S U M M A R YWe present a new time-varying model for palaeomagnetic axial dipole moment (PADM) for the past 2 Myr and compare it with earlier virtual axial dipole moment (VADM) reconstructions which have been based on stacking and averaging scaled relative palaeointensity records. The PADM is derived from both absolute and relative palaeointensity data and constructed using a new penalized maximum likelihood (PML) approach to recover a cubic B-spline representation of axial-dipole field variations on million year timescales. The PML method is explicitly intended to reduce bias in estimating the true axial dipole moment that arises in average VADM reconstructions. We apply the PML method to a set of 96 032 published data (1800 palaeointensities from igneous rocks, 3300 archaeointensities and 86 relative palaeointensity time-series of variable lengths and resolutions). Two models are discussed: PADM2Mp is a trial model based on a subset of the nine longest available sedimentary records; PADM2M uses a comprehensive data set (76 records, 81 446 data; 10 records were eliminated) and is our preferred model. PADM2M has a lower mean than existing VADM reconstructions but shows similarities in long-period variability. Some differences in timing, amplitude and resolution of certain features can be attributed to variations in age assignments. Others result from our more comprehensive data set and a reduction in bias attributable to PML modelling. PADM2M has an average axial dipole moment over 0-2 Ma of 5.3 × 10 22 Am 2 with a standard deviation of 1.5 × 10 22 Am 2 . The Brunhes chron average (6.2 × 10 22 Am 2 ) is higher than for earlier epochs of Matuyama (4.8 × 10 22 Am 2 ), as seen in some previous studies. The power spectrum for our model agrees with previous estimates of the global palaeomagnetic power spectrum for frequencies up to about 10 2 Myr −1 . We see no distinctive evidence in the power spectrum for orbital forcing of geodynamo behaviour.

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[1] Observations of Earth's magnetic field extending back to 3.45 billion years ago indicate that generation by a core dynamo must be sustained over most of Earth's history. However, recent estimates of thermal and electrical conductivity of liquid iron at core conditions from mineral physics experiments indicate that adiabatic heat flux is approximately 15 TW, nearly three times larger than previously thought, exacerbating difficulties for driving a core dynamo throughout Earth history by convective core cooling alone. Here, we explore the geomagnetic consequences of a basal magma ocean layer in the lowermost mantle, hypothesized to exist in the early Earth and perhaps surviving until well after the Archean. While the modern, solid lower mantle is an electromagnetic insulator, electrical conductivities of silicate melts are known to be higher, though as yet they are unconstrained for lowermost mantle conditions. We consider a range of possible electrical conductivities and find that for the highest electrical conductivities considered, a long-lived basal magma ocean could be a primary dynamo source region. This would suggest the proposed three magnetic eras observed in paleomagnetic data originate from distinct sources for dynamo generation: from 4.5 to 2.45 Ga within a basal magma ocean, from 2.25 to 0.4 Ga within a superadiabatically cooled liquid core, and from 0.4 Ga to present within a quasi-adiabatic core that includes a solidifying inner core.Components: 6,241 words, 3 figures.

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