Rachel E. Abercrombie

Earthquake source scaling relationships from −1 to 5 ML using seismograms recorded at 2.5-km depth

The scaling relationships of earthquake sources less than about magnitude 3 have been the subject of considerable controversy over the last two decades. Studies of such events have shown a tendency for the constant stress drop, self similarity of larger earthquakes to breakdown at small magnitudes, and an apparent minimum source dimension of about 100 m has been observed. Other studies showed that this apparent breakdown in scaling could be an artifact of severe near-surface attenuation, limiting the spatial resolution of surface data. In this study, source parameters are determined for over 100 nearby, tectonic earthquakes, from recordings at a depth of 2.5 km (in granite) in the Cajon Pass scientific drill hole, southern California. Comparison of the seismograms recorded at this depth with those at the wellhead clearly demonstrates the effect of the severe attenuation in the upper kilometers of the Earths crust. Source parameters are calculated by spectral modeling of three-component P and S waves, assuming four source models based on the Brune ω−2 (n = 2) model. In model l, n = 2 is fixed, and Q of P and S waves is determined to be 912 (581–1433) and 1078 (879–1323), respectively (the numbers in parentheses are ±1 standard deviation). In model 2, QP = QS = 1000 is assumed and n is allowed to vary. The ω−2 model is a good average for the data set, but there is some real scatter supported by the data. In model 3, QP = QS = 1000 is also assumed and ω−2 is constrained, and in model 4, attenuation is ignored and n is allowed to vary. Source dimensions of less than 10m are observed for all four models, 10 times smaller than the proposed “minimum”. No breakdown in constant stress drop scaling is seen in the downhole data (approximately ML-1 to 5.5, M0 = 109 - 1016 Nm). The ratio between radiated seismic energy (estimated by integrating the velocity squared spectra with adequate signal bandwidth) and seismic moment appears to decrease gradually with decreasing moment in the magnitude range −1 to 7. This is not incompatible with a constant stress drop but could result from errors in calculating energy. The ratio of the S wave energy to that radiated by the P waves is about 14, after correction for attenuation. This low value is consistent with the corner frequency shift of about 1.3. This corner frequency shift is observed for all four source models and therefore is interpreted as being source controlled.

A Common Origin for Aftershocks, Foreshocks, and Multiplets

We demonstrate that the statistics of earthquake data in the global Cen- troid Moment Tensor (CMT) and National Earthquake Information Center (NEIC) catalogs and local California Council of the National Seismic System (CNSS) catalog are consistent with the idea that a single physical triggering mechanism is responsible for the occurrence of aftershocks, foreshocks, and multiplets. Specifically, we test the hypothesis that tectonic earthquakes usually show clustering only as a result of an initial earthquake triggering subsequent ones and that the magnitude of each trig- gered earthquake is entirely independent of the magnitude of the triggering earth- quake. Therefore a certain percentage of the time, as determined by the Gutenberg- Richter magnitude-frequency relationship, an earthquake should by chance be larger than or comparable in size to the earthquake that triggered it. This hypothesis predicts that the number of times foreshocks or multiplets are observed should be a fixed fraction of the number of aftershock observations. We find that this is indeed the case in the global CMT and NEIC catalogs; the average ratios between foreshock, aftershock, and multiplet rates are consistent with what would be predicted by the Gutenberg-Richter relationship with b 1. We give special attention to the Solomon Islands, where it has been claimed that unique fault structures lead to unusually high numbers of multiplets. We use Monte Carlo trials to demonstrate that the Solomon Islands multiplets may be explained simply by a high regional aftershock rate and earthquake density. We also verify our foreshock results from the more complete recordings of small earthquakes available in the California catalog and find that foreshock rates for a wide range of foreshock and mainshock magnitudes can be projected from aftershock rates using the Gutenberg-Richter relationship with b 1 and the relationship that the number of earthquakes triggered varies with triggering earthquake magnitude M as c10M, where c is a productivity constant and is equal to 1. Finally, we test an alternative model that proposes that foreshocks do not trigger their mainshocks but are instead triggered by the mainshock nucleation phase. In this model, the nucleation phase varies with mainshock magnitude, so we would expect mainshock magnitude to be correlated with the magnitude, number, or spatial extent of the foreshocks. We find no evidence for any of these correlations.

