Finite-difference Modeling And Characteristics Analysis Of Rayleigh Waves In Viscoelastic-VTI Media

Rayleigh waves is a kind of seismic surface wave formed by interference of P-and SV-waves,which has the characteristics of strong energy,slow attenuation,high signal-to-noise ratio,strong anti-interference ability,and dispersion characteristics in layered media.It is suitable for inferring the internal structure and geotechnical parameters of solid Earth,and has been widely used in regional and global seismology,near-surface geophysical engineering and ultrasonic non-destructive testing.Especially in the field of near-surface geophysics,high-frequency Rayleigh waves has been increasingly used in practical engineering application and academic research due to its non-invasive,non-destructive,high-efficiency,economical,strong anti-interference,and high-resolution.So far,high-frequency Rayleigh-wave exploration methods are still based on the theoretical framework of isotropic elastic?IE?media.However,the Earth has been recognized as the anisotropy and viscoelastic materials with the significant effects on seismic waves propagation,especially on Rayleigh waves.Therefore,through the forward modeling method,it is of great significance to studying the attenuation and dispersion characteristics of Rayleigh waves in anisotropic-viscoelastic?AV?media for further broadening the application field of Rayleigh waves exploration and guiding the practical exploration work.Based on the research ideas from theory to practice,the author firstly investigated and summarized the current research status of the numerical simulation of wavefield and dispersion curves of Rayleigh waves.Then,aiming at the their shortage in AV media,in view of the generalized Zener viscoelastic model and VTI?Transversely Isotropy with A Vertical Axis of Symmetry,VTI?medium model,the author proposed the research topic of“Finite-difference Modeling and Characteristics Analysis of Rayleigh Waves in Viscoelastic-VTI Media”.Based on the first-order P-SV waves velocity-stress viscoelastic-VTI media wave equations,the author used the stress mirror image?SIM?method as the free boundary condition,adopted the multiaxial perfectly matched layer?M-PML?as the absorption boundary condition,and combined a grid high-order finite-difference algorithm with a fourth-order Runge-Kutta time integration method,to develop a viscoelastic-VTI medium Rayleigh wave finite-difference wavefield forward simulation program with 12th-order difference accuracy in space and4th-order difference accuracy in time.Because the Rayleigh wave dispersion function in the viscoelastic medium becomes a complex function,the rooting method in real number field cannot be used to calculate the dispersion curve.Based on previous researches,the author proposed a strategy to calculate approximately the dispersion curve in the real number domain by using phase velocity instead of complex velocity.Based on the simplified Delta Matrix method,the author extended the Rayleigh wave dispersion curve forward algorithm from the anisotropic elastic?AE?medium to the AV medium,and developed the fast and stable Rayleigh waves dispersion curve forward simulation program in viscoelastic-VTI media.By setting the Thomsen parameter?=?=0,the programs can simulate the result of the isotropic viscoelastic?IV?medium;by setting the relaxation time relationship^??₇)=^??₇),the programs can simulate the result of the AE medium;by setting both?=?=0 and^??₇)=^??₇),the programs can simulate the result of IE media.This paper achieves the forward simulation of Rayleigh waves in IE,IV,AE and AV media.By comparing the simulation results of IV and IE media,AE and IE media,and AV and AE media,the author studied deeply the characteristics of propagation,attenuation and dispersion in IV,AE,and AV media,respectively.First,the author studied the characteristics of Rayleigh waves in the homogeneous half-space model from three perspectives of the wavefield snapshot,the waveform curve,and the dispersive energy images.Then,the author studied the characteristics of Rayleigh wave in a typical layered media model using two-layer with velocity increasing,four-layer with velocity increasing,four-layer with low-velocity soft interlayer,and four-layer with high-velocity hard interlayer as examples.Finally,the authors studied the characteristics of Rayleigh waves in complex geological models using faults and voids models as examples.Research indicates:?1?In the dispersive energy images,the maximum peak values of Rayleigh waves dispersion energy can all agree with the corresponding theoretical dispersion curves in