Resolution of the slow earthquake/high apparent stress paradox for oceanic transform fault earthquakes

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B9, 2444, doi:10.1029/2002jb002312, 2003 Resolution of the slow earthquake/high apparent stress paradox for oceanic transform fault earthquakes X. Pérez-Campos Department of Geophysics, Stanford University, Stanford, California, USA J. J. McGuire Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USA G. C. Beroza Department of Geophysics, Stanford University, Stanford, California, USA Received 15 November 2002; revised 8 April 2003; accepted 12 May 2003; published 26 September 2003. [1] Oceanic transform fault earthquakes exhibit some interesting and apparently contradictory properties. A number of earthquakes on oceanic transforms have been identified as slow on the basis of their weak seismic radiation at high frequencies. On the other hand, transform fault events as a population have been found to have high apparent stress, indicating strong high-frequency radiation since the seismic energy is concentrated at and above the corner frequency. In an attempt to reconcile these observations, we analyze seventy 5.8 M w 8.3, strike-slip earthquakes from around the world. Four of these earthquakes have both exceptionally low apparent stress and large centroid time shifts for their seismic moment. All four of them are located on oceanic transform faults. If we include these events in the population, we find that continental and oceanic strike-slip earthquakes are not significantly different in their mean apparent stress but that there is greater variation for oceanic events. We also find that in contrast to the low correlation between centroid time shift and apparent stress for continental earthquakes, the oceanic ridge transform earthquakes have a high correlation between these two parameters. We also observe cases of both ordinary and slow earthquakes on adjacent sections of the same transform. These characteristics suggest significant differences in the faulting process between oceanic transforms and continental faults. INDEX TERMS: 7209 Seismology: Earthquake dynamics and mechanics; 7215 Seismology: Earthquake parameters; 7299 Seismology: General or miscellaneous; KEYWORDS: transform fault, slow earthquake, seismic energy, apparent stress Citation: Pérez-Campos, X., J. J. McGuire, and G. C. Beroza, Resolution of the slow earthquake/high apparent stress paradox for oceanic transform fault earthquakes, J. Geophys. Res., 108(B9), 2444, doi:10.1029/2002jb002312, 2003. 1. Introduction [2] A number of studies have found that earthquakes located on oceanic transforms are slow in that the rupture process is of unusually long duration given the seismic moment. In contrast, Choy and Boatwright [1995] observed that oceanic transform earthquakes have some of the highest levels of apparent stress, t a = me s /M 0, (rigidity modulus, m, times the ratio between the seismic energy, E s, and seismic moment, M 0 ) [Wyss and Brune, 1968], of any tectonic regime. Choy and McGarr [2002] also observed high apparent stresses for oceanic strike-slip earthquakes, and many of these events occurred near plate boundary triple junctions. [3] Slow earthquakes are identified by their anomalously large amplitudes at low frequencies. This signature has been seen in body waves by Kanamori and Stewart [1976] and Okal and Stewart [1982], who observed discrepancies Copyright 2003 by the American Geophysical Union. 0148-0227/03/2002JB002312$09.00 between magnitudes measured at long and short periods for earthquakes on transform faults. In surface waves, Shearer [1994] noticed that some transform earthquakes appeared anomalously strong in their low-frequency surface wave amplitudes relative to their predicted M S. Stein and Pelayo [1991] and Prozorov and Hudson [1983] observed that transform fault earthquakes had systematically larger M S compared to their body magnitude, m b, relative to other earthquakes. In free oscillations, Beroza and Jordan [1990] detected slow earthquakes with anomalously large characteristic durations, many of which were on oceanic transforms. Other researchers have observed an extremely slow rupture component, on the order of 100 s, for earthquakes located on ocean transforms [e.g., Ihmlé and Jordan, 1994; McGuire et al., 1996]. All these results suggest that oceanic transform fault earthquakes are enriched in low-frequency waves and depleted in high-frequency waves. On the other hand, most seismic energy is radiated around the corner frequency and at shorter periods, so a high apparent stress implies that earthquakes on ocean transforms are unusually ESE 15-1

