Frequency-domain Modeling Using Implicit and Explicit Finite-difference Operators

Several techniques have been developed to modeling the wave equation. In this paper we introduce the frequency-domain finite-difference (FDFD) modeling and its implementation using the explicit (2nd and 4th) and implicit (nine-point) centered difference operators for solving the scalar Helmholtz equation. We discuss some proprieties of the resulting linear system after the discretization of the wave equation and show that our implemented nine-point implicit scheme produces a much more accurate result in comparison with the 2nd and 4th schemes for seismic wave simulations in the frequency domain.