A Sparse Spike Deconvolution Algorithm Based on a Recurrent Neural Network and the Iterative Shrinkage-Thresholding Algorithm

Most deconvolution algorithms try to transform the seismic wavelet into spikes by designing inverse filters that remove an estimated seismic wavelet from seismic data. We assume that seismic trace subtle discontinuities are associated with acoustic impedance contrasts and can be characterized by wavelet transform spectral ridges, also called modulus maxima lines (WTMML), allowing us to improve seismic resolution by using the wavelet transform. Specifically, we apply the complex Morlet continuous wavelet transform (CWT) to each seismic trace and compute the WTMMLs. Then, we reconstruct the seismic trace with the inverse continuous wavelet transform from the computed WTMMLs with a broader band complex Morlet wavelet than that used in the forward CWT. Because the reconstruction process preserves amplitude and phase along different scales, or frequencies, the result looks like a deconvolution method. Considering this high-resolution seismic representation as a reflectivity approximation, we estimate the relative acoustic impedance (RAI) by filtering and trace integrating it. Conventional deconvolution algorithms assume the seismic wavelet to be stochastic, while the CWT is implicitly time varying such that it can be applied to both depth and time-domain data. Using synthetic and real seismic data, we evaluated the effectiveness of the methodology on detecting seismic events associated with acoustic impedance changes. In the real data examples, time and in-depth RAI results, show good correlation with real P-impedance band-pass data computed using more rigorous commercial inversion software packages that require well logs and low-frequency velocity model information.

During the propagation of seismic waves underground, the high-frequency seismic response of thin reservoir is absorbed and attenuated, which poses a challenge in seismic thin reservoir prediction. The high-resolution processing techniques have the capability to significantly expand the frequency range of the seismic data, so it becomes a key technique for thin reservoir prediction. Most of these techniques necessitate the extraction of seismic wavelets. However, the spatial and temporal variations of seismic data result in multiple solutions for wavelet extraction. Simultaneously, the majority of techniques fail to consider the influence of spatial tectonic features on the high-resolution processing. In this paper, we propose a novel solution to address these two fundamental challenges by utilizing seismic spectral expansion, sparse reflection coefficients, and spatial continuity constraints. First, we propose an innovative spectral fitting method that aims to expand the frequency bandwidth while adhering to the desired wavelet constraints. This method allows us to fully utilize the effective frequency information. It not only obtains broadband seismic data but also captures precise wavelets. Then, sparse deconvolution is employed to further extend the frequency range by utilizing the accurately expected wavelet and obtaining a high-resolution reflection coefficient. Finally, the Hessian matrix regularization is employed to constrain the spatial continuity of the reflection coefficient. This method is validated in both the model and real seismic data. Compared to traditional sparse deconvolution and spectral modeling deconvolution with spatial constraints, this method not only expands the frequency bandwidth and enhances seismic resolution but also preserves operational frequency information and improves the spatial continuity of seismic data. It has been verified that this approach can be used to forecast thin reservoir and reconstruct spatial tectonic characteristics.

Deep learning has been applied to tackle the seismic inversion problem, bringing more efficiency and accuracy. However, bad spatial continuity and poor generalizability limit the practical application. To solve these problems, we propose a 2D end-to-end seismic inversion method based on domain adaption. Firstly, the proposed 2D network learns the inversion mapping of seismic data under the constraint of domain adaption layer, which can reduce the difference between the features of real seismic data and synthetic seismic data, improving the generalization ability on real seismic data. Then, the trained model is finetuned with well logging data. In the first process, the spatial continuity of the inversion result is guaranteed by the 2D training scheme. Meanwhile, due to the constraint of the domain adaption layer, our model not only performs well on the synthetic data but also has good generalization ability on the real seismic data. And we carefully discuss the mechanism of domain adaption layer. In the second process, finetuning introduces well logging information, which can further improve the ability to invert details. Moreover, in order to improve the inversion accuracy on real seismic data, we develop a new training data generation method that can generate the synthetic samples close to the real samples, and a 2.5D training strategy is adopted to improve the continuity of the 3D data. The experiments on both synthetic and real seismic data show that our method performs better than both the recursive inversion method and the 1D closed-loop CNN methods.

