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The frequency band limitation of seismic data limits the resolution of full-waveform inversion (FWI) results. In addition, the high computational cost seriously affects the practical application of FWI. To alleviate these concerns, an FWI method based on superresolution (SR-FWI) is developed to improve the prediction efficiency and accuracy of the reservoir parameters. A channel attention mechanism is introduced for the multifrequency characteristics of the model images. A constrained residual channel attention network (CRCAN) is built for superresolution (SR) by adding structural constraints to the loss function of a deep learning network. A total of 65,000 sets of geologic models and natural images constitute the network training data, 90% of which are used for training with the rest used for testing. The iterative calculation for FWI is time-consuming; hence, SR is applied to the iterative process to reduce the number of iterations and accelerate the model update. Low-resolution images along with the synthetic and field data are used for the evaluation of the CRCAN and SR-FWI algorithms, respectively. The test results find that CRCAN can effectively improve the image resolution, whereas SR-FWI is beneficial due to its high efficiency and precision, especially in predicting the stratum edge and small-scale anomalies. Therefore, SR-FWI is a powerful means of reservoir static and dynamic detection and can provide high-resolution information for projects, such as resource development and CO2 storage.

Reservoir elastic parameters play an important role in resource exploration; however, the band-limited characteristics of seismic data and the ill-posed nature of seismic inversion significantly affect inversion accuracy. To alleviate this problem, a high-resolution prediction method for reservoir elastic parameters based on the progressive multitask learning network (PMLN) is proposed. Our network consists of three parts: network 1 for low-frequency extension (LFE), network 2 for reservoir parameter inversion, and network 3 for image superresolution (SR). Taking the seismic frequency band as the link, network 1 is first used to predict the low-frequency information of seismic data. Then, the nonlinear mapping relationship between the high-pass-filtered seismic data (and its envelope) and full-frequency seismic data is established. Second, network 2 directly predicts the reservoir elastic parameters using the seismic data after LFE. Finally, the SR of the inversion results is achieved from the image perspective based on network 3. The three networks have a progressive relationship and can share network features, which is beneficial for improving computing efficiency. As the features extracted by the network represent different contributions to the prediction target, a channel attention mechanism is introduced. Furthermore, the loss function of network 2 is improved using dip constraints to obtain high-precision reservoir parameters. Synthetic and field data analyses find that all three networks are competent for their respective tasks, and the PMLN can obtain high-resolution prediction results of reservoir elastic parameters. Compared with traditional full-waveform inversion, the PMLN effectively improves prediction accuracy. Therefore, the PMLN is expected to become a powerful tool for predicting the elastic parameters of reservoirs.

Seismic diffractions from small-scale discontinuities or inhomogeneities carry key geologic information and can provide high-resolution images of these objects. Because diffractions characterized by weak energy are easily masked by strong reflections, diffraction-enhancement processing is essential before subwavelength information detection. Therefore, a novel diffraction-separation method is developed that uses the Fourier-based geometric-mode decomposition (GMDF) algorithm to remove reflections and separate diffractions in the common-offset or poststack domain. The key idea of our method is that, in the frequency-wavenumber ( f- k) domain, strong reflections concentrate linearly along a certain dip direction, whereas weak diffractions are distributed over a wide range of wavenumbers owing to their variable dips in the time-space domain. The GMDF algorithm can effectively represent reflections with directional and linear geometric features by adaptively decomposing seismic data as a combination of the band-limited modes consisting of linear characteristics in the f- k domain. The alternating direction method of the multipliers algorithm is used to solve the GMDF optimization problem and obtain linear reflections. Because this method considers the energy sparsity property and linear geometric features of reflections in the f- k domain, kinematic and dynamic differences between reflections and diffractions are exploited to separate diffractions. Applied synthetic and field examples demonstrate the good performance of our method in removing strong reflections and separating weak diffractions, providing interpreters with detailed structural and stratigraphic information.

