Fast large-scale gravity modeling using a high-order compact cascadic multigrid strategy

Abstract

We develop a new high-order compact cascadic multigrid (MG) strategy for modeling large-scale complex gravity problems on nonuniform rectilinear grids. Firstly, we discretize the governing 3D Poisson’s gravitational potential equation using a novel high-order compact (HOC) difference scheme, which allows for Robin boundary conditions to further reduce the computational domain. Then, the resulting asymmetric linear system of equations is solved by a generalized extrapolation cascadic multigrid (gEXCMG) method augmented with a novel MG prolongation operator. The quartic interpolation and completed Richardson extrapolation assist this MG prolongation operator to produce a good initial guess for the biconjugate gradient stabilized (BiCGStab) smoother. In the end, two synthetic and SEG/EAGE salt models are examined to verify the presented approach. Results show that the proposed algorithm can efficiently and accurately produce the gravity signals for complex geological models. Moreover, the comparisons with the state-of-the-art algebraic MG solvers demonstrate that our gEXCMG solver offers substantially better efficiency with significantly less memory consumption. Therefore, our newly developed method has the potential for serving as a forward engine in large-scale gravity inversions.