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.