Time-averaged paleomagnetic field and secular variation: Predictions from dynamo solutions based on lower mantle seismic tomography

We compare three dynamo solutions incorporating laterally varying boundary heat flux with paleomagnetic models and data. The boundary condition is defined by the D″seismic shear-wave velocity and the three solutions have boundary anomalies with different amplitudes. The generated fields appear to divide into a stationary, boundary-locked part and a time-varying part with persistent centres of activity. Both parts contribute to the time average. A very long averaging time can be needed for nearly-locked solutions, but a rough time average that remains within the threshold set by the accuracy of paleomagnetic data is achieved in a few diffusion times. The locked part dominates for larger amplitude boundary anomalies. In previous work the locked field was shown to have strong similarities with the modern geomagnetic field. Previous dynamo solutions that were not locked to the boundary show similarities with our solutions with weak boundary forcing. The axisymmetric time average has small g20 and larger g30 components and peaks in inclination anomaly in high latitudes (associated with the locked field) and low latitudes (associated with the time average of the time-varying fields). The non-axisymmetric time average displays a striking longitudinal variation in inclination anomaly, with a large negative anomaly in the Pacific region in agreement with observations. None of the dominant geomagnetic coefficients are axisymmetric and g20 negligible in all three models. Secular variation is concentrated in equatorial latitudes, as in some recent paleomagnetic models. The locked field agrees with the inclination difference found between Hawai'i and Réunion, in agreement with paleomagnetic averages. The locked field agrees with the paleomagnetic time average rather better than the fields with less boundary variations. We conclude that, because the locked field agrees with the modern field as well as some aspects of the long-term time average, the geomagnetic field spends a considerable time in the present four-lobe configuration: it is not a coincidence that the present field resembles the time average. Longitudinal variations are likely to be at least as important as latitudinal variations in the paleomagnetic time average. This presents a challenge for dynamo theory, since a move to more geophysically realistic parameters would appear to destroy the locked solutions.