ESE 15-2 PÉREZ-CAMPOS ET AL.: SLOW EARTHQUAKE/HIGH APPARENT STRESS rich in high frequencies. Thus it seems contradictory to have both behaviors for oceanic transform earthquakes. [4] In this paper, we address the origin of this inconsistency. We estimate the apparent stress and obtain the centroid time shift, t (centroid time minus the origin time) for a population of 70 strike-slip earthquakes, located in both oceanic and continental crust (Figure 1). The oceanic earthquakes occurred either at ridge-ridge transforms or near subduction zones. We find four events with an anomalously large t given their M 0, that are accompanied by a low t a (Table 1). The low apparent stress is a consequence of their deficiency in high-frequency radiation, as reflected in their source spectra. We identify these events as slow earthquakes. These earthquakes tend to be excluded from the National Earthquake Information Center (NEIC) seismic energy analysis, due to their inherently low signal-to-noise ratio (SNR) between 0.1 and 1.0 Hz. When these earthquakes are included in the estimation of the average apparent stress of the oceanic transforms, the value we find is not significantly different than for other populations. Thus the resolution of the paradox is that there is a population of slow, low apparent stress earthquakes on oceanic transforms that have heretofore been excluded from routine analysis. Figure 1. Location of earthquakes. The gray scale represents t a, and the size of the symbols is proportional to t. The key at the bottom gives t and t a value of each symbol for a moment of 1 10 18 N m. The stars indicate the location of the four earthquakes identified as slow. 2. Large Centroid Time Shift [5] We select 70 strike-slip earthquakes, from 1992 to 2002, with moment magnitudes from 5.8 to 8.3, located both in oceanic or continental crust (Figure 1). These earthquakes were selected from the total population for these years based on their magnitude (M w > 5.5), the number of teleseismic stations that recorded the event (a minimum of three), and a fair SNR at high frequencies. For each earthquake, we use the t, location, focal mechanism, and M 0 from the Harvard centroid moment tensor (CMT) catalog [Dziewonski et al., 1981]. We identify Figure 2. Scaling of centroid time shift with moment. Gray symbols represent earthquakes with large t with respect to their M 0. Outlined symbols are the earthquakes identified as slow, with both high t given their M 0 and low t a. They are labeled with their source region. Solid line represents the regression of the data, and dashed lines are the 95% confidence interval. Figure 3. Moment normalized centroid time shift versus apparent stress. t has been normalized by the cube root of M 0 and referenced to M 0 =110 18 N m. Triangles are for continental earthquakes; squares are for oceanic events, excluding those at ridge or rise transforms, which are shown as solid circles; gray symbols are earthquakes with large t with respect to their M 0 ; outlined symbols are for the identified slow events. Solid lines represent the best fit for each population. Dashed lines are the 95% confidence intervals of the regressions. Thin black lines are for continental events; thin gray lines are for oceanic events (excluding ridge and rise transforms); and thick black lines are for ridge and rise transform events.

PÉREZ-CAMPOS ET AL.: SLOW EARTHQUAKE/HIGH APPARENT STRESS ESE 15-3 Table 1. Ridge Transform Earthquakes a Transform Event Date Latitude, deg Longitude, deg f s, d, l, deg M 0,Nm Mw t a,mpa t, s Owen 950526 26 May 1995 11.75 57.55 210, 64, 0 6.08E18 6.5 0.01 19.1 Owen b 960328 28 March 1996 12.01 57.72 208, 64, 2 1.60E18 6.1 1.51 2.9 Owen b 961001 1 Oct. 1996 12.30 57.89 207, 73, 7 4.90E18 6.4 20.20 7.8 Romanche 940314 14 March 1994 0.88 23.03 262, 61, 177 4.11E19 7.0 0.12 25.4 Romanche b 950518 18 May 1995 0.63 21.87 261, 73, 178 1.80E19 6.8 1.24 10.5 Conrad 950523 23 May 1995 55.89 2.14 353, 77, 166 1.48E19 6.7 0.20 15.8 Chile 970511 11 May 1997 36.46 98.23 93, 76, 174 6.04E18 6.5 0.17 10.4 Chile b 970529 29 May 1997 36.03 102.41 94, 82, 177 5.86E18 6.4 11.68 4.0 a Location, focal mechanism, moment, and t were obtained from Harvard CMT catalog. Depth of the events is 15 km, reported by the CMT Harvard catalog. Read 6.08E18 as 6.08 10 18. b Event was not identified as slow earthquake. potential slow earthquakes by their large centroid time shift for a given seismic moment. [6] Overall, the centroid time shift scales with seismic moment; as t / M 0 1/3, as predicted by a constant stress drop assumption; however, it is evident that for a given M 0, there are some earthquakes with an anomalously large t (Figure 2). These large t could be explained as a result of multiple events (e.g., the 10 May 1995 Iran earthquake [Berberian et al., 1999]) or as a result of long rupture durations due to low rupture velocities, which suggests a low apparent stress (i.e., low amplitudes at high frequencies). From the population of earthquakes with large t, we find that only four of them also have low apparent stress (Table 1). NEIC routinely estimates E s for events of M w Figure 4. Options for having a long centroid time shift. (left) In the time domain and (right) in the frequency domain. The centroid time shift is larger for the multiple and the slow event in contrast to the ordinary event, but the corner frequencies are different, being fc 1 fc 2 fc 3. This is assuming an omega square model for the spectral decay [Aki, 1967].

