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 The SEA-CALIPSO wide-angle seismic experiment revealed a high velocity region beneath the island of Montserrat. Field recordings show a decrease in the amplitude of seismic signals crossing this high velocity region. We constrain the geometry and nature of this attenuating body, by forward modeling of the seismic wave field with a viscoelastic finite-difference method. We interpret the attenuation observed as caused by a scattering region, which we model as a stochastic perturbation of the velocity field with characteristic length scale of 0.4 km. The scattering region approximately coincides with the top part of the high velocity region and is estimated to have a volume of about 800 km3. We argue that the scattering is caused by geological heterogeneities corresponding to a system of dikes and sills and to the complex structure of the volcanic edifice.
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 The magmatic systems of island arc volcanoes are complex structures, and can display highly irregular distributions of seismic velocity. The scale of heterogeneity can range over several orders of magnitude from small-scale blocky textures in breccias to kilometer-scale features such as lava domes and magma chambers. Seismic travel-time tomography can detect the presence of kilometer-scale heterogeneities but is unsuitable to study the fine scale structure [e.g., Hansen et al., 1999]. The nature of heterogeneities at this scale is best modeled as a stochastic field [Goff et al., 1994].
 The SEA-CALIPSO experiment collected active-source seismic data on and around Montserrat, to study the magmatic system of the Soufriére Hills Volcano (SHV) [Voight et al., 2010; E. Shalev et al., Three-dimensional seismic velocity tomography of Montserrat from the SEA-CALIPSO offshore/onshore experiment, submitted to Geophysical Research Letters, 2010]. This study focuses on the analysis of a profile across Montserrat for which a velocity model is available from travel-time inversion [Paulatto et al., 2010]. The model has two solid layers, an upper layer including oceanic sediments and the volcanic edifice and a lower layer corresponding to the upper crust plus sediments and volcanics from the early stages of arc formation (Figure 2a). A high velocity region beneath the island is interpreted to correspond to the cores of the SHV and Centre Hills Volcano (CHV) and to an associated intrusive dike and sill complex. Individual dikes or sills cannot be resolved by travel-time tomography but an intrusive complex is expected to cause scattering of seismic waves and its effect on first arrival amplitudes should be observable. We use first arrival amplitudes to identify regions of anomalously high seismic attenuation. By comparing these amplitudes with those of synthetic seismograms, we constrain the extent and nature of the attenuating region.
2. Finite Difference Modelling
 The data analyzed in this study are those used by Paulatto et al. , and initially included the vertical geophone recording on four ocean bottom seismometers (OBS) and four land stations of a radial shooting line to the south-east of Montserrat (Figure 1). These stations were selected because they are closest to the section. Unfortunately, two land stations (M11 and M30) were too noisy to be used for amplitude analysis.
 Synthetic seismograms were calculated with a two-dimensional viscoelastic finite difference algorithm [Robertsson et al., 1994]. Models were built as the sum of a background model V0(x, z), from Paulatto et al. , and a perturbation δV(x, z) and were sampled on a 20 × 20 m grid (Figure 2a). The S-wave velocities (vs) and density were calculated from the P-wave velocity (vp) using the empirical relations of Brocher , which apply to most lithologies, except mafic and calcium rich rocks. Qp (Figure 2b) was estimated from an interpretation of the solid layers of the vp model and Qs was calculated from vp, vs and Qp using the relation Qs = 4/3(vs/vp)2 [Müller, 1985]. The source wavelet was a Ricker wavelet with center frequency of 8.0 Hz, similar to the dominant frequency of the dataset.
3. Amplitude Analysis
 First, synthetic seismograms were calculated for the background model (Model-1) and the amplitudes of first arrivals were compared to the data (Figures 3a and 3b). The synthetics were scaled by a factor proportional to offset−0.5 to account for the difference of geometrical spreading in 2D and in 3D [e.g., Henstock and Levander, 2000]. The match between data and synthetics for O09 and O10 is good, showing that the background model is adequate in the offshore region to a depth of up to 6 km. In contrast, the medium offset (20–35 km) arrivals on O11 and O12, that travel beneath the island, have lower amplitudes than predicted by the background model. By studying the ray-paths of the arrivals involved (Figure 2a), the source of the amplitude reduction can be located beneath SHV and CHV at a depth of up to 6 km. Such amplitude reduction might be caused by one or more of the following three factors: geometric effects due to a low velocity zone, intrinsic attenuation, and scattering. We have assessed the contributions of these factors by forward modeling of the seismic wave field in perturbed models.
 Another discrepancy between data and synthetics is the difference in amplitudes of O11 and O12 at longer offset. Synthetic amplitudes for O11 are generally higher than those for O12, but observed amplitudes are similar. The difference in synthetic amplitudes may be the result of velocity gradients that are too high in the deep part of the model, where they are only loosely constrained by the tomographic inversion. A modified background model (Model-2) in which the velocity gradient at depths greater than 6 km was reduced by 40% (Figure 2c) shows a significantly improved amplitude fit for O11 and O12 (Figures 3c and 3d). Other stations are not affected. A measure of the goodness of amplitude fit is the χ2, defined here as the sum of the squares of the amplitude misfit between data and synthetics normalized by the synthetic amplitude. The χ2 for O11 and O12 is reduced by a factor 0.4 (Table 1). Since Model-2 provides a better amplitude fit and it does not alter significantly first arrival travel-times, it was adopted as the background model in all subsequent calculations.
