Abstract. In oceanic regions the effective elastic thickness Te of the lithosphere is generally estimated from the free air gravity field and approximately corresponds to the depth of the 450øC isotherm. In continental regions the Bouguer anomaly is commonly used and gives thicknesses for shields as great as 130 kin, where geotherms reach temperatures of 800-1000øC. If this result were correct, it would require the continental lithosphere to be able to support elastic stresses at considerably higher temperatures than the oceanic lithosphere can. However, detailed examination of the free air and Bouguer anomalies over continents shows that values of T, obtained from Bouguer anomalies over shields are often upper bounds, rather than estimates, because most of the short-wavelength topography has been removed by erosion, and what remains is incoherent with both the free air and Bouguer gravity anomalies. The present study uses free air anomalies, and topography as a load whose geometry is known. The main importance of subsurface density contrasts and their associated gravity anomalies is that they reduce the signal to noise ratio, without affecting the estimated value of T,. No estimates of T, from free air gravity and topographic data from North America, East Africa, Australia, the Indian peninsula, and the former Soviet Union exceed 25 kin, and all are smaller than the seismogenic thickness. The largest estimate, of 42 kin, comes from profiles across the Himalayan foredeep. The gravity in this region may be affected by dynamic effects. There is therefore no evidence that the continental lithosphere can support elastic stresses for geological times at temperatures above about 350øC.

S U M M A R YThe Earth's crust is magnetized down to the Curie-temperature depth at about 10 to 50 km. This limited depth extent of the crustal magnetization is discernible in the power spectra of magnetic maps of South Africa and Central Asia. At short wavelengths, the power increases as rapidly towards longer wavelengths as expected for a self-similar magnetized crust with unlimited depth extent. Above wavelengths of about 100 km the power starts increasing less rapidly, indicating the absence of deep-seated sources. To quantify this effect we derive the theoretical power spectrum due to a slab carved out of a self-similar magnetization distribution. This model power spectrum matches the power spectra of South Africa and Central Asia for a self-similarity parameter of p = 4 and Curie temperature depths of 15 to 20 km.

We have developed a new method for interpretation of gridded magnetic data which, based on derivatives of the tilt angle, provides a simple linear equation, similar to the 3D Euler equation. Our method estimates both the horizontal location and the depth of magnetic bodies, but without specifying prior information about the nature of the sources ͑struc-tural index͒. Using source-position estimates, the nature of the source can then be inferred. Theoretical simulations over simple and complex magnetic sources that give rise to noisecorrupted and noise-free data, illustrate the ability of the method to provide source locations and index values characterizing the nature of the source bodies. Our method uses second derivatives of the magnetic anomaly, which are sensitive to noise ͑high-wavenumber spectral content͒ in the data. Thus, an upward continuation of the anomaly may lead to reduce the noise effect. We demonstrate the practical utility of the method using a field example from Namibia, where the results of the proposed method show broad correlation with previous results using interactive forward modeling.