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Restoration with and without paleomagnetism

In document Ciencias de la Tierra (página 114-120)

After this round through the real deformation parameters we are going to test the incorporation of the paleomagnetic constraint into the restoration methods. We are going to unfold the surfaces with the piecewise approach using and not using paleomagnetism (Pmag3DRest and UNFOLD methods respectively) as well as with the parametric approach (gOcad method with and without the paleomagnetic constraint).

The piecewise restoration is quite sensitive to the pin-element selection, as we will see in Section 5.4, but for our current purpose we stick to the traditional approach ofplacing a pin-element in the undeformed area, although not in the border. The orientation of the paleomagnetic vector also has some influence in the results; for this example we try to select one oblique to the main structures that better registers the deformation, but of course this depends on the real geology setting in natural cases.

Eventually, in these simulations we consider paleomagnetism defined in all triangles.

We first analyze the piecewise restoration of the San Marzal model using and not using paleomagnetism (Fig. 5.5, Table 5.1). Restoration without paleomagnetism seems to be pretty good in terms of mean dilation (dmean without pmag < dmean with pmag) but restoration with paleomagnetism better locates real deformation (e with pmag < e without pmag). The restoration without paleomagnetism achieves the restored surface with minimum deformation because triangles are free to find the best fitting. However, the paleomagnetic constraint yields a restored surface more similar to the initial one.

Dilation values of the restored surface with paleomagnetism are mostly coherent with

the real dilation in the expected areas: expansion in the anticline and compression in the synclines. On the other hand, absolute values are always smaller than those expected (dmean < dreal_mean, e >> 0) because of the restoration method itself which try to minimize deformation.

Additionally, the anisotropy of deformation (strain ellipse) is coherent for the restoration with paleomagnetism and has less meaning for the restoration without paleomagnetism. The compression area with maximum strain ratio coincides with the real one and shares the same orientation. Moreover, the shape of the surface restored with paleomagnetism is closer to the expected rectangle.

This is a good example where piecewise restoration works well and paleomagnetism provides additional information about the real deformation of the surface. Let us compare now this results with the second method based on the parameterization.

The parametric approach without the incorporation of paleomagnetism is unable to reach a proper restoration of the surface (Fig. 5.6B) and mean dilation values are to high (dmean ≈ 10% [Table 5.1]). We can say that this restoration method is only valid for smoothly folded structures and not for complex folds such as this example. This method is too dependant on the initial solution and for this reason the usage of paleomagnetism is crucial to define it (particularly in non-cylindrical and non-coaxial structures).

The shape of the restored surface with paleomagnetism almost perfectly matches the expected one and orthogonality is preserved in the restored state. The distribution of maximum dilation values roughly corresponds with those expected, although the signs do not match in this case (restored surface does not show the contraction area). On the other hand, maximum strain orientation approximately coincides with the expected one.

The restoration method assumes isometric parameterization based on developable surfaces folded under flexural conditions but we have used it to restore globally developable surfaces with small deformation in complex folded areas. Therefore, the unfolding algorithm minimizes the deformation showing dilation patterns similar to those real, but it could never predict the real deformation. Because of that, we recommend the usage of several restoration methods in order to compare results. In this case for example, the strain orientation of the compression area with a maximum strain ratio is trustable because almost coincides with both techniques.

Figure 5.5: Piecewise restoration of the San Marzal model (regular triangulation, original mesh density).

Dashed black lines are useful to compare the restored surface with the initial one and real values of deformation (Fig. 5.2). The pin-element is highlighted with a red circle. A) Restoration using paleomagnetism (Pmag3DRest method). The red arrow is the paleomagnetic orientation. B) Restoration without paleomagnetism (UNFOLD method [Gratier et al., 1991]). 1) Dilation (d=(Afolded -Arestored)/Arestored). 2) Strain ratio: major axis / minor axis. 3) Strain orientation: major axis displayed in those triangles with meaningful strain ratio (>1.07).

Figure 5.6: Parametric restoration of the San Marzal model. Dashed black lines are useful to compare the restored surface with the initial one and real values of deformation (Fig. 5.2). A) Restoration using paleomagnetism: 1) dilation, 2) strain ratio, 3) strain orientation. B) Restoration without paleomagnetism with dilation values.

SAN MARZAL (dreal_mean=0.0433)

Piecewise restoration Parametric restoration

with pmag without with pmag without

e 0.0392 0.0442 0.0459 0.0964

dmean 0.0174 0.0086 0.0164 0.0925

Table 5.1: Mean dilation values for the restoration of San Marzal. Mean error between real and retro-dilation in absolute value: e=1N

dreald (Eq. [8]) Mean dilation in absolute value: dmean=1N

d

(Eq. [6]). Mean real dilation in absolute value: dreal_mean.

The next example (curved fold based on the Balzes Anticline) is more complicated than the previous because it has more deformation (higher dreal_mean) and the surface is less developable (higher Gaussian curvature). Moreover, the meshing is denser, hampering the piecewise restoration.

Piecewise restoration (Fig. 5.7, Table 5.2) is not as accurate for this example and the benefits of paleomagnetism are not as clear (e & dmean without pmag < e & dmean

with pmag). Dilation increases towards the opposite part of the pin-element due to the propagation of errors. Moreover, the dilation values seem to be more related to the areas of higher Gaussian curvature than with the real dilation, particularly in the interference syncline between both anticlines.

Figure 5.7: Piecewise restoration of the Balzes model. Dashed lines are useful to compare the restored surface with the initial one and real values of deformation (Fig. 5.4). The pin-element is highlighted with a red circle. A) Restoration using paleomagnetism (Pmag3DRest). The red arrow is the paleomagnetic orientation. B) Restoration without paleomagnetism (UNFOLD). 1) Dilation. 2) Strain ratio. 3) Strain orientation.

Figure 5.8: Parametric restoration of the Balzes model. Dashed lines are useful to compare the restored surface with the initial one and real values of deformation (Fig. 5.4). A) Restoration using paleomagnetism: 1) dilation, 2) strain ratio, 3) strain orientation. B) Restoration without paleomagnetism with dilation values.

In this situation, it seems more convenient to unfold the surface with the second restoration method, the parametric approach, because the results are really encouraging (Fig. 5.8). As in the example of San Marzal, the method does not work well without the paleomagnetic constraint. Thus, we focus on the restoration with paleomagnetism.

Dilation and strain ratio patterns are fairly similar to those expected. Strain orientation is more confuse this time.

BALZES (dreal_mean=0.0989)

Piecewise restoration Parametric restoration

with pmag without with pmag without

e 0.1087 0.0988 0.0856 0.1166

dmean 0.0415 0.0240 0.0228 0.0572

Table 5.2: Mean dilation values for the restoration of Balzes.

In document Ciencias de la Tierra (página 114-120)