[1] We have revisited the problem of mapping depth to the Curie temperature isotherm from magnetic anomalies in an attempt to provide a measure of crustal temperatures in the western United States. Such methods are based on the estimation of the depth to the bottom of magnetic sources, which is assumed to correspond to the temperature at which rocks lose their spontaneous magnetization. In this study, we test and apply a method based on the spectral analysis of magnetic anomalies. Early spectral analysis methods assumed that crustal magnetization is a completely uncorrelated function of position. Our method incorporates a more realistic representation where magnetization has a fractal distribution defined by three independent parameters: the depths to the top and bottom of magnetic sources and a fractal parameter related to the geology. The predictions of this model are compatible with radial power spectra obtained from aeromagnetic data in the western United States. Model parameters are mapped by estimating their value within a sliding window swept over the study area. The method works well on synthetic data sets when one of the three parameters is specified in advance. The application of this method to western United States magnetic compilations, assuming a constant fractal parameter, allowed us to detect robust long-wavelength variations in the depth to the bottom of magnetic sources. Depending on the geologic and geophysical context, these features may result from variations in depth to the Curie temperature isotherm, depth to the mantle, depth to the base of volcanic rocks, or geologic settings that affect the value of the fractal parameter. Depth to the bottom of magnetic sources shows several features correlated with prominent heat flow anomalies. It also shows some features absent in the map of heat flow. Independent geophysical and geologic data sets are examined to determine their origin, thereby providing new insights on the thermal and geologic crustal structure of the western United States.Citation: Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization,

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S U M M A R YIn a previous paper, Khokhlov et al. introduced a method to test the compatibility of so-called 'giant Gaussian process' (GGP) statistical models of the palaeomagnetic field against any palaeosecular variation database. This method did not take measurement errors into account. It therefore lacked practical usefulness. In the present paper, we remedy this and generalize the method to account for measurement errors in a way consistent with both the assumptions underlying the GGP approach and the nature of those errors. The method is implemented to test GGP models against any directional data set affected by Fisherian errors. Simulations show that the method can usefully discriminate which GGP model best explains a given data set.Applying the method to test six published GGP models against a test Bruhnes stable polarity data set extracted from the Quidelleur et al. database, it is found that all but one model (that of Quidelleur & Courtillot) should be rejected. Although this result should be taken with care, and does not necessarily imply that this model is superior to other models (Quidelleur & Courtillot precisely used the Quidelleur et al. database to infer their model), it clearly shows that in practice also, and with the databases currently available, the method can discriminate various candidate GGP models. It also shows that the statistical behaviour of the geomagnetic field at times of stable polarity can indeed be described in a consistent way in terms of a GGP model. This 'forward' testing method could ultimately be used to design an 'inverse' approach to GGP modelling of the palaeomagnetic field.

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International audienceBy relying on two numerical dynamo simulations for which such investigations are possible, we test the validity and sensitivity of a statistical palaeomagnetic field modelling approach known as the giant gaussian process (GGP) modelling approach. This approach is currently used to analyse palaeomagnetic data at times of stable polarity and infer some information about the way the main magnetic field (MF) of the Earth has been behaving in the past and has possibly been influenced by core–mantle boundary (CMB) conditions. One simulation has been run with homogeneous CMB conditions, the other with more realistic non-homogeneous symmetry breaking CMB conditions. In both simulations, it is found that, as required by the GGP approach, the field behaves as a short-term memory process. Some severe non-stationarity is however found in the non-homogeneous case, leading to very significant departures of the Gauss coefficients from a Gaussian distribution, in contradiction with the assumptions underlying the GGP approach. A similar but less severe non-stationarity is found in the case of the homogeneous simulation, which happens to display a more Earth-like temporal behaviour than the non-homogeneous case. This suggests that a GGP modelling approach could nevertheless be applied to try and estimate the mean µ and covariance matrix γ(τ) (first-and second-order statistical moments) of the field produced by the geodynamo. A detailed study of both simulations is carried out to assess the possibility of detecting statistical symmetry breaking properties of the underlying dynamo process by inspection of estimates of µ and γ(τ). As expected (because of the role of the rotation of the Earth in the dynamo process), those estimates reveal spherical symmetry breaking properties. Equatorial symmetry breaking properties are also detected in both simulations, showing that such symmetry breaking properties can occur spontaneously under homogeneous CMB conditions. By contrast axial symmetry breaking is detected only in the non-homogenous simulation, testifying for the constraints imposed by the CMB conditions. The signature of this axial symmetry breaking is however found to be much weaker than the signature of equatorial symmetry breaking. We note that this could be the reason why only equatorial symmetry breaking properties (in the form of the well-known axial quadrupole term in the time-averaged field) have unambiguously been found so far by analysing the real data. However, this could also be because those analyses have all assumed to simple a form for γ(τ) when attempting to estimate µ. Suggestions are provided to make sure future attempts of GGP modelling with real data are being carried out in a more consistent and perhaps more efficient way