Coal is a complex viscoelastic porous medium with fractal characteristics at different scales. To model the macroscale structure of coal, a fractal viscoelastic model is established, and the P-wave velocity dispersion and attenuation characteristics are discussed based on the complex modulus derived from this model. The numerical simulation results indicate that the fractional order [Formula: see text] and relaxation time [Formula: see text] greatly affect the P-wave velocity dispersion and attenuation. The fractal viscoelastic model indicates a full-band velocity dispersion between 1 Hz and 104 Hz. Meanwhile, the P-wave velocity has a weaker dispersion with the fractal viscoelastic model than with the Kelvin-Voigt model and Zener model between 1 Hz and 104 Hz for the same relaxation time and elastic modulus, but the velocity at 1 Hz based on the fractal viscoelastic model is higher with the Kelvin-Voigt model and Zener model. Simultaneously, the velocities of five coal samples are tested, and the attenuation factor is calculated using a low-frequency system. The experimental results indicate a strong dispersion in coal in the range of 10–250 Hz. The classic Kelvin-Voigt model and Zener model cannot describe the dispersion characteristics of coal, but the fractal viscoelastic model can describe them well by using the appropriate fractional order and relaxation time.

Time-lapse seismic difference refers to the comprehensive response of fluid saturation, pore pressure, and porosity. However, the contribution of different parameters to the seismic response is difficult to distinguish. The high-precision prediction of these reservoir parameters is of great significance in CO2 geologic storage and oil and gas development. Therefore, a simultaneous time-lapse reservoir multiparameter prediction method based on a multitask learning network is proposed. Combined with CO2 geologic storage monitoring, the process of generating training data is described, involving numerical simulation, petrophysical models, and seismic forward modeling. Moreover, the Hertz-Mindlin formula, which considers pressure changes, is used to establish the relationship between formation elasticity and physical parameters in CO2 storage. The effects of fluid saturation, pressure, and porosity on P- and S-wave velocities and densities are analyzed, and the amplitude-variation-with-offset response characteristics of fluid saturation, pressure, and porosity changes are discussed. In total, 4700 and 300 sets of reservoir parameters and seismic angle gather data are used for network training and testing, respectively. The prediction results of synthetic and field data find that the time-lapse reservoir multiparameter prediction method based on multitask learning can effectively distinguish changes in each parameter and simultaneously obtain high-precision prediction results of fluid saturation, pressure, and porosity. Once the network is constructed, the prediction will take only a few seconds, which will promote the further development of the CO2 geologic storage theory and technology.

Faults are geological structures that can cause disasters and thereby affect the safety of coal mines. To achieve improved fault interpretation accuracy during 3D seismic exploration of coal mines, we propose a seismic fault identification method based on a combination of kernel principal component analysis (KPCA), genetic particle swarm optimization (GPSO) and a support vector machine (SVM). The Dongwupan area of the Sihe Coal Mine in Shanxi Province, which mainly contains small faults, is the research area, and we extract 20 types of seismic attributes. According to the median difference between fault and nonfault data, we select the 12 leading seismic attributes with differences greater than 0.1 in descending order. Considering information redundancy and the nonlinear relationships among seismic attributes, we adopt the KPCA method to reduce and optimize the selected seismic attributes, thereby effectively capturing the main information contained in the data and eliminating noise. Moreover, we introduce the GPSO algorithm to effectively optimize the SVM model parameters, and we construct a KPCA-GPSO-SVM model to classify and predict faults. Through model testing, the average fault identification accuracy of the model is 98.89%. Relative to the KPCA-PSO-SVM, PCA-GPSO-SVM and GPSO-SVM models, the accuracy is improved by 3.3%, 7.8% and 16.7%, respectively. We apply the proposed model to predict the fault distribution in the research area, and we compare the predictions to the actual exposed faults. The results indicate that the KPCA-GPSO-SVM model can suitably realize fault distribution prediction in a mining area. Moreover, compared to manual fault interpretation, the proposed method is faster, more intuitive and can better identify small faults.

Diffractions produced by subsurface geological features are an effective means of imaging small-scale discontinuities at high resolution. We developed a novel diffraction imaging approach that combines the geometric mode decomposition (GMD) algorithm and least-squares Gaussian distribution fitting (LSGDF) technique. In the dip-angle domain, reflections tend to look like smiles and are mainly focused in areas related to Fresnel zones, whereas diffractions spread over a wide illumination area due to their uniform radiation propagation. The GMD algorithm can effectively and simultaneously extract line-like components consisting of reflected energy in the Fresnel zone and diffracted energy in dip-angle gathers. The energy discrepancies between the reflection and diffraction events in the extracted line-like components allow for the separation of diffractions and suppression of reflections in dip-angle gathers using LSGDF. Numerical applications illustrate that the proposed method can eliminate large continuous reflectors and reveal discontinuous subsurface features. A real data example demonstrates the capability of the diffraction-imaging workflow in enhancing the resolving power of the imaging of subsurface geologic structures.

