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Seismic instantaneous frequency (IF), as one of the instantaneous attributes, is widely used for seismic interpretation and stratigraphy analysis. The Hilbert transform (HT)-based complex analysis approaches are commonly used to extract seismic IF, which are sensitive to kinds of noise contained in field data. Although the normalized HT (NHT) improves the antinoise property of HT by normalizing the original trace, the HT-based methods are a global operator that is not suitable for the local analysis. For example, IF calculated by using the HT-based method is unstable when meeting strong seismic events. In this letter, we propose a workflow to extract local IF (LIF) and then apply it to describe superposed sands. Note that the proposed workflow extracts a stable IF result even when processing a seismic trace with strong events. To demonstrate the effectiveness of the proposed workflow, we apply it to both synthetic and field data. Compared with results from HT and NHT, the proposed workflow provides a stable IF extraction and offers potentials in precisely highlighting superposed sands.

In this work, we develop a novel abrupt-jump detection algorithm for seismic signal deconvolution. This new method significantly suppresses the effect of sidelobes. It begins with transforming a seismic trace to a series of innovations with a Kalman filter and then estimates the likelihood ratios of the reflectivity impulses from the innovations. Second, it modifies the likelihood ratios by imposing additional punishment on its asymmetry. Therefore, the likelihood ratios induced by the sidelobes are highly suppressed. Hence the reflectivity impulses recovered from the modified likelihood ratios are less affected by the sidelobes, leading to significantly enhanced resolution. The efficacy of the proposed method is numerically validated on a synthetic and a field dataset. The experimental results show that the proposed scheme is efficient and practical in enhancing the signal quality of seismograms than the original likelihood-ratio-based abrupt-jump detection.

Static corrections, especially in old land data, can be a challenging issue for adequate seismic processing and imaging. A frequently encountered problem is the lack of reliable elevation data for sources and receivers. In this work, we propose a simple method to reconstruct the elevation data for each seismic trace for a given dataset using freely available information. Such reconstruction enables all subsequent processing steps to be carried out in a proper way. As a proof of concept, we applied this methodology to a 30-year-old dataset from Parnaiba Basin, Brazil, and compared with refraction and residual statics results obtained with the elevation data recorded in the original seismic file header. The proposed method outperformed the original elevation results, being able to increase image quality and signal-to-noise ratio.

The seismic dip attribute is regularly used to aid structural interpretation and is commonly adopted as a compulsory input for computing other seismic geometric attributes. One disadvantage of current dip computation algorithms is that interpreters compute the dip attribute time sample by time sample and do not consider the relationship between dip values of nearby samples. The classic convolution theory suggests one formation boundary should have the corresponding seismic event. However, the seismic wavelet always has a certain time duration. As a result, one formation boundary has a corresponding seismic event that consists of several time samples. Ideally, the time samples, which belong to the same boundary, should have approximately the same dip attributes. In this research, a sample by sample computation procedure is treated as an independent optimisation procedure. Then, simultaneously computing the seismic dip of time samples of one seismic trace can be regarded as a multi-objective optimisation procedure. The proposed method is based on analysing features of seismic waveform within user-defined windows. Considering that nearby time samples should have continuous dip values, we the dynamic time warping to simultaneously compute seismic reflectors’ dip values of a seismic trace. We applied our method to a field seismic data to demonstrate its effectiveness.

Quality factor ( Q) and reflectivity are two important subsurface properties in seismic data processing and interpretation. They can be calculated simultaneously from a seismic trace corresponding to an anelastic layered model by a simultaneous inversion method based on the nonstationary convolutional model. However, the conventional simultaneous inversion method calculates the optimum Q and reflectivity based on the minimum of the reflectivity sparsity by sweeping each Q value within a predefined range. As a result, the accuracy and computational efficiency of the conventional method depend heavily on the predefined Q value set. To improve the performance of the conventional simultaneous inversion method, we have developed a dictionary learning-based simultaneous inversion of Q and reflectivity. The parametric dictionary learning method is used to update the initial predefined Q value set automatically. The optimum Q and reflectivity are calculated from the updated Q value set based on minimizing not only the sparsity of the reflectivity but also the data residual. Synthetic data and two field data sets are used to test the effectiveness of our method. The results demonstrate that our method can effectively improve the accuracy of these two parameters compared to the conventional simultaneous inversion method. In addition, the dictionary learning method can improve computational efficiency up to approximately seven times when compared to the conventional method with a large predefined dictionary.

