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The inverse problem in Seismology is tackled in this paper under threeparticular circumstances. First, the inverse problem is defined as thedetermination of the seismic-moment tensor from the far-field seismic waves (Pand S waves). We use the analytical expression of the seismic waves in ahomogeneous isotropic body with a seismic-moment source of tensorial forces,the source being localized both in space and time. The far-field waves providethree equations for the sixth unknown parameters of the general tensor of theseismic moment. Second, the Kostrov vectorial (dyadic) representation of theseismic moment is used. Third, the fourth missing equation is derived from theenergy conservation and the covariance condition. The four equations derivedhere are solved, and the seismic moment is determined, thus solving the inverseproblem in the conditions described above. It is shown that a useful picture ofthe seismic moment is the conic represented by the associated quadratic form,which is a hyperbola (seismic hyperbola). Also, it is shown that the far-fieldseismic waves allow an estimation of the volume of the focal region, focalstrain, duration of the earthquake and earthquake energy; the later quantity isa direct measure of the magnitude of the seismic moment. The special case of anisotropic seismic moment is presented.

The inverse problem in Seismology. Seismic moment and energy of earthquakes. Seismic hyperbola