic image. The first method extracts horizons one at a time; the second generates at once an entire volume of horizons. The most significant new aspect of both methods is the ability to specify, perhaps interactively during interpretation, a small number of control points that may be scattered through- out a 3D seismic image. Examples show that control points enable the accurate extraction of horizons from seismic images in which noise, unconformities, and faults are apparent. These points represent constraints that we implement simply as preconditioners in the conjugate gradient method used to construct horizons.
    Wu, X. and D. Hale, 2015, Horizon volumes with interpreted constraints. Geophysics, 80 (2), IM21-IM33. [PDF]
    Technical talk:
    This paper was recognized as “Geophysics Bright Spots” by The Leading Edge

    Horizon surface extraction

    We first introduce a globally optimal method to efficiently extract a horizon from a seismic image. We then use scattered control points as constraints to enable our horizon-extraction method to extract sequence boundaries. Finally, we propose an active-surface method to refine the globally optimized horizons to align with amplitude peaks or troughs and thereby reveal more geologic details.
    The cartoon shows Xinming's interactive implementation of this algorithm for Transform/Drillinginfo during his 2014 summer intern.
    Wu, X. and D. Hale, 2013, Extracting horizons and sequence boundaries from 3D seismic images. 83rd Annual International Meeting, SEG. [Expanded Abstracts]
    Technical talk:

    Graph-cut-based phase unwrapping

    We propose a robust phase unwrapping method to compute a relative geologic time volume from a 3D seismic instantaneous phase volume. We provide a convenient way to incorporate interpreted horizons and unconformities into our phase unwrapping method to obtain more reliable results in cases complicated by noise, faults, and unconformities. Using a computed RGT volume, we further automatically generate a 3D seismic Wheeler volume.
    Wu, X. and G. Zhong, 2012, Generating a relative geologic time volume by improved 3D graph-cut-based phase unwrapping method with horizon and unconformity constraints. Geophysics, 77 (4), O21-O34. [PDF]