Geophysical Prospecting - Volume 72, Issue 5, 2024

Estimating clean seismic signals from noisy single‐channel records is a hot research topic in the field of microseismic data processing. Due to the existence of strong random noise, the signal‐to‐noise ratio of such data is low, presenting a challenge for signal restoration. In this paper, we propose a denoising method of microseismic data based on a single‐channel phase space reconstruction and independent component analysis algorithm. Specifically, we first apply the phase space reconstruction to transform the one‐dimensional seismic signal into a high‐dimensional phase space in which signal and noise have different trajectories. We then employ independent component analysis to the reconstructed data for noise separation. Experimental results on real microseismic data verify that our proposed denoising method is useful for noise suppression and can enhance the signal‐to‐noise ratio of data, which can be further used for signal identification and event positioning in microseismic monitoring.

We developed an algorithm to simulate two‐dimensional frequency domain acoustic‐wave response in a transversely isotropic medium with a tilted symmetry axis. The algorithm employs a support operator finite‐difference method for modelling. This method constructs a nine‐point stencil finite‐difference scheme for second‐order elliptic equations for generalized anisotropic physical properties. The medium's properties are described as P‐wave velocity on the symmetric axis, density, Thomsen's anisotropic parameters (epsilon and delta) and the tilt angle. The benchmarking analysis of the modelled amplitude is illustrated using an isotropic whole‐space model. Several synthetic experiments are conducted to evaluate the accuracy of the scheme for anisotropic models. The results suggest that the developed algorithm simulates the P‐wave solution and the fictitious S‐wave mode as reported in the literature. Simulation for a heterogeneous model with a spatially varying tilt angle of the medium symmetry axis is performed to ascertain the algorithm's robustness. The outcomes of the numerical experiments demonstrate that the developed algorithm can accurately simulate the frequency domain response of acoustic waves in the tilted anisotropic media.

The potential application of conducting Scholte‐wave analysis using electroseismic pressure fields excited by an electric current source due to the electrokinetic effect in fluid‐saturated porous seabed sediments is investigated. First, we develop a numerical modelling algorithm by combining the Luco–Apsel–Chen generalized reflection and transmission method with the peak‐trough averaging method to simulate the electroseismic wave fields in stratified fluid/porous media. The modelling results show that the electroseismic pressure signals recorded on the seafloor are mainly composed of evanescent electroseismic waves, and Scholte waves are the dominant wave pattern. Their amplitudes are generally within the order of magnitudes capable of being detected by current seismic instruments. Then, the modified frequency–Bessel transform method is extended to extract the Scholte‐wave dispersion curves from electroseismic pressure fields. Results demonstrate that Scholte‐wave dispersion curves extracted from electroseismic records are superior to those extracted from conventional seismic wave fields excited by an airgun source under the same source–receiver geometry because they contain many overtones and are almost free from the interferences of dispersive guided waves. Furthermore, the Scholte‐wave dispersion inversion results obtained by employing the Levenberg–Marquardt method show that the shear‐wave velocity model inverted by Scholte‐wave dispersion curves extracted from the electroseismic pressure field is more accurate than those obtained by dispersion curves extracted from the seismic wave fields with the guided‐wave removal. The above results indicate that the electroseismic Scholte‐wave analysis method has the potential to evaluate the shear‐wave velocities of shallow‐water seabed sediments.

Random noise attenuation is a fundamental task in seismic data processing aimed at improving the signal‐to‐noise ratio of seismic data, thereby improving the efficiency and accuracy of subsequent seismic data processing and interpretation. To this end, model‐based and data‐driven seismic data denoising methods have been widely applied, including f–x deconvolution, K‐singular value decomposition, feed‐forward denoising convolutional neural network and U‐Net (an improved fully convolutional neural network structure), which have received widespread attention for their effectiveness in attenuating random noise. However, they often struggle with low‐signal‐to‐noise ratio data and complex noise environments, leading to poor performance and leakage of effective signals. To address these issues, we propose a novel approach for random noise attenuation. This approach employs a multi‐model stacking structure, where the parameters governing this structure are optimized using a particle swarm optimizer. In the model‐based denoising method, we choose the f–x deconvolution method, whereas in the data‐driven denoising method, we choose K‐singular value decomposition for shallow learning and U‐Net for deep learning as components of the multi‐model stacking structure. The optimal parameters for the multi‐model stacking structure are obtained using a particle swarm optimizer, guided by the proposed novel hybrid fitness function incorporating weighted signal‐to‐noise ratio, structural similarity and correlation parameters. Finally, the effectiveness of the proposed method is verified with three synthetic and two real seismic datasets. The results demonstrate that the proposed method is effective in attenuating random noise and outperforms the benchmark methods in denoising both synthetic and real seismic data.

