Seismic Forward Modeling And Ensemble Source Encoding Full Waveform Inversion Algorithm

Full waveform inversion(FWI) is the frontier of the researches in seismic exploration. It is prospecting in oil and gas exploration and research of earth’s crust for its potential in high-resolution imaging. FWI requires huge computation, most of which is taken up by seismic forward modeling. It is urgent to improve the accuracy and efficiency of forward modeling methods. FWI also suffers from inaccurate initial models and data noise, making methods to tackle these problems the hotspots of research. This dissertation proposes 3 finite difference methods for seismic forwarding with high efficiency and accuracy, and a FWI method which has large convergence domain and strong anti-noise ability. The main contents are as follows:(1) A numerical dispersion minimized nearly analytic discrete method(DMNAD) is proposed. The method represent the wave fields by the displacement and its gradient. I derive the spatial differentiator to approximate the high-order spatial derivatives by minimizing the wavenumber error, under the constrains from truncated Taylor expansion. The spatial differentiator is applied to solve scalar wave equations. It suppresses the numerical dispersion effectively on coarse grids. In the 3D acoustic wave equation, when the Courant number is 0.4, the maximum relative phase velocity error is as low as 3.21% even in the extreme case with 2 sampling points per minimum wavelength. Under the condition of effectively suppressing the numerical dispersion, the computational time of DMNAD is 11.2%, 34.7% and 11.5% comparing with the 4th-order and 24th-order Lax-Wendroff correction method(LWC4 and LWC24), and the 4th-order staggered grid method(SG4), respectively.(2) A time-space domain optimized nearly analytic discrete(TSNAD) method is proposed. The method is derived by adding a high-order infinitesimal as compensation to improve the nearly analytic discrete scheme, in order to minimize the phase velocity error generated by both temporal and spatial discretization. I further reduce the computation by fitting the coefficients using the Courant numbers, avoiding consecutively loading of the interpolation coefficients for different velocities. Stability adjustment allows larger time steps. Comparing to DMNAD, TSNAD further reduces the numerical dispersion error. When the phase velocity error is less than 0.1 and the Courant number is 0.1, the max grid step of TSNAD is 3.1% larger, and its computational time decreases by 13.8%, comparing with DMNAD.(3) A regularized dispersion relation preserving(RDRP) method for elastic wave equations is proposed. An optimized spatial differentiator for 2nd-order cross derivatives is derived by minimizing the 2-norm of wave number domain error. An auto-adapting regularizing term is added to the objective function to solve the ill-conditioned optimizing problem. For the 3D elastic wave equation in isotropic media, under the condition of effectively suppressing the numerical dispersion, the computational time of RDRP is 56.8% comparing with LWC12, while their radius of difference operator are both 6.(4) An ensemble full wave inversion method with source encoding(EnFWI) is proposed. The ensemble Kalman filter(EnKF) is applied in FWI, which refines an ensemble of the model parameters, and approximate the error covariance by the ensemble covariance. Consequently, it approximates the total inversion with affordable computation, to suppress the error caused by the initial model and data noise. Regularized source encoding FWI is applied to refine the model parameters samples with low computational costs, improving the representation ability of the low rank ensemble approximation. The anisotropic regularization factors are optimized by EnKF to utilize the layered structure of the earth media. Numerical experiments show that EnFWI has larger range of convergence, stronger anti-noise ability, and lower computation, comparing with traditional FWI.