Objective Determination of Source Parameters and Similarity of Earthquakes of Different Size
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The omega-squared spectral model with two independent parameters (stress drop, moment) provides a simple parameterization of ground motion spectra for statistical analysis. Accurate determination of source parameters of small earthquakes requires accounting for distortion of the source spectrum by each site response spectrum. Record spectra are inverted here to find separate station and event spectra. Source parameters are found by an automated objective method using integrals of each event spectrum. Quantitative estimates of error are carried through the entire analysis. These methods are applied to digital records of aftershocks of the 1980 Mammoth Lakes California earthquake sequence. Stress drop is found to be independent of source radius for the 90 events with best-determined source parameters. The ratio of Hanks to Brune stress drop is remarkably constant and independent of source radius, showing that the spectra, on average, have a constant shape that is scaled by two parameters, corner frequency and low-frequency level. Stress drops have a log-normal distribution with the standard deviation being about a factor of 2.Keywords:
Seismic moment
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Asperity (geotechnical engineering)
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Abstract The well-recorded strong ground motion data for the 23:19 aftershock of the 15 October 1979 Imperial Valley earthquake provide a good opportunity to study the high-frequency source characteristics and the path effects at near-source distances. The best-fitting point source model has a strike-slip mechanism, N40°W, which is nearly identical to the main event. The estimated stress drop is extremely high, roughly 500 bars, with a triangular time history (0.1, 0.1 sec) but with a moment of 1.0 × 1024 dyne-cm. A double-source model found by inversion fits the high-frequency data better but indicates complex faulting: the first source (with strike = N319°E, dip = 42°NE, and slip angle = 165°) has a moment of 0.7 × 1024 dyne-cm, the second source (with strike = N324°E, dip = 82°SW, and slip angle = 181°) lies about 0.5 km to the north and has a seismic moment twice that of the first source. Source dimensions appear very small for this amount of energy release. Many of the anomalous behaviors observed at certain stations for the main event are, also, present in the aftershock data. These features are examined in terms of path effects.
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Source parameter estimates based on the homogeneous and inhomogeneous source models have been examined for an anomalous sequence of seven mine-induced events located between 640 and 825 m depth at Strathcona mine, Ontario, and having magnitudes ranging between m N 0.8 and 2.7. The derived Brune static stress drops were found to be similar to those observed for natural earthquakes (~ 30 bars), whereas dynamic stress drops were found to range up to 250–300 bars. Source radii derived from Madariaga's model better fit documented evidence of underground damage. These values of source radii were similar to those observed for the inhomogeneous model. The displacement at the source, based on the observed attenuation relationship, was about 60 mm for three magnitude 2.7 events. This is in agreement with slip values calculated using peak velocities and assuming the asperity as a Brune source within itself (72 mm). By using Madariaga's model for the asperity, the slip was over 3 times larger than observed. Peak velocity and acceleration scaling relations with magnitude were investigated by incorporating available South African data, appropriately reduced to Canadian geophysical conditions. The dynamic stress drop scaled as the square root of the seismic moment, similar to reported results in the literature for crustal earthquakes. This behavior suggests that the size of the asperities responsible for the peak ground motion, with respect to the overall source size, follow distributions that may be similar over a wide range of magnitudes. Measurements of source rupture complexity (ranging from 2 to 4) were found to agree with estimates of overall source to asperity radii, suggesting, together with the observed low rupture velocities (0.3 β to 0.6 β), that the sources were somewhat complex. Validation of source model appropriateness was achieved by direct comparison of the predicted ground motion level to observed underground damage in Creighton mine, located within the same regional stress and geological regime as Strathcona mine. Close to the source (<100 m), corresponding to relatively higher damage levels, a good agreement was found between the predicted peak particle velocities for the inhomogeneous model and velocities derived based on established geomechanical relationships. The similarity between asperity radii and the regions of the highest observed damage provided additional support for the use of the inhomogeneous source model in the assessment of damage potential.
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Although the Brune source model describes earthquake moment release as a single pulse, it is widely used in studies of complex earthquakes with multiple episodes of high moment release (i.e., multiple subevents). In this study, we investigate how corner frequency estimates of earthquakes with multiple subevents are biased if they are based on the Brune source model. By assuming complex sources as a sum of multiple Brune sources, we analyze 1,640 source time functions (STFs) of Mw 5.5-8.0 earthquakes in the SCARDEC catalog to estimate the corner frequencies, onset times, and seismic moments of subevents. We identify more subevents for strike-slip earthquakes than dip-slip earthquakes, and the number of resolvable subevents increases with magnitude. We find that earthquake corner frequency correlates best with the corner frequency of the subevent with the highest moment release (i.e., the largest subsevent). This suggests that, when the Brune model is used, the estimated corner frequency and therefore the stress drop of a complex earthquake is determined primarily by the largest subevent rather than the total rupture area. Our results imply that the stress variation of asperities, rather than the average stress change of the whole fault, contributes to the large variance of stress drop estimates.
