We have developed convolutional sparse coding (CSC) to attenuate noise in seismic data. CSC gives a data-driven set of basis functions whose coefficients form a sparse distribution. The noise attenuation method by CSC can be divided into the training and denoising phases. Seismic data with a relatively high signal-to-noise ratio are chosen for training to get the learned basis functions. Then, we use all (or a subset) of the basis functions to attenuate the random or coherent noise in the seismic data. Numerical experiments on synthetic data show that CSC can learn a set of shifted invariant filters, which can reduce the redundancy of learned filters in the traditional sparse-coding denoising method. CSC achieves good denoising performance when training with the noisy data and better performance when training on a similar but noiseless data set. The numerical results from the field data test indicate that CSC can effectively suppress seismic noise in complex field data. By excluding filters with coherent noise features, our method can further attenuate coherent noise and separate ground roll.

Full-waveform inversion of seismic data is often plagued by cycle-skipping problems such that an iterative optimization method often gets stuck in a local minimum. To avoid this problem, we simplify the objective function so that the iterative solution can quickly converge to a solution in the vicinity of the global minimum. The objective function is simplified by only using parsimonious and important portions of the data, which are defined as skeletonized data. We have developed a mostly nonmathematical tutorial that explains the theory of wave-equation inversion of skeletonized data. We also demonstrate its effectiveness with examples.

To image deeper portions of the earth, geophysicists must record reflection data with much greater source-receiver offsets. The problem with these data is that the signal-to-noise ratio (S/N) significantly diminishes with greater offset. In many cases, the poor S/N makes the far-offset reflections imperceptible on the shot records. To mitigate this problem, we have developed supervirtual reflection interferometry (SVI), which can be applied to far-offset reflections to significantly increase their S/N. The key idea is to select the common pair gathers where the phases of the correlated reflection arrivals differ from one another by no more than a quarter of a period so that the traces can be coherently stacked. The traces are correlated and summed together to create traces with virtual reflections, which in turn are convolved with one another and stacked to give the reflection traces with much stronger S/Ns. This is similar to refraction SVI except far-offset reflections are used instead of refractions. The theory is validated with synthetic tests where SVI is applied to far-offset reflection arrivals to significantly improve their S/N. Reflection SVI is also applied to a field data set where the reflections are too noisy to be clearly visible in the traces. After the implementation of reflection SVI, the normal moveout velocity can be accurately picked from the SVI-improved data, leading to a successful poststack migration for this data set.

Many explorationists think of surface waves as the most damaging noise in land seismic data. Thus, much effort is spent in designing geophone arrays and filtering methods that attenuate these noisy events. It is now becoming apparent that surface waves can be a valuable ally in characterizing the near-surface geology. This review aims to find out how the interpreter can exploit some of the many opportunities available in surface waves recorded in land seismic data. For example, the dispersion curves associated with surface waves can be inverted to give the S-wave velocity tomogram, the common-offset gathers can reveal the presence of near-surface faults or velocity anomalies, and back-scattered surface waves can be migrated to detect the location of near-surface faults. However, the main limitation of surface waves is that they are typically sensitive to S-wave velocity variations no deeper than approximately half to one-third the dominant wavelength. For many exploration surveys, this limits the depth of investigation to be no deeper than approximately 0.5–1.0 km.

We have developed the theory and practice of 3D supervirtual interferometry (SVI) for enhancing the signal-to-noise ratio (S/N) of refraction arrivals in 3D data. Unlike 2D SVI, 3D SVI requires an extra integration along the inline direction to compute the stationary source-receiver pairs for enhanced stacking of the refraction events. The result is a significant increase in the S/N of first arrivals in the far-offset traces. We have evaluated 3D synthetic and field data examples to demonstrate the effectiveness of the proposed method. For the synthetic data tests, SVI has extended the source-receiver offset range of pickable traces from 11 to 15 km. In the field data example, SVI has extended the source-receiver offset of traces with pickable first-arrival traveltimes from 12 km to a maximum of 18 km, and the total number of reliable traveltime picks has increased by 12%, which contributes to a deeper velocity update in the traveltime tomogram.