**3. Tomographic inversion and crustal seismic structure**

The inversion of a 1-D or 3-D seismic model of the crustal structure is based on the sourcestation travel times of seismic waves, generally by minimizing the time residual (difference between observed and theoretical travel times) due to disturbances introduced in the hypocentral coordinates and model properties. The dependence or coupling between the hypocentral parameters and the velocity structure being modelled is usually resolved by way of damped least-squares (Menke, 1984); a more detailed discussion on these methodologies can be found at Thurber (1993), Kissling et al. (1994), Thurber et al. (2000) or Thurber (2003). The resolution of this coupling problem requires the use of seismic events with stable hypocentral solutions, a criterion which must be balanced with the best spatial coverage possible (Thurber, 1993; Kissling et al., 1994; Thurber et al., 1999).

The methods used for the inversion of the velocity structure are implemented in programs like VELEST (Kissling et al., 1994; Kissling, 1995) for 1-D structure and SIMUL2000/SIMULPS (Thurber, 1983; Thurber et al., 1999) for 3-D structure. In the first case the model is parameterized by plane horizontal layers where seismic properties like P-wave velocity, Vp, or the Vp/Vs ratio remain constant, while in the former the model parameterization is done using a three-dimensional grid where on each node the value of these properties is set, with the values in other regions obtained by linear interpolation. Given the lower quality usually associated with S-waves readings compared to P-waves, both methods invert directly to the Vp and Vp/Vs structures, the Vs structure being latter derived from them.

Figure 2 displays the best (minimum) 1-D model obtained for the area between the islands of Faial, Pico and São Jorge, labelled FAIAL98 (Matias et al., 2007). Considering the P and S velocities and the Vp/Vs ratio of the model, and comparing with values associated with typical oceanic crusts (Tanimoto, 1995; Karson, 1998) it is possible to make a generic interpretation in petrological terms of the crustal structure of the area under study. The results indicate a basaltic composition for the layer located between 1 and 3 km in depth (Layer 2), with the velocities values suggesting a succession from lava flows to pillow lava and basaltic dikes. Between 3 and 12.5 km, the values of Vp and Vp/Vs indicate the presence of a Layer 3 with increased thickness, whose composition corresponds to Gabbro type mafic rocks. The location of the Moho at 12.5 km is an effect arising from the numerical modelling, the crust-mantle transition being more gradual and located between 12 and 14 km depth. The Moho associated Vp values will be intermediate values between 7.3 and 7.7 km/s, a possible evidence of a gradual increase of ultra-mafic rocks intrusion in the lower crust or the effect of variations in the depth of the Moho.

In order to determine the 3-D crustal structure in the tomographic inversion process (Dias et al. 2007) the above 1-D model was used as initial model, parameterized in the 3-D grid of Figure 3. After relocation of the earthquakes used in the 1-D modelling, the stability criteria for the hypocentral solutions were strengthened, with only 688 events used (cf. Fig. 3).

Fig. 2. Vertical profiles of P and S waves velocities and Vp/Vs ratio distribution corresponding to the new 1-D model FAIAL98, together with its petrological interpretation (Dias, 2005; Matias et al., 2007).

Any tomographic modelling process leads to a mathematic solution where it is important to estimate the quality of such solution in physical terms, namely by defining the regions of the model that can be considered well resolved. This evaluation can be accomplished through analysis of mathematical parameters related to the model resolution, reflecting the distribution of information and associated resolution, and also by performing sensitivity tests that use synthetic models or data. Only after such tests were performed, and together with joint analysis of the resolution parameters, is possible to define the resolved areas that will later be interpreted in physical terms. For discussion on the tomographic resolution of tomographic models see for example Menke (1984), Eberhart-Phillips (1993), Kissling et al. (1994), or Kissling et al. (2001); for the quality assessment of the model presented here see Dias (2005) and Dias et al. (2007).

In order to determine the 3-D crustal structure in the tomographic inversion process (Dias et al. 2007) the above 1-D model was used as initial model, parameterized in the 3-D grid of Figure 3. After relocation of the earthquakes used in the 1-D modelling, the stability criteria for the hypocentral solutions were strengthened, with only 688 events used (cf.

Fig. 2. Vertical profiles of P and S waves velocities and Vp/Vs ratio distribution

(Dias, 2005; Matias et al., 2007).

Dias (2005) and Dias et al. (2007).

corresponding to the new 1-D model FAIAL98, together with its petrological interpretation

Any tomographic modelling process leads to a mathematic solution where it is important to estimate the quality of such solution in physical terms, namely by defining the regions of the model that can be considered well resolved. This evaluation can be accomplished through analysis of mathematical parameters related to the model resolution, reflecting the distribution of information and associated resolution, and also by performing sensitivity tests that use synthetic models or data. Only after such tests were performed, and together with joint analysis of the resolution parameters, is possible to define the resolved areas that will later be interpreted in physical terms. For discussion on the tomographic resolution of tomographic models see for example Menke (1984), Eberhart-Phillips (1993), Kissling et al. (1994), or Kissling et al. (2001); for the quality assessment of the model presented here see

Fig. 3).

Figure 4 shows the tomographic model obtained, in horizontal planes of Vp and Vp/Vs structures at depth, with resolved areas outlined. Given the information distribution (source-station paths), the resolved areas are located around the NNW area of the Faial -Pico channel and essentially between depths of 4 to 10 km. At the shallower level (1.0 km) there is good agreement between the anomalies of the tomographic model and the surface geological structure, particularly with the several volcanic units, but the most relevant feature of the tomographic model is the presence of a high-velocity body (Vp>6.3 km/s) located under the NW area of the island of Faial and extending from 6-7 km to a depth of approximately 13 km, which is enclosed in the northeast and east by deeper seismicity.

Fig. 3. Horizontal grid nodes positions (crosses) of the 3-D grid, seismic network (cf. Fig. 1) and epicenters (red dots) of the 688 selected events. A white cross marks the center of the grid, and the X and Y coordinates of Figure 4 are represented laterally to the grid. The horizontal distance between nodes was of 4-8 km, and vertically the nodes were placed in layers located at depths Z = 1, 4, 7, 10, 13, 17 km.

In the deepest levels (Z = 7, 10 km, see Figure 4) there is a strong lateral gradient to NNE in the direction of the S. Jorge channel, mainly of the Vp/Vs ratio that drops from 1.82 to less than 1.72; since this transition is partly coincident with the NNE limit of the high-velocity body and simultaneously runs parallel to the Faial-Pico alignment, it probably reflects the presence of an important tectonic feature. Under the central area of Faial, there is the presence of a low velocity zone (Vp <6.0 km/s), with a 5-10% lateral gradient on Vp and extending between 4 and 7 km in depth; under Pico there is the suggestion of the presence of a similar anomaly. The location of these anomalies is consistent with the estimated position for the magmatic chambers of the main volcanic edifices of Faial and Pico (Machado et al., 1994).

Fig. 4. Horizontal depth planes of the 3-D Vp (left) and Vp/Vs (right) models, at selected depths. Triangles: seismic stations, crosses: grid nodes, dots: epicenters within 1 km vertical range of the plane. Lateral XY coordinates according to the 3-D grid of Fig. 3.