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ABSTRACT Although the Brune source model describes earthquake moment release as a single pulse, it is widely used in studies of complex earthquakes with multiple episodes of high moment release (i.e., multiple subevents). In this study, we investigate how corner frequency estimates of earthquakes with multiple subevents are biased if they are based on the Brune source model. By assuming complex sources as a sum of multiple Brune sources, we analyze 1640 source time functions of Mw 5.5–8.0 earthquakes in the seismic source characteristic retrieved from deconvolving teleseismic body waves catalog to estimate the corner frequencies, onset times, and seismic moments of subevents. We identify more subevents for strike-slip earthquakes than dip-slip earthquakes, and the number of resolvable subevents increases with magnitude. We find that earthquake corner frequency correlates best with the corner frequency of the subevent with the highest moment release (i.e., the largest subsevent). This suggests that, when the Brune model is used, the estimated corner frequency and, therefore, the stress drop of a complex earthquake is determined primarily by the largest subevent rather than the total rupture area. Our results imply that, in addition to the simplified assumption of a radial rupture area with a constant rupture velocity, the stress variation of asperities, rather than the average stress change of the whole fault, contributes to the large variance of stress-drop estimates.
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Abstract Time and frequency domain analyses are applied to strong motion data recorded in Friuli, Italy, during 1976 to 1977. An inversion procedure to estimate spectral parameters (low frequency level, corner frequency, and high frequency decay) has been applied to displacement spectra using a simple earthquake source model with a single corner frequency. The data were digitized accelerograms from ENEA-ENEL portable and permanent networks. Instrument-corrected SH waves were selected from a set of 138 three-component, hand-digitized records and 28 automatically digitized records. Thirty-eight events with stations having 8 to 32 km epicentral distance were studied. Different stress drop estimates were performed showing high values (200 to 300 bars, on the average) with seismic moments ranging from 2.8 × 1022 to 8.0 × 1024 dyne-cm. The observation of systematic higher values of Brune stress drop (obtained from corner frequencies) with respect to other time and frequency domain estimates of stress release, and the evidence on time series of multiple rupture episodes suggest that the observed corner frequencies are most probably related to subevent ruptures rather than the overall fault size. Seven events recorded at more than one station show a good correlation between rms, Brune, and dynamic stress drops, and a constant scaling of this parameter as a function of the seismic moment. When single station events are also considered, a slight moment dependence of these three stress drop estimates is observed differently. This may be explained by an inadequacy of the ω−2 high-frequency decay of the source model or by high-frequency attenuation due to propagation effects. The high-frequency cutoff of acceleration spectra indicates the presence of an Fmax in the range of 5 to 14 Hz, except for the stations where local site effects produce spectral peaks.
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Although the Brune source model describes earthquake moment release as a single pulse, it is widely used in studies of complex earthquakes with multiple episodes of high moment release (i.e., multiple subevents). In this study, we investigate how corner frequency estimates of earthquakes with multiple subevents are biased if they are based on the Brune source model. By assuming complex sources as a sum of multiple Brune sources, we analyze 1,640 source time functions (STFs) of Mw 5.5-8.0 earthquakes in the SCARDEC catalog to estimate the corner frequencies, onset times, and seismic moments of subevents. We identify more subevents for strike-slip earthquakes than dip-slip earthquakes, and the number of resolvable subevents increases with magnitude. We find that earthquake corner frequency correlates best with the corner frequency of the subevent with the highest moment release (i.e., the largest subsevent). This suggests that, when the Brune model is used, the estimated corner frequency and therefore the stress drop of a complex earthquake is determined primarily by the largest subevent rather than the total rupture area. Our results imply that the stress variation of asperities, rather than the average stress change of the whole fault, contributes to the large variance of stress drop estimates.
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Dynamic stress
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SUMMARY Time-domain analyses of seismic waveforms have revealed diverse source complexity in large earthquakes (Mw > 7). However, source characteristics of small earthquakes have been studied by assuming a simple rupture pattern on the frequency domain. This study utilizes high-quality seismic network data from Japan to systematically address the source complexities and radiated energies of Mw 3–7 earthquakes on the time domain. We first determine the apparent moment-rate functions (AMRFs) of the earthquakes using the empirical Green's functions. Some of the AMRFs show multiple peaks, suggesting complex ruptures at multiple patches. We then estimate the radiated energies (ER) of 1736 events having more than ten reliable AMRFs. The scaled energy (eR = ER/M0) does not strongly depend on the seismic moment (M0), focal mechanisms, or depth. The median value of eR is 3.7 × 10−5, which is comparable to those of previous studies; however, eR varies by approximately one order of magnitude among earthquakes. We measure the source complexity based on the radiated energy enhancement factor (REEF). The values of REEF differ among earthquakes, implying diverse source complexity. The values of REEF do not show strong scale dependence for Mw 3–7 earthquakes, suggesting that the source diversity of smaller earthquakes is similar to that of larger earthquakes at their representative spatial scales. Applying a simple spectral model (e.g. the ω2-source model) to complex ruptures may produce substantial estimation errors in source parameters.
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