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Simultaneous source acquisition technology can greatly improve seismic acquisition efficiency. However, due to continuous shooting and serious crosstalk noise of the adjacent sources in seismic data, simultaneous source data cannot be directly used in conventional data processing procedures. Therefore, simultaneous source data need to be deblended to obtain the conventional shot record. Under densely sampled sources, we have developed a novel unsupervised deep learning (UDL) method based on the double-deep neural networks for iterative inversion deblending of simultaneous source data. Our UDL, which is mainly composed of the residual neural network (R-net) and the U-net neural network, has excellent nonlinear optimization ability. The total loss function design can optimize our UDL in the correct direction and avoid the problem of overfitting. By minimizing the total loss function, the R-net and U-net branches of the UDL can extract the coherent effective signals of all sources and suppress the crosstalk noise. The most prominent advantage of our UDL method is that it does not require label data, and the training data set does not contain raw unblended data, thus solving the problem of missing training data sets. The examples with two synthetic and one field data set are used to prove the effectiveness of iterative inversion deblending of simultaneous source data based on our UDL method when sources are within a small distance of each other. By comparing our UDL method with the traditional curvelet-based and contourlet-based methods, the superiority of our method in the quality of separation results is demonstrated.

SUMMARY Understanding the effects of pressure and rock microstructure on seismic elastic properties of fully saturated rocks is of considerable importance in a range of geophysical applications, especially at seismic frequency range. A recently proposed theoretical model of squirt attenuation and dispersion can be used to interpret the stress and frequency dependence of elastic properties on the basis of a triple porosity structure. The poroelastic model requires the knowledge of a variety of pore microstructure parameters, in particular, the compliant pores with a discrete distribution of aspect ratio. We performed laboratory measurements of (compressional and shear wave) velocity dispersion and attenuation, associated with the pressure-related closure of compliant pores on three dry and wet sandstones, to verify the effects of squirt flow arising from compressibility heterogeneities in the rock microstructure on the pressure dependence of dynamic elastic moduli and attenuation. Ultrasonic velocities experimentally measured on dry rocks were applied to extract pressure-dependent pore aspect distribution of compliant pores and the effective porosity of three types of pores with distinct aspect ratios, via fitting of the poroelastic model to the pressure dependence of elastic compressibilities. Under the assumption of frequency-independent dry elastic properties, inferred velocities and the associated attenuation of the saturated rocks from the forced oscillation experiments, which are still scarcely investigated, are in fairly good agreement with the predictions of the squirt model of three porosity types at seismic frequencies. The Gassmann's relation was found, nevertheless, underpredicts the ultrasonic saturated velocity measurements. The results validate applicability of the recently developed squirt model to account for dispersion and attenuation of phase velocities at varying effective pressures.

Seismic multiples in marine seismic data can affect the identification of oil and gas reservoirs. The efficiency of traditional multiple suppression methods, such as the Radon transform, depends on the accuracy of the velocity model for primaries and multiples, and the assumption of random background noise. To attenuate multiples with background noise, a method of primary reconstruction using a deep neural network based on data augmentation training is proposed. The designed deep neural network (DNN) includes convolutional encoding and decoding processes. The convolutional encoding process uses convolutional layers and maximum pooling layers to learn the features of the primaries, multiples, and background noise in a seismic data set. The convolutional decoding process uses these features to reconstruct the primaries and suppress the multiples and background noise. Using the data augmentation training method in the training phase, the full-wavefield data and the predicted multiples are added to background noise and then rotated to constitute the augmented data sets. This allows the DNN to have a better multiple suppression effect and better robustness. A well-trained DNN can be used for primary reconstruction in the same work area directly or in other work areas with a transfer learning method. Three examples of synthetic data with two simple models and a Pluto model verify the effectiveness, efficiency, stability, and good generalization of the proposed method for primary reconstruction and multiple suppression. Another example from field data finds that the proposed method can efficiently suppress seismic multiples under complex conditions.

SUMMARY The simultaneous source data obtained by simultaneous source acquisition contain crosstalk noise and cannot be directly used in conventional data processing procedures. Therefore, it is necessary to deblend the blended wavefield to obtain the conventionally acquired single-shot recordings. In this study, we propose an iterative inversion method based on the unsupervised deep neural network (UDNN) to deblend the simultaneous source data from a denser shot coverage survey (DSCS). In the common receiver gather (CRG), the coherent effective signals in the blended data of the primary and secondary sources are similar. We exploit the excellent nonlinear optimization capability of the U-net network to extract similar coherent signals from the blended data of the primary and secondary sources by minimizing the total loss function. The proposed UDNN method does not need to use the raw unblended data as label data, which solves the problem of missing label data and is suitable for deblending the simultaneous source data in different work areas with complex underground structures. One synthetic data and one field data examples are used to prove that the proposed method can suppress crosstalk noise and protect weak effective signals effectively, and achieve good effectiveness for the separation of simultaneous source data.

