Abstract: A method for seismic imaging of a subsurface using a full waveform inversion, FWI, includes the steps of obtaining an initial P-velocity model that describes how a seismic wave propagates through the subsurface, generating an S-velocity model based on the initial P-velocity model, generating an elastic synthetic dataset p based on the initial P-velocity model and the S-velocity model, receiving a recorded seismic dataset d of the subsurface, updating the P-velocity model based on a comparison between the synthetic dataset p and the recorded seismic dataset d, updating a reflectivity at various locations in the subsurface based on the updated P-velocity model, and generating an image of the subsurface based on the reflectivity.

Abstract: A method for imaging a formation of a subsurface includes receiving input data d related to the subsurface, generating synthetic data u related to the subsurface, by applying an implicit finite-difference approach to a reflectivity model r, updating a velocity model V based on the input data d and the synthetic data u, and generating an image of the formation in the subsurface based on the updated velocity model, wherein the formation is used to locate natural resources.

Abstract: A method for seismic imaging of a subsurface using a full waveform inversion, FWI, includes the steps of obtaining an initial P-velocity model that describes how a seismic wave propagates through the subsurface, generating an S-velocity model based on the initial P-velocity model, generating an elastic synthetic dataset p based on the initial P-velocity model and the S-velocity model, receiving a recorded seismic dataset d of the subsurface, updating the P-velocity model based on a comparison between the synthetic dataset p and the recorded seismic dataset d, updating a reflectivity at various locations in the subsurface based on the updated P-velocity model, and generating an image of the subsurface based on the reflectivity.

Abstract: Embodiments of the present disclosure describe methods for efficient wavefield solutions, the methods including defining a wave equation as a linear portion and as a nonlinear portion; and solving the wave equation via an iterative process, the iterative process including, at each iteration, performing LU decomposition before solving the nonlinear portion, or obtaining best finite difference coefficients by solving an optimization equation.

Abstract: Embodiments of the present disclosure describe methods for efficient wavefield solutions, the methods including defining a wave equation as a linear portion and as a nonlinear portion; and solving the wave equation via an iterative process, the iterative process including, at each iteration, performing LU decomposition before solving the nonlinear portion, or obtaining best finite difference coefficients by solving an optimization equation.