As dense seismic arrays at different scales are deployed, the techniques to make full use of array data with low computing cost become increasingly needed. The wave gradiometry method (WGM) is a new branch in seismic tomography, which utilizes the spatial gradients of the wavefield to determine the phase velocity, wave propagation direction, geometrical spreading, and radiation pattern. Seismic wave propagation parameters obtained using the WGM can be further applied to invert 3D velocity models, Q values, and anisotropy at lithospheric (crust and/or mantle) and smaller scales (e.g., industrial oilfield or fault zone). Herein, we review the theoretical foundation, technical development, and major applications of the WGM, and compared the WGM with other commonly used major array imaging methods. Future development of the WGM is also discussed.

Teleseismic traveltime tomography is an important tool for investigating the crust and mantle structure of the Earth. The imaging quality of teleseismic traveltime tomography is affected by many factors, such as mantle heterogeneities, source uncertainties and random noise. Many previous studies have investigated these factors separately. An integral study of these factors is absent. To provide some guidelines for teleseismic traveltime tomography, we discussed four main influencing factors: the method for measuring relative traveltime differences, the presence of mantle heterogeneities outside the imaging domain, station spacing and uncertainties in teleseismic event hypocenters. Four conclusions can be drawn based on our analysis. (1) Comparing two methods, i.e., measuring the traveltime difference between two adjacent stations (M1) and subtracting the average traveltime of all stations from the traveltime of one station (M2), reveals that both M1 and M2 can well image the main structures; while M1 is able to achieve a slightly higher resolution than M2; M2 has the advantage of imaging long wavelength structures. In practical teleseismic traveltime tomography, better tomography results can be achieved by a two-step inversion method. (2) Global mantle heterogeneities can cause large traveltime residuals (up to about 0.55 s), which leads to evident imaging artifacts. (3) The tomographic accuracy and resolution of M1 decrease with increasing station spacing when measuring the relative traveltime difference between two adjacent stations. (4) The traveltime anomalies caused by the source uncertainties are generally less than 0.2 s, and the impact of source uncertainties is negligible.

Waveforms of seismic events, extracted from January 2019 to December 2021 were used to construct a test dataset to investigate the generalizability of PhaseNet in the Shandong region. The results show that errors in the picking of seismic phases (P- and S-waves) had a broadly normal distribution, mainly concentrated in the ranges of −0.4–0.3 s and −0.4–0.8 s, respectively. These results were compared with those published in the original PhaseNet article and were found to be approximately 0.2–0.4 s larger. PhaseNet had a strong generalizability for P- and S-wave picking for epicentral distances of less than 120 km and 110 km, respectively. However, the phase recall rate decreased rapidly when these distances were exceeded. Furthermore, the generalizability of PhaseNet was essentially unaffected by magnitude. The M4.1 earthquake sequence in Changqing, Shandong province, China, that occurred on February 18, 2020, was adopted as a case study. PhaseNet detected more than twice the number of earthquakes in the manually obtained catalog. This further verified that PhaseNet has strong generalizability in the Shandong region, and a high-precision earthquake catalog was constructed. According to these precise positioning results, two earthquake sequences occurred in the study area, and the southern cluster may have been triggered by the northern cluster. The focal mechanism solution, regional stress field, and the location results of the northern earthquake sequence indicated that the seismic force of the earthquake was consistent with the regional stress field.

The number of dispersion curves increases significantly when the scale of a short-period dense array increases. Owing to a substantial increase in data volume, it is important to quickly evaluate dispersion curve quality as well as select the available dispersion curve. Accordingly, this study quantitatively evaluated dispersion curve quality by training a convolutional neural network model for ambient noise tomography using a short-period dense array. The model can select high-quality dispersion curves that exhibit a ≤ 10% difference between the results of manual screening and the proposed model. In addition, this study established a dispersion curve loss function by analyzing the quality of the dispersion curve and the corresponding influencing factors, thereby estimating the number of available dispersion curves for the existing observation systems. Furthermore, a Monte Carlo simulation experiment is used to illustrates the station-pair interval distance probability density function, which is independent of station number in the observational system with randomly deployed stations. The results suggested that the straight-line length should exceed 15 km to ensure that loss rate of dispersion curves remains < 0.5, while maintaining the threshold ambient noise tomography accuracy within the study area.

In this study, the broadband ground motions of the 2021 M7.4 Maduo earthquake were simulated to overcome the scarcity of ground motion recordings and the low resolution of macroseismic intensity map in sparsely populated high-altitude regions. The simulation was conducted with a hybrid methodology, combining a stochastic high-frequency simulation with a low-frequency ground motion simulation, from the regional 1-D velocity structure model and the Wang WM et al. (2022) source rupture model, respectively. We found that the three-component waveforms simulated for specific stations matched the waveforms recorded at those stations, in terms of amplitude, duration, and frequency content. The validation results demonstrate the ability of the hybrid simulation method to reproduce the main characteristics of the observed ground motions for the 2021 Maduo earthquake over a broad frequency range. Our simulations suggest that the official map of macroseismic intensity tends to overestimate shaking by one intensity unit. Comparisons of simulations with empirical ground motion models indicate generally good consistency between the simulated and empirically predicted intensity measures. The high-frequency components of ground motions were found to be more prominent, while the low-frequency components were not, which is unexpected for large earthquakes. Our simulations provide valuable insight into the effects of source complexity on the level and variability of the resulting ground motions. The acceleration and velocity time histories and corresponding response spectra were provided for selected representative sites where no records were available. The simulated results have important implications for evaluating the performance of engineering structures in the epicentral regions of this earthquake and for estimating seismic hazards in the Tibetan regions where no strong ground motion records are available for large earthquakes.