Diffractions possess the potential to reveal subsurface discontinuities, such as faults, collapsed columns, and the rough edges of the salt body. We have developed a novel diffraction separation method that first flattens the dominant reflections and then identifies the diffraction wavefields through an orthogonal polynomial transform (OPT). Based on the plane-wave assumption and local slope, the reflection events can be predicted and flattened using plane-wave differential equations. To enhance the stability of the flattening process, a sliding window algorithm and three finite-difference forms are adopted. As the dominant coherent event, a reflection often corresponds to low-order coefficients in the OPT. To better preserve the diffraction energy, a time-varying order threshold is used when removing the dominant reflections. Two field data applications are presented to demonstrate the feasibility and effectiveness of the proposed diffraction separation strategy.

Seismic diffractions encoding subsurface small-scale geologic structures have great potential for high-resolution imaging of subwavelength information. Diffraction separation from the dominant reflected wavefields still plays a vital role because of the weak energy characteristics of the diffractions. Traditional rank-reduction (RR) methods based on the low-rank assumption of reflection events have been commonly used for diffraction separation. However, these methods using truncated singular-value decomposition (TSVD) suffer from the problem of reflection-rank selection by singular-value spectrum analysis, especially for complicated seismic data. In addition, the separation problem for the tangent wavefields of reflections and diffractions is challenging. To alleviate these limitations, we have developed an effective diffraction separation strategy using an improved optimal RR (ORR) method to remove the dependence on the reflection rank and improve the quality of separation results. The improved RR method adaptively determines the optimal singular values from the input signals by directly solving an optimization problem that minimizes the Frobenius-norm difference between the estimated and exact reflections instead of the TSVD operation. This improved method can effectively overcome the problem of reflection-rank estimation in the global and local RR methods and adjusts to the diversity and complexity of seismic data. The adaptive data-driven algorithms indicate good performance in terms of the trade-off between high-quality diffraction separation and reflection suppression for the ORR operation. Applications of our strategy to synthetic and field examples demonstrate the superiority of diffraction separation in detecting and revealing subsurface small-scale geologic discontinuities and inhomogeneities.

Diffracted waves provide an opportunity to detect small-scale subsurface structures because they give wide illumination direction of geologic discontinuities, such as faults, pinch outs, and collapsed columns. However, separating diffracted waves is challenging because diffracted waves have greater geometric amplitude losses and are generally weaker than reflections. To retain more diffracted waves, we have developed a prestack diffraction separation method based on the local slope pattern and plane-wave destruction (PWD) method. In general, it is difficult to distinguish between hyperbolic reflections and hyperbolic diffractions using data-driven local slope estimation in the shot domain. Therefore, we transfer slope estimation in the shot domain to velocity analysis in the common-midpoint domain and ray parameter calculation in the stack domain. The connection between local slope and the normal moveout velocity and the surface-ray parameter is known, which provides a novel approach for estimating the local slope of hyperbolic reflected waves in the shot domain. The estimated slope can provide an exact slope-based operator for the PWD method, thus allowing the PWD to separate diffracted waves from reflected waves in the shot domain. Synthetic and field data tests demonstrate the feasibility and effectiveness of our prestack diffraction separation method.

Diffraction imaging is an important technique for high-resolution imaging because of the close relationship between diffractions and small-scale discontinuities. Therefore, we we have developed a diffraction imaging method using a mathematical morphological filter (MMF). In a common image gather, reflections have an evident energy band associated with the Fresnel zone and stationary point, whereas diffractions can be observed in a wide illumination direction and therefore have no energy band. Based on these phenomena, we analyze the amplitude distributions of the diffractions and reflections and develop a time-varying structuring element (SE) in the MMF. Based on the time-varying SE, our method can effectively suppress reflections and has the advantage of automatically preserving the diffractions energy near the stationary point. Numerical and field experiments demonstrate the efficient performance of the proposed method in imaging diffractions and obtaining high-resolution information.

