Application of linear inversion theory toward the estimation of seismic source parameters

摘要

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.A discussion is given concerning the development of methods for obtaining an accurate representation of the forward elastostatic problem of describing the processes which accompany faulting. A method is suggested by which a more complicated and arbitrary static dislocation function could be approximated with the formulations derived for simple dislocation sources. A stochastic inverse is used to provide optimum estimates of the source description when observed elastostatic phenomena are systematically related to the media response of the various source parameters. This method is applied to the observed static displacement data from the 1964 Alaska earthquake and the 1971 San Fernando, California, earthquake.For the Alaskan event, the surface static displacements are calculated with the finite-element numerical modeling technique in which the effects of known geologic heterogeneities of the region are taken into account. The fault model used is that of a shallow angle fault underthrusting the Alaskan continental block. The calculated optimum static offset, stress drop, and strain energy density along the fault were found to be variable with a maximum offset of about 30 m. The region of maximum stress drop (218 bars) and maximum strain energy density change is found to correspond to the region of maximum compressional wave radiation. The resolution and resolvability of the calculated static fault model is discussed.For the San Fernando earthquake, the static dislocation along the assumed fault plane was also found to vary considerably. The observed surface displacements are fit to a high degree of accuracy by the given model. Included in the inversion data set are changes in the local gravity field caused by the earthquake. These changes can be predicted from known changes in elevation when a Bouguer correction is applied to the gravity data.The spatial and frequency distribution of path-corrected Rayleigh waves from the San Fernando earthquake are systematically related to the faulting process. The surface wave source is taken to be a depth-distributed set of double couples. A least-squares inversion is used to find the set of source parameters which optimally fit the variance-weighted data. The inversion results indicate a depth-distributed moment of 1.7 x [...] dyne-cm. The slip angles of the sources varied in such a way along the fault that the displacements became more predominantly dip slip as the dislocation propagated upward from the point of initial rupture at about 3.0 km/sec. A sophisticated error analysis is performed to estimate the uncertainties of the calculated model variables.An appendix is included in which the analytical expressions are derived for the complete strain field due to a dislocation on an arbitrarily inclined fault in a homogeneous half-space. Although the expressions are lengthy, the strain values can be calculated quickly on a computer since no numerical integration is necessary.