Reflection Waveform Inversion And GPU Realization In Time Domain

The staggered-grid finite-difference(SGFD)method has been widely used in seismic forward modeling.The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration.Numerical dispersion is one of the problems in this method.The window function method can reduce dispersion by replacing the finite-difference operators with window operators,obtained by truncating the spatial convolution series of the pseudo-spectral method.Although the window operators have high precision in the low-wavenumber domain,their precision decreases rapidly in the high-wavenumber domain.We develop a least squares optimization method to enhance the precision of operators obtained by the window function method.We transform the SGFD problem into a least squares problem and find the best solution iteratively.The window operator is chosen as the initial value and the optimized domain is set by the error threshold.The conjugate gradient method is also adopted to increase the stability of the solution.Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.The traditional seismic data processing flow usually includes: modeling the velocity by travel time and waveform tomography,to provide an accurate velocity field for subsequent processing,and performing the imaging based on the known background velocity field in order to accurately describing the main underground layer.Accurate velocity field modeling is the premise and guarantee for high-precision imaging.With the increasingly complex exploration conditions,higher requirements are also put forward for the velocity field modeling method.Full waveform inversion(FWI)can theoretically make full use of effective information such as amplitude,phase,travel time and waveform contained in the seismic data and has made great progress in different domains and different media.In the global inversion of the structure and exploration geophysics,FWI has achieved good results.However,the full waveform inversion is a very strong nonlinear problem.One of the most effective solutions is to iteratively obtain the optimal solution through the local optimization method.In this case,an initial model that is very close to the global optimal solution is required.The conventional full waveform inversion method lacks the ability to recover the medium and long wavelength components,so the initial velocity field is required to provide accurate long-wavelength information.In recent years,the rise of the reflected wave full waveform inversion played an increasingly important role in terms of recovering the long and middle wavelength component,providing an accurate initial model for conventional FWI and migration.Reflected Waveform Inversion(RFWI)provides a more accurate initial velocity field for traditional full waveform inversion(FWI)by alternately updating the low and high wavenumber components of the model.