Summary Seismic velocity analysis is the basis for seismic imaging and understanding complex subsurface geological structures. Although the performance of automatic velocity analysis methods based on CMP data or velocity spectra is encouraging, particularly deep learning methods. However, most methods ignore the complementarity between CMP data and velocity spectrum, and only one of them is selected for velocity modeling. We propose a multimodal neural network (MMN) that combines the advantages of CMP data details representation and simplification of velocity spectrum. MMN includes multi-layer convolution structures and auto-encoder structures, which are used to extract time-space amplitude information from CMP gathers and energy groups features from velocity spectra, respectively. This paper compared MMN with the CMP single-modal network (CSN) and the velocity spectra single-modal network (VSSN). Based on synthetic data, we investigated their differences in terms of continuity, accuracy, noise resistance, and generalization. The MMN prediction results makes a trade-off between the overall continuity and local details. Visualization analysis of the intermediate feature maps explains the MMN velocity prediction mechanism, that is, the multi-angle representation and complementary fusion of velocity information. Finally, the performance of the proposed method is demonstrated using the braided river deposited field data example.

Ultrasonic tomography, which is widely used in the study of the fracturing process of rocks, often exhibits low resolution due to insufficient ray coverage, particularly while evaluating the three-dimensional (3D) fractures. To resolve this issue, we adopted sparseness regularisation in tomography to reconstruct the ultrasonic velocity of rocks. Both numerical and laboratory experiments demonstrate that tomography with sparseness regularisation generates velocity images with clear fracture morphology than that with Tikhonov regularisation. Dynamic monitoring of the fracturing process of a granite slab with two-dimensional (2D) velocity images can reveal the accurate development of the fracturing process. The experiment on the internal structure of tight sandstone after hydraulic fracturing reveals demarcated low-velocity regions in the 3D ultrasonic velocity images of tomography with sparseness regularisation. These low-velocity regions correspond to the positions of the fractures when compared to the X-ray scanning images. Thus, tomography with sparseness regularisation can improve the resolution of ultrasonic velocity images, which can be used to accurately describe the fracture development and strain localisation during rock deformation.

Manually picking regularly and densely distributed first breaks (FBs) are critical for shallow velocity-model building in seismic data processing. However, it is time consuming. We employ the fully-convolutional SegNet to address this issue and present a fast automatic seismic waveform classification method to pick densely-sampled FBs directly from common-shot gathers with sparsely distributed traces. Through feeding a large number of representative shot gathers with missing traces and the corresponding binary labels segmented by manually interpreted fully-sampled FBs, we can obtain a well-trained SegNet model. When any unseen gather including the one with irregular trace spacing is inputted, the SegNet can output the probability distribution of different categories for waveform classification. Then FBs can be picked by locating the boundaries between one class on post-FBs data and the other on pre-FBs background. Two land datasets with each over 2000 shots are adopted to illustrate that one well-trained 25-layer SegNet can favorably classify waveform and further pick fully-sampled FBs verified by the manually-derived ones, even when the proportion of randomly missing traces reaches 50%, 21 traces are missing consecutively, or traces are missing regularly.

Full waveform inversion (FWI) plays a central role in the field of exploration geophysics due to its potential in recovering the properties of the subsurface at a high resolution. A starting model with ample long wavelength components is essential for the success of most FWI algorithms. Reflection waveform inversion (RWI) is one popular way to invert for the long wavelength velocity components from the short offset seismic data by decomposing the gradient of FWI into migration and tomographic terms. However, the transmitted part of Born scattering in conventional RWI still produces high-wavenumber artifacts, which would hinder its convergence. Thus, in this letter, an efficient nontransmission energy norm Born scattering is used in RWI to overcome the drawbacks of conventional RWI. Finally, we use numerical examples to show that the energy norm Born scattering can provide clean reflection energy from the reflector and enhance the low-wavenumber information in the RWI gradient.

Low-frequency information is important in reducing the nonuniqueness of absolute impedance inversion and for quantitative seismic interpretation. In traditional model-driven impedance inversion methods, the low-frequency impedance background is from an initial model and is almost unchanged during the inversion process. Moreover, the inversion results are limited by the quality of the modeled seismic data and the extracted wavelet. To alleviate these issues, we have investigated a double-scale supervised impedance inversion method based on the gated recurrent encoder-decoder network (GREDN). We first train the decoder network of GREDN called the forward operator, which can map impedance to seismic data. We then implement the well-trained decoder as a constraint to train the encoder network of GREDN called the inverse operator. Besides matching the output of the encoder with broadband pseudowell impedance labels, data generated by inputting the encoder output into the known decoder match the observed narrowband seismic data. The broadband impedance information and the already-trained decoder largely limit the solution space of the encoder. Finally, after training, only the derived optimal encoder is applied to unseen seismic traces to yield broadband impedance volumes. Our approach is fully data driven and does not involve the initial model, seismic wavelet, and model-driven operator. Tests on the Marmousi model illustrate that our double-scale supervised impedance inversion method can effectively recover low-frequency components of the impedance model, and we determine that low frequencies of the predicted impedance originate from well logs. Furthermore, we apply the strategy of combining the double-scale supervised impedance inversion method with a model-driven impedance inversion method to process field seismic data. Tests on a field data set indicate that the predicted impedance results not only reveal a classic tectonic sedimentation history but also match the corresponding results measured at the locations of two wells.