Diffractions are the seismic responses of subsurface small-scale geologic discontinuities or inhomogeneities, whose energy is much weaker than that of reflections. To eliminate the masking effect of strong reflections on weak diffractions, a prestack diffraction separation method is proposed based on the common virtual source gather (CVSG) and the median filter. The reflection generated from a reflector can be regarded as originating from a virtual source (or a focused area). According to this behavior, the reflection can be transformed into its corresponding virtual source position to build the CVSG. Unlike the reflection, diffraction cannot be regarded as originating from one virtual source. Therefore, diffractions have a curved shape, whereas reflections are flat in the CVSG. Based on the traveltime moveout method, the reflection traveltime is calculated for describing reflection events and generating CVSG. Theory and a simple synthetic data test demonstrate that there is almost no energy lost when transforming between a shot gather and CVSG. Then, for removing the reflection, the median filter is used in the CVSG where the reflection appears as a linear event. Complex synthetic and field examples demonstrate that the proposed method can flatten reflection events and thus can separate diffraction events from strong reflections in the prestack domain.

Traditional diffraction images without a specific migration kernel for promoting focusing abilities may cause confusion to seismic interpretation because diffraction images may show a finite-array response of diffracted/scattered waves. Because diffractors are discontinuous and sparsely distributed, a least-squares diffraction-imaging method is formulated by solving a hybrid L1-L2 norm minimization problem that imposes a sparsity constraint on diffraction images. It uses two different forward modeling operators for reflections and diffractions and L2 and L1 regularizations for penalizing the amplitudes of the reflection and diffraction images, respectively. A classic Kirchhoff diffraction demigration operator is implemented on an initial diffraction image model to synthesize diffracted/scattered waves. A Kirchhoff reflection demigration operator, formulated by considering the local reflection slopes and a cosine attenuation weighting function, is implemented on an initial reflection image to synthesize the reflected waves. A modified alternating direction approach of multipliers is developed for iteratively solving this minimization problem to create diffraction images and their separated diffractions. The depths and local reflection slopes of the reflection images are fixed during this iteration. To alleviate the energy leakage between diffractions and reflections, after performing the plane-wave destruction method on the conventional migration data, its estimated reflection image and residual image are provided as the initial reflection and diffraction images, respectively. Our method can remove steep-slope reflections, increase the focusing power of the diffractions, and eliminate noise. Two numerical experiments demonstrate its capability of separating and imaging small-scale discontinuities and inhomogeneities. The exposed geologic structures in the tunnel of field coal mining further illustrate this method’s potential in ascertaining hidden faults, edges, and collapsed columns. A safety warning should be definitely required if a mining working surface is advancing these hidden geologic disasters because an emergency of water bursting or gas leakage may happen.

Accurate measurement of coalbed methane (CBM) content is the foundation for CBM resource exploration and development. Machine-learning techniques can help address CBM content prediction tasks. Due to the small amount of actual measurement data and the shallow model structure, however, the results from traditional machine-learning models have errors to some extent. We have developed a deep belief network (DBN)-based model with the input as continuous real values and the activation function as the rectified linear unit. We first calculated a variety of seismic attributes of the target coal seam to highlight the features of the coal seam, then we preprocessed the original attribute features, and finally developed the performance of the DBN model using the preprocessed features. We used 23,374 training data to train our model, 23,240 for pretraining, and 134 for fine-tuning. For the purpose of demonstrating the advantages of the DBN model, we compared it with two typical machine-learning models, including the multilayer perceptron model and the support vector regression model. These two models were trained based on the same labeled training data. The results, obtained from different models, indicated that the DBN model has the least error, which means that it is more accurate than the other two models when used to predict CBM content.

