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SUMMARY The variation of temperature in the crust is difficult to quantify due to the sparsity of surface heat flow observations and lack of measurements on the thermal properties of rocks at depth. We examine the degree to which the thermal structure of the crust can be constrained from the Curie depth and surface heat flow data in Southeastern Australia. We cast the inverse problem of heat conduction within a Bayesian framework and derive its adjoint so that we can efficiently find the optimal model that best reproduces the data and prior information on the thermal properties of the crust. Efficiency gains obtained from the adjoint method facilitate a detailed exploration of thermal structure in SE Australia, where we predict high temperatures within Precambrian rocks of 650 °C due to relatively high rates of heat production (0.9–1.4 μW m−3). In contrast, temperatures within dominantly Phanerozoic crust reach only 520 °C at the Moho due to the low rates of heat production in Cambrian mafic volcanics. A combination of the Curie depth and heat flow data is required to constrain the uncertainty of lower crustal temperatures to ±73 °C. We also show that parts of the crust are unconstrained if either data set is omitted from the inversion.

SUMMARY Based on a critical evaluation of several different spectral magnetic depth determination techniques on areally large synthetic layered and random magnetization models, we recommend the following considerations in the usage of the methods as necessary prerequisites to successful bottom depth determinations: (1) using windows with sufficient width to ascertain that the response of the deepest magnetic layer is captured and by verifying the spectra and computing the depth estimates with the largest possible windows (>300‐500 km); (2) avoiding filtering to remove arbitrary regional fields, accomplished by compiling magnetic anomalies derived from modern spherical harmonic degree 13 Earth’s main field models [e.g. recent International Geomagnetic Reference Field models (IGRF) or Comprehensive models (CM)]; (3) ascertaining the near-circularity of the autocorrelation function to avoid analysing biased spectra containing strong anomaly trends; and (4) avoid determining the slopes from the exponential, low wavenumber part of the spectra in the cases of layered magnetization. We also describe the details of the new spectral peak forward modelling method and discuss the conditions under which the method can lead to useful results. We found that, despite all these precautions, in some cases, the results can still be erroneous and, therefore, we recommend a critical evaluation of the results by modelling heat flow and taking into account seismic information on the crustal and lithospheric thicknesses and seismic velocities wherever possible. In the southcentral US, east of the Rockies, where the surface heat flow ranges between 40 and 65 mW m −2 ,w e obtained the magnetic bottom depth of 40 ± 10 km using the approach of the forward modelling of the spectral peak. This range is similar to the seismically derived crustal thickness of 45‐ 50 km, suggesting, therefore, that the entire crust may be magnetic in this region. Because of the uncertainties in the various heat flow contributing parameters, such as the variations in thermal conductivity, radiogenic heat and hydraulic regime, we could not constrain the lithospheric thickness beyond an estimate ranging approximately from 100 to 200 km.

SUMMARY A Curie-point isotherm map of the whole of Turkey has been prepared from aeromagnetic data by means of a spectral analysis technique. The most characteristic signature of this map is that the shallow depths generally correlated with the young volcanic rocks and the thinned crustal thicknesses in the west reveal geothermal fields and several hot springs. The orogenic Pontide belt of the Black Sea region in the north, the western Taurus belt in the south, and some high plateaus in eastern Turkey show that the deepest Curie isotherm depths range between 20 and 29 km. Depth contour lines elongating in an almost E–W direction are due to the overlapping percentage of adjacent data blocks of 50 per cent in the E–W direction and to magnetic anomalies trending in the E–W direction. Curie isotherm depths are in the range 6 to 10 km in the Aegean region and are characterized by E–W- and NE–SW-trending graben structures, as expected, since the region has crustal thinning and many hot springs and geothermal fields. These imply the existence of shallow heat sources that could be utilized for electricity, heating of towns and cities, greenhouse and health purposes.

Summary. We study aeromagnetic maps from four areas in the Western United States: Utah High Plateaus, Yellowstone National Park, Southern Great Basin, and Uinta Basin. In the first area we try to infer depth-to-bottom of magnetic source by comparison of individual anomalies with theoretical fields of vertical prisms. We conclude that this task is impossible, at least for the few anomalies considered. Assuming a bottomless prism a fit can be obtained which is not significantly worse than the best fit obtainable with any prism model. This is documented by both nonlinear and linear inverse theory. We then turn to a spectral theory like that of Spector & Grant. The advantage of spectral analysis is that the broad, low-amplitude negative flanks of positive anomalies are included even though they may be covered by adjacent positive anomalies. The disadvantage is sensitivity to finite data length: the spectra are interpreted with models derived by Fourier transformation in an infinite domain. Anomalies which are only partly included in the map can degrade the estimated spectrum. We try several techniques to deal with this problem, but none seem universally applicable. These techniques include elimination of part of the map and subtraction of a low-order polynomial. For computation of the spectral estimate our favourite procedure is: (1) average autocovariance over azimuth, (2) extrapolate to large lags as r-5, (3) Hankel transform the radial autocovariance profile to a radial power profile. Our usual model for interpretation of the low-frequency spectra is a truncated right circular cone defined by the four parameters ZT (depth to top), ZB (depth to bottom), RT (top radius) and RB (bottom radius). For the Utah High Plateaus and Uinta Basin we find a distinct preference for sloping sides, i.e. RB > RT. In analysing individual anomalies as well as spectra we find anticorrelation of ZT and ZB. We attribute this to the centroid of the average source body being better determined than its thickness.

Summary A first order estimate of Curie depth and lithospheric thickness variation beneath the Indian region has been obtained using the available geothermic data. The Curie depth is found to vary from 18 to 68 km and the lithospheric thickness from 38 to 186 km. These estimates conform well with the MAGS AT and seismological findings. Both the parameters exhibit covariancy and suggest the possibility of approximating heat flow values and lithospheric thickness in geothermally uncharted areas using Curie point geotherm depths derived from air/satellite-borne magnetic anomalies. Interestingly, the areas with shallow Curie depth and lithospheric thickness are found to be associated with a thin crust, higher heat flow, higher geothermal gradients and positive gravity anomalies, and vice versa. Large thickness estimate of magnetic crustal layer, extending below the Moho, demands a new conceptual understanding. The study has brought out a good case for wider use of magneto-thermometry and provides understanding of the geodynamic evolution of the Indian subcontinent.