ESE 15-4 PÉREZ-CAMPOS ET AL.: SLOW EARTHQUAKE/HIGH APPARENT STRESS 15 14 13 12 11 10 9 30 0 ATD 0 30 60 90 960328 961001 950526 8 54 56 58 60 62 Figure 5. (bottom) Location of the three events on the Owen transform and (top) the location of station ATD ( =15 ). 5.5 using the technique of Choy and Boatwright [1995]; however, energy was computed for only one of the four identified slow earthquakes (14 March 1994) owing to their low SNR at 0.1 1 Hz. This criterion for choosing what events to analyze will bias the data set to exclude slow events, and we believe it is the major source of the slow earthquake/high apparent stress paradox for oceanic transform fault earthquakes. 3. Low Apparent Stress [7] We estimate E s for all the earthquakes using the technique described by Boatwright and Choy [1986], as modified by Pérez-Campos and Beroza [2001] and Pérez- Campos et al. [2003]. We use the IASP91 velocity model [Kennett, 1991] for continental earthquakes and an oceanic crustal velocity model for oceanic earthquakes [Gaherty et al., 1996]. We use a slightly different attenuation model than Choy and Cormier [1986], Boatwright and Choy [1986], or Boatwright et al. [2002]. This model not only has a stronger attenuation at all frequencies but also depends on the source region, with a stronger attenuation correction at high frequencies, above 0.3 Hz, for earthquakes originating in subduction zones. We adopt the new attenuation model based on the observation that at subduction zones, such as Japan, attenuation is stronger than the global average [e.g., Boatwright and Choy, 1989]. Also, Pérez- Campos et al. [2003] found that to reconcile local and teleseismic seismic energy estimates for earthquakes in the subduction zone of Mexico, the attenuation correction had to be stronger at high frequencies than average global models. [8] We also include a site correction. Since Global Seismic Network (GSN) stations are mostly located at hard rock sites, we used a site correction for a hard rock environment [Boore and Joyner, 1997; Boatwright et al., 2002; Pérez-Campos et al., 2003]. This correction takes into account the amplification and attenuation at the station, is frequency dependent, and tends to reduce estimates of the seismic energy, since it predicts amplification. Since we used the weighting scheme proposed by Pérez-Campos and Beroza [2001], we are accounting for known uncertainties in the location, depth, focal mechanism, and corner frequency in the seismic energy estimation. [9] We calculate t a using the corrected E s estimates and find that the mean apparent stress for the four identified earthquakes, t a = 0.09 + 0.22/ 0.06 MPa, is much lower than for the other oceanic earthquakes, either ridge transform or subduction events, t a = 1.51 + 3.41/ 1.05 MPa. However, the mean t a for earthquakes in continental crust (2.00 + 4.12/ 1.35 MPa) is not significantly different than that for earthquakes in oceanic crust (1.41 + 4.62/ 1.08 MPa) or for ridge transform fault events (1.22 + 7.62/ 1.05 MPa) once we included the four events with low apparent stress. We note that all four slow earthquakes are located near or on ridge-ridge oceanic transforms not on continents or in other tectonic settings. [10] Figure 3 shows the centroid time shift normalized by the cube root of the seismic moment and referenced to M 0 = 1 10 18 N m, against the apparent stress. The continental earthquakes are indistinguishable from the oceanic earthquakes (subduction and ridge transform) in this plot, with some scatter and a low correlation coefficient (0.1 and 0.2, respectively); however, the ridge transform events including the four identified earthquakes, represent a different population with a larger correlation coefficient of 0.65. These four events are characterized by both a very low apparent stress and a large centroid time shift (Table 1) and can be classified as slow earthquakes. Their spectra indicate that they are deficient in high-frequency seismic radiation. 4. Signal Characteristics [11] For two earthquakes with the same moment, we expect to observe very different signals, both in the time and the frequency domains, for a simple event, a multiple event, and a slow event. For the first two, the spectra might be similar, with similar corner frequency and spectral decay but with larger centroid time shift for the multiple event. When we compare against a slow event, the centroid time shift might be as large as that for a multiple event; however, the spectrum is going to be different, with a much lower corner frequency for the slow earthquake (Figure 4). [12] We compare three earthquakes with similar seismic moment and focal mechanism, all located in the Arabian Sea on the Owen transform fault (950526, 960328, and 951001) (Figure 5). Even though they have similar M 0, their t are very different (Table 1). This should be reflected in