To enable a mathematical description, geologic fractures are considered as infinitely thin planes embedded in a homogeneous medium. These fracture structures satisfy linear slip boundary conditions, namely, a discontinuous displacement and continuous stress. The general finite-difference (FD) method described by the elastic wave equations has challenges when attempting to simulate the propagation of waves at the fracture interface. The FD method expressed by velocity-stress variables with the explicit application of boundary conditions at the fracture interface facilitates the simulation of wave propagation in fractured discontinuous media that are described by elastic wave equations and linear slip interface conditions. We have developed a new FD scheme for horizontal and vertical fracture media. In this scheme, a fictitious grid is introduced to describe the discontinuous velocity at the fracture interface and a rotated staggered grid is used to accurately indicate the location of the fracture. The new FD scheme satisfies nonwelded contact boundary conditions, unlike traditional approaches. Numerical simulations in different fracture media indicate that our scheme is accurate. The results demonstrate that the reflection coefficient of the fractured interface varies with the incident angle, wavelet frequency, and normal and tangential fracture compliances. Our scheme and conclusions from this study will be useful in assessing the properties of fractures, enabling the proper delineation of fractured reservoirs.

Seismic diffractions are the responses of small-scale discontinuous structures. They contain subwavelength geologic information. Thus, diffractions can be used for high-resolution imaging. The energy of diffractions is generally much weaker than that of reflections. Therefore, diffracted energy is typically masked by specular reflected energy. Diffraction/reflection separation is a crucial preprocessing step for diffraction imaging. To resolve the diffraction-separation problem, we have developed a method based on the multichannel singular-spectrum analysis (MSSA) algorithm for diffraction separation by reflection suppression. The MSSA algorithm uses the differences in the kinematic and dynamic properties between reflections and diffractions to suppress time-linear signals (reflections) and separate weaker time-nonlinear signals (diffractions) in the common-offset or poststack domain. For the time-linear signals, the magnitudes of the singular values are proportional to the energy strength of the signals. The stronger the energy of a component of the linear signals is, the larger the corresponding singular values will be. The singular values of reflections and diffractions have dissimilar spatial distributions in the singular-value spectrum because of the differences in their linear properties and energy. Only the singular values representing diffractions are selected to reconstruct seismic signals. Synthetic data and field data are used to test our method. The results reveal the good performance of the MSSA algorithm in enhancing diffractions and suppressing reflections.

Seismic weak responses from subsurface small-scale geologic discontinuities or inhomogeneities are encoded in 3D diffractions. Separating weak diffractions from a strong reflection background is a difficult problem for diffraction imaging, especially for the 3D case when they are tangent to or interfering with each other. Most conventional diffraction separation methods ignore the azimuth discrepancy between reflections and diffractions when suppressing reflections. In fact, the reflections associated with a specific pair of azimuth-dip angle possess sparse characteristics, and the diffractions adhering to Huygens’ principle behave as low-rank components. Therefore, we have developed a 3D low-rank diffraction imaging method that uses the Mahalanobis-based low-rank and sparse matrix decomposition method for separating and imaging 3D diffractions in the azimuth-dip angle image matrix. The advantages of our 3D diffraction imaging method not only includes the handling of interfering events but also includes ensuring a better protection of weak diffractions. The numerical experiment illustrates the good performance of our method in imaging small-scale discontinuities and inhomogeneities. The field data application of carbonate reservoirs further confirms its potential value in resolving the masked small-scale cavities that can provide storage spaces and a migration pathway for petroleum.

Interpretation of geologic structures entails ambiguity and uncertainties. It usually requires interpreter judgment and is time consuming. Deep exploitation of resources challenges the accuracy and efficiency of geologic structure interpretation. The application of machine-learning algorithms to seismic interpretation can effectively solve these problems. We analyzed the theory and applicability of five machine-learning algorithms. Seismic forward modeling is a key connection between the model and seismic response, and it can obtain seismic data of known geologic structures. Based on the modeling data, we first optimized the seismic attributes sensitive to the target geologic structure and then we verified the accuracy of the five machine-learning algorithms by the cross-checking method. In this case, the random forest algorithm had the highest accuracy. So we examined the structural interpretation method based on a random forest using the 3D seismic reflection data from coalfield exploration. The prediction effect of this interpretation workflow is verified by comparison with known geologic structures on the plane and profile. The results suggest that the random forest algorithm is feasible to indicate geologic structure interpretations in the case of collapsed column and fault structures and it can effectively improve the efficiency of seismic interpretation and its accuracy. The machine-learning-based workflow provides a new technique for seismic structure interpretation in coal mining.

