| In the dissertation, I have proposed and developed new approaches for seismic modeling, migration, and full-waveform inversion in the frequency domain.;For 3D scalar-wave simulations in the frequency-space domain, we develop a fourth-order compact finite-difference (FD) form with a high-order spatial accuracy (4-5 grid points per shortest wavelength), and optimal one-way wave-equation (OWWE) absorbing boundary conditions (ABCs) with only one outer layer; these strategies greatly reduce the total number of the model grid points, and thus the overall computational cost.;For reverse-time migration (RTM) using the cross-correlation imaging condition in the time domain, extra disk storage or wavefield simulations are required to make the forward propagated source and backward-propagated receiver wavefields available at the same time. We propose a new method to implement RTM in the frequency domain. Using virtual sources for the backward propagation of the receiver wavefield, we can straightforwardly implement the excitation-time and cross-correlation imaging conditions at each frequency without any disk storage or I/O and with complete spatial coverage of the migrated images.;As both time and frequency domains have their own advantages for the inversion, we implement a hybrid scheme to combine both advantages in elastic full-waveform inversion (FWI). We simulate the wavefields using a time-domain high-precision finite-element (FE) modeling parallelized over shots with the message passing interface (MPI), and implement the inversion in the frequency domain via Fourier transform. Thus, we can easily apply both frequency-selection and time-windowing techniques to reduce the nonlinearity in inversion. To decouple different parameters in elastic FWI, we propose a new multi-steplength gradient approach to assign individual weights separately for each parameter gradient, and search for an optimal steplength along the composite gradient direction. As variations in the results are usually underestimated (smoothed) for Vp and Vs, and correspondingly overestimated (sharpened) for rho, we further calculate the impedances Ip and Is from the velocity and density products to compensate for the under or over estimations of their variations. Using both FE and finite-difference (FD) synthetic data (without surface waves) from the elastic Marmousi-2 model, we obtain satisfactory results for Vp, Vs, rho, Ip, and Is with stable convergences. |