different media,which verifies the correctness of the numerical modeling results.?2?The viscoelasticity of the medium will cause the amplitude attenuation of Rayleigh waves;the high-frequency components will attenuate more seriously than the lower-frequency components;the center frequency of the amplitude spectrum of the seismic record moves toward the low frequency side;the degree of attenuation are getting severe increasingly with the offset increasing.The viscoelasticity of the medium will cause the phase velocity dispersion of Rayleigh waves;the overall trend of the dispersion is that the degree of dispersion increases as the frequency increases.The viscoelasticity of the medium will reduce the resolution of the Rayleigh wave dispersion energy.The effects of the viscoelasticity are getting severe increasingly with the quality factor decreasing.?3?The reference frequency will not affect the degree of the amplitude attenuation and phase velocity dispersion of Rayleigh waves caused by the viscoelasticity of the medium,but it will affect the phase velocity value and determine the frequency position where the phase velocities of the viscoelastic and elastic media are equal.?4?Being similar to the IE medium,the Rayleigh waves amplitude of the AE medium hardly changes with the offset changing,and the Rayleigh waves phase velocity,which is a constant value,is not dispersive in a homogeneous half-space.Being different from IE media,Rayleigh waves of AE media show the significant differences in amplitude,waveshape?or waveform?and wave velocity?or travel time?;the differences will obviously change if Thomsen parameter values changed.For example,in the waveforms comparison of the homogeneous half-space models,when?=0.2 is constant,the Rayleigh wave will takes off more and more late and the amplitude becomes larger and larger as?decreases from 0.3 to 0.1;when?=0.3,the take-off time of Rayleigh waves of AE medium is earlier than that of the IE medium,and the amplitude is smaller than that of the IE medium.When?=0.1,the take-off time of Rayleigh wave of the AE medium is later than that of the IE medium,and the amplitude is larger than that of the IE medium.These reflects the complexity of the anisotropy of the medium.?5?Under certain Thomsen parameters??=0.4 and?=0.2?,in the layered media,compared with IE media,the Rayleigh wave events on the shot gathers of AE media are more centralized,the inclination and number of the events are significantly reduced.The Rayleigh waves phase velocities on the dispersion energy image of AE medium are obviously higher;the distance between adjacent modes is greater;the number of AE high-order modes is markedly less;the dispersion energy of AE high-order modes is more continuous.?6?The Rayleigh waves characteristic in AV medium is actually the effect result of both the anisotropy and the viscoelasticity of the medium.Therefore,the comparison conclusion of simulation results of AV and IE medium can be obtained through the comparison of AE and IE media and comparison of AV and AE media.The original contributions in this dissertation are as follows:1.A numerical simulation scheme,which combines the standard staggered grid high-order finite-difference algorithm,the fourth-order Runge-Kutta time integration method,the free boundary condition of SIM,and the absorption boundary condition of M-PML,is applied in the wavefield numerical simulation of Rayleigh waves basing on the first-order P-SV wave velocity-stress viscoelastic-VTI medium wave equations.It greatly improves the accuracy of numerical simulation and avoids confusion between numerical dispersion and physical dispersion.2.The dispersion curve forward algorithm of Rayleigh waves based on the simplified Delta Matrix method is extended from the elastic-VTI medium to the viscoelastic-VTI medium,achieving a stable and efficient forward calculation of the Rayleigh waves dispersion curve.It provides the foundation for dispersion curve inversion of Rayleigh waves in viscoelastic-VTI media,and also provides a powerful tool for verifying the correctness of wavefield modeling results of Rayleigh waves and assisting analysis of dispersion characteristics of Rayleigh waves.3.The propagation,attenuation and dispersion characteristics of Rayleigh waves in isotropic-viscoelastic media,anisotropic-elastic media,and anisotropic-viscoelastic media are deeply studied.It is of great significance for helping people to better understand Rayleigh-wave behaviors in Earth media,further improving the accuracy of inversion and interpretation of Rayleigh waves and broadening the filed of exploration applications of Rayleigh waves.