Dataset for the article "Prediction of dispersion and attenuation for partially saturated rock based on the fluid distribution from three-dimensional (3D) micro-CT image" submitted to RMRE. Please refer to the ReadMe file or to kang2008ping2008@163.com for more details.

Gas-bearing prediction of tight sandstone reservoirs is significant but challenging due to the relationship between the gas-bearing property and its seismic response being nonlinear and complex. Although machine learning (ML) methods provide potential for solving the issue, the major challenge of ML applications to gas-bearing prediction is that of generating accurate and interpretable intelligent models with limited training sets. The k nearest neighbor ( kNN) method is a supervised ML method classifying an unlabeled sample according to its k neighboring labeled samples. We have introduced a kNN-based gas-bearing prediction method. The method can automatically extract a gas-sensitive attribute called the gas-indication local waveform similarity attribute (GLWSA) combining prestack seismic gathers with interpreted gas-bearing curves. GLWSA uses the local waveform similarity among the predicting samples and the gas-bearing training samples to indicate the existence of an exploitable gas reservoir. GLWSA has simple principles and an explicit geophysical meaning. We use a numerical model and field data to test the effectiveness of our method. The result demonstrates that GLWSA is good at characterizing the reservoir morphology and location qualitatively. When the method applies to the field data, we evaluate the performance with a blind well. The prediction result is consistent with the geologic law of the work area and indicates more details compared to the root-mean-square attribute.

Noise attenuation has been a long-standing but still active topic in seismic data processing. The deep convolutional neural networks (CNNs) have been recently adopted to remove the learned random noise from noisy seismic data, but it is still difficult to improve the generalization ability of learned denoisers due to the limited diversity of training data sets. In this letter, we investigate an end-to-end deep denoising CNNs (DCNNs) with a novel data generation method involving multidimensional geological structure features for seismic denoising. To learn an optimized network denoiser, seismic amplitude data are extracted from 3-D synthetic seismic data along three directions (i.e., two spatial directions and one temporal direction) to prepare a training data set. Compared with using seismic data from only a certain single direction to generate all training samples, this strategy enables DCNNs to learn abundant geological structural information from three directions, and helps DCNNs have a better performance on noise reduction. Another 3-D synthetic seismic data and 3-D real land data examples with plentiful faults and fluvial channels are used to illustrate that the optimized network denoiser can be directly extended to attenuate random noise. The denoising results demonstrate that DCNNs learned from the multidimensional geological structures can accomplish the self-adaptive random noise attenuation, and meanwhile preserve spatial geological structures.

Full-waveform inversion (FWI) has the potential to provide a high-resolution detailed model of the earth’s subsurface, but it often fails to do so if the starting model differs significantly from the true one. Reflection waveform inversion (RWI) is a popular method for building a sufficiently accurate initial model for FWI. In traditional RWI, the low-wavenumber updates are always computed and captured by smearing the data misfit along the reflection path with the help of migration/demigration. However, the success of RWI relies heavily on accurately reproducing the data in demigration. Thus, we have introduced a new generalized internal multiple imaging-based RWI (GIMI-RWI) implementation, in which we avoid the Born modeling and update the primary reflection kernel directly. In GIMI-RWI, we store one reflection kernel for each source-receiver pair, preserving the unique wavepath for every single source-receiver trace. Subsequently, the convolution between the data residuals and the corresponding reflection kernel can build the tomographic velocity updates. In this situation, the long-wavelength tomographic updates are free of migration footprints and will contribute a smoother background velocity to reduce the cycle-skipping risk and stabilize the followed FWI process. In addition, the GIMI-RWI method is source independent because it entirely relies on the data. Using a synthetic example extracted from the Sigsbee2A model, we find the reliable performance of the GIMI-RWI technique.

Physical and/or economic constraints cause acquired seismic data to be incomplete; however, complete data are required for many subsequent seismic processing procedures. Data reconstruction is a crucial and long-standing topic in the exploration seismology field. We extended our previous works on deep learning (DL)-based irregularly and regularly missing 2-D data reconstruction to 3-D data. A key motivation is that the 3-D convolutional neural network (CNN) can take full advantage of the 3-D nature of the data, and the additional dimension allows more information to contribute to the data reconstruction. DL also avoids many assumptions (e.g., linearity, sparsity, and low-rank) limiting conventional nonintelligent reconstruction methods. We built an artificial neural network (ANN) based on an end-to-end U-Net encoder–decoder-style 3-D CNN. The ANN was trained on large quantities of various synthetic and field 3-D seismic data using a mean-squared-error (MSE) loss function and an Adam optimizer. We demonstrated that the developed 3-D CNN reconstruction method appears to outperform the 2-D CNN for 3-D restoration. We benchmarked the ANN’s generalization capacity for recovery of irregularly and regularly sampled 3-D data on several typical seismic data sets, particularly those with high missing percentages or large gaps. An ANN trained with irregularly sampled data can be partly applied to regularly sampled cases. We investigated how a key parameter, i.e., the learning rate, can be experimentally determined. In the context of the presented examples, our methodology provided a substantial improvement over an open-source state-of-the-art rank-reduction-based approach in terms of data fidelity and efficiency.

