I. Earthquake source models, magnitudes and scaling relations. II. Amplitudes of rotationally split normal modes for the 1960 Chilean and 1964 Alaskan earthquakes

Abstract

In Part I several fundamental concepts in seismology are examined in detail. The different teleseismic seismic magnitude scales are studied on the basis of Gutenberg and Richter's original notepads. The presented by Richter and Duda are shown to be basically body wave magnitudes which are converted to the surface wave basis. These revised magnitudes are systemically higher (by an average of 0.22) than the magnitudes published by Gutenberg and Richter in Seismicity of the Earth, which are basically surface wave magnitudes. Use of the revised magnitudes has led to substantial over-estimates of the moment of great earthquakes. Fault area, rather than magnitude, should be used for moment estimates when the moment is unavailable. A dataset of 41 moderate and large earthquakes is used to derive scaling laws relating kinematic fault parameters such as magnitudes, moment and fault dimensions. If effective stress and static stress drop are equal, then, fault rise time, τ, and fault area, S, are related by τ = 16S^½ /(7π^(3/2)β), where β is shear velocity. Fault length (parallel to strike) and width (parallel to dip) are empirically related by L = 2W. Observed data agree well with the predicted scaling relations. Fault width (i.e. the two dimensionality of faults) must not be neglected. Inclusion of width leads to different average source spectra for surface waves and body waves. The m_b versus M_s relation from this study differs significantly from the Gutenberg-Richter relation, because the Gutenberg-Richter equation was derived for body waves with a predominant period of about 5 sec and thus does not apply to modern 1 sec m_b determinations. Previous investigators who assumed that the Gutenberg-Richter relation was derived from 1 sec data were in error. In Part II, the theory necessary to calculate the amplitudes of the earth's rotationally and elliptically split free oscillations is developed. The amplitude of each singlet is explicitly given as the product of factors for fault geometry, seismic moment, source depth, earth structure and the geographic coordinates of the source and receiver. These results are applicable for the synthesis of either spectra or time domain records for which splitting is an important factor. The splitting of the earth's normal modes was observed for both the 1960 Chilean and 1964 Alaskan earthquakes. The theoretical results for the excitation of singlets are used to predict the relative amplitude of observed split peaks. Good agreement is obtained for thrust fault source models derived from long period surface waves. However, other mechanisms, such as a slow isotropic volume change, are also consistent with the split mode relative amplitudes, and are excluded only by additional data. The split modes are observed for the 1960 Chilean earthquake by analysis in the time domain. One hundred fifty hours of the Isabella, California strain record are filtered to isolate individual multiplets. Synthetic seismograms with and without splitting are used to confirm the splitting of _0S_2 and _0S_3 and to demonstrate the splitting of _0S_4, _0S_5, _0T_3 and _0T_4. Different techniques for measuring the Q of split modes are studied. It is concluded that Q determinations from comparison of time domain synthetics to data give much more stability than frequency domain techniques. Uncertainties in the calibration of the instrumental absolute amplitudes rule out a direct determination of the moment of the Chilean earthquake. However, by comparing Isabella records for Chile and Alaska, the long-period moment of the Chilean earthquake is found to be 3.3 times that of the Alaskan event. By using the moment estimated for Alaska from long period surface waves, the moment of the Chilean earthquake is estimated to be 2.4 x 10^(30) dyne cm.