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.

Simultaneous-source method is usually adopted, as one of the most efficient ways, to reduce the computation cost of full waveform inversion (FWI). Unfortunately, this method is facing with the problem of crosstalk noise, degrading the quality of inversion results. To avoid this problem, we propose an algorithm of time–frequency hybrid-domain simultaneous-source FWI based on the time-domain finite difference with phase sensitive detection method. The harmonic sine functions with different frequencies are used as wavelet signals for different sources within one super shot. Based on the orthogonality of trigonometric integral within an integer multiple of one period, the amplitude and phase fields of each source are deblended from the blended multisource wavefield. With this approach, the frequency-domain wavefield can be obtained, no need of the discrete Fourier transform. Consequently, we can calculate the gradient in the frequency domain using the deblended wavefield without the influence of crosstalk noise. Through controlling the frequencies of simultaneous sources, it is natural to perform the multi-scale inversion. In order to improve the quality of inversion results, several key strategies are applied. Finally, the synthetic examples show the feasibility, high efficiency and accuracy of our method.

Accurate estimation of source wavelet is crucial in a successful full-waveform inversion (FWI); however, it cannot be guaranteed in the case of real seismic data. We have developed time-domain source-independent elastic FWI using the convolution-based objective function that was originally developed for acoustic FWI. We have applied a new time window on the reference traces in the objective function to suppress the noises induced by the convolution and crosscorrelation operations. Also, we have adopted ${\ell }_1$-, Huber-, and hybrid-norm objective functions to improve the antinoise ability of our algorithm. We implemented a multiscale inversion strategy to conduct the tests with a quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to reduce the sensitivity to initial models and to improve the quality of inversion results. Synthetic tests verified that the new added time window can not only improve the inversion results, but also accelerate the convergence rate. Our method can be implemented successfully without a priori knowledge or accurate estimation of the source wavelet and can be more robust to Gaussian and spike noises, even for a Dirac wavelet. Finally, we applied our method to real seismic data. The similarity between the observed and modeled seismic data, the higher resolution of the migration image, and flatter common image gathers corresponding to the inverted models proved the relevance of our algorithm.

Time-frequency analysis always plays a central role in the field of seismic processing due to the advantage in characterizing nonstationary signals. In this letter, we present a novel technique for seismic time-frequency analysis based on the high-order synchrosqueezing transform, which obtains more accurate instantaneous frequencies by using the higher order approximations for both amplitude and phase in order to achieve a highly energy-concentrated time-frequency representation. A synthetic example is employed to demonstrate the validity of the proposed method in sharpening time-frequency representation. Application on field data example further proves its potential in enhancing time-frequency resolution and delineating stratigraphic characteristics with higher precision and renders that this technique is promising for seismic data analysis.

Simultaneous source acquisition, which allows a temporal overlap between shot records, has significant advantages to improve data quality (e.g., denser shooting) and reduce acquisition cost (e.g., efficient wide-azimuth shooting). We have developed a novel shot-domain deblending approach for a wide-azimuth simultaneous shooting survey based on an inversion scheme. The inverse problem is formulated by introducing two convolution operators that can respectively destruct the signal and interference and is solved by a conjugate-gradient algorithm in the least-squares sense. Our approach breaks down the limit that source separation can only be implemented in some domains other than the shot domain based on the incoherency principle. Our shot-domain approach does not require the random dithering time; thus, it is very flexible to use in a wide-azimuth simultaneous shooting survey. Three numerically blended synthetic examples were developed to demonstrate the excellent performance of our method. The feasibility has been further validated via a field-data example that is numerically blended from two realistic marine towed streamers.