Seismic anisotropy, wave attenuation, and dispersion are critical phenomena of wave propagation in real media. Full-wavefield modeling of wave behavior in such media plays an important role in investigating dynamic features of the earth’s interior and in full-waveform inversion of anisotropic parameters and velocity dispersion. We have developed a numerical scheme to model the full-waveform response from a point source in a vertically varying viscoelastic medium of arbitrary anisotropy. The method is implemented in the frequency domain, so the complexity of anelasticity and anisotropy can be described by a complex elastic stiffness matrix and frequency-dependent moduli can also be readily incorporated. In our scheme, we solve the elastodynamic equations for general anisotropy through finite-element method in the frequency-wavenumber domain and we use the stiffness reduction method to suppress reflections from artificial boundaries along the depth direction. A nonuniform 2D Fourier transform strategy is developed to reconstruct the spatial-domain counterparts from the wavenumber-domain solutions. The time-domain responses are then obtained by taking inverse fast Fourier transform with respect to frequency. We validate the method by comparing the numerical results with the exact solutions for a homogeneous transversely isotropic model and a two-layered model. In the application example, we further proved the feasibility and generality of the scheme using an attenuative, dispersive model with velocity and attenuation anisotropy. Our scheme enjoys significant advantages in incorporating various viscoelastic/dispersive behaviors and general anisotropy, and thus provides a useful tool for numerical simulation of dynamic responses in practical application.

Multidimensional Fourier transform on an irregular grid is a useful tool for various seismic forward problems caused by complex media and wavefield distributions. Using a shape-function-based strategy, we have developed four different algorithms for 1D and 2D nonuniform Fourier transforms, such as two high-accuracy Fourier transforms (the linear shape-function-based Fourier transform [LSF-FT] and the quadratic shape-function-based Fourier transform [QSF-FT]) and two nonuniform fast Fourier transforms (NUFFTs) (the linear shape-function-based NUFFT [LSF-NUFFT] and the quadratic shape-function-based NUFFT [QSF-NUFFT]), respectively, based on their linear and quadratic shape functions. The main advantage of incorporating shape functions into the Fourier transform is that triangular elements can be used to mesh any complex wavefield distribution in the 2D case. Therefore, these algorithms can be used in conjunction with any irregular sampling strategies. The accuracy and efficiency of the four nonuniform Fourier transforms are investigated and compared by applying them in frequency-domain seismic wave modeling. All of the algorithms are compared with the exact solutions. Numerical tests indicate that the quadratic shape-function-based algorithms are more accurate than those based on the linear shape function. Moreover, LSF-FT/QSF-FT exhibits higher accuracy but much slower calculation speed, whereas LSF-NUFFT/QSF-NUFFT is highly efficient but has lower accuracy at near-source points. In contrast, a combination of these algorithms, by using QSF-FT at near-source points and LSF-NUFFT/QSF-NUFFT at others, achieves satisfactory efficiency and high accuracy at all points. Although our tests are restricted to seismic models, these improved NUFFT algorithms may also have potential applications in other geophysical problems, such as forward modeling in complex gravity and magnetic models.

SUMMARY Elastic moduli and velocities of tight sandstones are strongly influenced by rock-frame heterogeneity, pore microstructure and fluid in addition to pressure and probing-wave frequency. The effects of pressure and frequency on the elastic moduli and velocities are different from those of conventional sandstones with high porosity and high permeability due to complexity of pore microstructure. To investigate these effects, we measured two tight sandstone samples for their velocities in the dry and fluid saturation conditions using the ultrasonic transmission technique and the low-frequency stress–strain method. The variations in the ultrasonic velocities with pressure see a transition from non-linear to linear increase for the dry samples, in contrast to a gradual increase for the fluid-saturated samples. The low frequency velocities of the saturated sample T1 and T2 directly show significant dispersion in a wide range of frequencies (1–100 Hz), and the magnitudes of the dispersion are suppressed by the pressure. The low-frequency velocities also increase with pressure, showing increasing trends bounded by the ultrasonic velocity–pressure curves for the dry and fluid saturation conditions. An elaborate rock physics model, considering a discrete aspect ratio spectrum and the simple squirt flow model, was constructed to account for the pressure and frequency dependence of the velocities. The predictions from the modified squirt flow model can fit well the measured velocities at varying pressures, both in the low-frequency range and the ultrasonic frequency range. The real measurements and the modelling results suggest that the pressure- and frequency-dependence cannot be modelled without considering such aspect ratio spectra. The effects of pressure and frequency are coupled in that they are interconnected by the microstructure of the pores. Changes in the pressure and fluid saturation (and thus wave frequency) both contribute to stiffening of the rock frame, and they both strongly depend on the presence of microcracks in the rock. Therefore, this rock physics model could be applied in extraction of pore microstructure and fluid properties provided elastic moduli or velocities can be estimated accurately.

