Wave Equation-based Dynamic Inversion Algorithm

Full waveform inversion?FWI?is a research hotspot in the field of seismic exploration,and it is prospecting in oil and gas exploration and crustal research.The calculation of full waveform inversion is huge,and most of them are used to simulate the seismic wave field.Therefore,it is of great theoretical and practical value to improve the numerical accuracy and computational efficiency of forward modeling method.At the same time,the FWI results strongly depend on the initial models.It is urgent to extend the convergence domain and reduce the dependence of the inversion process on the initial model.In this dissertation,two efficient high-precision finite difference algorithms and a full waveform inversion method with large convergence domain are proposed.The main contents include:?1?We propose a new finite difference scheme for solving the wave equation,named the dispersion relation preserving stereo-modeling method?DRPSM?,which is practical for seismic forward modeling beyond the Nyquist frequency.The basic idea is to use both the displacement field and its gradient field to reconstruct the high order spatial partial derivative.Then,the interpolation coefficients of the space operator are obtained by wave number domain optimization.It is found that when the operator radius is 4,the maximum phase offset between adjacent grid points can reach 1.2?,and only 5/3 sampling points per minimum wavelength,goes beyond the Nyquist sampling frequency.Theoretical analysis and numerical experiments show that the method is superior to the 60^th-order Lax-Wendroff correction method and the pseudo spectral method in terms of computational efficiency and simulation accuracy,making it a highly useful tool for seismic modeling.?2?To solve 3D scalar wave equation,we optimize the temporal and spatial error simultaneously forpiecewise Courant numbers,forming an optimized time-space-domain FD method with piecewise constant interpolation coefficients?CTSFD?.The method suppresses numerical dispersion effectively on coarse grids,and promotes the computational efficiency by significantly reducing the extra time cost for consecutively loading the coefficients.In numerical experiments,when the numerical dispersion is effectively suppressed,the computational efficiency of CTSFD is 2.5 times and 1.8 times comparing to central FD and time-space-domain FD methods with the same stencil length.It is also effective in complex models.?3?We have taken a new perspective on the dynamic inversion method and used acceleration approaches to reduce the computational time and memory usage to improve its ability of performing high-resolution imaging.The dynamic inversion method obtains sensitivities of the seismic displacement field with respect to earth properties directly by solving differential equations for them instead of constructing sensitivities from the displacement field itself.Full wave-field information is utilized as much as possible at the expense of a larger amount of calculations.To mitigate the computational burden,two ways are proposed to accelerate the method from a computer-implementation point of view.One is source encoding which uses a linear combination of all shots,and the other is to reduce the amount of calculations on forward modeling.We present some inversion results to demonstrate the validity of this method through layered model,checkerboard and Marmousi models.It shows that this method is also convergent even with big deviations for the initial model.Besides,parallel calculations can be easily implemented due to its unique construction.