Deghosting is an important technique in the marine seismic industry, as it plays a crucial role in mitigating the effects of ghost reflections from the sea surface, which can significantly impact the accuracy and resolution of subsurface imaging. In recent years, various acquisition‐based techniques have been developed to tackle the challenge of removing receiver–ghost reflections, which is the focus of our paper. These state‐of‐the‐art approaches, such as dual‐sensor or multicomponent towed streamer acquisitions, have demonstrated exceptional accuracy by combining pressure and particle motion data. However, such methods face limitations when dealing with low frequencies due to heavy noise contamination in the particle motion data. Consequently, ghost‐free data reconstruction at low frequencies typically relies on processing‐based approaches, which exclusively utilize recorded pressure data. This study presents a novel deghosting method for low‐frequency applications based on parabolic dictionary learning, which relies solely on recorded pressure data. The proposed method has the advantage of being applicable directly in a compressed domain, eliminating the need for data decompression prior to the deghosting process when compression is applied before the processing steps. This not only reduces costs related to data storage and transfer but also provides a cost‐effective alternative to conventional deghosting by operating directly on the compressed data format, which is smaller in size. The effectiveness of the proposed method was evaluated using both synthetic and field datasets. The results obtained from a synthetic data example indicate that the proposed method achieves similar results to an industry‐standard frequency–wavenumber method, while achieving a compression rate of over 7. Furthermore, the method was tested using a field dataset consisting of a full sail‐line of marine seismic acquisition. The comparison of 2D pre‐stack migrated images between the proposed method and the industry‐standard frequency–wavenumber method revealed insignificant differences, while achieving a compression ratio higher than 5 when our method was used.

Geostatistical seismic inversion is an important method for establishing high‐resolution reservoir parameter models. There is no accurate representation method for reservoir structural features, and prior information about structural features cannot be incorporated into geostatistical inversion. Based on the assumption of the sparsity of stratigraphic sedimentary features, the same type of structural feature is used to represent the sedimentary pattern of reservoirs within the same facies. Different sparse representation patterns are used to represent the differences in sedimentary patterns between facies. Although changes in depositional environment might result in the multi‐scale characteristics of geological structures for varying sedimentary rhythms, this paper proposes a facies‐constrained geostatistical inversion method based on multi‐scale sparse representation to better accommodate such situation. Using the method of sparse representation combined with wavelet transform, the multi‐scale sedimentary structural features of reservoirs are learned from well‐logging data. Seismic facies and multi‐scale features are used as prior information for geostatistical inversion. Further, the likelihood function is constructed using seismic data to obtain the posterior probability distribution of reservoir parameters. Finally, the accurate inversion result is obtained by using multi‐scale sparse representation as a constraint in the posterior probability distribution of reservoir parameters. Compared with conventional geostatistical methods, this algorithm can better match the structural features of reservoir parameters with varying geological conditions. Field data tests have shown the effectiveness of this method in improving the accuracy and resolution of reservoir parameter structural features.

Improving the resolution of seismic migration images plays an important role for geophysical interpreters to characterize underground reservoirs. However, the classical image domain least‐squares migration method based on the local‐stationary assumption cannot obtain a satisfactory high‐resolution seismic image due to the significant spatial variant characteristics of the point spread function. To mitigate this problem, we proposed a high‐resolution point spread function deconvolution method and applied it to two‐dimensional cases. Nevertheless, extending the two‐dimensional method to three‐dimensional problems directly would fail due to the intrinsic complexity in three‐dimensional cases. In this study, we resolve the differences encountered in the point spread function deconvolution method for two‐ and three‐dimensional cases and provide specific strategies for achieving high‐resolution imaging with low computational cost when extending the point spread function deconvolution method to three‐dimensional cases. The main schemes include (1) incorporating the analytical expression of the point spread function to guide the generation of three‐dimensional point spread function distributions, (2) extending the point spread function filter calculation method from a two‐dimensional square to a three‐dimensional rectangular prism and (3) interpolating to obtain more compact point spread functions for reducing migration artefacts. Results from the three‐dimensional synthetic Overthrust model and field data set demonstrate that our techniques could effectively enhance the spatial resolution of the migration images with reduced migration artefacts. With these specific strategies, the space‐variant point spread function deconvolution algorithm shows superior performance on three‐dimensional cases at a much lower computational cost compared with the classical least‐squares migration method and the local‐stationary deblurring method. Synthetic tests and real data applications confirm that the space‐variant point spread function deconvolution method has distinct advantages over both two‐ and three‐dimensional problems and can be widely adopted in practice.

