Causes And Attenuation Of “Crossed” Artifacts In Passive Surface Wave Dispersion Analysis

In China,the rapidly urbanization has posed a challenge to urban underground development.The depth of urban underground development(water resources utilization,underground rail development)has expanded from tens of meters to more than 100 meters.There is an urgent need for an effective and environmentally friendly method to estimate earth layer parameters of the near surface to protect the development of urban underground space.Due to the severe electromagnetic and noise interference in the highly populated urban area,traditional geophysical methods can not be properly applied.The passive surface wave method has gained much attention among geophysical and civil engineering communities because of its capability of determining near-surface shear wave velocities from traffic noise in urban areas.The measured dispersion energy with traditional dispersion analysis methods,however,would usually be contaminated by a type of “crossed” artifacts at high frequencies."Crossed" artifacts in the dispersion image is essentially the spatial aliasing introduced by applying the reverse directional velocity scan on the unidirectional propagation energy.There are two different causes of "crossed" artifacts in the traditional ambient noise dispersion analysis algorithms:(1)the bidirectional velocity scan in the dispersion analysis algorithms;(2)applying the forward directional velocity scan on the reverse directional propagation energy.Although the causes are different,the distribution range of "crossed" artifacts in the dispersion image is the same.Corresponding processing methods need to be adopted to avoid "crossed" artifacts,to obtain a wider frequency range of multi-mode surface wave dispersion energy.Higher mode information of surface waves is important in dispersion curve inversion for shear wave velocity structure.The frequency– Bessel(F-J)transform method is an effective tool for multimode surface wave extraction,which has been applied to multiscale investigations of the Earth structure.The measured dispersion energy with the F-J method,however,would also be contaminated by “crossed”artifacts,which are caused by spatial aliasing and bidirectional velocity scan of dispersion analysis methods.The “crossed” artifacts usually cross and smear the true dispersion energy in the frequency–velocity domain.I propose a modified frequency–Bessel(MFJ)transform method in which the Bessel function is replaced by the Hankel function for dispersion analysis of empirical Green's function.The MFJ method performs a unidirectional velocity scanning on the outgoing wave to avoid the ‘crossed'artifacts.Synthetic and real-world examples demonstrate the effectiveness of the proposed MFJ method in improving the accuracy of Rayleigh wave multimode dispersion measurements.However,this traditional passive surface wave methods are currently limited to the vertical component ambient noise recording dispersion analysis,and only Rayleigh wave dispersion curves can be obtained.In recent years,three-component seismic sensors have been gradually applied to the passive surface wave survey in urban areas,and Love wave can be obtained through three-component ambient noise collection Love wave can provide a complementary constraint on the Earth structures.I extend the MFJ method to the full multicomponent empirical Green's function tensor,including the radial-radial,transverse-transverse,and mixed-component empirical Green's function.Using the newly derived formulation,not only the signal of higher?mode Rayleigh wave phase velocity dispersion can be determined,but also the multimode Love wave phase velocity dispersion curves can be extracted.A synthetic example demonstrates verifies the accuracy of the multicomponent MFJ method.In a field case,the multi-component MFJ method is compared with several developed ambient noise dispersion analysis methods(roadside passive multichannel analysis of surface wave method,the multichannel analysis method of passive surface waves,FJ method,and spatial autocorrelation method),the result shows that the multicomponent MFJ method has significant advantages in high-mode surface wave dispersion imaging from multicomponent ambient noise recordings.In the dispersion image generated by multichannel analysis of passive surface waves method,however,a type of “crossed” artifacts usually overlaps and smears the true dispersion energy in a high frequency range.The “crossed” artifacts are spatial aliasing of a reverse-directional propagating wave with a directional velocity scan.In urban areas,the coherent noise signals could be repetitively induced by traffic in a short time segment,which will produce repetitive signals in the cross-correlation function,leading to spurious reverse-directional propagating waves in the causal or acausal part.I propose to use the Wiener filter based on singular value decomposition(SVD)to attenuate the spurious signals in the cross-correlation functions to reduce “crossed”artifacts in the dispersion image.A synthetic example demonstrates that the “crossed”artifacts related to spurious signals in the dispersion image can be well attenuated by applying the SVD-based Wiener filter(SVDWF)to cross-correlation functions.Two field examples suggest that high-mode dispersion energy in the dispersion images generated from the SVDWF denoised cross-correlation functions becomes more continuous and clearer in high-frequency bands,which benefits from the advantages of both SVD and Wiener filters.