Vessels constructed in electrically conductive materials give rise to frequency-dependent, induced magnetic fields when waves of water cause them to roll in the Earth's magnetic field. These fields, typically referred to as roll-induced magnetic vortex fields, are a component of the ship's overall signature, where signature refers to measurable quantities which can reveal or identify objects. It is crucial for military platforms to keep the signature low and thereby increase the possibilities of operation. For magnetic signatures, this is done through strategic design and construction of the platform or by using magnetic silencing systems. The signature is then decreased to minimize the risk of detection from naval mines and marine detection systems.  This report covers the initial research on the subject of an inverse source model for roll induced magnetic fields. By limiting the analysis to two basic objects and applying a time variant magnetic field to them, we induce a magnetic field which we then model. The inverse modeling is done using magnetic dipoles as sources which are placed around the area of the object. The parameters of the model are then found by applying a least squares algorithm coupled with Tikhonov regularization. The focus of this report is the configuration of this setup in terms of measurements and sources, as well as finding a proper regularization parameter. Since the applied magnetic field is dependent on the roll frequency, also the inverse model depends on a frequency parameter in addition to the geometry and material of the object. The objects here studied are of two simple geometries, a rectangular block and a hollow cylinder. Both objects are constructed in an aluminum alloy with well known material parameters. Measurement data is gathered using a numerical solver utilizing the finite element method for solving the partial differential equations. The numerical measurement data is compared to physical measurements as well. The physical measurement data is gathered by placing the objects in a Helmholtz-cage which is used to apply a homogeneous time variant magnetic field upon them. The project was carried out at the Swedish Defence Research Agency (FOI) at the department of underwater research.