We present a numerical pure-shear stretching model to study the effect of the ''depth of lithospheric necking'' on the state of flexure at extensional basins. This model avoids the need for low flexural rigidities during synrift basin subsidence. The model also accounts for long-standing rift flank uplifts in the absence of significant thermal anomalies or underplating beneath rift shoulders, and it predicts low β factors beneath basin centers. Numerical modeling of synthetic continental rift zones and rifted continental margins together with the gravity characteristics demonstrates that isostatic residual anomalies are sensitive indicators of the state of flexure at extensional basins, particularly at basin margins. Isostatic residual anomalies are particularly useful to study the state of lithospheric flexure because the results are not biased by assumptions on the loads that have to be made in a forward modeling approach. Previous studies of lithospheric flexure and gravity modeling might have underestimated flexural rigidities at extentional basins. Comparison of predicted gravity anomaly signatures with gravity data suggests that at narrow rift basins and young rifted continental margins, upward flexure occurs more commonly than does downward flexure. This can be explained by intermediate or deep levels of necking (>15 km). For rifted continental margins, the apparent transition in the state of flexure during basin evolution from upward to downward flexure points to intermediate levels of necking (15--20 km).

The occurrence of intermediate to deep levels of necking at narrow rift basins and intermediate levels of necking at rifted margins is in accordance with brittle-ductile rheological models of the lithosphere. An intermediate depth range for the level of lithospheric necking at rifted continental margins is consistent with a scenario in which rifting preferentially occurs in an area where the lithosphere is weakened by a thickened crust. Rifting in areas of stronger lithosphere, as for example cratons, is probably more often associated with a deep level of necking, explaining the widespread occurrence of rift shoulders at failed rift basins. We have tested several depths of necking and a model of local isostasy for the Gulf of Lions margin in the northwestern Mediterranean. At positions of deep synrift grabens, model with depths of necking of 25--35 km predict crustal thicknesses that are more in accordance with observations than are models with a shallower level of necking. It appears that local isostasy cannot account for the present-day basin configuration and at the same time reproduce the observed strongly laterally varying bathymetry at the end of rifting, supporting a significant postrift flexural rigidity. ¿ American Geophysical Union 1992