2D/2.5D Seismic Wave Modeling And Reverse-time Migration In Complex Media Including Undulating Topography

Numerical stimulation of seismic wave propagation has always been considered a crucial step towards a more detailed understanding and interpreting seismic data,as well as imaging structure of the Earth’s shallow or deep interior.In order to obtain a high-accurate seismic wave solution,various numerical simulation methods and seismic wave theories have been put forward and continuously improved.In addition,various seismic wave modeling methods have gradually developed from 2-D to 3-D in order to highly restore the real geological model.But 3-D seismic wave modelling is usually very time-consuming and requires huge computer memory,which leads to its inefficiency for seismic imaging in a large scalar 3D problem.Meanwhile,the 2-D seismic wave modelling replaces the point source which is used in practice with an artificial line source and results in difficulty to match 3-D dynamic features of the real observed seismograms with the 2-D numerical solutions,and 3-D-to-2-D data transformation methods can only be reliably applied to very simplistic models,e.g.,homogeneous or flat-layered isotropic media,far-field approximation,and no overlapping arrivals.What’s more,it is still not very clear when seismic wave propagates through irregular and undulating topography.And furthermore,it is very helpful to know the features when the seismic wave propagates across the complex fluid-solid interface,which can help better understand of seismic data obtained from multi-component ocean seismograph,and further investigate the physical phenomena associated with the fluid-solid interface.To overcome the above problems,in this thesis,I present a generalized 2-D/2.5-D first-order time-domain governing equation to model seismic wave propagation in different(acoustic,elastic isotropic and anisotropic)media,and then deduce different formula that incorporate topographic free-surfaces(air-water and air-solid)and water-solid interface.Furthermore,I numerical solved the generalized wave equation by the curvilinear grid finite-difference method and subdomain Chebyshev spectral method.The 2.5-D forward-modelling method considers the medium be symmetric in the out-of-plane direction,so that one can apply the Fourier transform with respect to the symmetry axis and the 3-D problem is reduced to a repeated 2-D computational problem,which is much more economical than full 3-D wave modeling.Numerical tests of this thesis verify the correctness of the 2.5-D method and its advantages over the 2-D and 3-D numerical methods in term of computational accuracy and efficiency.The results of numerical experiments show that the proposed 2.5-D method can simulate seismic wave propagation in various media having different boundary conditions,including a free-surface(air-water or air-solid)and a water-solid interface,what’s more,the methods of this thesis can also solve the seismic wave propagation problems including undulating interface by using curvilinear-grid FD method.In addition,unlike the problems encountered in 2-D numerical solutions for a real 3-D application,the 2.5-D method can be directly employed as the forward modeling method in seismic reverse-time migration.Reverse time migration(RTM)is an important method for complex structure imaging,this thesis also completed 2-D reverse time migration imaging of acoustic medium,isotropic medium,anisotropic medium and solid-fluid coupling medium by using the curvilinear-grid FD method.Through a series of model tests,such as the layered model with undulating surface,the salt model and the Marmousi model,the correctness and adaptability of the reverse time migration method in this thesis are verified.It needs to be stated that the 2-D reverse time migration method can be extended to the 2.5-D reverse time migration method,which can be directly applied to real 3-D seismic data.The theory of two-phase media takes into account the influence of the natural structure of the medium,the properties of the fluid,and the interaction between the solid skeleton and the pore fluid in the propagating elastic wave,therefore,the two-phase model more accurately describes the actual geological structure and the nature of the formation.In this thesis,the corresponding equations in curvilinear coordinate system based on the first-order velocity stress equation of two-phase isotropic media based on the improved BISQ model are derived,then the equations are numerically solved by an optimized high-order non-staggered finite difference scheme,that is,DRP/opt Mac Cormack scheme.To implement the free-surface undulated topography,we derive the analytical relationship between derivatives of velocity components and use the compact finite-difference scheme and traction-image method.The curvilinear grid finite difference method using body-conforming grid to describe the free surface,thus avoids of numerical approximation caused by scattering.In the undulating free surface and the undulating interface of two-phase medium,the complex reflection wave and transmission wave can be clearly demonstrated by the numerical simulation results.The simulation results show that the curvilinear-grid finite-difference method can accurately solve the propagation problem of seismic waves in a two-phase isotropic medium when an undulating surface is presented.