A Contribution to the Determination and Interpretation of Seismic Source Parameters

Citation

Hanks, Thomas Colgrove (1972) A Contribution to the Determination and Interpretation of Seismic Source Parameters. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DGY7-DE54. https://resolver.caltech.edu/CaltechTHESIS:08262011-111631645

Abstract

Two models of the seismic source are reviewed as a prelude to the determination and interpretation of seismic source parameters from far-field shear displacement spectra. Within several limitations, the far-field shear displacement spectra of Brune (1970) and Haskell (1964) are grossly similar although the results differ in detail. These similarities imply that there is no gross discrepancy between Brune (1970) and Haskell (1964) with respect to the determination of seismic moment and source dimension. The source parameters seismic moment (M_o), source dimension (r), shear stress drop (Δσ), effective shear stress (σ_(eff)), radiated energy (E_s), and apparent stress (ησ) can all be expressed in terms of three spectral parameters which specify the far-field shear displacement of the Brune (1970) seismic source model l no (the long-period spectral level), f_o (the spectral corner frequency) and E, which controls the high frequency (f > f_o) decay of spectral amplitudes. All of the above source parameters can be easily extracted from a log-log plot of Ω_o versus f_o (ε when < 1 entering as a parameter), but only three of them are independent. The apparent stress is proportional to the effective shear stress, not the average shear stress. The Ω_o-f_o diagram is especially convenient for comparisons within a chosen suite of seismic and/or explosive sources. The equation on which the Gutenberg-Richter energy (E_(GR))-magnitude (M_L) relation was originally based is cast into an approximate spectral form; E_(GR) can then be easily compared with E_s on the Ω_o-f_o diagram for an earthquake of any M_L. Within the framework of the (Ω_o, f_o, ε) relations, it is a simple matter to construct an earthquake magnitude scale directly related to the radiated energy (E_s). The source parameters seismic moment and source dimension are estimated with teleseismic body-wave spectra for four intermediate magnitude earthquakes for which these source parameters can be obtained from field observations, The spectral and field estimates for these quantities agree within estimated uncertainties, when the spectral observations are scaled with the Brune (1970) model, The seismic moment and source dimension may be obtained as reliably with P-wave spectra as with S-wave spectra for these earthquakes, with the assumption that the P-wave corner frequency should be shifted from the S-wave corner frequency in proportion to the ratio of the compressional to shear wave velocities. Observational and theoretical uncertainties in the determination and interpretation of high frequency (f > f_o) spectral amplitude constitute a major barrier in the understanding of dynamical aspects of earthquake occurrence. Two of several problems concerning the generation of high frequency spectral amplitudes are discussed from a conceptual point of view. The source finiteness or directivity function is altered significantly from the result of Ben-Menahem (1961) for easily imaginable variations of displacement on the fault surface. The far-field shear displacement spectrum of Brune (1970) for the case of small fractional stress drop is structurally similar to that of Haskell (1964) when the rise time of displacement on the fault surface is much smaller than the fault length divided by the shear-wave velocity. The effective stress of Brune (1970) may be interpreted as a stress difference associated with the emplacement of rupture. The idea of a stress difference associated with the emplacement of rupture is investigated observationally for the case of the San Fernando, California, earthquake (February 9, 1971). Compressional and shear radiation emanating from the emplacement of rupture at depth beneath the San Gabriel Mountains is identified on the Pacoima Dam accelerograms. The S-P time obtained from this identification suggests a hypocentral depth of 12-15 km, somewhat greater than that of the local hypocentral location of the main shock, but consistent with that indicated by teleseismic observations of the reflected phases pP and sP. With less certainty, the radiation emanating from the rupture of the Earth's surface is identified on the Pacoima Dam accelerograms and WWSSN stations at teleseismic distances. Within several assumptions, the initial rupture event is separated from the subsequent motion on the Pacoima Dam accelerograms, and the source parameters are estimated for it from the associated shear wave. The stress drop accompanying the initial rupture is estimated to be 430 bars, approximately an order of magnitude greater than the average stress drop obtained from teleseismic spectral estimates and static dislocation models.

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