# AVO-Friendly Velocity Analysis Based on the High-Resolution PCA-Weighted Semblance
## 1 Introduction  
Velocity analysis is an essential step in seismic exploration, which can estimate an appropriate velocity model for subsequent seismic signal processing and imaging. The normal-moveout (NMO)-based velocity analysis with the semblance spectrum [1, 2] is widely applied in industry due to its straightforward implementation and relatively minor computational cost. The semblance spectrum uses a series of scanning velocities to apply NMO corrections with hyperbolic trajectories [3, 4] and then measures the spatial coherence of the corrected seismic events to obtain the corresponding semblance. When an accurate velocity is used, the corrected seismic events have a strong spatial coherence [5], and the peak value will appear in the semblance spectrum. The velocity values corresponding to the peaks in the semblance spectrum are then picked for velocity modeling [6, 7]. The resolution of the semblance spectrum determines its ability to distinguish and pick individual peaks, and the high-resolution semblance can significantly improve the accuracy of the velocity modeling [8, 9, 10]. Advanced velocity modelling methods [11, 12, 13, 14], such as full waveform inversion [15], usually require the NMO-based semblance spectrum to provide an effective initial model. However, due to insufficient resolution, the peak broadening of the conventional semblance spectrum leads to picking uncertainty, which makes it difficult to provide an effective initial model. To improve the resolution of the semblance spectrum, many scholars have improvedthe coherence measurement in the semblance spectrum [16] and proposed a new semblance based on the coherence measurement of the covariance matrix. The covariance matrix of the NMO-corrected seismic events is sensitive to far-offset traces, which improves the ability to distinguish individual peaks [17; 18; 19] and to develop a new coherence measurement based on the bootstrapped differential semblance. The bootstrapping approach estimates statistical properties of the NMO-corrected seismic events with a coherency estimator, which can significantly improve the resolution of the semblance spectrum. In addition, many scholars have developed the semblance spectra through the singular value decomposition (SVD) of the data matrix [20; 21; 22; 23]. The SVD-based semblance is sensitive to the spatial coherency of the NMO-corrected seismic events, thus improving the ability to distinguish individual peaks. On the other hand, many scholars have constructed the weighting functions to improve the resolution. The weighting functions are usually sensitive to the coherency of the NMO-corrected seismic events. [23] constructed a weighting function by measuring the local similarity between the reference data and each trace. This similarity-weighted function can significantly improve the resolution of semblance. Then, [24] applied the similarity-weighted function to the simultaneous-source data, and achieved better results than the traditional methods.The similarity-weighted function requires an appropriate reference trace as a judging criterion. However, how to select a reliable reference trace needs further study [25]. Coherence measurement in the semblance spectrum assumes that there is no variation of amplitudes or phases along with seismic events. However, the amplitudes of seismic events that exhibit the amplitude-variation-with-offset phenomenon are usually variable [26]. The conventional semblance spectrum based on this assumption cannot deal with the amplitude variation, and the energy clusters in the conventional semblance spectrum will be lost, making it impossible to pick up the effective velocity value. To overcome the problem that the conventional spectrum cannot deal with AVO anomalies, [27] introduced a trend-based semblance operator to account for the effect of AVO anomalies on the semblance spectrum. This semblance operator, referred to as the AB semblance. Ref.