New FD Operators to Solve Second Order Elastic Wave Equation

The finite difference method (FDM) is one of the most applied and studied numerical methods for seismic wave propagation due to its computational efficiency. There are several available algorithms based on FDM, each one presenting advantages and disadvantages. Concerning offshore elastic wave simulations, it is well known that numerical schemes based on staggered grids are the most applied and successful schemes, but they spend a great amount of computational memory. It is because of the need to store both velocity and stress components. On the other hand, simple grid FDM based schemes based on second-order elastic wave equations in terms of only displacement components present unacceptable responses when modelling high Poisson ration material layers (specially water). This paper presents a new FDM staggered-grid scheme (ESG) based only in displacements – where new stable DF approximations are applied directly to the second-order wave equation – able to model offshore regions as well as staggered grid schemes. The ESG has the same stability and accuracy characteristics as staggered grid schemes but spends as memory as simple grid schemes. In other words, it is presented a staggered grid scheme that takes advantage of the two better features of staggered and simple grid schemes.