SYSTEM AND METHOD FOR SEISMIC INVERSION
A method for elastic wave modeling up to tilted orthorhombic symmetry in anisotropy involves applying a curved grid adapting to a free-surface topography and transforming this the curved grid to a rectangular grid. Calculations using numerical discretization methods such as finite-difference are performed. The boundary condition for any free-surface is σ ij ·n j =0, which requires vanishing the global stresses' normal components to the free-surface. This resulting model more accurately simulates surface effects and better inversion for subsurface earth properties.
1 . A method for simulating seismic waves, comprising:
reading a plurality of parameters of a grid and a plurality of seismic acquisition data into a model;
reading a plurality of parameter of a medium of a earth formation into the model;
applying a free-surface boundary condition to the model, wherein the free-surface boundary conditions are applied in a curved grid;
converting the free-surface boundary condition in the curved grid to a rectangular computational grid;
constructing a Hooke's law equation (4) in the rectangular computational grid;
constructing momentum conservation equations (15)-(17) in the rectangular computational grid;
solving the Hooke's law equation and the momentum conservation equations in the rectangular computation grid by applying the free-surface boundary conditions; and
obtaining a resulting data, wherein the output data are seismograms or snapshots of seismic pressure, or stress components, or particle velocities of the seismic wave.
2 . The method of claim 1 , wherein the curved grid has a planar bottom and a curvilinear top that coincides with the free-surface topology.
3 . The method of claim 1 , wherein the free-surface boundary condition is vanishing normal traction at any point on a surface of the curved grid.
4 . The method of claim 1 , wherein the medium of the earth formation is an elastic medium of anisotropy of tilted orthorhombic symmetry.
5 . The method of claim 1 , wherein a numerical discretization method is employed in solving the Hooke's law equation and the momentum conservation equations in the rectangular computation grid.
6 . The method of claim 5 , where in the numerical discretization method is a finite-difference (FD) method, a finite element (FE) method, a spectral element (SE) method.
7 . The method of claim 1 , further comprising inputting the resulting data into a seismic imaging method, a full waveform inversion (FWI) method, an elastic reverse time migration method.