The conventional equation for 3D edge diffractions in the Cartesian coordinate system lacks angle information for studying the energy patterns in 3D seismic prestack data. Here, a new calculation method is presented for determining 3D edge-diffraction coefficients in a spherical coordinate system that can formulate the coefficients according to the azimuth and emergence angles. To avoid the singularity phenomenon, a Haar wavelet operator matrix is used for this new method. Analysis of the edge-diffraction coefficients variations with azimuth in the common-shot domain, common-receiver domain, and common-midpoint domain reveals that the variation curves of the coefficients can be used to identify the trend of a fault. The phenomenon of polarity reversal of the edge-diffraction coefficients is observed in the different domains, and the coefficients in the common-shot domain are more sensitive than in other domains.

The bulk density and bulk modulus of adsorbed coalbed methane are required to calculate the undrained bulk and shear moduli as well as the fluid-saturated density of the coal reservoir. We derived the formula for the bulk modulus and bulk density of adsorbed methane using the Langmuir equation for isothermal adsorption. The bulk density of adsorbed methane is positively correlated with the gas pressure and Langmuir volume, but it is negatively correlated with the Langmuir pressure and adsorbed methane saturation. The bulk density of adsorbed methane is greater than that of free-state methane for the same gas pressure. The bulk modulus of adsorbed methane is positively correlated with the gas pressure and negatively correlated with the Langmuir pressure; it is much larger than that of free methane, but it is still much smaller than that of water within the normal gas pressure range. Coal samples from the study area demonstrate that the water saturation is less than 95%. Considering adsorbed methane as a pseudosolid, calculations yield a very small difference in the bulk modulus of coal under room-dry conditions. Considering adsorbed methane as a gas, calculations based on spatially uniform or patchy saturation indicate that multiphase fluid saturation produces a very small difference in the elastic parameters and wave velocity of the fluid-saturated coal from the dual-phase fluid (water and free methane).

Seismic diffractions contain valuable information regarding small-scale inhomogeneities or discontinuities, and therefore they can be used for seismic interpretation in the exploitation of hydrocarbon reservoirs. Velocity analysis is a necessary step for accurate imaging of these diffractions. A new method for diffraction velocity analysis and imaging is proposed that uses an improved adaptive minimum variance beamforming technique. This method incorporates the minimum variance, coherence factor, and correlation properties to improve the signal-to-noise ratio and enhance correlations. Our method can make seismic diffractions become better focused in semblance panels, allowing for the optimal migration velocity for diffractions to be accurately picked. Synthetic and field examples demonstrate that the migration velocity for the diffractions can differ from that for the reflections. The results suggest that the diffraction velocity analysis and imaging method is feasible for accurately locating and identifying small-scale discontinuities, which leads to the possibility of using this approach for practical application and seismic interpretation.

With the incident P-wave, we derive approximate formulas for amplitudes and polarizations of waves reflected from and transmitted through a planar, horizontal boundary between an overlying isotropic medium and an underlying tilted transversely isotropic (TTI) medium assuming that the directions of the phase and group velocities are consistent. Provided that the velocities in the isotropic medium are equal to the velocities along the symmetry axis direction, we derive the relational expression between the propagation angle in the TTI medium and the propagation angle in the hypothetical isotropic medium, under the condition that the horizontal slowness is the same, and then we update the approximate formula of the polarization in the TTI medium. Provided that the slow and fast transverse waves (qS and SH) are generated simultaneously in the anisotropic interface, we linearize for a six-order Zoeppritz equation, derive the azimuthal formula of longitudinal and S-waves, and determine their detailed expressions within the symmetry axis plane. According to the derived azimuthal AVO formula, we establish medium models, compare the derived AVO with the precision, and obtain the following conclusions: (1) The dip angle for the symmetry axis with respect to the vertical may have a sufficiently large impact on AVO, and the vertical longitudinal wave can generate an S-wave. (2) For the derived AVO formula, within the symmetry axis plane, the fitting effect of the approximate and exact formulas is good; however, within the other incident planes, taking the azimuth angle 45° as an example, the approximation is suitable for the large impedance contrast if the anisotropic parameters are set properly. (3) The error between the approximation and precision is mainly caused by the difference between the reflected and transmitted angles, the velocities’ derivation with respect to azimuth, and the division of approximation into isotropic and anisotropic parts.

