A paper was published that treats the problem of determining the source of scattered waves (Gritto et al., Pure Appl. Geophys., 156, 557-589, 1999). This problem of scattered waves is commonly encountered both in the study of seismic sources and in the imaging of subsurface structure. It is a strongly nonlinear problem and the linearized approaches that are typically used are only valid for weak scattering. In this paper it is shown that in the low frequency regime it is possible to obtain an exact solution to the full nonlinear inverse problem. It is also shown how these results can be extended to higher frequencies through the use of the Mie approximation. The method is quite general in that it can be used for arbitrary geometrical arrangements of sources and receivers and for large contrasts in medium properties. The use of this approach to complement conventional travel time tomography is being further investigated.
Considerable research has been done on a general method of solving both the forward and inverse problems for elastic waves in realistic three-dimensional media. The method includes non-stationary ray paths, remains valid at caustics, and involves sensitivity functions for both velocity and attenuation. It can be applied to media which are both visco-elastic and poro-elastic. It includes frequency dependent effects for waves propagating in media that are heterogeneous in both velocity and attenuation. The inclusion of both velocity and attenuation in the inverse problem leads to a significant improvement in the ability to explain observational data and permits estimation of several relevant material properties, including velocity, intrinsic attenuation, porosity, and permeability.