We construct a model of remanence for the oceans, combine it with a model of induced magnetization for the whole Earth from a previous study, compute the predicted lithospheric geomagnetic field and compare the result with a model, MF7, that is based on satellite data. Remanence is computed by assigning magnetizations to the oceanic lithosphere acquired at the location and time of formation. The magnetizing field is assumed to be an axial dipole that switches polarity with the reversal time scale. The magnetization evolves with time by decay of thermal remanence and acquisition of chemical remanence. The direction of remanence is calculated by Euler rotation of the original geomagnetic field direction with respect to an absolute reference frame, significantly improving previous results which did not include realistic oceanic magnetization computed this way. Remanence only accounts for 24 per cent of the energy of the oceanic magnetization, the induced magnetization being dominant, increasing slightly to 30 per cent of the part of the magnetization responsible for generating geomagnetic anomalies and 39 per cent of the Lowes energy of the geomagnetic anomalies. This is because our model of oceanic crust and lithosphere is fairly uniform, and a uniform layer magnetized by a magnetic field of internal origin produces no external field. The largest anomalies are produced by oceanic lithosphere magnetized during the Cretaceous Normal Superchron. Away from ridges and magnetic quiet zones the prediction fails to match the MF7 values; these are also generally, but not always, somewhat smaller than the observations. This may indicate that the magnetization estimates are too small, in which case the most likely error is in the poorly-known magnetization deep in the crust or upper mantle, or it may indicate some other source such as locally underplated continental lithosphere or anomalous oceanic crust, or even small-scale core fields.