PÉREZ-CAMPOS ET AL.: SLOW EARTHQUAKE/HIGH APPARENT STRESS ESE 15-5 Figure 6. (top) Comparison of the smoothed source spectrum of the slow event (black) and the regular events (gray). (bottom) Comparison of the accumulation of the seismic energy released by each event with respect to frequency. The smoothed spectra were obtained using a loess function, with a linear interpolation for a neighborhood parameter of 0.5 [Cleveland, 1993]. their corner frequency if the 1995 event is not a multiple earthquake. The fact that they have a different t a should be apparent in different high-frequency amplitudes. Comparing the source spectra of these earthquakes, the regular earthquakes have a higher corner frequency than the slow event. At 0.05 Hz, the seismic energy is comparable for these earthquakes, after that, the slow event is depleted (Figure 6), and overall it radiated only 5% of the total energy of the fast event despite having a slightly larger seismic moment. [13] In Figure 7, we compare the two of these earthquakes that were recorded at the station ATD (Figure 5). This station is a nearby, quiet GEOSCOPE station ( = 15 ) that recorded both earthquakes with high SNR at high frequencies. The broadband signals are very different for the two events. After applying progressively lower, lowpass two-pole Butterworth filters, down to 20 s, the time signals become increasingly similar. If we track the cumulative energy with increasing frequency, the signals accumulate energy at the same rate up to 0.05 Hz, but at higher frequencies, the slow event is depleted. It is also interesting to note that after applying the filters of 10 and 20 s, the arrival times are the same but the two events exhibit a difference in the slope of the initial pulse. [14] Abercrombie and Ekström [2003] have argued that at least some, and perhaps all, previous identifications of slow earthquakes on oceanic transforms are suspect. Much of this argument is based on the effect of crustal structure in the source region on surface wave amplitudes and on the uncertainties in modeling procedures. Our observations of the P waves of the two Owen transform earthquakes suggest that some oceanic transform earthquakes are indeed slow. We observe that all four of the events we identified have spectra depleted at frequencies above 40 mhz, allowing us to classify them as slow earthquakes. All of these are on oceanic transforms. [15] Owing to the limited frequency band (0.01 1 Hz) in which teleseismic P waves are well recorded for moderate sized (M w 6.5) transform earthquakes, the estimates of t a determined in this study do not directly address the connection between our observed slow earthquakes and those studied by previous authors using low-frequency (0.001 0.01 Hz) surface wave measurements [e.g., Shearer, 1994; Ihmlé and Jordan, 1994; McGuire et al., 1996; Abercrombie and Ekström, 2001]. What is resolved by our P wave derived estimates of t a is the existence of a population of M w 6.5 oceanic transform earthquakes (such as 950526 and 970511) with durations on the order of 20 40 s. These durations are a lower bound estimated from the inverse of the corner frequency [Boore, 1983]. These anomalous earthquakes appear to be sufficiently slow to cause the surface wave anomalies observed in other studies. For instance, Shearer [1994] used a matched filter approach applied to low-frequency (0.003 0.015 Hz) surface waves and found numerous oceanic transform earthquakes that had greater surface wave amplitudes than would be predicted by their M S (a measure of earthquake size using 20 second period surface waves). Many of these earthquakes were located on the Chile and Eltanin transform faults. Figure 8 shows seismograms at the low noise station LPAZ from the 970511 ( = 33 ), a M w 6.5, slow earthquake on the Chile transform (Table 1) compared to those of an ordinary event (970529, Table 1) on the same fault. The large centroid time shift of the low t a event is accompanied by a long ringing P wave in Figure 8a as

ESE 15-6 PÉREZ-CAMPOS ET AL.: SLOW EARTHQUAKE/HIGH APPARENT STRESS Figure 7. Comparison of the slow Owen transform event (thick black line) and the regular event (thin gray line) on the same transform recorded at station ATD. (left) Time domain signals and (right) the cumulative seismic energy with frequency. Top curves are the original signals aligned at the arrival times. The signals are very different for the two earthquakes. Bottom curves are after applying a low-pass twopole Butterworth filter at 2 s, 10 s, and 20 s. The time signals become increasingly similar, accumulating energy at the same rate up to 0.05 Hz, but at higher frequencies, the slow event is depleted. compared to the impulsive arrival shown for the high t a event. Figures 8b, 8c, and 8d present recordings of the first orbit rayleigh wave arrival at LPAZ. In both the raw (Figure 8b) and low-pass filtered (0.03 Hz corner, Figure 8c) the low t a event has a significantly smaller amplitude than the high t a event. It is only at periods longer than about 100 s (see Figure 8d) that the two events produce similar amplitudes. Thus measures of earthquake size based on M S, which is based on the amplitude of 20 s surface waves, would see this event as significantly smaller than would measures based on long period surface waves. 