Imaging of crustal scatterers using multiple seismic arrays

Array seismology is an useful tool to perform a detailed investigation of the Earth’s interior. Seismic arrays by using the coherence properties of the wavefield are able to extract directivity information and to increase the ratio of the coherent signal amplitude relative to the amplitude of incoherent noise. The Double Beam Method (DBM), developed by Krüger et al. (1993, 1996), is one of the possible applications to perform a refined seismic investigation of the crust and mantle by using seismic arrays. The DBM is based on a combination of source and receiver arrays leading to a further improvement of the signal-to-noise ratio by reducing the error in the location of coherent phases. Previous DBM works have been performed for mantle and core/mantle resolution (Krüger et al., 1993; Scherbaum et al., 1997; Krüger et al., 2001). An implementation of the DBM has been presented at 2D large-scale (Italian data-set for Mw=9.3, Sumatra earthquake) and at 3D crustal-scale as proposed by Rietbrock & Scherbaum (1999), by applying the revised version of Source Scanning Algorithm (SSA; Kao & Shan, 2004). In the 2D application, the rupture front propagation in time has been computed. In 3D application, the study area (20x20x33 km3), the data-set and the source-receiver configurations are related to the KTB-1994 seismic experiment (Jost et al., 1998). We used 60 short-period seismic stations (200-Hz sampling rate, 1-Hz sensors) arranged in 9 small arrays deployed in 2 concentric rings about 1 km (A-arrays) and 5 km (B-array) radius. The coherence values of the scattering points have been computed in the crustal volume, for a finite time-window along all array stations given the hypothesized origin time and source location. The resulting images can be seen as a (relative) joint log-likelihood of any point in the subsurface that have contributed to the full set of observed seismograms.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).