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

The aim of this study is to calibrate synthetic seismic data to the real reservoir for a proposed seismic modelling and inversion studies. For this purpose, well tie was done by generating reflectivity series from log data in TWT, convolving it with Ricker wavelet. Optimal match was then explored by adapting the phase of the wavelet and correlating the resulting synthetic trace with neighbouring traces of the real data. Thus, synthetic post-stack seismic data was simulated using a convolution model in an iterative approach, extracting a wavelet from the seismic data. After a satisfactory calibration, forward prestack seismic modelling was applied to investigate the AVO response of different interfaces. Both the simulated post-stack and prestack models were then verified against real seismic data. Results show a perfect fit of synthetic-to-seismic calibration at WTR well. Good match between the petrophysical and the seismic attributes then implies that well data has been tied to the seismic data (lithologic units can be assigned to logs and seismic parameters at these wells). Therefore, further seismic modelling and inversion can be performed to study the acoustic response of the reservoir in-fills and extract the seismic attributes in this reservoir using these data sets.

It is important to separate the near‐surface seismic scattered waves from low signal‐noise data in mountain seismic exploration, and seismic interferometry is one of promising methods. The seismic interferometry representations of the near‐surface scattered wave are derived according to the seismic interferometry theory and the scattering theory. Those representations are composed of interferometry between actual wavefield and background wavefield and include cross‐correlation type and convolution type seismic interferometry expression. According to the near‐surface scattered wave separation theory and the geometry of land seismic exploration, the mixed configuration of convolution type and deconvolution type seismic interferometry is used. The application effect of the near‐surface scattered wave method is showed using the real land seismic data. The theoretical analysis and real data tests in gravel area indicate that the seismic interferometry method can separate not only scattered wave generated by scattering sources on survey lines, but also partial side scattered wave. The advantages of this technology are that it adapts to the uneven terrain and the complex near‐surface structure without information about topography and near‐surface velocity. In this article, the subtraction method of multi‐traces self‐adaptive matched filter is used to eliminate the near‐surface scattered wave from the real seismic data, and gets preferable results in gravel area.

Most deconvolution algorithms try to transform the seismic wavelet into spikes by designing inverse filters that attempts to remove an estimated seismic wavelet from seismic data. Considering that seismic trace singularities are associated with acoustic impedance contrasts, and can be characterized by wavelet transform modulus maxima lines (WTMML), we show how to improve seismic resolution by using the wavelet transform. Specifically, we apply complex Morlet continuous wavelet transform (CWT) to each seismic trace and compute the WTMML‟s. Then, we reconstruct the seismic trace with the inverse continuous wavelet transform (ICWT) from the computed WTMML‟s with a slightly different complex Morlet wavelet than that used in the forward CWT. As the reconstruction process preserves amplitude and phase along different scales, or frequencies, the result resembles a deconvolution process. Using synthetic and real seismic data we show the effectiveness of the methodology on detecting seismic events associated with acoustic impedance changes.

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

ABSTRACTAutomatic feature detection from seismic data is a demanding task in today's interpretation workstations. Channels are among important stratigraphic features in seismic data both due to their reservoir capability or drilling hazard potential. Shearlet transform as a multi‐scale and multi‐directional transformation is capable of detecting anisotropic singularities in two and higher dimensional data. Channels occur as edges in seismic data, which can be detected based on maximizing the shearlet coefficients through all sub‐volumes at the finest scale of decomposition. The detected edges may require further refinement through the application of a thinning methodology. In this study, a three‐dimensional, pyramid‐adapted, compactly supported shearlet transform was applied to synthetic and real channelised, three‐dimensional post‐stack seismic data in order to decompose the data into different scales and directions for the purpose of channel boundary detection. In order to be able to compare the edge detection results based on three‐dimensional shearlet transform with some famous gradient‐based edge detectors, such as Sobel and Canny, a thresholding scheme is necessary. In both synthetic and real data examples, the three‐dimensional shearlet edge detection algorithm outperformed Sobel and Canny operators even in the presence of Gaussian random noise.

Seismic impedance inversion is a geophysical technique that transforms seismic data into quantitative subsurface properties, primarily acoustic impedance. This process enables the identification of rock boundaries, hydrocarbon reservoirs, and lithological variations, thus supporting informed drilling decisions and reducing exploration risks. However, conventional inversion methods face limitations such as noise sensitivity, low resolution, and reduced effectiveness in geologically complex areas, often resulting in oversimplified subsurface models. This study addresses these challenges by employing deep learning approaches, specifically LeNet, AlexNet, and conventional CNN architectures, to improve seismic resolution and synthetic seismogram generation. The methodology involves preprocessing seismic and well-log data, calculating acoustic impedance and reflection coefficients, and applying Continuous Wavelet Transform (CWT) for feature extraction. The models are trained using synthetic seismograms and validated against real seismic data. Among the models evaluated, AlexNet demonstrates superior performance in seismic data reconstruction, achieving the lowest MSE (0.0031), RMSE (0.0557), and MAE (0.052), along with the highest R2 score (0.993). The proposed technique demonstrates superior predictive accuracy, refined subsurface characterization, and reduced geological risk, thereby establishing a robust benchmark for advanced geophysical data analysis.