Reliable estimate of the anelastic attenuation factor- $Q$ from seismic records is highly desirable for improving seismic resolution. However, the conventional equivalent- $Q$ or horizontal interval- $Q$ estimation ignores that $Q$ -distribution should hold the same ability for the subsurface structure characterization as seismic data. To pursue an accurate $Q$ -model, we propose a technique for joint reflectivity and structural interval- $Q$ estimation by using nonstationary sparse inversion. We designed a structural interval- $Q$ model by dividing the seismic data into several structural layers with the interpreted horizon(s). Attenuations in each layer are close to each other and can be described by an equivalent- $Q$ or gradient- $Q$ . Based on the attenuation theory, the nonstationary sparse inversion is solved iteratively, where, at each iteration, the equivalent- $Q$ of only one layer is optimized by searching for the corresponding optimum inverted reflectivity, leading to a structural interval- $Q$ model. The main advantages of our method are its objectivity and accuracy because of the integration of the prior structural information from interpreted horizons into joint reflectivity-estimation and $Q$ -estimation. The test of synthetic and field data clearly illustrates that the proposed method enables high-precision structural interval- $Q$ estimation and sufficiently compensates for $Q$ -related attenuation.

SUMMARY We conducted stress–strain oscillation experiments on dry and partially oil-saturated Fontainebleau sandstone samples over the 1–2000 Hz band at different confining pressures to investigate the wave-induced fluid flow (WIFF) at mesoscopic and microscopic scales and their interaction. Three tested rock samples have similar porosity between 6 and 7 per cent and were partially saturated to different degrees with different oils. The measurement results exhibit a single or two attenuation peaks that are affected by the saturation degree, oil viscosity and confining pressure. One peak, exhibited by all samples, shifts to lower frequencies with increasing pressure, and is mainly attributed to grain contact- or microcrack-related squirt flow based on modelling of its characteristics and comparison with other experiment results for sandstones. The other peak is present at smaller frequencies and shifts to higher frequencies as the confining pressure increases, showing an opposite pressure dependence. This contrast is interpreted as the result of fluid flow patterns at different scales. We developed a dual-scale fluid flow model by incorporating the squirt flow effect into the patchy saturation model, which accounts for the interaction of WIFFs at microscopic and mesoscopic scales. This model provides a reasonable interpretation of the measurement results. Our broad-frequency-band measurements give physical evidence of WIFFs co-existing at two different scales, and combining with modelling results, it suggests that the WIFF mechanisms, related to pore microstructure and fluid distribution, interplay with each other and jointly control seismic attenuation and dispersion at reservoir conditions. These observations and modelling results are useful for quantitative seismic interpretation and reservoir characterization, specifically they have potential applications in time-lapse seismic analysis, fluid prediction and reservoir monitoring.

Phase information of seismic signals is sensitive to subsurface discontinuities. However, 1D phase attributes are not robust when dealing with noisy data. In addition, variations of seismic phase attributes with azimuth are seldom explored. To address these issues, we have developed 6D phase-difference attributes (PDAs) derived from azimuthal phase-frequency spectra. For the seismic volume of a certain azimuth and frequency, we first construct stacked phase traces at each common-depth point along a certain decomposed trending direction. Then, the 6D PDA is extracted by calculating the complex-valued covariance at a 6D phase space. The proposed method enables characterization of the subsurface discontinuities and indicates seismic anisotropy. Moreover, we provide one q-value attribute obtained by singular value decomposition to describe the variation intensity of PDA along different azimuths. Simulated and field wide-azimuth seismic data sets are used to illustrate the performance of the proposed 6D PDA and the derived q-value attribute. The results show that PDA at different frequencies can image various geologic features, including faults, fracture groups, and karst caves. Our field data example shows that PDA is able to discern the connectivity of karst caves using large-azimuth data. In addition, PDA along different azimuths and the q-value attribute provide a measurement of azimuthal variations, as well as the anisotropy. Our 6D PDA method can be used as a potential tool for wide-azimuth seismic data interpretation.

An important application of spectral decomposition (SD) is to identify subsurface geological anomalies such as channels and karst caves, which may be buried in full-band seismic data. However, the classical SD methods including the wavelet transform (WT) are often limited by relatively low time–frequency resolution, which is responsible for false high horizon-associated space resolution probably indicating more geological structures, especially when close geological anomalies exist. To address this issue, we impose a constraint of minimizing an lp (0 p l1-norm constraint, the modified ISD (MISD) using an lp-norm constraint can yield a more compact spectrum contributing to detect the distributions of close geological features. We design a 3D synthetic dataset involving frequency-close thin geological anomalies and the other 3D non-stationary dataset involving time-close anomalies to demonstrate the effectiveness of MISD. The application of 4D spectrum on a 3D real dataset with an area of approximately 230 km2 illustrates its potential for detecting deep channels and the karst slope fracture zone.