Due to environmental and economic constraints on their acquisition, seismic data are always irregularly sampled and include bad or missing traces, which can cause problems for seismic data processing. Recently, many researchers have attempted to improve seismic data reconstruction using machine learning (ML) techniques, such as convolutional neural networks, which are inspired by computer vision and imaging processing. In this letter, we propose a novel approach for reconstructing missing traces in seismic data using ML techniques, especially recurrent neural network (RNN) algorithms. Instead of processing seismic data as an image, the proposed approach performs seismic trace interpolation using traces that are sequences of time-series data. More specifically, we adopt deep bidirectional long short-term memory (LSTM) for seismic trace interpolation and test models with and without skip connections. Field seismic data are used to demonstrate the effectiveness of the proposed approaches, and the deep bidirectional LSTM (DBiLSTM) with skip connections shows the best performance compared to cubic interpolation, minimum weighted norm interpolation (MWNI), and DBiLSTM without skip connection.

We propose a stable ${Q}$ -estimation approach based on the compensation of amplitude spectra in the time–frequency domain after a synchrosqueezed wavelet transform (SSWT). SSWT employing a post-processing frequency reallocation method to the original representation of a continuous wavelet transform (CWT) for improving its readability provides the sharper time–frequency representation of a signal when compared with the other traditional time–frequency methods such as CWT or S-transform. For ${Q}$ -estimation, we transform a seismic trace into the time–frequency domain using SSWT at first. Then, we derive the amplitude compensation in the SSWT domain. By searching the predetermined ${Q}$ range, the comparison between the compensated amplitude spectrum and the reference one in the SSWT domain is carried out. The output optimized ${Q}$ -factor estimation is evaluated by the minimum of the mean square error. For the robust and fast stabilization form of the amplitude compensation in the SSWT domain with noise amplification damping, the seismic pulse is truncated with a limited length and the obtained time–frequency maps using an SSWT are smoothed. The synthetic vertical seismic profiling data and the real stacked seismic data applications illustrate the effectiveness and the ability of the proposed method.

This paper presents a rigorous but pragmatic and data driven approach to the science of making seismic-to-well ties. This pragmatic approach is consistent with the interpreter’s desire to correlate geology to seismic information by the use of the convolution model, together with least squares matching techniques and statistical measures of fit and accuracy to match the seismic data to the well data. Three wells available on the field provided a chance to estimate the wavelet (both in terms of shape and timing) directly from the seismic and also to ascertain the level of confidence that should be placed in the wavelet. The reflections were interpreted clearly as hard sand at H1000 and soft sand at H4000. A synthetic seismogram was constructed and matched to a real seismic trace and features from the well are correlated to the seismic data. The prime concept in constructing the synthetic is the convolution model, which represents a seismic reflection signal as a sequence of interfering reflection pulses of different amplitudes and polarity but all of the same shape. This pulse shape is the seismic wavelet which is formally, the reflection waveform returned by an isolated reflector of unit strength at the target depth. The wavelets are near zero phase. The goal and the idea behind these seismic-to-well ties was to obtain information on the sediments, calibration of seismic processing parameters, correlation of formation tops and seismic reflectors, and the derivation of a wavelet for seismic inversion among others. Three seismic-to-well ties were done using three partial angle stacks and basically two formation tops were correlated. Keywords: seismic, well logs, tie, synthetics, angle stacks, correlation