Numerical 3D high-resolution models of subsurface petroelastic properties are key tools for exploration and production stages. Stochastic seismic inversion techniques are often used to infer the spatial distribution of the properties of interest by integrating simultaneously seismic reflection and well-log data also allowing accessing the spatial uncertainty of the retrieved models. In frontier exploration areas, the available data set is often composed exclusively of seismic reflection data due to the lack of drilled wells and are therefore of high uncertainty. In these cases, subsurface models are usually retrieved by deterministic seismic inversion methodologies based exclusively on the existing seismic reflection data and an a priori elastic model. The resulting models are smooth representations of the real complex geology and do not allow assessing the uncertainty. To overcome these limitations, we have developed a geostatistical framework that allows inverting seismic reflection data without the need of experimental data (i.e., well-log data) within the inversion area. This iterative geostatistical seismic inversion methodology simultaneously integrates the available seismic reflection data and information from geologic analogs (nearby wells and/or analog fields) allowing retrieving acoustic impedance models. The model parameter space is perturbed by a stochastic sequential simulation methodology that handles the nonstationary probability distribution function. Convergence from iteration to iteration is ensured by a genetic algorithm driven by the trace-by-trace mismatch between real and synthetic seismic reflection data. The method was successfully applied to a frontier basin offshore southwest Europe, where no well has been drilled yet. Geologic information about the expected impedance distribution was retrieved from nearby wells and integrated within the inversion procedure. The resulting acoustic impedance models are geologically consistent with the available information and data, and the match between the inverted and the real seismic data ranges from 85% to 90% in some regions.

In forecasting foreign currencies, or known as foreign exchange, fundamental analysis and technical analysis can be used. Fundamental analysis relies on external factors or news happening in the market. In comparison, technical analysis studies the price itself by relying on graphs and mathematical formulas. This study combines fundamental value and technical analysis to predict the Rupiah (IDR) against the Dollar (USD). In this study, the artificial neural network architecture that is compared is Backpropagation and Recurrent Neural Networks (RNN). The RNN architecture used in this research is Elman and Jordan with Backpropagation Through Time (BPTT) learning algorithm. Technical analysis is applied by entering the USD exchange rate against IDR at a certain time. At the same time, fundamental analysis is applied in the form of entering some data on the value of fundamental factors as a training data set. Fundamental data used in this research are inflation rate, interest rate, money supply, and the number of exports and imports in Rupiah. In this study, the prediction system is also compared, the prediction system uses technical data, and the prediction system uses technical and fundamental data. This research results in the prediction system using the Elman RNN algorithm, which is better than the Backpropagation and Jordan RNN algorithms. A prediction system using training data in time series and fundamental data is better than only training data. So, it means in this study that the best prediction system uses the Elman RNN Algorithm with training data in the form of time series data USD sell exchange rate against IDR and fundamental data.

In this paper, we address the problem of sparse multichannel seismic deconvolution. We introduce multichannel sparse spike inversion as an iterative procedure, which deconvolves the seismic data and recovers the Earth two-dimensional reflectivity image, while taking into consideration the relations between spatially neighboring traces. We demonstrate the improved performance of the proposed algorithm and its robustness to noise, compared to competitive single-channel algorithm through simulations and real seismic data examples.

Compressed sensing (CS) reconstruction of nonsparse scenes is one of the difficulties in synthetic aperture radar (SAR) imaging technology. Although the conventional CS method with sparse representation has proven applicable for nonsparse SAR reconstruction, its disadvantages are unsatisfactory imaging quality and high computational complexity under downsampling. In this paper, a novel deep learning approach for nonsparse SAR scene reconstruction is proposed based on sparse representation and the iterative shrinkage threshold algorithm (ISTA). Specifically, we first develop a sparse representation-based imaging model associated with the ℓ₁ sparse regularizer in nonlinear transform domains. Then, the advantages of the recurrent neural network (RNN) and convolutional neural network (CNN) are incorporated into an ISTA-inspired deep unfolded network (DUN) called SR-ISTA-Net, in which all the parameters are layer-varied rather than handcrafted. The experiments verify that the proposed SR-ISTA-Net can provide high-quality reconstruction results under nonsparse scenes while substantially reducing imaging time.

Enhancing the detection of small coal structures by seismic diffraction imaging