Geophysical prospecting signals encompass subsurface structural information and incorporate textual messages generated in accordance with a specific pattern. These signals can be employed in places without radio access to ensure public and worker safety. Therefore, the use of seismic signals to transmit information through the earth has attracted the attention of researchers in the last decade. Presently, achievements in seismic communication are mainly in the coding, generation, and propagation of seismic signals. Little work has been done on methods to convert seismic signals generated by vibroseis sources into text and broadcast them vocally. Therefore, we built a seismic communication system with 6‐bit code using the American Standard Code for Information Interchange. To better recommend the seismic communication system scheme, the origin, state and principles of seismic communication system are illustrated in detail. Then, a seismic transmitting system is devised with a 500 N vibroseis source, which compiles seismic signals through amplitude modulation. After seismic signals propagate through the earth, they are received by geophones and recorded in seismographs. Through data acquisition based on a compression algorithm, seismic signals are converted into text and voice signals, which significantly reduces the storage and transmission of seismic data.

Marine vibrators represent an alternative seismic source technology that could come to market in the near future. A key challenge related to marine vibrator seismic data is the effect that phase dispersion from source motion has on the signal during transmission. As such, the recorded moving vibrator data will benefit from being phase corrected, so that the data appear as if they had been shot with a stationary source. This transformation is called the source motion correction. Previous source motion corrections used either specific dephasing operators for specific sweep types or pre‐correlation methods for any sweep type. A source motion correction dephasing operator has been derived, demonstrated and applied to real seismic data collected during a Marine Vibrator Joint Industry Project field trial of an array of marine vibrators. This dephasing operator has been made more general so that any strictly monotonic sweep through time may be used for this correction regardless of sweep type (e.g. linear or exponential). Moreover, the correction uses the pilot sweep as a direct input, measuring from it, the instantaneous frequency which can then be used to build the dephasing operator. This new more general form brings two key advantages over previous dephasing operator corrections: (1) Non‐analytically defined sweeps can now be source motion corrected, and (2) even when an analytically defined sweep (e.g. linear) is used, the transmitted sweep from the marine vibrator can vary from the theoretical input sweep; this correction can account for these changes. Furthermore, given that this source motion correction is a dephasing operator, it can be applied pre‐ or post‐correlation of the raw data with the pilot sweep, thus allowing greater flexibility in the processing. Lastly, some previously derived source motion corrections based on dephasing operators contained errors in their derivation; this new derivation addresses these errors resulting in an improved correction.

The presence of coherent noise in seismic data leads to errors and uncertainties, and as such it is paramount to suppress noise as early and efficiently as possible. Self‐supervised denoising circumvents the common requirement of deep learning procedures of having noisy‐clean training pairs. However, self‐supervised coherent noise suppression methods require extensive knowledge of the noise statistics. We propose the use of explainable artificial intelligence approaches to ‘see inside the black box’ that is the denoising network and use the gained knowledge to replace the need for any prior knowledge of the noise itself. This is achieved in practice by leveraging bias‐free networks and the direct linear link between input and output provided by the associated Jacobian matrix; we show that a simple averaging of the Jacobian contributions over a number of randomly selected input pixels provides an indication of the most effective mask to suppress noise present in the data. The proposed method, therefore, becomes a fully automated denoising procedure requiring no clean training labels or prior knowledge. Realistic synthetic examples with noise signals of varying complexities, ranging from simple time‐correlated noise to complex pseudo‐rig noise propagating at the velocity of the ocean, are used to validate the proposed approach. Its automated nature is highlighted further by an application to two field data sets. Without any substantial pre‐processing or any knowledge of the acquisition environment, the automatically identified blind masks are shown to perform well in suppressing both trace‐wise noise in common shot gathers from the Volve marine data set and coloured noise in post‐stack seismic images from a land seismic survey.