Reservoir prediction is often a primary objective in seismic exploration, especially for deep hydrocarbon detection with its potential for assessing oil and gas resources. Time–frequency analysis has become a successful method for detecting subsurface features and can also be used to identify potential hydrocarbon reservoirs. However, current applications for hydrocarbon detection often occur at low resolution, due to the influence of the windowing functions and lack of prior constraints, thereby affecting gas prediction for thin reservoirs. To rectify this issue, we investigate the use of sparse inverse spectral decomposition (SISD) based on the wavelet transform, which adopts an lp norm to constrain the time–frequency spectra, and thereby provides a more highly concentrated time–frequency representation than conventional spectral decomposition techniques. The main objective of this paper is to investigate the performance of spectral attributes derived from lp-norm constrained SISD and its application to the characterization of deep-marine dolomite reservoirs in southwest China. The gas-bearing zones in target reservoir are predicted well by extracting and analyzing the spectral amplitude responses of different frequency components. The predicted favorable gas-bearing areas are closely related to local structures in the target reservoir, which are also in good agreement with gas-testing results at three well locations and may be used to guide subsequent exploration well development in this region.

The coherence attribute has been widely used to detect faults and channels as well as other structural and stratigraphic discontinuities since its introduction. Currently, the most commonly used algorithm for coherence computation is the eigenstructure-based coherence method (C3). When seismic data are of a low signal-to-noise ratio, more traces should be involved in coherence computation to improve the robustness to noise; thus, a larger analysis window shall be used. However, this will lead to increased time costs and blurred coherence images. To address these issues, we have adopted a modified eigenstructure-based coherency algorithm (C3m) based on an inverse distance weighting method and dimensionality reduction of the covariance matrix for eigendecomposition in the case of a large lateral analysis window whose size is larger than [Formula: see text] (nine traces). To further improve the computational efficiency, the add-drop algorithm is also used for covariance matrix construction. In the case of large analysis windows, the time cost by C3m is less than the time cost by C3 as demonstrated in synthetic and field data studies; also, the coherence results computed via C3m are superior to those computed via the traditional C3 method, and the new method is more favorable to seismic interpretation. Thus, our method shall be a potentially efficient and robust alternative to C3 for coherence attribute computation.

The following files (.xlsx) are included: --- Regarding Figure 1a&b /file Figure1_a&b The evolution of water volume saturated the sample, porosity and crack fractions during effective pressure loading/unloading(compaction process). The data are obtained directly from quzix pump. --- Regarding Figure 1c&d&e&f /file Figure1_c&d&e&f Dry sample : Vp and Vs velocities and the deduced aspect ratio and crack density base on CPEM theory (introduced in the paper). --- Regarding Figure 2c&d / file Figure2_c&d Intact/compacted dry sample : Young's modulus and related attenuation obtained directly from from axial oscillations. --- Regarding Figure 3a-d and Figure S1 / file Figure3&supplementary Intact/compacted glycerin sample : Young's modulus, and related attenuation obtained directly from axial oscillations. ----->The Intact sample measured at drained and undrained boundary: Figure 3a&b and Figure S1 in subpplementary . ----->The compacted sample measured at undrained boundary: Figure 3c&d. &nbsp

It is an effective way in seismic imaging to make full use of lateral seismic response to break through the limitation of vertical resolution and to improve the accuracy of interpretation. On zero-crossing-time (ZCT) amplitude slices, there is a clearer imprint of underground beds than on non-ZCT slices, providing an important foundation for characterizing interbedded thin beds. However, picking ZCTs is time-consuming with significant manual efforts. In the assumption of horizontally layered media with lateral invariance, we deduce the variation of the cluster number on ZCT and non-ZCT slices with the number of thin beds. Furthermore, based on the statistical analysis on all cluster numbers of a 3-D seismic data set, ZCT, and non-ZCT slices are distinguished according to the difference of the cluster number. As a result, all ZCTs are picked automatically. Considering the influence of noise, the method provides the estimated values and the estimated intervals for all ZCTs to improve reliability. No label is required with this unsupervised learning method. The feasibility and practicability of the proposed method have been verified with numerical and real data experiments.

Frequency‐dependent amplitude variation with offset offers an effective method for hydrocarbon detections and analysis of fluid flow during production of oil and natural gas within a fractured reservoir. An appropriate representation for the frequency dependency of seismic amplitude variation with offset signatures should incorporate influences of dispersive and attenuating properties of a reservoir and the layered structure for either isotropic or anisotropic dispersion analysis. In this study, we use an equivalent medium permeated with aligned fractures that simulates frequency‐dependent anisotropy, which is sensitive to the filled fluid of fractures. The model, where pores and fractures are filled with two different fluids, considers velocity dispersion and attenuation due to mesoscopic wave‐induced fluid flow. We have introduced an improved scheme seamlessly linking rock physics modelling and calculations for frequency‐dependent reflection coefficients based on the propagator matrix technique. The modelling scheme is performed in the frequency‐slowness domain and can properly incorporate effects of both bedded structure of the reservoir and velocity dispersion quantified with frequency‐dependent stiffness. Therefore, for a dispersive and attenuated layered model, seismic signatures represent a combined contribution of impedance contrast, layer thickness, anisotropic dispersion of the fractured media and tuning and interference of thin layers, which has been avoided by current conventional methods. Frequency‐dependent amplitude variation with offset responses was studied via considering the influences of fracture fills, layer thicknesses and fracture weaknesses for three classes amplitude variation with offset reservoirs. Modelling results show the applicability of the introduced procedure for interpretations of frequency‐dependent seismic anomalies associated with both layered structure and velocity dispersion of an equivalent anisotropic medium. The implications indicate that anisotropic velocity dispersion should be incorporated accurately to obtain enhanced amplitude variation with offset interpretations. The presented frequency‐dependent amplitude variation with offset modelling procedure offers a useful tool for fracture fluid detections in an anisotropic dispersive reservoir with layered structures.