5. Discussion [16] Ide et al. [2003] observed a strong correlation between the apparent stress and the Brune stress drop for small earthquakes. If this were also valid for large earthquakes, our observations would imply that a slow event has a very small Brune stress drop, which seems to be unfeasible, since we would need an unrealistically large source dimension to match the given M 0. [17] A more plausible option is that the slip during the earthquake was slow and/or that the rupture velocity is low due to frictional properties of the transform faults. This suggests that the rupture process for transform faults may be different, radiating less energy as seismic waves and expending more energy as fracture energy. [18] Mikumo [1981] discussed the possibility of the occurrence of a slow earthquake and a normal earthquake on the same fault at different times, arguing that the strength of the asperities would become different at the time of a succeeding earthquake. In the case of the Owen transform earthquakes, given the Harvard CMT catalog locations, their rupture areas probably did not overlap, making it impossible

PÉREZ-CAMPOS ET AL.: SLOW EARTHQUAKE/HIGH APPARENT STRESS ESE 15-7 Figure 8. Vertical component broadband seismograms recorded at station LPAZ in South America for two M w 6.5 earthquakes on the Chile transform ( =33 ). The 11 May 1997 event was a low apparent stress, large centroid time shift earthquake and the 28 May 1997 event was an ordinary event. (a) Unfiltered P wave recordings for the two events, aligned on their largest amplitude arrivals (at about 150 s). The slow event s P wave begins about 15 s before its largest arrival, while the fast event begins with an impulsive large arrival. The slow event s P wave has been multiplied by a factor of 3 in amplitude to make it visible on the same scale. (b) Unfiltered recordings of the first orbit Rayleigh wave for the two events shown at the same scale. The slow event has a much smaller R1 amplitude at high frequencies. (c) and (d) The same Rayleigh wave records as Figure 8b after low-pass filtering with a corner frequency of 0.033 Hz and 0.01 Hz, respectively. At periods >100 s the two events have identical surface wave amplitudes (and hence estimated seismic moments), while at shorter periods the slow event appears significantly smaller. to rule out absolutely that the fault has different frictional properties in the two locations. The similarity of the propagation path for the two events, however, demonstrates that the anomalous nature of the slow event is a source, rather than a propagation effect. [19] The apparent stress is a measure of how energetic an earthquake is with respect to its size. For a given value of M 0 there is a wide range of values of t a [e.g., Choy and Boatwright, 1995; Pérez-Campos and Beroza, 2001]. This dispersion is at least partially explained by the uncertainty in the estimates of the seismic energy; however, we believe that after the improvements used in our analysis, the uncertainty is substantially reduced and that much of the dispersion observed in t a is real and a signature of the source. 6. Conclusions [20] From our analysis we conclude that slow earthquakes can be identified using a combination of a large centroid time shift and a low apparent stress. These earthquakes are deficient in high-frequency radiation, which distinguishes them from regular or multiple events. All of the slow strikeslip earthquakes we identified are located on oceanic ridge transform fault systems. When these low apparent stress

ESE 15-8 PÉREZ-CAMPOS ET AL.: SLOW EARTHQUAKE/HIGH APPARENT STRESS events are included in the calculation of characteristic t a, we cannot distinguish the average apparent stress between continental and oceanic events or between ridge transform earthquakes and events in other tectonic settings. The mean behavior of ridge transform earthquakes is characterized neither by slow earthquakes nor by high apparent stresses. They have regular events with high apparent stress but also slow events with low apparent stress that reduce the characteristic t a of the ridge transforms to average values of t a found for other tectonic settings. Our observations seem to indicate, however, that in terms of apparent stress, there is greater variation in the behavior of oceanic transform fault earthquakes than there is for continental strikeslip faults. Thus the apparent contradiction of oceanic transform earthquakes having both high apparent stress and a slow nature is resolved. 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Res., 73, 4681 4694, 1968. G. C. Beroza, Department of Geophysics, Stanford University, 397 Panama Mall, Stanford, CA 94305-2215, USA. (beroza@geo.stanford.edu) J. J. McGuire, Department of Geology and Geophysics, MS 24, Woods Hole Oceanographic Institution, Woods Hole, MA 02540, USA. (jmcguire@ whoi.edu) X. Pérez-Campos, Seismological Laboratory, MS 252-21, California Institute of Technology, 1200 East California Blvd., Pasadena, CA 94305-2215, USA. (xyoli@pangea.stanford.edu)