3D-marine tCSEM inversion using model reduction in the Rational Krylov subspace

Wednesday, 17 December 2014
Malte Sommer and Marion D Jegen, GEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany
Computationally, the most expensive part of a 3D time domain CSEM inversion is the computation of the Jacobian matrix in every Gauss-Newton step. An other problem is its size for large data sets. We use a model reduction method (Zaslavsky et al, 2013), that compresses the Jacobian by projecting it with a Rational Krylov Subspace (RKS). It also reduces the runtime drastically, compared to the most common adjoint approach and was implemented on GPU.
It depends on an analytic derivation of the implicit Anzatz function, which solves Maxwell's diffusion equation in the Eigenspace giving a Jacobian dependent on the Eigenpairs and its derivatives of the forward problem. The Eigenpairs are approximated by Ritz-pairs in the Rational Krylov subspace. Determination of the derivived Ritz-pairs is the most time consuming and was fully GPU-optimized. Furthermore, the amount of inversion cells is reduced by using Octree meshes. The gridding allows for the incorporation of complicated survey geometries, as they are encountered in marine CSEM datasets.
As a first result, the Jacobian computation is, even on a Desktop, faster than the most common adjoint approach on a super computer for realistic data sets. We will present careful benchmarking and accuracy tests of the new method and show how it can be applied to a real marine scenario.