Can One Determine Seismic Focal Parameters from the Far‐Field Radiation?

Summary A number of postulates concerning the nature of faulting have been used in the construction of kinematical models, which give the source parameters of seismic moment, fault length, and stress drop from the spectral properties of d.c. level and knee frequency. Several one‐dimensional models of faulting, calculated as well‐posed boundary value problems, are obtained which give both the source parameters and the far‐field radiation, providing a test for these empirical relations. The results for these models show that the high‐frequency content of the seismogram is usually associated not with the onset of fracture, but with the onset of healing, that is, when the cessation of relative motion on the fault begins. In some cases, the high‐frequency part of the seismogram is also associated with the termination of rupture. For different distributions of tectonic stress, dynamical friction and cohesion, healing can take place sonically, supersonically, or instantaneously over the entire fault. The final state of stress may be less than or greater than the dynamical friction. For four selected models of one‐dimensional faulting, the calculation of fault parameters from the theoretical seismograms give internally consistent estimates of seismic moment. Unfortunately, the theory shows that the estimates of fault length and stress drop made from the empirical formulas may be completely without value, without additional information not usually derived from the radiation spectrum.