Variations between Q values estimated from damped terrestrial eigenvibrations

Abstract

A general probabilistic model is used to investigate the variations in Q values as a function of time for two large earthquakes and a regional network of stations. The time series is assumed to be a linear combination of exponentially damped harmonics in the presence of noise. The analysis is by complex demodulation, which provides instantaneous amplitude and phase at each eigenfrequency as a function of time. Parameter estimation is also made by nonlinear regression for the same statistical model. Q values and their variances have been calculated using records from the ultra‐long‐period instruments at Berkeley (three components), Jamestown (vertical component), and Whiskeytown (vertical component). Time series following the earthquakes of August 1976 (Philippines) and August 1977 (Indonesia) provide estimates of Q for a number of well‐resolved fundamental spheroidal and torsional vibrations. Representative Q values and standard errors from well‐resolved torsional modes for the 1977 Indonesia data at Berkeley for 0T11, 0T12, and 0T35 are 230±81, 213±47, and 244±33. In a number of cases, intercomparison of Q values shows differences for the same mode greater than twice the formal standard error. For example, Q values for the sharp peak 0S16 after the Philippine earthquake are 326±64 at Berkeley and 244±24 at Whiskeytown. In contrast, the mode 0S21 is well excited on the periodograms for Berkeley from both the Indonesia and the Philippine data; Q values are, however, 204±39 and 354±70, respectively, an unacceptable difference. Partial explanation of these differences is helped by the complex demodulates which show varying lengths of coherency of phase angle with time probably due to nonstationary noise and varying interference from neighboring modes. These results suggest that estimates of Q values from eigenspectra should not be accepted at full weight unless specified coherency tests are satisfied.