Summary: We investigate a problem of potential interest to geophysicists. Namely, we attempt to find the shape of a magnum chamber lying in the earth crust below a volcano. This is posed as an inverse acoustics problem where we use scattered seismic waves to determine the location and form of the chamber. A simplification is to consider the finite crust to be over a semi-finite magma region. An earlier work of ours discussed the inverse problem associated with the Perkeris model, whereas the present work represents the crust with volcano as a perturbation of this model. In order to reformulate this inverse problem in integral equation form we first construct the Green’s function for this problem. A numerical example is presented for the case of the bump being a half circle.
For the entire collection see [Zbl 1169.00011].