An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods.
It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.
We study certain Fourier integral operators arising in the inversion of data from reflection seismology.
The displacement field caused by the classic earthquake mechanism model consisting of a slip along the fault is extended to the case when besides the slip, also an opening occurs caused by tensional forces. The tensor matrix describing the moment tensor does not necessarily have a nil trace. The direct problem is solved finding the radiation pattern for and waves. A method to solve the inverse problem of the determination of the four parameters describing the source is presented and tested on...