Subproject I

WP 1.01 – Benchmarking of various existing 3D MT and 3D CSMT forward and inversion codes.

WP 1.02 – Extension of a 3D code for joint inversion of CSMT und MT: the development of the joint inversion will combine the modular, open source code from Egbert et al., which presently includes a range of options for MT modelling and more generally applicable inversion schemes, with existing CSEM modelling codes (Streich, 2009; Streich and Becken, 2011). In addition, optimized strategies for regularization and design of the inversion meshes for a joint CSMT and MT inversion must be defined, considering the different and complementary sensitivities of the two methods (WP 1.04). Furthermore, global weighting of the individual methods as described by Commer and Newman (2009) can be used.

WP 1.03 – Efficient parallelization of implemented algorithms: We will develop and implement parallelization strategies that are specific to each individual method. For instance, when using iterative solvers, the MT forward problem can be computed in parallel for each period and polarisation, and the sensitivity matrix can be computed for all receivers autonomously. We will also utilize parallelized direct solvers, initially for CSEM modelling and inversion. Direct solution approaches are memory-intensive, but advantageous if solutions for many sources and sensitivities for many receivers are required. Inversion techniques which so far have been considered impractical because of the large number of forward modelling solutions required may thus become feasible. In addition to these different levels of parallelization within our modelling and inversion algorithms, we shall also use and possibly adapt parallelized algorithms for matrix operations, such as PETSc, PSBLAS or ScaLAPACK (see also WP 1.09 and 1.10).

WP 1.04 – Multi-grid methods and adaptive meshes for multi-scale problems: Scaling properties of CSMT and MT models may be comparable, but the spatial behaviour of the associated electromagnetic fields differs significantly between the two methods. Whereas the external magnetic source fields in MT can be treated as quasi-homogenous plane waves, the source fields and secondary currents in the vicinity of a CSMT transmitter are extremely heterogeneous and exhibit strong gradients. Consequently, numerical CSMT simulations generally require much finer meshes than MT simulations, and local mesh refinements near the source can be advantageous for CSMT simulations. To generate optimized meshes that permit accurate computations of EM fields using as few cells as possible but as many as necessary, adaptive methods for grid refinement shall be applied in the forward computations. Similarly, for the inversion, we will develop adaptive methods that adjust the mesh according to the model sensitivities. Adaptive inversion meshes will also be used in the multi-scale inversion of combined borehole and surface measurements (see also WP 1.05).

WP 1.05 – Optimisation of regularisation schemes: All electrical and electromagnetic inverse problems are ill-posed and require regularization. Common regularization schemes impose smoothness constraints on the electrical conductivity structure. The solution is then determined as a trade-off between the model norm (or an a priori defined semi-norm) and the data residuals. Usually, model structure is penalized with a (weighted) global constraint, which may lead to over-regularisation of well resolved model domains and under-regularization of badly resolved regions. Such global penalties are inappropriate for multi-scale inversion algorithms. We therefore aim to develop a posteriori regularization strategies that depend on the model resolution on a local scale, possibly making use of strategies similar to Scherzer et al., 1993; Kaltenbacher und Schicho, 2002; Raus und Hämarik, 2009, which are not yet widely used for EM inversion.

In multi-grid approaches, a resolution-dependent regularization can be found by discretizing the model space depending on the resolution and defining the regularization operator in the model space: Well-resolved model regions are finely discretized and thus require little regularization. Kaltenbacher und Schicho (2002) show that such an approach converges for ill-posed non-linear problems. In this work package, we attempt to develop an implicit local regularization by adaptive model parameter discretization for multi-scale problems, such as the joint inversion of surface and borehole data. This first requires testing strategies for adaptive model refinement (see also WP 1.04).

WP 1.06 – Wavelet parameterisation: To reduce the number of degrees of freedom in the model and the associated size of the inverse problem, the model parameters can also be represented in the wavelet domain. A major challenge in using wavelet parameterisation is identifying the significance of coefficients, as predicting the significance of coefficients for the next iteration will be necessary when solving nonlinear equation systems iteratively. For an efficient inversion, these predictions must be achieved without explicitly computing the wavelet coefficients. To this end, we attempt to transfer methods for adaptive model discretization of WP 1.04 to the wavelet domain.

WP 1.07 – Application to existing field data: The newly developed inversion schemes will be applied to and tested with existing field data. MT data sets with areal site coverage that are suitable for 3D inversion are available from various projects (Namibia, South Africa, Dead Sea Transform, San Andreas Fault, North-German basin, Groß Schönebeck). Within the ongoing GeoEn project, the GFZ working group has acquired a large CSMT data set in the vicinity of the CO₂ sequestration test site near Ketzin. Since MT data were also collected in the same survey, these data may be used for testing the multi-scale joint inversion.

WP 1.08 – Communication Platform: Implementation of a web-based communication platform that will serve as a tool for an exchange of experiences, to publish best practice guides, and to document project and administrational matters. The platform will be available throughout the project and after the project has ended.

WP 1.09 – Implementation of parallel computing and open source packages on the compute cluster: For the development of parallel algorithms, several Message Passing Interface (MPI) software packages, which are capable of using the infiniband network, and compatible Fortran and C compilers (Intel, Portland, GNU) are installed on the GFZ computer cluster. In this work package we will investigate the combination of distributed memory, MPI-based and shared-memory (OpenMP) parallelization that can be used within multi-core cluster nodes.

WP 1.10 – Development of scheduling algorithms for distributed computing: In addition to the compute cluster of the GFZ, the project aims to facilitate the use of Grid computing technologies, such as the D-GRID network (Klump and Häner, 2005). Besides parallelization of algorithms, the distributed nature of the Grid requires development of scheduling algorithms to orchestrate distributed compute jobs dispatched to remote Grid computing nodes. The Grid resources will be made accessible through a web portal. The results of this work package will be disseminated to the project partners and a wider user community via the workshops and the project communication platform (WP 1.08). A longer-term goal of this work package is to facilitate access to the compute and storage resources of the Grid for the geosciences community to provide computing resources which are well beyond the current means of individual research groups. We have initiated discussions to coordinate these efforts with the BMBF-funded WissGrid project.