The inversion of electromagnetic sounding data does not yield a unique solution, but inevitably a single model to interpret the observations is sought. We recommend that this model be as simple, or smooth, as possible, in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models.To obtain smooth models, the nonlinear forward problem is linearized about a starting model in the usual way, but it is then solved explicitly for the desired model rather than for a model correction. By parameterizing the model in terms of its first or second derivative with depth, the minimum norm solution yields the smoothest possible model.Rather than fitting the experimental data as well as possible (which maximizes the roughness of the model), the smoothest model which fits the data to within an expected tolerance is sought. A practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models, resulting in a stable and rapidly convergent algorithm. The inversion of both magnetotelluric and Schlumberger sounding field data, and a joint magnetotelluric-resistivity inversion, demonstrate the method and show it to have practical application.

We present a synthesis of 0–5 Ma paleomagnetic directional data collected from 17 different locations under the collaborative Time Averaged geomagnetic Field Initiative (TAFI). When combined with regional compilations from the northwest United States, the southwest United States, Japan, New Zealand, Hawaii, Mexico, South Pacific, and the Indian Ocean, a data set of over 2000 sites with high quality, stable polarity, and declination and inclination measurements is obtained. This is a more than sevenfold increase over similar quality data in the existing Paleosecular Variation of Recent Lavas (PSVRL) data set, and has greatly improved spatial sampling. The new data set spans 78°S to 53°N, and has sufficient temporal and spatial sampling to allow characterization of latitudinal variations in the time‐averaged field (TAF) and paleosecular variation (PSV) for the Brunhes and Matuyama chrons, and for the 0–5 Ma interval combined. The Brunhes and Matuyama chrons exhibit different TAF geometries, notably smaller departures from a geocentric axial dipole field during the Brunhes, consistent with higher dipole strength observed from paleointensity data. Geographical variations in PSV are also different for the Brunhes and Matuyama. Given the high quality of our data set, polarity asymmetries in PSV and the TAF cannot be attributed to viscous overprints, but suggest different underlying field behavior, perhaps related to the influence of long‐lived core‐mantle boundary conditions on core flow. PSV, as measured by dispersion of virtual geomagnetic poles, shows less latitudinal variation than predicted by current statistical PSV models, or by previous data sets. In particular, the Brunhes data reported here are compatible with a wide range of models, from those that predict constant dispersion as a function of latitude to those that predict an increase in dispersion with latitude. Discriminating among such models could be helped by increased numbers of low‐latitude data and new high northern latitude sites. Tests with other data sets, and with simulations, indicate that some of the latitudinal signature previously observed in VGP dispersion can be attributed to the inclusion of low‐quality, insufficiently cleaned data with too few samples per site. Our Matuyama data show a stronger dependence of dispersion on latitude than the Brunhes data. The TAF is examined using the variation of inclination anomaly with latitude. Best fit two‐parameter models have axial quadrupole contributions of 2–4% of the axial dipole term, and axial octupole contributions of 1–5%. Approximately 2% of the octupole signature is likely the result of bias incurred by averaging unit vectors.

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[1] Steadily increasing numbers of archeomagnetic and paleomagnetic data for the Holocene have allowed development of temporally continuous global spherical harmonic models of the geomagnetic field extending present and historical global descriptions of magnetic field evolution. The current work uses various subsets of improved data compilations, details of which are given in a companion paper by Donadini et al. (2009), and minor modifications of standard modeling strategies (using temporally and spatially regularized inversion of the data and cubic spline parameterizations for temporal variations) to produce five models with enhanced spatial and temporal resolution for 0-3 ka. Spurious end effects present in earlier models are eliminated by enforcing large-scale agreement with the gufm1 historical model for 1650-1990 A.D. and by extending the model range to accommodate data older than 3 ka. Age errors are not considered as a contribution to data uncertainties but are included along with data uncertainties in an investigation of statistical uncertainty estimates for the models using parametric bootstrap resampling techniques. We find common features but also significant differences among the various models, indicating intrinsic uncertainties in global models based on the currently available Holocene data. Model CALS3k.3 based on all available archeomagnetic and sediment data, without a priori quality selection, currently constitutes the best global representation of the past field. The new models have slightly higher dipole moments than our previous models. Virtual axial dipole moments (VADMs) calculated directly from the data are in good agreement with all corresponding model predictions of VADMs. These are always higher than the spherical harmonic dipole moment, indicating the limitations of using VADMs as a measure of geomagnetic dipole moments.