We propose an algorithm for seismic trace interpolation using generative adversarial networks, a type of deep neural network. The method extracts feature vectors from the training data using self‐learning and does not require any pre‐processing to create the training labels. The algorithm also does not make any prior explicit assumptions about linearity of seismic events or sparsity of the data, which are often required in the traditional interpolation methods. We create the training labels by removing traces from different receiver indices of the original datasets to simulate the effect of missing traces. We adopt the framework of the generative adversarial networks to train the network and add additional loss functions to regularize the model. Numerical examples using land and marine field datasets demonstrate the validity and effectiveness of the proposed approach. With minimal computational burden and proper training, the proposed method can be applied to three‐dimensional seismic datasets to achieve accurate interpolation results.

This article proposes an innovative scheme for recovering sparse reflectivity series from uniformly quantized seismic signals. In this scheme, the statistically less affected impulses by the quantization error are assigned higher weights than the ones with a larger error. First, the orthogonal matching pursuit (OMP) algorithm is applied on a quantized seismic trace to obtain a set of conservative estimates of the reflectivity impulses. Second, the quantization error is formulated as a systematic uncertainty within a neighborhood of the obtained conservative estimates from the OMP. Finally, a robust worst case (RWC) deconvolution method is developed to recover an improved estimate of the reflectivity impulses. The proposed scheme significantly increases the robustness and enhances the recovered reflectivity impulses obtained by the OMP algorithm. This is substantiated by experiments on both synthetic and real seismic data. Specifically, the falsely or overly estimated impulses are significantly suppressed, and the robustness to the change of the quantization interval is enhanced.

The presence of seismic absorption distorts seismic record and reduces seismogram resolution, which can be partially compensated by application of absorption compensation algorithms. Conventional absorption compensation techniques are based on 1D forward model with each seismic trace being compensated independently. Therefore, the 2D results combined by each compensation trace may be noisy and discontinuity. To eliminate this issue, we extend the 1D forward model to the 2D forward system and further add an additional lateral constraint to the compensation algorithm for enforcing the lateral continuity of the compensated section. Solving the proposed laterally constrained absorption compensation (LCAC) problem, we simultaneously obtain the multiple compensated traces with lateral smoother transition and higher signal-to-noise ratio (S/N). We testify the effectiveness of the proposed method by applying both synthetic and field data. Synthetic data examples demonstrate the superior performance of the LCAC algorithm in terms of improving algorithmic stability and protecting lateral continuity. The field data tests further indicate its ability to not only improve seismic resolution, but also inhibit the amplification of high-frequency noise.

The conventional impedance inversion method ignores the attenuation effect, transmission loss and inter‐layer multiple waves; the smooth‐like regularization approach makes the corresponding impedance solution excessively smooth. Both fundamentally limit the resolution of impedance result and lead to the inadequate ability of boundary characterization. Therefore, a post‐stack impedance blocky inversion method based on the analytic solution of viscous acoustic equation is proposed. Based on the derived recursive formula of reflections, the 1D viscous acoustic wave equation is solved analytically to obtain zero‐offset full‐wave field response. Applying chain rule, the analytical expression of the Frechet derivative is derived for gradient‐descent non‐linear inversion. Combined with smooth constraints, the blocky constraints can be introduced into the Bayesian inference framework to obtain stable and well‐defined inversion results. According to the above theory, we firstly use model data to analyse the influence of incompleteness of forward method on seismic response, and further verify the effectiveness of the proposed method. Then the Q‐value sensitivity analysis of seismic trace is carried out to reduce the difficulty of Q‐value estimation. Finally, the real data from Lower Congo Basin in West Africa indicate that the proposed approach provide the high‐resolution and well‐defined impedance result. As a supplement and development of linear impedance inversion method, the non‐linear viscous inversion could recover more realistic and reliable impedance profiles.

