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Two-dimensional thermal models of the lithosphere under the Basin and Range Province, the Rio Grande rift and the Colorado Plateau have been constructed using a numerical method for solution of the equation of conservation of energy for the transient temperature field. It is established that the crust in the Basin and Range Province and the Rio Grande rift is still heating on a regional scale. We suggest that intrusion of asthenospheric material in the shape of wide upwellings was a cause of lithospheric heating. The time elapsed since asthenospheric material reached the base of the crust of the Basin and Range Province and the Rio Grande rift is estimated as 2–4 m.y. About the same time a great dyke intrusion into the crust beneath the Rio Grande rift occurred. The asthenospheric surface under the Colorado Plateau reached the present depth (about 60 km) not less than 30 m.y. ago.

The analysis of geological and geophysical data on Late-Cenezoic rift zones indicates that the anomalous mantle occurring in asthenospheric upwellings beneath these rift zones has a relatively low density, this being conditioned only by its heating and partial melting. After the crystallization of the liquid phase and cooling, this material becomes more dense than the mantle part of the lithosphere beneath the adjacent regions, which leads to isostatic subsidence of the crustal surface and to formation of postrift sedimentary basins. Numerical modelling of this process shows that the theoretical curve of basin subsidence is in line with empiral data. The theoretical reconstruction of paleogeotherms indicates the important role of the sedimentary infill of paleorifts in oil and gas generation.

Geophysical data indicate that beneath Late Cenozoic continental rift zones there are asthenospheric upwellings with their upper surfaces reaching the Moho at depths of 30–40 km. Under neighboring stable regions the asthenospheric surface is situated at a depth over 100 km. Evidently, rifting was causally related with the development of such upwellings. The authors performed numerical two-dimensional modellings of the formation process of the asthenospheric upwelling, assuming progressive partial melting of lithosphere. It turned out that correlation of the time period required with the time of development of Late Cenozoic rift zones (15–40 m.y.) requires the heat flow into the base of the lithosphere to be very high (200–300 mW m−2). Such values of heat flow would cause an intensive melting of the lower crust, and the composition of volcanics shows that this does not take place during the late stages of evolution of rift zones. Most probably, the asthenospheric material mechanically replaces lithosphere along weak zones: blocks are detached from the lithosphere and sink into the asthenosphere. Plastic flow in the solid part of the mantle is of secondary importance. We simulated this replacement through an upward movement of the 1200°C isotherm (temperature of mantle solidus). Deformations of the mantle and crust were neglected. Above this isotherm the temperature field in the lithosphere was computed by means of a numerical solution of the equation of energy conservation. Two-dimensional models have been constructed for rift zones of the Baikal, the Rio-Grande and the Basin and Range Province. Regional values of heat flow of these regions were successfully correlated with geophysical data on Curie depths and on the structure of the upper mantle, assuming that the asthenosphere reached the Moho some million years ago and the crust is still being heated on a regional scale. These estimates of time are in good agreement with the beginning of the stage of most rapid rifting in these zones. With such models it is not difficult to reconcile the total time for the development of the asthenospheric upwellings with the observed duration of rifting. In the rift zones mentioned above, crustal cooling is possible only on individual narrow segments with local anomalies of heat flow which may be produced by basalt dikes situated at comparatively small depths.