Seismic Responses To A Point Source In Horizontally Stratified Transversely Isotropic Porous Media

In early seismological research,people usually regarded the surface medium as an isotropic medium,and studied the propagation characteristics of seismic waves based on the isotropic theory.With the further understanding of underground media,it is found that if people only use isotropic theory for research,it will bring some difficulties to the development of complex oil and gas reservoirs and the interpretation of seismic exploration data.This is because the actual strata are not all isotropic,and some strata have anisotropic characteristics.For example,during the deposition of sedimentary rocks,the particles will be arranged horizontally to form a horizontal layered structure.The propagation properties of seismic waves in all directions of the layered plane are the same,but the propagation properties in the direction outside the plane are different.Such a medium is called transversely isotropic medium,which is one of anisotropic medium,and it is widely distributed in the surface medium.In addition to the anisotropic properties of the medium,it should also be noted that natural media(rocks)contain pores,which are filled with fluid(such as water,oil,gas,etc.).The movement of fluid relative to the skeleton may have an impact on the propagation of waves.Therefore,in order to simulate the propagation of seismic waves in underground media more realistically,the anisotropy and porosity of the media must be considered at the same time.Based on this consideration,this paper studies the propagation characteristics of seismic waves in transversely isotropic porous media with a vertical axis of symmetry(VTI).This results are of great significance for seismic data interpretation,oil and gas development,and anisotropic inversion.In this paper,we propose a semi-analytical method to calculate the 3D seismic wave field excited by point source(including point force source and seismic moment tensor source)in VTI porous media.By introducing a set of harmonic basis functions,the displacement,stress and other variables are transformed into a new coordinate system,and then substituted into the wave equations of the VTI porous medium,we decouple the wave equations into two sets of first-order differential equations in frequencywavenumber domain.These two sets of equations have the same form and can be solved by the global matrix method to obtain the wavefield in the frequency-wavenumber domain.Finally,we obtain the wavefield response in the three-dimensional time-space domain by using discrete wavenumber method and fast Fourier transform.We degrade VTI porous media into isotropic porous media and VTI elastic solid media respectively,and compare the calculation results of this method with those of other existing methods to verify the correctness of this method.Then we carry out numerical simulation to study the characteristics of seismic waves in VTI porous media.The calculation results show that the wave field response in the VTI porous medium is obviously different from that of isotropic porous media.For example,in VTI porous media,the explosive source can simultaneously generate q P wave and q SV wave,and q SV wave can cause the change of pore pressure,but SH waves cannot.In addition,the research results also show that seismic waves in VTI porous media have velocity anisotropy and attenuation anisotropy.The semi-analytical method proposed in this paper has high computational efficiency and provides a convenient and efficient simulation tool for the rapid evaluation of seismic response in VTI porous media in the future.The knowledge gained provides theoretical reference for the interpretation of seismic data in the future.