Velocity analysis using the semblance spectrum can provide an effective velocity model for advanced seismic imaging technology, in which the picking accuracy of velocity analysis is significantly affected by the resolution of the semblance spectrum. However, the peak broadening of the conventional semblance spectrum leads to picking uncertainty, and it cannot deal with the amplitude-variation-with-offset (AVO) phenomenon. The well-known AB semblance can process the AVO anomalies, but it has a lower resolution compared with conventional semblance. To improve the resolution of the AB semblance spectrum, we propose a new weighted AB semblance based on principal component analysis (PCA). The principal components or eigenvalues of seismic events are highly sensitive to the components with spatial coherence. Thus, we utilized the principal components of the normal moveout (NMO)-corrected seismic events with different scanning velocities to construct a weighting function. The new function not only has a high resolution for velocity scanning, but it is also a friendly method for the AVO phenomenon. Numerical experiments with the synthetic and field seismic data sets proved that the new method significantly improves resolution and can provide more accurate picked velocities compared with conventional methods.

Staggered-grid finite-difference (FD) method is widely used to solve the wave equation for the numerical seismic modeling, and it is a key step of the advanced seismic imaging and inversion problem. However, the conventional FD method is prone to instability and dispersion error due to the insufficient approximation accuracy. In this work, we propose an efficient temporal high-order finite-difference (FD) scheme with the cross-rhombus stencil. Compared with the standard cross-rhombus method, the new method has less computational cost due to we simplify the FD scheme. Moreover, the dispersion relation of the new method is easy to obtain the dispersion-relation-preserving (DRP) FD coefficients, which can significantly alleviate the spatial and temporal dispersion errors. Dispersion and stability analyses indicate that the new scheme has better performance in seismic modeling than the conventional method, and numerical experiments also indicate that the new scheme can effectively mitigate dispersion error and improve the numerical accuracy.