The seismic sedimentology is an emerging inter-discipline originating from the seismic stratigraphy and sequence stratigraphy. However, implementation of the seismic sedimentological research is found with high difficulties, due to influences imposed by structural and depositional background data (including strong reflections). In this paper, seismic records are regarded as a combination of the reflection from the depositional background and lithological data volumes, and moreover, the seismogram of the depositional background data is characterized by the low frequency and stable phase. Subsequently, the Kernel Hebbian Algorithm (KHA) has been modified to remove the influence of the depositional background data. The seismic trace data are used as the training set, and an innovative attempt has been made to incorporate the Ricker wavelet kernel function. Finally, a depositional background data volume extraction methodology with respect to input of higher-dimension seismic data has been developed, on the basis of the Modified KHA (MKHA), so as to obtain the lithological data volume. Utilizing the unsupervised online learning capabilities of the MKHA, iterative calculation of Kernel PCA can greatly reduce the computational complexity and can be adapted to big data problems. This paper introduces the Ricker wavelet kernel function to transform the original seismic data into the feature space through the inner-product operation, extract the non-linear features, and solve the problem that the seismic data of the original sample space is linearly inseparable. The seismic sedimentological analysis based on the lithological data volume that is able to reflect hidden sand bodies can achieve elaborate carving of the reservoir. The proposed method has been tested in Working Block A of the East-1 district in the Sulige gas field, the Ordos Basin, China. The case study demonstrates that the presented method is capable of efficiently removing the depositional background data, and making great contributions to improving accuracy of the seismic sedimentological analysis of the effective reservoir, with the help of higher-dimension seismic data.

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.

Seismic wavelets are dynamic components that result in a seismic trace when convolved with reflectivity series. The seismic wavelet is described by three components: amplitude, frequency, and phase. Amplitude and frequency are considered static because they mainly affect the appearance of a seismic event. Phase can have a large effect on seismic appearance by changing the way it describes the subsurface. Knowing the wavelet properties of certain seismic data facilitates the process of interpretation by providing an understanding of the appearance of regional geologic markers and hydrocarbon-bearing formation behavior. The process through which seismic data wavelets are understood is called seismic well tie. Seismic well tie is the first step in calibrating seismic data in terms of polarity and phase. It ensures that the seismic data are descriptive to regional markers, well markers, and discoveries (if they exist). The step connects well data to seismic data to ensure that the seismic correctly describes well results at the well location. It then extends the understanding of seismic behavior to the rest of the area covered by the seismic data. Good seismic well tie will greatly reduce uncertainties accompanying seismic interpretation. One important outcome of the seismic well tie process is understanding the phase of seismic data, which affects how seismic data will reflect a known geologic marker or hydrocarbon-bearing zone. This understanding can be useful in quantifying discoveries attached to seismic anomalies and extending knowledge from the well location to the rest of the area covered by seismic data.

Deconvolution is an essential step for high‐resolution imaging in seismic data processing. The frequency and phase of the seismic wavelet change through time during wave propagation as a consequence of seismic absorption. Therefore, wavelet estimation is the most vital step of deconvolution, which plays the main role in seismic processing and inversion. Gabor deconvolution is an effective method to eliminate attenuation effects. Since Gabor transform does not prepare the information about the phase, minimum‐phase assumption is usually supposed to estimate the phase of the wavelet. This manner does not return the optimum response where the source wavelet would be dominantly a mixed phase. We used the kurtosis maximization algorithm to estimate the phase of the wavelet. First, we removed the attenuation effect in the Gabor domain and computed the amplitude spectrum of the source wavelet; then, we rotated the seismic trace with a constant phase to reach the maximum kurtosis. This procedure was repeated in moving windows to obtain the time‐varying phase changes. After that, the propagating wavelet was generated to solve the inversion problem of the convolutional model. We showed that the assumption of minimum phase does not reflect a suitable response in the case of mixed‐phase wavelets. Application of this algorithm on synthetic and real data shows that subtle reflectivity information could be recovered and vertical seismic resolution is significantly improved.

