A rare foreshock sequence of the 20 January 2007 Odaesan, Korea, earthquake to measure the existence of preseismic velocity changes

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2012jb009232, 2012 A rare foreshock sequence of the 20 January 2007 Odaesan, Korea, earthquake to measure the existence of preseismic velocity changes David P. Schaff 1 and Won-Young Kim 1 Received 13 February 2012; revised 5 April 2012; accepted 11 May 2012; published 27 June [1] Dilatancy theory and laboratory studies predict that there may be changes in the velocity of seismic waves in the Earth s crust preceding large earthquakes due to cracks opening up in response to stress changes. These changes, however, have been extremely difficult to find in the field. Because we do not know where or when the next earthquake will strike, often there is not sufficient instrumentation to capture such a signal if it exists with active sources. But natural sources such as repeating earthquakes offer hope of measuring a preseismic signal. To date, however, they have not measured a preseismic signal, perhaps due to insufficient temporal sampling, especially if the signal is short lived. We examine a rare foreshock sequence of nine near-repeating events with fine temporal sampling all occurring within 3 days of the M w 4.6 main shock with the last event occurring an hour before. The nearest event occurred within 114 m of the main shock hypocenter. This presents a unique opportunity to measure preseismic velocity changes at the depth of the main shock, which is 9.4 km. Because the foreshocks are not exact repeats, slight position differences bias the velocity change measurements. The locations of these events are known precisely, however, which allows for us to correct for these biases by treating the events as a source array, improving the measurement precision by up to an order of magnitude. We observe no apparent preseismic velocity change signal, but we are able to place an upper bound on its existence ranging from 0.01% to 0.08%. Citation: Schaff, D. P., and W.-Y. Kim (2012), A rare foreshock sequence of the 20 January 2007 Odaesan, Korea, earthquake to measure the existence of preseismic velocity changes, J. Geophys. Res., 117,, doi: /2012jb Introduction [2] Coseismic and postseismic velocity changes are now well established and confirmed for many earthquakes using repeating events [e.g., Schaff and Beroza, 2004; Rubinstein and Beroza, 2004a, 2004b, 2005; Peng and Ben-Zion, 2006; Rubinstein et al., 2007] and controlled sources [Li et al., 1998, 2003, 2006; Li and Vidale, 2001]. Some clusters of repeating events have an event before the main shock enabling a coseismic measurement compared to the events after the main shock. Typically the coseismic velocity changes are on the order of a 3% decrease occurring in the unconsolidated materials at the surface or in highly damaged fault zones. In the postseismic period this change is often seen to heal following a logarithmic recovery [Schaff and Beroza, 2004; Peng and Ben-Zion, 2006]. [3] Temporal monitoring using ambient noise has also recently emerged as a new technique to measure velocity changes. Wegler and Sens-Schönfelder [2007] measured a coseismic velocity change of 0.6% for the 2004 M w Lamont-Doherty Earth Observatory, Earth Institute at Columbia University, Palisades, New York, USA. Corresponding author: D. P. Schaff, Lamont Doherty Earth Observatory, Earth Institute at Columbia University, 61 Rt. 9W, Palisades, NY 10964, USA. (dschaff@ldeo.columbia.edu) American Geophysical Union. All Rights Reserved /12/2012JB Mid-Niigata earthquake using ambient noise at a single station averaging over a single day at a time. The measurement precision they observed was on the order of 0.1%. There was no observable preseismic signal above the background scatter. Following a similar method using ambient noise on single day stacks, Ohmi et al. [2008] measured a 1.7% coseismic velocity change for the 2007 M w 6.6 Not Hanto earthquake, Central Japan. They report gradual changes in the time shifts of their measurements in the two weeks preceding the main shock. Both Brenguier et al. [2008] and Hadziioannou et al. [2011] observe a coseismic decrease in velocity and subsequent logarithmic postseismic healing for both the 2003 M w 6.5 San Simeon and 2004 M w 6.0 Parkfield earthquakes. They measure a coseismic decrease in velocity of 0.1% for the Parkfield earthquake. Cheng et al. [2010] measured a coseismic decrease of 0.4% for the M w 7.9 Wenchuan earthquake using ambient noise. The coseismic velocity changes measured by ambient noise are typically smaller than those measured by repeating events and controlled sources. One reason for this may be if the changes have shallow origin [e.g., Schaff and Beroza, 2004; Rubinstein and Beroza, 2004a, 2004b, 2005; Peng and Ben- Zion, 2006] and the longer wavelengths that sample deeper in the Earth s crust average out those changes. [4] Despite techniques being established to reliably measure coseismic and postseismic velocity changes, confirming the existence of a preseismic velocity change signal 1of16

