Patent ID: 8423332

Claim:
A method for processing seismic data, the method comprising: synthesizing numerical operators for conducting a numerical analysis of seismic wave motion propagated in a finite region defined by an interior section of the earth using a time-domain finite-difference method employing a predictor-corrector scheme to solve the following implicit finite-difference equation T ′ ⁢ 1 Δ ⁢ ⁢ t 2 ⁢ ( c + - 2 ⁢ c 0 + c - ) = - H ′ 12 ⁢ ( c + + 10 ⁢ c 0 + c - ) + f , (where Δt denotes a time step, c + , c 0 , and c − denote state vectors (which give components of the displacement vector at discrete grid points in an analysis target space) at times t+Δt, t, and t−Δt, respectively, f denotes an external force vector at each discrete grid point, T′ denotes a mass matrix, and H′ denotes a stiffness matrix), which synthesizes operators H′ and δT num (where T is a positive definite diagonal mass matrix) given by δT num =T′−T, the residual of the mass matrix, wherein H′ is generated using a spatial first-order difference operator P i (where i is an integer in the range of 1≦i≦I and I is a natural number which depends on a dimensionality of the analysis target space), which operates on the state vectors at each discrete grid point and an elastic constant matrix C on the basis of the following equation, H ′ = ∑ i ⁢ a i ⁢ P i T ⁢ CP i , (where a i is a positive scalar coefficient, the operator P i T is a transposed matrix operator of P i ), and wherein δT num is defined so that an operation result of the operator δT num on the state vectors corresponding to rotations and translations is 0; receiving the seismic data; and using the synthesized numerical operators to carry out the numerical analysis and to produce a model of the interior section of the earth.