Seismic noise suppression plays an important role in seismic data processing and interpretation. The time–frequency peak filtering (TFPF) is a classical method for seismic noise attenuation defined in the time–frequency domain. Nevertheless, we obtain serious attenuation for the seismic signal amplitude when choosing a wide window of TFPF. It is an unsolved issue for TFPF to select a suitable window width for attenuating seismic noise effectively and preserving valid signal amplitude effectively. To overcome the disadvantage of TFPF, we introduce the empirical wavelet transform (EWT) to improve the filtered results produced by TFPF. We name the proposed seismic de-noising workflow as the TFPF based on EWT (TFPF-EWT). We first introduce EWT to decompose a non-stationary seismic trace into a couple of intrinsic mode functions (IMFs) with different dominant frequencies. Then, we apply TFPF to the chosen IMFs for noise attenuation, which are selected by using a defined reference formula. At last, we add the filtered IMFs and the unprocessed ones to obtain the filtered seismic signal. Synthetic data and 3D field data examples prove the validity and effectiveness of the TFPF-EWT for both attenuating random noise and preserving valid seismic amplitude.

Instantaneous phase is a commonly used attribute for structural and stratigraphic feature characterization. The conventional calculation method is to construct the complex-valued seismic trace, then get the ratio of the imaginary part to the real part and finally compute the antitangent of the ratio as the instantaneous phase attribute. In this way, the phase result at one time sample point is the total phase rotation from the beginning of the trace to this point, which means the traditional instantaneous phase is cumulative. Furthermore, the phase obtained by arctangent is usually entangled, which makes it more difficult to apply to seismic interpretation. To address the two issues above, we proposed a new way to calculate the improved local phase variation attributes. Firstly, we calculate traditional instantaneous phase and unwrap it. Then we set a time window on the unwrapped phase to compute the local phase variation by using some difference methods. Finally, we slide the time window on the whole trace to obtain the final phase variation attributes. This strategy turns the whole cumulative value into local variational value, which makes the obtained local phase variation nearly zero in the continuous region but changed greatly at the interface or the abnormal structure areas. Tested by the numerical model and the real data, the proposed attributes have a good application effect in channel detection, which provides a train of thought to seismic structure interpretation with phase attributes.

Seismic trace interpolation is an important technique because irregular or insufficient sampling data along the spatial direction may lead to inevitable errors in multiple suppression, imaging, and inversion. Many interpolation methods have been studied for irregularly sampled data. Inspired by the working idea of the autoencoder and convolutional neural network, we have performed seismic trace interpolation by using the convolutional autoencoder (CAE). The irregularly sampled data are taken as corrupted data. By using a training data set including pairs of the corrupted and complete data, CAE can automatically learn to extract features from the corrupted data and reconstruct the complete data from the extracted features. It can avoid some assumptions in the traditional trace interpolation method such as the linearity of events, low-rankness, or sparsity. In addition, once the CAE network training is completed, the corrupted seismic data can be interpolated immediately with very low computational cost. A CAE network composed of three convolutional layers and three deconvolutional layers is designed to explore the capabilities of CAE-based seismic trace interpolation for an irregularly sampled data set. To solve the problem of rare complete shot gathers in field data applications, the trained network on synthetic data is used as an initialization of the network training on field data, called the transfer learning strategy. Experiments on synthetic and field data sets indicate the validity and flexibility of the trained CAE. Compared with the curvelet-transform-based method, CAE can lead to comparable or better interpolation performances efficiently. The transfer learning strategy enhances the training efficiency on field data and improves the interpolation performance of CAE with limited training data.