As an approximation of the spherical-wave reflection coefficient (SRC), the plane-wave reflection coefficient does not fully describe the reflection phenomenon of a seismic wave generated by a point source. The applications of SRC to improve analyses of seismic data have also been studied. However, most of the studies focus on the time-domain SRC and its benefit to using the long-offset information instead of the dependency of SRC on frequency. Consequently, we have investigated and accounted for the frequency-dependent spherical-wave reflection coefficient (FSRC) and analyzed the feasibility of this type of inversion. Our inversion strategy requires a single incident angle using reflection data for inverting the density and velocity ratios, which is distinctly different from conventional inversion methods using amplitude variation with offset. Hence, this investigation provides an alternative approach for estimating media properties in some contexts, especially when the range of aperture of the reflection angles is limited. We apply the FSRC theory to the inversion of noisy synthetic and field data using a heuristic algorithm. The multirealization results of the inversion strategy are consistent with the feasibility analysis and demonstrate the potential of the outlined method for practical application.

We investigated reflection dispersion characteristics of a poroelastic layer with patchy saturations in seismic low-frequency range. Frequency-dependent attenuation and dispersion of phase velocity...

Inspired by image-to-image translation, we applied deep learning (DL) to regularly missing data reconstruction, aimed at translating incomplete data into their corresponding complete data. With this purpose in mind, we first construct a network architecture based on an end-to-end U-Net convolutional network, which is a generic DL solution for various tasks. We then meticulously prepare the training data with both synthetic and field seismic data. This article is implemented in Python based on Keras (a high-level DL library). We described the network architecture, the training data, and the training settings in detail. For training the network, we employed a mean-squared-error loss function and an Adam optimization algorithm. Next, we tested the trained network with several typical data sets, achieving good performances (even in the presence of big gaps) and validating the feasibility, effectiveness, and generalization capability of the assessed framework. The feature maps for a sample going through the well-trained network are uncovered. Compared with the f-x prediction interpolation method, DL performs better and is capable of avoiding several assumptions (e.g., linearity, sparsity, etc.) associated with conventional interpolation methods. We demonstrated the influences of the network depth, the kernel size of the convolution window, and the pooling function on the DL results. We applied the trained network to dense data reconstruction successfully. The proposed method can overcome noise to some extent. We finally discussed some practical aspects and extensions of the evaluated framework.

Seismic wave propagation through a fluid‐saturated poroelastic layer might be strongly affected by media heterogeneities. Via incorporating controlled laboratory simulation experiments, we extend previous studies of time‐lapse seismic effects to evaluate the wave scattering influence of the heterogeneous nature of porous permeable media and the associated amplification effects on 4D seismic response characteristics of reservoir fluid substitution. A physical model consisted of stratified thin layers of shale and porous sandstone reservoir with rock heterogeneities was built based on the geological data of a real hydrocarbon‐saturated reservoir in Northeast China. Multi‐surveys data of good quality were acquired by filling poroelastic reservoir layers with gas, water and oil in sequence. Experimental observations show that reservoir heterogeneity effect causes significantly magnified abnormal responses to the fluid‐saturated media. Specifically, reflection signatures of the gas‐filled reservoir are dramatically deviated from those of the liquid fluid‐filled reservoir, compared with ones of the homogeneous media. By removing the influences unrelated to reservoir property alterations, 4D seismic estimates of travel‐time and frequency‐dependent characteristic are reasonably consistent with fluid variations. Nevertheless, strong 4D amplitude difference anomalies might not correspond to the regions where fluid variations occur. We also find that 4D seismic difference attributes are evident between oil‐ and water‐filled models, whereas significant between oil‐ and gas‐filled models. Meanwhile, rock physics modelling results reveal the predicted 4D seismic differences are obviously smaller than those calculated from seismic observations. The results in this paper, therefore, implicate that the effect of a reservoir's heterogeneous nature might be beneficial for hydrocarbons detection as well as monitoring small variations in pore fluids.

