Gauss-Newton Inversion with Node-Based Basis Functions: Application#xD;to Imaging of Seabed Minerals in an Area with Rough Bathymetry#xD;

Abstract

The Gauss-Newton method has good convergence properties when employed for the solution of both seismic and electromagnetic inversion problems. One main issue is high numerical cost. The numerical cost can be reduced if the optimization domain can be decoupled from the simulation domain and such that the number of optimization parameters is much smaller than the number of grid nodes required for accurate simulation results. Overparameterization can be avoided. The decoupling can be achieved in a rigorous manner with the use of node-based basis functions. We provide a generic derivation of the method that is easily specialized to seismic and electromagnetic problems. The transformations between the optimization domain and the simulation domain are most effective if both domains can be described by rectilinear grids. A variable seabed depth causes a difficulty. We introduce a transform from the true bathymetry to a flat seabed that solves this problem. The method is validated by application to both synthetic and real electromagnetic data sets. The real data was acquired at the slow spreading Mohns ridge located east of Greenland and southwest of Svalbard. We provide a discussion on the interpretation of these data for an inverse scheme using the VTI (Transverse Isotropy with a Vertical symmetry axis) approximation. We offer some insights on how to interpret inversion results in the case of exploration for marine minerals. The interpretation differs from a hydrocarbon exploration setting owing to the presence of vertical conductors due to formation water circulation and vertical resistors due to volcanic intrusions.