How to estimate anisotropic attenuation exploiting prior isotropic knowledge

The pattern of the highest intensities in macroseismic fields of volcanic areas is strongly anisotropic because of the linear extension of the fault. In the isotropic approach to the estimation of the probability distribution of the site intensity the analysis starts considering the sites inside circular bins, with fixed width, around the epicentre. To consider the source effect it seems natural to shift epicentre to the rupture length and circular bins to elliptical ones. To exploit prior information on the attenuation trend in Italian seismological and volcanic areas we transform the plane so that an ellipse becomes a circle with diameter equal to its minor axis, and then estimate the probability distribution of the site intensity applying the method proposed in Zonno et al. (2009) to the transformed data points.