Table 1. χ2 of the Maximum Amplitude of First Arrivals, Smoothed With a 0.5 km Running Average
 The first perturbed model tested (Model-3) has an elliptical low-vp zone representing a small magma chamber of the size predicted by geodetic studies of SHV [e.g., Voight et al., 2006] (Figure 2d). The perturbation has a horizontal axis of 4 km and a vertical axis of 2 km and is centered at 4 km depth (Figure 2d). Inside the low velocity region vp is reduced by 10% with respect to the background model and Qp is reduced to a value of 200.
 The second perturbed model (Model-4) has an elliptical zone characterized by high intrinsic attenuation (low Q), centered at 1.8 km depth beneath SHV with horizontal axis of 15.6 km and vertical axis of 6.4 km (Figure 2e). Iterative forward modeling was used to define the perturbation geometry and strength. In the best fitting model, Qp is reduced to a value of 20, and Qs is modified to match.
 The third perturbed model (Model-5) was built to test the hypothesis that the amplitude variations observed are caused by scattering and to constrain the spatial distribution of scatterers. The magmatic system was modeled as a stochastic medium using the approach of Goff et al. . A continuous von Kármán field perturbation, with the same geometry as the perturbation in Model-3, with RMS amplitude of 0.7 km s−1, Hurst number of 1.5, and characteristic length scale of 0.4 km, was added to the background model (Figure 2f). These values were determined by iterative forward modeling and are only loosely constrained.
 The amplitudes for Model-3 were very similar to those of Model-2 and are not shown. First arrival amplitudes were reduced as expected, but the reduction was not large enough to match the observations. A larger perturbation would have generated travel-time anomalies and therefore would have been detected by the tomographic inversion. For Model-4, amplitudes of first arrivals on O11 and O12 are reduced in the appropriate offset range. The fit for B94 and C46 is also improved, but the decay of amplitude with offset is larger than observed. (Figures 3e and 3f). The χ2 is reduced to about 0.5 times that of Model-2 (Table 1). The effect of Model-5 on OBS first arrival amplitudes is similar. For C46 the decay of amplitudes with offset is slower (Figures 3f and 3h), but the χ2 does not vary significantly (Table 1).
 The models may be further evaluated by comparing observed and synthetic receiver gathers (Figure 4). For Model-1 synthetics are characterized by a sharp first arrival and at short offset they are dominated by a slow phase travelling in layer 1 (Figure 4, feature 1). Synthetics for Model-2 and Model-3 are not shown since they are very similar to Model-1. For Model-4 the most significant features are a reduction in the high-frequency content and a reduction of first arrival amplitudes at short offset (Figure 4, feature 2). The first arrival remains sharp and even though the amplitude variations match the observed values well, the visual match of the synthetics is poor. In contrast, the synthetic seismograms for Model-5 are more similar to the field recordings especially for the land stations. In particular there is a greater high frequency content and the first arrivals at short offset are weaker (Figure 4, feature 3). For O12 the amplitude ratio between first and later arrivals is higher than observed for all models (Figure 4, feature 4), possibly because our models do not fully account for reverberations within the sediment layer.
 The amplitude analysis shows that the observed attenuation can be explained equally well by intrinsic attenuation or by scattering, but the scattering model gives a better match when full waveforms are compared. Moreover the only simple mechanism that can account for strong intrinsic attenuation in the crust beneath Montserrat is the presence of a partial melt zone, but such a large volume of partial melt would have other detectable effects, e.g., lower vp. Intrinsic attenuation due to the presence of partial melt may play a role in the observed amplitude reduction, but scattering is likely to be the dominant mechanism.
Martinez-Arévalo et al.  measured attenuation beneath Deception Island and their results also suggest that in these regions scattering is predominant over intrinsic attenuation. The presence of similar highly heterogeneous regions has been inferred beneath other active volcanoes [e.g., Del Pezzo et al., 1996]. In such regions scattering may affect the quality of seismic recordings by reducing the signal to noise ratio and hence may negatively affect our ability to image the subsurface with wide-angle seismic surveys.
5. Discussion and Conclusions
 By comparing field recordings with synthetic seismograms, a region of anomalously high seismic attenuation has been identified beneath the island of Montserrat, approximately coincident with a high velocity region at depth of up to 5 km. Assuming radial symmetry, the heterogeneous region is estimated to have a volume of about 800 km3. The observed attenuation is best explained as scattering from a geologically heterogeneous region, modeled as a continuous stochastic field. Petrological and seismological evidence [e.g., Barclay et al., 1998; Aspinall et al., 1998], suggests that the top of the active magma body may be at a depth of around 5 km and so may contribute to the attenuation. However, a model with a magma chamber at these depths does not reproduce the observations. We infer that the lower part of the scattering region consists of an intrusive complex with bodies a few hundred meters in size, consistent with a network of dykes or sills or both. In the upper part of this region, heterogeneities are more likely to be controlled primarily by fractures, weathering, alteration, and variations in porosity between the dense lava domes forming the cores of the volcanic edifices and the softer flanks. This interpretation is consistent with observations of the surface geology, with the presence of abundant xenoliths with hypabyssal textures in Montserrat lavas (E. Kiddle et al., Crustal structure beneath Montserrat, Lesser Antilles, constrained by xenoliths, seismic velocity structure and petrology, submitted to Geophysical Research Letters, 2009) and with models for formation of high level crustal intrusive complexes and magma chambers by amalgamation of numerous intrusive events [e.g., Annen, 2009].
 We thank Steve Sparks, Barry Voight, Brian Baptie and two anonymous reviewers for their insightful comments on our analysis. This study forms part of a PhD studentship partly funded by the British Geological Survey (BGS). The dataset used was collected as part of the SEA-CALIPSO project, funded by the National Science Foundation, the National Environmental Research Council, BGS, the Incorporated Research Institutions for Seismology, Discovery Channel TV and the British Foreign and Commonwealth Office.