Mimetic Operators for Seismic Exploration

Abstract

SUMMARYMimetic operators are a kind of discrete operators which, on staggered grids, can accomplish "mimetic" properties analogous to their continuous counterparts. Furthermore, they can attain identical convergence order everywhere in the domain, including at or near the domain's boundaries in non-periodic problems. This property makes mimetic finite difference (MFD) operators attractive whenever high-contrast interfaces or physical boundary conditions are present in our models. In the seismic case, the strongest boundary condition is the interface between Earth and air, the so-called free surface. This surface is typically represented as a traction-free boundary condition and, although it is of critical importance for achieving accurate results, due to its vicinity to the sources and receivers, it is still a problem for current FD implementations. Despite efforts in the past, few FD schemes have attained convergence of order beyond two in results involving the free surface. Here we summarize the properties of mimetic operators applied to the elastic wave equation, as well as the changes required in order to incorporate into current explicit staggered grid codes the mimetic approach of the free-surface condition