Source parameters of small earthquakes recorded at 2.5 km depth, Cajon Pass, southern California: Implications for earthquake scaling

A 2.5 km deep triaxial seismometer at Cajon Pass in southern California has recorded several hundred earthquakes <ML4.0 occurring within the San Andreas fault system. At 2.5 km seismic background noise is below amplifier sensitivity and the 2–250 Hz spectral range of recorded seismic motion is wider and higher than that of most natural event catalogs. Compared with downhole recorded motion, seismic amplitudes at the surface are amplified below 10 Hz and severely attenuated above 30 Hz. We estimate that QS is at least 1000 for wave motion at 2.5 km and below and QP is over 2000. The range of source dimensions in the downhole recorded catalog is ∼10 m to ∼70 m (ML∼−2.0, Mo∼108 Nm to ML∼2.7, Mo∼1013 Nm). The plot of log(source-radius) vs log(moment) has a straight line trend compatible with earthquake scaling at constant stress drop; inferred stress drops are scattered between 1 and 500 bars. There is no evidence in the catalog for the proposed minimum source dimension at ∼100 m. When the Cajon Pass borehole catalog, containing some of the smallest recorded natural earthquakes, is combined with 800 larger events from previous studies, the moment-radius trend suggests that natural earthquakes are self-similar over a magnitude range M∼−2 to ∼8. We suggest that inferences of minimum source dimension are more likely due to bias in bandlimited individual catalogs than to properties of the seismic crust.

Depth dependence of earthquake frequency-magnitude distributions in California: Implications for rupture initiation

Statistics of earthquakes in California show linear frequency-magnitude relationships in the range of M2.0 to M5.5 for various data sets. Assuming Gutenberg-Richter distributions, there is a systematic decrease in b value with increasing depth of earthquakes. We find consistent results for various data sets from northern and southern California that both include and exclude the larger aftershock sequences. We suggest that at shallow depth (∼0 to 6 km) conditions with more heterogeneous material properties and lower lithospheric stress prevail. Rupture initiations are more likely to stop before growing into large earthquakes, producing relatively more smaller earthquakes and consequently higher b values. These ideas help to explain the depth-dependent observations of foreshocks in the western United States. The higher occurrence rate of foreshocks preceding shallow earthquakes can be interpreted in terms of rupture initiations that are stopped before growing into the mainshock. At greater depth (9-15 km), any rupture initiation is more likely to continue growing into a larger event, so there are fewer foreshocks. If one assumes that frequency-magnitude statistics can be used to estimate probabilities of a small rupture initiation growing into a larger earthquake, then a small (M2) rupture initiation at 9 to 12 km depth is 18 times more likely to grow into a M5.5 or larger event, compared to the same small rupture initiation at 0 to 3 km.

The 1994 Java tsunami earthquake: Slip over a subducting seamount

On June 2, 1994, a large subduction thrust earthquake (Ms 7.2) produced a devastating tsunami on the island of Java. This earthquake had a number of unusual characteristics. It was the first recorded large thrust earthquake on the Java subduction zone. All of the aftershock mechanisms exhibit normal faulting; no mechanisms are similar to the main shock. Also, the large tsunami and the relatively low energy radiated by the main shock have led to suggestions that this earthquake might have involved slow, shallow rupture near the trench, similar to the 1992 Nicaragua earthquake. We first relocate the main shock and the aftershocks. We then invert long-period surface waves and broadband body waves to determine the depth and spatial distribution of the main shock slip. A dip of 12°, hypocenter depth of 16 km and moment of 3.5×l020 N m (Mw 7.6) give the best fit to the combined seismic data and are consistent with the plate interface geometry. The source spectrum obtained from both body and surface waves has a single corner frequency (between 10 and 20 mHz) implying a stress drop of ∼0.3 MPa. The main energy release was preceded by a small subevent lasting ∼12 s. The main slip occurred at ∼20 km depth, downdip and to the NW of the hypocenter. This area of slip is collocated with a prominent high in the bathymetry that has been identified as a subducting seamount. We interpret the Java earthquake as slip over this subducting seamount, which is a locked patch in an otherwise decoupled subduction zone. We find no evidence for slow, shallow rupture. No thrust aftershocks are expected if the entire locked zone slipped during the main shock, but extension of the subducting plate behind the seamount would promote normal faulting as observed. It seems probable that such a source model could also explain the size and timing of the observed tsunami.

Stress drops and radiated energies of aftershocks of the 1994 Northridge, California, earthquake

We study stress levels and radiated energy to infer the rupture characteristics and scaling relationships of aftershocks and other southern California earthquakes. We use empirical Green functions to obtain source time functions for 47 of the larger (M ≥ 4.0) aftershocks of the 1994 Northridge, California earthquake (M6.7). We estimate static and dynamic stress drops from the source time functions and compare them to well-calibrated estimates of the radiated energy. Our measurements of radiated energy are relatively low compared to the static stress drops, indicating that the static and dynamic stress drops are of similar magnitude. This is confirmed by our direct estimates of the dynamic stress drops. Combining our results for the Northridge aftershocks with data from other southern California earthquakes appears to show an increase in the ratio of radiated energy to moment, with increasing moment. There is no corresponding increase in the static stress drop. This systematic change in earthquake scaling from smaller to larger (M3 to M7) earthquakes suggests differences in rupture properties that may be attributed to differences of dynamic friction or stress levels on the faults.

