Context. A large number of magnetic white dwarfs discovered inthe SDSS have so far only been analyzed by visual comparison of theobservations with relatively simple models of the radiation transportin a magnetised stellar atmosphere. Aims. We model the structure of the surface magnetic fields of the hydrogen-rich white dwarfs in the SDSS. Methods. We calculated a grid of state-of-the-art theoreticaloptical spectra of hydrogen-rich magnetic white dwarfs (WDs) withmagnetic field strengths of between 1 MG and 1200 MG for differentangles between the magnetic field vector and the line of sight, and foreffective temperatures between 7000K and 50000K. Weused a least squares minimization scheme with an evolutionary algorithmto find the best-fit magnetic field geometry of the observed data. Weused centered dipoles or dipoles that had been shifted along the dipoleaxis to model the coadded SDSS fiber spectrum of each object. Results. We analyzed the spectra of all known magnetichydrogen-rich (DA) WDs from the SDSS (97 previously published, plus44newly discovered) and also investigated the statisticalproperties of the magnetic field geometries of this sample. Conclusions. The total number of known magnetic white dwarfs hasalready been more than tripled by the SDSS and more objects areexpected after more systematic searches. The magnetic fields havestrengths of between 1and 900MG. Our results further support the claims thatAp/Bppopulation is insufficient in generating the numbers andfield strength distributions of the observed MWDs, and that of eitheranother source of progenitor types or binary evolution is needed. Clearindications of non-centered dipoles exist in about 50%, of the objects which is consistent with the magnetic field distribution observed in Ap/Bpstars. Key words: stars: white dwarfs - stars: magnetic fields - stars: atmospheres
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