We have developed a numerical scheme for the second‐order acoustic wave equation based on the Lie product formula and Taylor‐series expansion. The scheme has been derived from the analytical solution of the wave equation and in the approximation of the time derivative for a wavefield. Through these two equations, we obtained the first‐order differential equation in time, where the time evolution operator of the analytic solution of this differential equation is written as a product of exponential matrices. The new numerical solution using a Lie product formula may be combined with Taylor‐series, Chebyshev, Hermite and Legendre polynomial expansion or any other expansion for the cosine function. We use the proposed scheme combined with the second‐ or fourth‐order Taylor approximations to propagate the wavefields in a recursive procedure, in a stable manner, accurately and efficiently with even larger time steps than the conventional finite‐difference method. Moreover, our numerical scheme has provided results with the same quality as the rapid expansion method but requiring fewer computations of the Laplacian operator per time step. The numerical results have shown that the proposed scheme is efficient and accurate in seismic modelling, reverse time migration and least‐squares reverse time migration.

The high precision identification of coal–rock layers is a significant challenge in intelligent mining. There is a large amount of electromagnetic noise and metal reflector signals in the full space detection environment of mining roadway, which makes it hard to distinguish the reflected waves at interface from a set of echo signals generated by the interface due to the similar amplitudes among them. So the method of identifying layers solely based on amplitude characteristics has poor stability and accuracy in coal mining environments. This paper proposes a method for identifying coal–rock layers based on Hilbert transform and tracking–scanning–stacking technology. There are two steps to achieve the recognition of air–coal–rock interfaces. First, by analysing the instantaneous amplitude spectrum obtained from the Hilbert transform, the first extreme point that is always the maximum value within a wavelength range is determined as the rough position of the air–coal interface. To solve the problem of recognition errors caused by noise and energy dispersion, the density difference method is used to remove discrete points. Second, the precise position of the air–coal interface is determined by tracking the extreme points within the 1.5 wavelength range around the rough position, and using the amplitude stacking method to quantitatively analyse and compare the degree of energy concentration. The data between zero time and the reflected waves at the air–coal interface is removed to avoid the impact of them on the recognition of the coal–rock interface. Results of physical model experiments and actual coal mine experiments show that this method yields better results and has high stability compared to conventional recognition method. Moreover, the average relative thickness errors are 4.5% for air layer and 4.2% for coal layer.

Deep learning has gained attraction amongst geophysicists for solving complex longstanding problems. Nevertheless, proper hyperparameter optimization methodologies remain critically underexplored in geophysical deep learning research. This paper attempts to first highlight the importance of hyperparameter optimization and then showcase two geophysics‐related deep learning examples where a grid search and Optuna framework (an automated optimization approach) were used for hyperparameter optimization. We consider two geophysical problems related to denoising seismic traces and the inversion of seismic traces for velocity information. In both cases, models created based on Optuna hyperparameter optimization were able to perform better than those created through grid search. The most significant advantage of Optuna, however, is having quantifiable results to justify the choice of a neural network architecture, depth and other hyperparameters rather than relying on inefficient methods of exploring the hyperparameter space such as a trial‐and‐error or grid search. This study aims to stimulate further exploration and adoption of these frameworks, pushing the boundaries of current deep learning based geophysical problem‐solving methodologies towards full automation.

Reservoir monitoring is essential to guarantee safe operations for all activities involving the production and injection of fluids into the subsurface, such as hydrocarbon production, gas storage and the exploitation of geothermal reservoirs. For this purpose, microseismic monitoring networks are operated in real time in order to identify and locate any possible seismic events in the vicinity of the reservoir. The goal of this study is to investigate whether the large amount of ambient seismic noise recorded by seismic reservoir monitoring networks can be used to infer a one‐dimensional shear‐wave velocity profile representative of the area covered by the network. Shear‐wave velocities are generally difficult to characterize and constrain, yet they are key to precisely locate seismic events. The adopted workflow consists of three steps: first, the cross‐correlation functions between all station pairs are retrieved, using 1 year of continuous data; second, the average group‐ and phase velocity dispersion curves are extracted; third, a joint group and phase velocity inversion is done. For validation, the obtained average shear‐wave velocity profile is compared with a regional model of the area as well as with local shear‐wave velocity measurements from a sonic log.

Seismic inversion is an important tool for reservoir characterization. The inversion results are significantly impacted by a reliable initial model. Conventional well interpolation methods are not able to meet the needs of seismic inversion for lateral heterogeneous reservoirs. Inspired by the sequence modelling network and seismic inversion in the Laplace–Fourier domain, we propose an initial model‐building method using semi‐supervised learning strategy. The proposed method considers spatial information to ensure the horizontal continuity of the initial model. Based on the fact that the low‐frequency components of seismic signals in the Laplace–Fourier domain are easier to obtain, we use the forward model in the Laplace–Fourier domain to replace the time‐domain forward model. The proposed workflow was validated using the Marmousi II model. Although the training was carried out on a small number of low‐frequency impedance traces, the proposed workflow was able to build low‐frequency model for the entire Marmousi II model with a correlation of 98%. Field data examples demonstrate the feasibility and effectiveness of the proposed method. For lateral heterogeneous reservoirs, the proposed method performs better than the well interpolation method. By utilizing the model obtained by the proposed method as the initial low‐frequency model of the conventional inversion method, it is possible to estimate better inversion results. The results of different combinations of training sets demonstrate the stability of the proposed method. This method may still be a viable choice if there is lateral heterogeneity underground but not much well‐logging label data.

