Effect of lateral heterogeneity on 2-D Rayleigh wave ZH ratio sensitivity kernels based on the adjoint method: Synthetic and inversion examples

The ratio between vertical and radial amplitudes of Rayleigh waves(hereafter,the Rayleigh wave ZH ratio)is an important parameter used to constrain structures beneath seismic stations.Some previous studies have explored crust and upper mantle structures by joint inversion of the Rayleigh wave ZH ratio and surface wave dispersion.However,all these studies have used a 1-D depth sensitivity kernel,and this kernel may lack precision when the structure varies a great deal laterally.Here,we present a systematic investigation of the two-dimensional(2-D)Rayleigh wave ZH ratio kernel based on the adjoint-wavefield method and perform two synthetic tests using the new kernel.The 2-D ZH ratio kernel is consistent with the traditional 1-D sensitivity kernel but has an asymmetric pattern with a preferred orientation toward the source.The predominant effect caused by heterogeneity can clearly be seen from kernels calculated from models with 2-D heterogeneities,which confirms the necessity of using the new 2-D kernel in some complex regions.Inversion tests using synthetic data show that the 2-D ZH ratio kernel has the potential to resolve small anomalies as well as complex lateral structures.

Improved Reliability Analysis Method Based on the Failure Assessment Diagram

With the uncertainties related to operating conditions,in-service non-destructive testing（NDT） measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram（FAD） approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics（PFM） assessment method is proposed.By integrating 2D kernel density estimation（KDE） technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures.