GNGTS 2015 - Atti del 34° Convegno Nazionale

with the receiver (station position) is composed by several segments, whose associated travel time t i is defined by: where d j represents the single straight line of the ray i which belong to the single pixel j , s j is the slowness of the same pixel and m is the total number of pixels in the model. To minimize time residuals, SIRT method uses an iterative procedure which leads to convergence. In formulas, where ∆ s j is the upgraded velocity of pixel j , ∆ t i is the time residual associated to ray i, N is the number of rays (travel times) and M is the number of pixels in the model. The computation of ray paths in the model follows the principle of minimum time, using an iterative algorithm based on Snell’s law (Böhm et al. , 1999a). Initial model, data processing and reliability of the tomographic system. As we can see in Fig. 1b, the rays distribution is not homogeneous in the considered area. The greater ray density reflects the higher seismicity of the area, distributed in the center of the model, with the most intense activity concentrated along the Friuli region and in correspondence of the geologic junction between southern Alps and External Dinarides. We adopted the 1-D velocity structure computed by Costa et al. (1992) as initial velocity model. Futhermore, the Friuli plain constitutes an important part of our zone and obviously does not represent a seismic area, therefore we constrained, for the first layers, some voxels of the model with the velocity values coherent with real data considering the geological information by Slejko et al. (1987). The volume of our investigation, whose dimensions are 180 x 60 x 51 km, is discretized by 18 voxels along X direction, 6 voxels alongYdirection and 60 layers in depth, obtaining a spatial resolution of 10 x 10 km in two horizontal directions and 0.85 km in the vertical component, which it coincides with the half of thinnest layer of the base model. The choice of this grid, which we called “base grid”, represents a compromise between two opposite requirements: the resolution and the reliability of the model. In this work, inside the tomographic process, we used the staggered grids method (Böhm et al. , 1999b), which provides a high resolution velocity model by summing and averaging different inversions obtained from low resolution but well-constrained in a base grid that has been perturbed in the space. In our case, we applied two shifts in both horizontal directions ( x , y ) and one shift in vertical direction z . In tomographic inversion, the homogeneity of earthquake’s distribution is fundamental to obtain a reliable 3-D velocity model. The reliability of tomographic system (model discretization and ray geometry) can be computed in different ways. The ray density represents only a simple method to evaluate the reliability of the model, while the map of null space is a more complex and expensive in computation time. Nevertheless, null space evaluation is the most correct methodology to measure the reliability of a tomographic system; it utilizes the single value decomposition technique (SVD) (Stein and Wysession, 2003) in which the instability of the system is defined by the presence of singular values equal or close to zero. After defining a threshold value, it is possible to map the null space values in the whole model, by summing the squares of the elements of each column of the diagonal matrix of the singular values. To verify the consistency of the inversion quality, we adopted the checkboard test, which represents one of the most popular test used to verify the inversion’s quality. This technique consists of creating a model on which velocities are distributed between low (in our case, GNGTS 2015 S essione 1.2 69