Picking stack velocity from seismic velocity spectra is a fundamental method in seismic stack velocity analysis. With the increase in the scale of seismic data acquisition, manual picking cannot achieve the required efficiency. Therefore, an automatic picking algorithm is urgently needed now. Despite some supervised deep learning–based picking approaches that have been proposed, they heavily rely on sufficient training samples and lack interpretability. In contrast, utilizing physical knowledge to develop semi‐data‐driven methods has the potential to efficiently solve this problem. Thus, we propose a semi‐supervised ensemble learning method to reduce the reliance on manually labelled data and improve interpretability by incorporating the interval velocity constraint. Semi‐supervised ensemble learning fuses the information of the estimated spectrum, nearby velocity spectra and few‐shot manual picking to recognize the velocity picking. Test results of both the synthetic and field datasets indicate that semi‐supervised ensemble learning achieves more reliable and precise picking than traditional clustering‐based techniques and the currently popular convolutional neural network method.

Due to the intrinsic attenuation of the earth, the study of wave propagation characteristics, considering seismic attenuation plays an important role in high‐precision reservoir prediction. Therefore, we investigate the propagation and reflection characteristics of seismic waves in viscoelastic vertical transverse isotropic media in the complex frequency domain. Specifically, we analyse the response characteristics of velocity, propagation vector and attenuation vector with respect to viscosity media with different attenuation intensities. Furthermore, based on the quasi‐Zoeppritz equation, the variation of reflection coefficient amplitude with offset at different attenuation angles and different attenuation intensities is studied. We also compare the trends in the amplitude variation of reflection coefficients with offset in elastic isotropic, elastic anisotropic and viscoelastic anisotropic media. Due to the complexity of the exact reflection coefficient expression, we first propose the approximate expression of the attenuation–anisotropy parameters and then derive the approximate expression of the reflection coefficient. The numerical simulation results show that the approximate expression of the reflection coefficient is still accurate, even in media with strong anisotropy. Finally, the accuracy evaluations of the reflection coefficient formulas using four typical theory models demonstrate that the approximate reflection coefficient formulas are highly accurate in both weak and strong anisotropic media.

The strong sensitivity of velocity to stress observed in many sandstones originates from the response of stress‐sensitive discontinuities such as grain contacts and microcracks to a change in effective stress. If the change in stress is anisotropic, then the change in elastic wave velocities will also be anisotropic. Characterization of stress‐induced elastic anisotropy in sandstones may enable estimation of the in situ three dimensional stress tensor with important application in solving problems occurring during drilling, such as borehole instability, and during production, such as sanding and reservoir compaction. Other applications include designing hydraulic fracture stimulations and quantifying production‐induced stresses which may lead to rock failure. Current methods for estimating stress anisotropy from acoustic anisotropy rely on third‐order elasticity, which ignores rock microstructure and gives elastic moduli that vary linearly with strain. Elastic stiffnesses in sandstones vary non‐linearly with stress. Using P‐ and S‐wave velocities measured on Gulf of Mexico sandstones, this non‐linearity is found to be consistent with a micromechanical model in which the discontinuities are represented by stress‐dependent normal and shear compliances. Stress‐induced anisotropy increases with increasing stress anisotropy at small stress but then decreases at larger stresses as the discontinuities close and their compliance decreases. When the ratio of normal‐to‐shear compliance of the discontinuities is unity, the stress‐induced anisotropy is elliptical, but for values different from unity, the stress‐induced anisotropy becomes anelliptic. Although vertical stress can be obtained by integrating the formation's bulk density from the surface to the depth of interest, and minimum horizontal stress can be estimated using leak‐off tests or hydraulic fracture data, maximum horizontal stress is more difficult to estimate. Maximum horizontal stress is overpredicted based on third‐order elasticity using measured shear moduli, with estimates of pore pressure, vertical stress and minimum horizontal stress as input. The non‐linear response of grain contacts and microcracks to stress must be considered to improve such estimates.