The lack of low-frequency signals in seismic data makes the full-waveform inversion (FWI) procedure easily fall into local minima leading to unreliable results. To reconstruct the missing low-frequency signals more accurately and effectively, we have developed a data-driven low-frequency recovery method based on deep learning from high-frequency signals. In our method, we develop the idea of using a basic data patch of seismic data to build a local data-driven mapping in low-frequency recovery. Energy balancing and data patches are used to prepare high- and low-frequency data for training a convolutional neural network (CNN) to establish the relationship between the high- and low-frequency data pairs. The trained CNN then can be used to predict low-frequency data from high-frequency data. Our CNN was trained on the Marmousi model and tested on the overthrust model, as well as field data. The synthetic experimental results reveal that the predicted low-frequency data match the true low-frequency data very well in the time and frequency domains, and the field results show the successfully extended low-frequency spectra. Furthermore, two FWI tests using the predicted data demonstrate that our approach can reliably recover the low-frequency data.

Efficient modeling schemes currently exist to handle the spatially variable-order fractional Laplacians in the fractional Laplacian viscoacoustic wave equation. The simplest approach is to change the spatially variable-order fractional Laplacians into a linear combination of several constant fractional-order Laplacians. We generalize the constant fractional-order scheme to a spatially variable fractional-order viscoelastic wave equation and develop an almost-equivalent constant fractional-order viscoelastic wave equation. Our constant fractional-order scheme avoids the simulation error introduced by directly averaging the spatially varying fractional order; thus, our scheme simulates seismic wave propagation in viscoelastic media with sharp [ ] contrasts well. The fast Fourier transform is used in the approximation of the fractional Laplacians, which improves the spectral accuracy in space. Several simulation examples are performed to verify that the numerical solution of a homogeneous [ ] model obtained by solving our constant fractional-order viscoelastic wave equation agrees well with that obtained by solving the original viscoelastic wave equation. The numerical simulations for spatially varying [ ] models obtained by the new wave equation are more straightforward than those currently in use and match the reference solutions obtained by accurate, but inefficient, methods. This match of simulation results verifies the accuracy of our viscoelastic wave equation.

The natural damping effect of the Earth typically results in significant distortion of seismic waveforms, which greatly diminishes the precise of subsequent processes such as parameter inversion, migration imaging, and reservoir description. Compensating for this attenuation is crucial to achieving precise underground parameter measurements. While inversion or imaging techniques that rely on wave path compensation have the potential to address attenuation effects better, they encounter challenges, including heightened demands for input models, rapidly escalating algorithm intricacy, and computational burdens. Consequently, developing novel attenuation compensation methods that balance computational efficiency and accuracy is important in enhancing the precision of exploring complex reservoirs. This study utilizes a groundbreaking convolutional neural network, which integrates an attention mechanism and residual learning. This network establishes an inherent link between attenuated seismic data and their non-attenuated counterparts, effectively accomplishing data-driven compensation for seismic data attenuation. The more advanced acoustic (non-attenuated) full waveform inversion or reverse time migration framework is directly applied to enhance the modeling or imaging of attenuated seismic data with improved accuracy and efficiency. Simulation data and actual test results confirm that the suggested Q-compensation approach successfully enhances the amplitude of deep structural reflection signals, rectifies phase distortion induced by attenuation, and widens the seismic frequency range. This mitigates issues like the cycle-skipping problem associated with low-frequency absence in traditional FWI and the numerical instability and increased computational complexity found in attenuation compensation FWI. Furthermore, the imaging profile’s resolution is further heightened due to the effective attenuation correction and enhancement of high-frequency components.

Microseismic monitoring is an indispensable technique in characterizing the physical processes that are caused by extraction or injection of fluids during the hydraulic fracturing process. Microseismic data, however, are often contaminated with strong random noise and have a low signal-to-noise ratio (S/N). The low S/N in most microseismic data severely affects the accuracy and reliability of the source localization and source-mechanism inversion results. We have developed a new denoising framework to enhance the quality of microseismic data. We use the method of adaptive sparse dictionaries to learn the waveform features of the microseismic data by iteratively updating the dictionary atoms and sparse coefficients in an unsupervised way. Unlike most existing dictionary learning applications in the seismic community, we learn the features from 1D microseismic data, thereby to learn 1D features of the waveforms. We develop a sparse dictionary learning framework and then prepare the training patches and implement the algorithm to obtain favorable denoising performance. We use extensive numerical examples and real microseismic data examples to demonstrate the validity of our method. Results show that the features of microseismic waveforms can be learned to distinguish signal patches and noise patches even from a single channel of microseismic data. However, more training data can make the learned features smoother and better at representing useful signal components.

Elastic full waveform inversion (FWI) is more suitable to process multicomponent seismic data and can provide more subsurface medium information than acoustic FWI often with lower efficiency. Except for the parallel algorithms, source-encoding methods are usually adopted to improve the efficiency of FWI, but it often includes crosstalk noise. Besides, the additional source estimation process, critical for a successful FWI, would counteract the high-efficiency advantage of the source-encoding algorithm. We propose an elastic FWI with source-independent crosstalk-free encoding algorithm to solve the above problems. Arbitrary-phase harmonic sine functions are used as new source wavelets to perform the time-domain wavefield simulation regardless of the true wavelet. Treating the harmonic wavelet as the encoding operator and based on the orthogonality of trigonometric functions within integer periods, the amplitude and phase of each source are recovered from the blended source and adjoint wavefields so that the influence of crosstalk noise is avoided. With the deblended data, the proposed algorithm can be naturally applied to unfixed-spread acquisition systems. Moreover, we can conveniently perform the multiscale inversion by controlling the frequencies of simultaneous-source signals as conventional frequency-domain FWI does. Synthetic examples show that the proposed algorithm has high efficiency and accuracy with a strong robustness to the incorrect wavelets.