Instantaneous seismic attributes are commonly used in assisting seismic interpretation and stratigraphy analysis. We compute the instantaneous seismic attributes using 1-D seismic traces and the corresponding quadrature (Hilbert transformed) traces. However, the 1-D seismic trace and the corresponding quadrature trace are sensitive to noise and seismic processing artifacts. To improve the lateral continuity of instantaneous seismic attributes, we propose to compute instantaneous attributes using multichannel seismic traces. Dynamic time warping (DTW) is used to align the seismic traces centered at the analysis point which mitigates the effect of structure dip on the multichannel complex seismic trace analysis (MCSTA). We fine interpolate the 1-D seismic traces to minimize the possible error in the computation of the error matrix of DTW. We also define a constraint in the backtracking of DTW to avoid severe strain (stretch or squeeze) between seismic traces. We obtain the “robust” 1-D complex seismic trace by applying Gaussian smoothing to the aligned complex seismic traces. We finally obtain instantaneous seismic attributes from the smoothed 1-D seismic trace and the corresponding quadrature trace. We show the superiority of new instantaneous attributes by applying our method to real seismic data.

The recorded seismic signals are attenuated and spatially correlated due to their propagation through an elastic earth and the sedimentary rule of strata. This attenuation phenomenon is quantified by means of the earth quality factor (Q) or the attenuation factor (1∕Q). Nowadays, the related Q-compensation and multi-trace inversion for the seismic data are two challenging problems when used for enhancing the temporal resolution and preserving the spatial continuity. Separately estimating Q and reflectivity are difficult and produce the uncertainty or ill-condition problems. To overcome these limitations, we have developed a multi-trace nonstationary sparse inversion with structural constraint. Using prior dipping-angle information and reflectivity sparsity property, the proposed method simultaneously estimates equivalent-Q and reflectivity with structural constraint. Constructed by the source wavelet and different scanned equivalent-Q, a series of time-varying (nonstationary) wavelet matrices are provided for the forward-modeling schemes and the corresponding inversions. When the Q-model is infinitely close to the true attenuation mechanism, the corresponding inverted reflectivity is comparatively sparse and quantified as maximum sparsity or minimum sparse representation. A sparse representation function, such as l0.1-norm, is used for sparsity measurement of the inverted reflectivity corresponding to each scanned Q. Through optimizing these sparse representation values, a suitable equivalent-Q, as well as the corresponding inverted reflectivity with structural preservation and Q-attenuation, is determined. The synthetic and field examples both confirmed a substantial improvement on seismic records, especially for Q-estimation, structure preservation and Q-compensation.

Normal moveout (NMO) correction is a routine step in seismic data processing, which has an important impact on other seismic processing procedures, seismic inversion, and interpretation. We propose a goal-oriented inversion-based NMO correction method using a convex $l_{2,1}$ -norm. The proposed method corrects the superresolution multichannel offset-dependent reflectivity rather than the bandlimited data itself sample by sample, block by block, or wavelet by wavelet. Therefore, the proposed method can essentially reduce the amplitude and even phase distortion introduced by data-based NMO correction methods in the presence of strong wavelet interference. We impose two goal-oriented constraints including both the temporal sparsity and the horizontal continuity of reflectivity, which are approximately represented by a convex $l_{2,1}$ -norm, on the geometric moveout relationship from offset-dependent trajectories to zero offsets to build a new objective function for NMO correction. The goal-desired temporal sparsity of reflectivity can induce the superresolution solution; meanwhile, the goal-desired horizontal continuity introduces a reasonable intrinsic structure to further limit the solution space and is particularly suitable to processing interfering reflections. Attributing to these two additional constraints, the new NMO correction method can flatten the interfering events and the intersecting events with favorable offset-dependent amplitude and phase variations even in the presence of noise. Synthetic and real data examples are adopted to verify the performance of our method. The results show that goal-oriented inversion-based NMO correction using the $l_{2,1}$ -norm is a potentially effective, stable, and high-quality NMO correction tool, especially for strong wavelet interference and at far offsets.

Dataset for the article "Fluid distribution effect on seismic dispersion and attenuation in biphasic saturated limestone- Direct measurement." by Chao SUN, Jérôme Fortin, Jan V.M. Borgomano, Shangxu Wang, Tom Bultreys, Veerle Cnudde submitted to Journal of Geophysical Research: Solid Earth. Please refer to the ReadMe file or to kang2008ping2008@163.com for more details.

Seismic interpolation can provide complete data for some multichannel processing techniques such as time lapse imaging and wave equation migration. However, field seismic data often contains random noise and noisy data interpolation is a challenging task. A traditional method applies interpolation and denoising separately, but this needs two workflows. Simultaneous interpolation and denoising combines interpolation and denoising in one workflow and can also get acceptable results. Most existing interpolation methods can only recover missing traces but fail to attenuate noise in sampled traces. In this study, a novel thresholding strategy is proposed to remove the noise in the sampled traces and meanwhile recover missing traces during interpolation. For each iteration, the residual is multiplied by a weighting factor and then added to the iterative solution, after which the sum in the transformed domain is calculated using the thresholding operation to update the iterative solution. To ensure that the interpolation and denoising results are robust, the exponential method was chosen to reduce the threshold values in small quantities. The curvelet transform was used as sparse representation and three interpolation methods were chosen as benchmarks. Three numerical tests results proved the effectiveness of the proposed method on removing noise in the sampled traces when the minimum threshold values are correctly chosen.