Secondary Aftershocks and Their Importance for Aftershock Forecasting

The potential locations of aftershocks, which can be large and damaging, are often forecast by calculating where the mainshock increased stress. We find, however, that the mainshock-induced stress field is often rapidly altered by aftershock-induced stresses. We find that the percentage of aftershocks that are secondary aftershocks, or aftershocks triggered by previous aftershocks, increases with time after the mainshock. If we only consider aftershock sequences in which all aftershocks are smaller than the mainshock, the percentage of aftershocks that are secondary also increases with mainshock magnitude. Using the California earthquake catalog and Monte Carlo trials we estimate that on average more than 50% of aftershocks produced 8 or more days after M ≥5 mainshocks, and more than 50% of all aftershocks produced by M ≥7 mainshocks that have aftershock sequences lasting at least 15 days, are triggered by previous aftershocks. These results suggest that previous aftershock times and locations may be important predictors for new aftershocks. We find that for four large aftershock sequences in California, an updated forecast method using previous aftershock data (and neglecting mainshock-induced stress changes) can outperform forecasts made by calculating the static Coulomb stress change induced solely by the mainshock. Manuscript received 20 November 2002.

The 14 November 2001 Kokoxili (Kunlunshan), Tibet, Earthquake: Rupture Transfer through a Large Extensional Step-Over

The 14 November 2001 Kokoxili, Tibet, earthquake ( M w 7.8) ruptured ∼400 km of the western Kunlun fault in northern Tibet. We apply two inversion methods to P and SH waves recorded by the Global Seismographic Network to recover the spatial and temporal history of the rupture process. The observed surface rupture consists of two strike-slip segments, offset by an extensional step-over. Little surface rupture was observed in the graben system in this step-over, which is approximately 45 km long and over 10 km wide. Our results imply that the rupture did not jump this large gap, but that the rupture was continuous through the graben. The earthquake began with a small strike-slip subevent, presumably along the westernmost of the two segments. This was followed 5 sec later by a subevent of about the same magnitude but having an oblique mechanism with a large normal-faulting component. The likely location for this subevent is within the graben. This oblique-slip event probably enabled transfer of the rupture onto the main Kunlun fault. The main moment release began ∼18 sec after rupture initiation and propagated over 350 km eastward along the Kunlun fault. Slip on this segment was very heterogeneous, averaging ∼2 m for the first 200 km, followed by a sharp increase to a maximum of 7.5 m within the next 50 km, and then a rapid decline. The average rupture velocity along the main segment was high (∼3.6 km sec -1 ) and probably exceeded the local shear-wave velocity. The M w 7.8 Kokoxili earthquake had a longer surface rupture and faster average rupture velocity, radiated more energy, and probably had a lower average fracture energy than the November 2002, M w 7.9 Denali fault (Alaska) earthquake. Evidence suggests that the velocity of the rupture front dropped significantly after passing the point of maximum slip, implying a large difference in frictional strength between the two ends of the fault. Online material : Waveform fits to teleseismic body waves.

The magnitude-frequency distribution of earthquakes recorded with deep seismometers at Cajon Pass, southern California

A means for detecting wear of the exposed surface of a transparent member such as a sight glass, forming at least a portion of the wall of an enclosure such as a vessel or a conduit, containing a fluid capable of physically or chemically attacking such exposed surface, generally comprising a nontransparent means disposed on the transparent member on a line of sight therethrough, which when worn away either by physical or chemical action of the fluid will indicate that the exposed surface of the transparent member has worn away a predetermined amount.

Investigating uncertainties in empirical Green's function analysis of earthquake source parameters

I use a well-recorded earthquake sequence to investigate the uncertainties of earthquake stress drops calculated using an empirical Greens function (EGF) approach. The earthquakes in the largest (M ~ 2.1) repeating sequence targeted by the San Andreas Observatory at Depth (SAFOD), Parkfield, California, are recorded by multiple borehole stations and have simple sources, well-constrained stress drops, and abundant smaller earthquakes to use as EGFs. I perform three tests to estimate quantitatively the likely uncertainties to arise in less optimal settings. I use EGF earthquakes with a range of cross-correlation values and separation distances from the main earthquakes. The stress drop measurements decrease by a factor of 3 as the quality of the EGF assumption decreases; a good EGF must be located within approximately one source dimension of the large earthquake, with high cross correlation. I subsample the large number of measurements for the main earthquakes to investigate the expected stress drop uncertainties in studies where fewer stations or EGFs are available. If only one measurement is available, the uncertainties are likely to be at least 50%. The uncertainties decrease to <20% with five or more measurements; using multiple EGFs is a good alternative to multiple stations. To investigate the effects of limited frequency bandwidth, I recalculate the corner frequencies after progressively decimating the sample rate. Decreasing the high-frequency limit of the bandwidth decreases the estimate of the corner frequency (and stress drop). The corner frequency may be underestimated if it is within a factor of 3 of the maximum frequency of the signal.