The mechanical meshes of a few of the 15 models are shown in Figure 5, Figure 6, Figure 7, and Figure 9. For models following path 4, the steps shown are roughly equally spaced (in the time domain) from beginning to end. For paths 3 and 5, we show the beginning, middle, and end of both the first and the second rifting phases. Note that, for these paths, the mesh at the end of the first rifting phase (25 Ma) is roughly the same as the mesh at the beginning of the second (70 Ma), because between these two times, no extension was applied to the models. Keep in mind that these models represent one-half of a symmetrical rifting margin. For clarity, after each model name in the text and figure captions we list in parentheses the percentages of total extension for each phase.
The following conclusions were drawn from the generic model suite:
At any point in time, the upper mantle extension will localize where the Moho is hottest. For the power law creep rheology, strength is inversely related to temperature; cooling the mantle only a little will greatly strengthen it. In the models in which mantle extension migrates laterally, cooling is sufficiently fast relative to the rate of extension that the upper mantle becomes stronger than the neighboring hotter (and weaker) mantle. Because the upper mantle is the strongest portion of a vertical slice of lithosphere in most cases, when the upper mantle strength decreases, the strength of the entire lithosphere decreases. Indeed, the mantle weakness becomes a mantle strength once it cools sufficiently, preventing further significant extension at that location. This increase in strength from cooling is the same phenomenon presented by England (1983) and discussed most recently by Bassi et al. (1993). This effect is also similar to the phenomenon proposed by Steckler and ten Brink (1986), in which rifting in the Red Sea region was directed away from the previously thinned (and thus stronger) Mediterranean continental margin. In the models presented here, however, the phase of extension affected by earlier rifting occurs relatively soon after the original episode and is roughly parallel to the original orientation of rifting. The upper mantle may become shallow enough to enter the brittle failure regime (Sawyer, 1985), but it still remains stronger than neighboring hotter mantle. It is this strengthening of the zone of initial rifting that causes the locus of extension to move laterally outward from the center of the model. This effect would be diminished in cases where heavy sedimentation reduces the cooling rate, but is nonetheless present in instances of lighter sedimentation (as our model represents).
This behavior is exhibited by many of the generic models, where the locus of extension migrates laterally. In model MW4 (20.8, 37.5, 41.7), the rate of extension is slow enough to allow the mantle in the center to cool and strengthen and cause a shift in necking location (Fig. 5). Necking begins in the center of this model, but the locus of necking moves closer to the edges of the model as time progresses; extension is roughly evenly distributed across the original mantle weakness. This mesh looks very similar to the "runaway thinning" model presented by Bassi et al. (1993).
In model MW3 (30, 0, 70), the second phase of rifting occurs at the outer flanks of original wide weakness, where the Moho is deepest and hottest (Fig. 6). The center of the model stretches a bit more in the second phase, but by the end of the second phase, necking on the flanks of the original mantle weakness has taken over.
During the first phase, model CW5 (50, 0, 50) necks more in the center then the aforementioned models, because the most extension is assigned to the first phase in this path (Fig. 7). At 25 Ma, strain is concentrated entirely in middle of the model. At the beginning of the second rifting phase, the upper mantle is extremely cold and strong at the center, and the necking shape created in the first phase is practically frozen (Fig. 7, Fig. 8). Figure 8 shows that the strain rate is extremely low in the center of the model throughout the second phase of rifting; the area of highest strain rate always stays about halfway between the model's center and its outer edge. The strain rate is fairly high even at the outer edge of the model.
The location of crustal weaknesses will be the initial location of crustal extension. Once the mantle lithosphere becomes sufficiently thinned at a different location, however, crustal thinning will proceed there. Early during extension, the crustal weakness (with a granite lithology) is partly in the ductile deformation regime and is thus weaker than the surrounding quartz diorite crust. As the crustal weakness is necked and cools, it enters the brittle deformation field entirely. Because Byerlee's (1978) law is insensitive to rock type, the granite crustal weakness is no longer weaker than the neighboring "normal" quartz diorite crust. Once the crust becomes equally strong everywhere, crustal deformation is controlled by the location of upper mantle strain, and hence the entire lithosphere begins to strain at the same location.
Model BS4 (20.8, 37.5, 41.7) exhibits such a migration of crustal extension (Fig. 9, Fig. 10). In this mesh, both crustal and mantle extension are more evenly distributed throughout the model; this difference is probably the result of the relatively low extension rate. In the strain rate plot in Figure 10, the area of highest mantle strain rate moves from center outward; the strain rate decreases more slowly in the crust at the center than in the mantle. Extension is always more diffuse in the crust, and produces pervasive shear just above the Moho. (This lower crust shear provides a "reasonable" mechanism for decoupling crust and mantle stretching, which Rowley and Sahagian [1986] claimed was lacking in previous nonuniform stretching models.) It is clear that, at each time from 70 Ma onward, the highest strain rate occurs in a location slightly outward from the most highly necked area (Fig. 10); this mechanism allow the locus of necking to migrate outward. The phenomenon of the mantle weakness controlling the later stages of rifting is a similar result to that reached by Harry and Sawyer (1992a).
These models suggest that the occurrence of a resting phase between two episodes of rifting should greatly affect the morphology of a continental rift. In most cases, the site of the original rift will not be favored for extension when stretching begins anew. If extension in the first phase is significant, the crust will be thinned and the Moho elevated. During the resting phase, the upper mantle will cool and strengthen. When rifting begins anew in the second phase, the original site of rifting will be a lithospheric strong zone, and second-phase rifting will occur in a different, weaker location. Furthermore, a resting phase (or other variation through time in the rate of rifting) could serve as a possible explanation for areas where the location of rifting is observed to migrate through time. While the temperature boundary conditions presented here probably represent the "cooler end" of the spectrum of possible rifting thermal regimes, we do not feel that the thermal conditions are unreasonably cool. Of the models in the generic model suite, model MW3 (30, 0, 70) demonstrates this phenomenon the best (Fig. 6).