Search

The Padul Fault is located in the Central Betic Cordillera, formed in the framework of the NW-SE Eurasian-African plate convergence. In the Internal Zone, large E-W to NE-SW folds of western Sierra Nevada accommodated the greatest NW-SE shortening and uplift of the cordillera. However, GPS networks reveal a present-day dominant E-W to NE-SW extensional setting at surface. The Padul Fault is the most relevant and best exposed active normal fault that accommodates most of the NE-SW extension of the Central Betics. This WSW-wards dipping fault, formed by several segments of up to 7 km maximum length, favored the uplift of the Sierra Nevada footwall away from the Padul graben hanging wall. A non-permanent GPS network installed in 1999 constrains an average horizontal extensional rate of 0.5 mm/yr in N66°E direction. The fault length suggests that a (maximum) 6 magnitude earthquake may be expected, but the absence of instrumental or historical seismic events would indicate that fault activity occurs at least partially by creep. Striae on fault surfaces evidence normal-sinistral kinematics, suggesting that the Padul Fault may have been a main transfer fault of the westernmost end of the Sierra Nevada antiform. Nevertheless, GPS results evidence: (1) shortening in the Sierra Nevada antiform is in its latest stages, and (2) the present-day fault shows normal with minor oblique dextral displacements. The recent change in Padul fault kinematics will be related to the present-day dominance of the ENE-WSW regional extension versus ~ NNW-SSE shortening that produced the uplift and northwestwards displacement of Sierra Nevada antiform. This region illustrates the importance of heterogeneous brittle extensional tectonics in the latest uplift stages of compressional orogens, as well as the interaction of folding during the development of faults at shallow crustal levels. This research was funded by PAIUJA 2017/2018, UJA2016/00086/001 project, CGL2016-80687-R AEI/FEDER, UE project and RNM148 and RNM282 research groups of Junta de Andalucía.

The supporting vectors of a matrix A are the solutions of max ∥ x ∥ 2 = 1 ∥ A x ∥ 2 2 . The generalized supporting vectors of matrices A 1 , ⋯ , A k are the solutions of max ∥ x ∥ 2 = 1 ∥ A 1 x ∥ 2 2 + ⋯ + ∥ A k x ∥ 2 2 . Notice that the previous optimization problem is also a boundary element problem since the maximum is attained on the unit sphere. Many problems in Physics, Statistics and Engineering can be modeled by using generalized supporting vectors. In this manuscript we first raise the generalized supporting vectors to the infinite dimensional case by solving the optimization problem max ∥ x ∥ = 1 ∑ i = 1 ∞ ∥ T i ( x ) ∥ 2 where ( T i ) i ∈ N is a sequence of bounded linear operators between Hilbert spaces H and K of any dimension. Observe that the previous optimization problem generalizes the first two. Then a unified MATLAB code is presented for computing generalized supporting vectors of a finite number of matrices. Some particular cases are considered and three novel examples are provided to which our technique applies: optimized observable magnitudes by a pure state in a quantum mechanical system, a TMS optimized coil and an optimal location problem using statistics multivariate analysis. These three examples show the wide applicability of our theoretical and computational model.