We propose a new method to tackle the mapping challenge from time-series data to spatial image in the field of seismic exploration, i.e., reconstructing the velocity model directly from seismic data by deep neural networks (DNNs). The conventional way of addressing this ill-posed inversion problem is through iterative algorithms, which suffer from poor nonlinear mapping and strong nonuniqueness. Other attempts may either import human intervention errors or underuse seismic data. The challenge for DNNs mainly lies in the weak spatial correspondence, the uncertain reflection-reception relationship between seismic data and velocity model, as well as the time-varying property of seismic data. To tackle these challenges, we propose end-to-end seismic inversion networks (SeisInvNets) with novel components to make the best use of all seismic data. Specifically, we start with every seismic trace and enhance it with its neighborhood information, its observation setup, and the global context of its corresponding seismic profile. From the enhanced seismic traces, the spatially aligned feature maps can be learned and further concatenated to reconstruct a velocity model. In general, we let every seismic trace contribute to the reconstruction of the whole velocity model by finding spatial correspondence. The proposed SeisInvNet consistently produces improvements over the baselines and achieves promising performance on our synthesized and proposed SeisInv data set according to various evaluation metrics. The inversion results are more consistent with the target from the aspects of velocity values, subsurface structures, and geological interfaces. Moreover, the mechanism and the generalization of the proposed method are discussed and verified. Nevertheless, the generalization of deep-learning-based inversion methods on real data is still challenging and considering physics may be one potential solution.

Seismic sensors continuously record a wide range of ground vibrations that are not necessarily related to earthquake activity, but are rather caused by human activity such as industrial processes, urban and air traffic. In this paper we show that human-generated seismic noise provides valuable information about the economic developments of a particular area, thus offering policymakers a useful tool for monitoring the heartbeat of that economy. We adopt a set of techniques developed within the seismic literature to disentangle sources of ground motion and propose a novel, daily indicator measuring vibrations caused by human activity. To demonstrate the usefulness of our procedure, we collect a huge data set made of nearly 20 years of continuously recorded seismic data in Beijing, China, and use our vibration indicator to forecast daily variations in regional industrial production. Our findings suggest that seismic data closely tracks business cycle fluctuations, with significant enhancements in the forecasting performance during economic crises. Our results support the usefulness of seismology as a nowcasting and forecasting tool in the area of economics and business, particularly for monitoring regional economies, for which timely and up-to-date indicators of economic activity are often not available, or for tracking national economies in periods of disruption of many key statistics.

The modern seismic acquisition produces a large data volume that significantly increases the cost of storage and transmission. Therefore, it is desirable to reduce the cost by compressing the seismic data. In this work, we propose a model-based compression scheme to deal with the large data volume. First, each seismic trace is modeled as a superposition of multiple exponential decaying sinusoidal waves (EDSWs). Each EDSW represents a model component and is determined by a set of parameters. Secondly, a single component parameter estimation algorithm is proposed accordingly using the particle swarm optimization (PSO) technique. We extend the algorithm for multiple model components by sequentially estimating the parameter set wave by wave. A suitable number of model components for each trace is selected according to the level of the energy of residuals. Next, the residuals are encoded using quantization coding techniques to improve the reconstruction quality. Comparison of PSO, genetic algorithm (GA), and simulated annealing (SA) is presented where the proposed model estimation technique outperforms the comparative models. The proposed model-based compression scheme is experimentally compared with the discrete cosine transform (DCT) on a real seismic dataset. The performance of the proposed model-based exhibits superiority to that of the DCT.

In this work, we develop a novel abrupt-jump detection algorithm for seismic signal deconvolution. This new method significantly suppresses the effect of side lobes. It begins with transforming a seismic trace to a series of innovations with a Kalman filter and then estimates the likelihood ratios of the reflectivity impulses from the innovations. Secondly, it modifies the likelihood ratios by imposing an additional punishment on its asymmetry. Therefore, the likelihood ratios induced by the side lobes are highly suppressed. Hence the reflectivity impulses recovered from the modified likelihood ratios are less effected by the side lobes, leading to significantly enhanced resolution. The efficacy of the proposed method is numerically validated on a synthetic and a field dataset. The experimental results show that the proposed scheme is efficient and practical in enhancing signal quality of seismograms than the original likelihood-ratio-based abrupt-jump detection.