Clarifying and locating small-scale discontinuities or inhomogeneities in the subsurface, such as faults and collapsed columns, plays a vital role in safe coal mining because these discontinuities or inhomogeneities may destroy the continuity of layers and result in dangerous mining accidents. Diffractions carry key information from these objects and therefore can be used for high-resolution imaging. However, diffracted/scattered waves are much weaker than reflected waves and consequently require separation before being imaged. We have developed a Mahalanobis-based diffraction imaging method by modifying the classic Kirchhoff formula with an exponential function to account for the dynamic differences between reflections and diffractions in the shot domain. The imaging method can automatically account for destroying of reflected waves, constructive stacking of diffracted waves, and strengthening of scattered waves. The method can overcome the difficulties in handling Fresnel apertures, and it is suitable for high-resolution imaging because of the consistency of the waveforms in the shot domain. Although the proposed method in principle requires a good migration velocity model for calculating elementary diffraction traveltimes, it is robust to an inaccurate migration velocity model. Two numerical experiments demonstrate the feasibility of the proposed method in removing reflections and highlighting diffractions, and one field application further confirms its efficiency in resolving masked faults and collapsed columns.

The State Key Laboratory of Coal Resources and Safe Mining at the China University of Mining and Technology organized a workshop on the large-scale geophysical laboratory model site (LGLMS) in Lincheng County, Hebei Province, People's Republic of China on 9 June 2018. The theme of the workshop was on the design and construction of the LGLMS.

There are similarities and differences in employing amplitude variation with offset (AVO) to explore for gas-sand reservoirs, as opposed to coal-bed methane (CBM) reservoirs. The main similarity is that large Poisson’s ratio contrasts, resulting in AVO gradient anomalies, are expected for both kinds of reservoirs. The main difference is that cleating and fracturing raise the Poisson’s ratio of a coal seam as it improves its reservoir potential for CBM, while gas always lowers the Poisson’s ratio of a sandstone reservoir. The top of gas sands usually has a negative AVO gradient, leading to a class one, two, or three anomaly depending on the impedance contrast with the overlying caprock. On the other hand, the top of a CBM reservoir has a positive AVO gradient, leading to a class four anomaly. Three environmental factors may limit the usage of AVO for CBM reservoirs: the smaller contrast in Poisson’s ratio between a CBM reservoir and its surrounding rock, variations in the caprock of a specific CBM reservoir, and the fact that CBM is not always free to collect at structurally high points in the reservoir. However, other factors work in favor of using AVO. The strikingly high reflection amplitude of coal improves signal/noise ratio and hence the reliability of AVO measurements. The relatively simple characteristics of AVO anomalies make them easy to interpret. Because faults are known to improve the quality of CBM reservoirs, faults accompanied by AVO anomalies would be especially convincing. A 3D-AVO example offered in this paper shows that AVO might be helpful to delineate methane-rich sweet spots within coal seams.

For converted waves, stacking traces with a common reflection point, forming gathers, and performing dip moveout (DMO) all require accurately calculating the location of conversion points. Because of the asymmetrical paths of converted waves, even for horizontally layered media, the calculation of a conversion point for converted waves is complicated. Previous authors have obtained analytic solutions for the conversion point for converted waves in a horizontally layered media. We extend those results to the more general case of converted waves from a dipping reflector with a homogeneous, isotropic overburden. By using Snell's law, we derive a quartic equation and solve it uniquely for the conversion point. The resultant analytic expression is a function of offset, compressional-, and shear-wave velocities; normal reflector depth; and dip angle at the conversion point. This solution can be readily used to generate accurate synthetic seismic responses for converted waves based on ray theory. It also can be extended to operators for stacking converted waves and applying DMO correction.

The precision of C-wave traveltime approximations directly affects the velocity analysis and migration. Different types of traveltime approximations always have different kinds of parameterization and applicability. Because of the shallow depth of coal seam, it is difficult for conventional approximations to ensure the accuracy of converted wave exploration about x/z>2.5 (offset/depth > 2.5). Based on the fraction expansion of traveltime approximation, a revised moveout equation for converted wave is derived. The results of synthetic and real coalfield data show that the revised moveout equation is superior to the conventional approximations in the far offsets in the coalfield C-wave exploration.