Estimation of the Crustal Bulk Properties Beneath Mainland Portugal from P-Wave Teleseismic Receiver Functions

In this work, we present results from teleseismic P-wave receiver functions (PRFs) obtained in Portugal, Western Iberia. A dense seismic station deployment conducted between 2010 and 2012, in the scope of the WILAS project and covering the entire country, allowed the most spatially extensive probing on the bulk crustal seismic properties of Portugal up to date. The application of the H-κ stacking algorithm to the PRFs enabled us to estimate the crustal thickness (H) and the average crustal ratio of the P- and S-waves velocities V p/V s (κ) for the region. Observations of Moho conversions indicate that this interface is relatively smooth with the crustal thickness ranging between 24 and 34 km, with an average of 30 km. The highest V p/V s values are found on the Mesozoic-Cenozoic crust beneath the western and southern coastal domain of Portugal, whereas the lowest values correspond to Palaeozoic crust underlying the remaining part of the subject area. An average V p/V s is found to be 1.72, ranging 1.63-1.86 across the study area, indicating a predominantly felsic composition. Overall, we systematically observe a decrease of V p/V s with increasing crustal thickness. Taken as a whole, our results indicate a clear distinction between the geological zones of the Variscan Iberian Massif in Portugal, the overall shape of the anomalies conditioned by the shape of the Ibero-Armorican Arc, and associated Late Paleozoic suture zones, and the Meso-Cenozoic basin associated with Atlantic rifting stages. Thickened crust (30-34 km) across the studied region may be inherited from continental collision during the Paleozoic Variscan orogeny. An anomalous crustal thinning to around 28 km is observed beneath the central part of the Central Iberian Zone and the eastern part of South Portuguese Zone.

Mantle beneath the Gibraltar Arc from receiver functions

P and S receiver functions (PRF and SRF) from 19 seismograph stations in the Gibraltar Arc and the Iberian Massif reveal new details of the regional deep structure. Within the high-velocity mantle body below southern Spain the 660-km discontinuity is depressed by at least 20 km. The Ps phase from the 410-km discontinuity is missing at most stations in the Gibraltar Arc. A thin (similar to 50 km) low-S-velocity layer atop the 410-km discontinuity is found under the Atlantic margin. At most stations the S410p phase in the SRFs arrives 1.0-2.5 s earlier than predicted by IASP91 model, but, for the propagation paths through the upper mantle below southern Spain, the arrivals of S410p are delayed by up to +1.5 s. The early arrivals can be explained by elevated Vp/Vs ratio in the upper mantle or by a depressed 410-km discontinuity. The positive residuals are indicative of a low (similar to 1.7 versus similar to 1.8 in IASP91) Vp/Vs ratio. Previously, the low ratio was found in depleted lithosphere of Precambrian cratons. From simultaneous inversion of the PRFs and SRFs we recognize two types of the mantle: 'continental' and 'oceanic'. In the 'continental' upper mantle the S-wave velocity in the high-velocity lid is 4.4-4.5 km s(-1), the S-velocity contrast between the lid and the underlying mantle is often near the limit of resolution (0.1 km s(-1)), and the bottom of the lid is at a depth reaching 90 100 km. In the 'oceanic' domain, the S-wave velocities in the lid and the underlying mantle are typically 4.2-4.3 and similar to 4.0 km s(-1), respectively. The bottom of the lid is at a shallow depth (around 50 km), and at some locations the lid is replaced by a low S-wave velocity layer. The narrow S-N-oriented band of earthquakes at depths from 70 to 120 km in the Alboran Sea is in the 'continental' domain, near the boundary between the 'continental' and 'oceanic' domains, and the intermediate seismicity may be an effect of ongoing destruction of the continental lithosphere.

Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulation

This work provides an assessment of layerwise mixed models using least-squares formulation for the coupled electromechanical static analysis of multilayered plates. In agreement with three-dimensional (3D) exact solutions, due to compatibility and equilibrium conditions at the layers interfaces, certain mechanical and electrical variables must fulfill interlaminar C-0 continuity, namely: displacements, in-plane strains, transverse stresses, electric potential, in-plane electric field components and transverse electric displacement (if no potential is imposed between layers). Hence, two layerwise mixed least-squares models are here investigated, with two different sets of chosen independent variables: Model A, developed earlier, fulfills a priori the interiaminar C-0 continuity of all those aforementioned variables, taken as independent variables; Model B, here newly developed, rather reduces the number of independent variables, but also fulfills a priori the interlaminar C-0 continuity of displacements, transverse stresses, electric potential and transverse electric displacement, taken as independent variables. The predictive capabilities of both models are assessed by comparison with 3D exact solutions, considering multilayered piezoelectric composite plates of different aspect ratios, under an applied transverse load or surface potential. It is shown that both models are able to predict an accurate quasi-3D description of the static electromechanical analysis of multilayered plates for all aspect ratios.

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

Estimation of rotational frequency response functions

As it is widely known, in structural dynamic applications, ranging from structural coupling to model updating, the incompatibility between measured and simulated data is inevitable, due to the problem of coordinate incompleteness. Usually, the experimental data from conventional vibration testing is collected at a few translational degrees of freedom (DOF) due to applied forces, using hammer or shaker exciters, over a limited frequency range. Hence, one can only measure a portion of the receptance matrix, few columns, related to the forced DOFs, and rows, related to the measured DOFs. In contrast, by finite element modeling, one can obtain a full data set, both in terms of DOFs and identified modes. Over the years, several model reduction techniques have been proposed, as well as data expansion ones. However, the latter are significantly fewer and the demand for efficient techniques is still an issue. In this work, one proposes a technique for expanding measured frequency response functions (FRF) over the entire set of DOFs. This technique is based upon a modified Kidder's method and the principle of reciprocity, and it avoids the need for modal identification, as it uses the measured FRFs directly. In order to illustrate the performance of the proposed technique, a set of simulated experimental translational FRFs is taken as reference to estimate rotational FRFs, including those that are due to applied moments.

Algebraic structure for interaction on mixed models

Binary operations on commutative Jordan algebras, CJA, can be used to study interactions between sets of factors belonging to a pair of models in which one nests the other. It should be noted that from two CJA we can, through these binary operations, build CJA. So when we nest the treatments from one model in each treatment of another model, we can study the interactions between sets of factors of the first and the second models.