2 associated with large earthquakes has still eluded us. These changes are predicted to exist based both on theoretical grounds and laboratory experiments. Perhaps the most familiar is dilatancy theory where cracks open up in response to stress changes before an impending earthquake [Brace et al., 1966; Scholz, 1968; Nur, 1972; Scholz et al., 1973]. The opening of the cracks causes the moduli of the material to be weaker and the velocity changes to decrease. Pore fluids can also be involved with the cracks also affecting the velocities of P and S waves differently. [5] One of the reasons why preseismic velocity changes have not been reliably observed with almost all existing techniques and data may be due to insufficient temporal sampling to resolve the presence of such a signal. Repeating aftershocks which follow Omori s law in frequency [Schaff et al., 1998] provide excellent temporal sampling to measure the postseismic velocity changes associated with large earthquakes since they occur frequently in the days and months following the earthquake where the signal is most rapidly changing. Since we do not know where or when the next earthquake will strike, campaign controlled source studies do not typically have the temporal sampling required to determine either a preseismic or coseismic velocity change signal, with the exception of Parkfield which had a data point before the main shock [Li et al., 2006]. Ambient noise monitoring has continuous measurements before and after the earthquake but there is a tradeoff with the number of days that are averaged over and the measurement precision. [6] A survey of the studies in the literature using repeating events reveal the difficulty in obtaining fine temporal sampling in the preseismic period. The 1994 Morgan Hill earthquake had repeating aftershocks but no events before because there were no digital data before 1984 [Schaff and Beroza, 2004]. For the 1989 Loma Prieta earthquake there were four clusters of repeating events that each had one event before so a coseismic measurement was possible but not preseismic measurements [Schaff and Beroza, 2004]. The multiplets on the Calaveras Fault for the Morgan Hill earthquake also measured the coseismic velocity change on the San Andreas Fault due to Loma Prieta. They had recurrence intervals of about a year just before the Loma Prieta earthquake and did not measure any preseismic velocity change with that temporal resolution [Schaff and Beroza, 2004]. Rubinstein and Beroza [2005] studied the 2004 Parkfield earthquake using two repeating event clusters. Both had events that occurred about a year before the main shock and so were probably too far out in time to capture a preseismic signal. Peng and Ben-Zion [2006] analyzed the 1999 İzmit and Düzce earthquakes which had 36 clusters of repeating events. The recurrence intervals in the preseismic period of the Düzce ranged from days to months. There was no apparent preseismic velocity change signal that could be clearly interpreted partly because the preseismic period for the Düzce earthquake overlapped with changes from the İzmit aftershock period. [7] The one exception to not being successfully observed in the field and the most convincing evidence for the existence of a preseismic velocity change for two earthquakes has come from a remarkable experiment at the Parkfield SAFOD drill site [Niu et al., 2008]. The experiment was conducted for two months with a piezoelectric source and a three-component accelerometer which were deployed inside the pilot and main boreholes at 1 km depth. Cross correlation was used to measure time delays in the stacked seismograms and corresponded to a detectable threshold of velocity perturbations of s or 11 ppm. Two significant excursions in the delay times emerged, the largest associated with a M 3 earthquake approximately 5 km away from the test site and a smaller anomaly associated with a M 1 earthquake 1.5 km away. The excursion for the larger earthquake began 10.6 h before the M 3 event and the deviation for the smaller earthquake began 2.5 h before the M 1 event. In both cases the magnitude of the preseismic signal was approximately equal to the magnitude of the coseismic velocity change perhaps because the measurements were taken at depth. The M 3 event was the largest event in the two month period whereas the M 1 event was the second closest event. The closest event was 1.3 km away from the site, but it was only an M 0.34 and so was not expected to produce a large change. The amazing sensitivity of this extremely well controlled experiment was able to reliably measure preseismic velocity changes, surprisingly, for events as small as M 1. Based on these two events, it appears that both the magnitude and duration of preseismic velocity changes scales with the magnitude of the future event. Therefore for larger earthquakes such as M 6s and 7s there is hope that a larger preseismic velocity change signal may exist for a longer time period leading up to the main shock. [8] The Parkfield experiment was unique and cost prohibitive to be done on a large scale. It would be beneficial to be able to confirm the results found in that experiment through alternate means such as naturally occurring repeating events or ambient noise. As we have seen above, though, it is rare to find repeating events with sufficient temporal sampling in the preseismic period. The reason for this probably lies in the physical mechanism of how repeating events are generated. A common model is that they occur on asperities or stuck patches embedded in a sea of creep that loads the fault and repeatedly sets up the same initial conditions for failure. Therefore the recurrence intervals are periodic at places such as Parkfield ranging from several months to years allowing enough stress to build up in the characteristic earthquake model [Nadeau et al., 1995; Waldhauser et al., 2004]. Either that or the events occur as repeating aftershocks in response to the stress of the main shock and have recurrence intervals that follow Omori s law [Schaff et al., 1998]. This seems to be the general case for repeating events that are true colocated within the location errors of a few meters. It appears to be physically impossible to rapidly rerupture the same fault patch after the stress has been relieved. In cases where events are not exactly colocated, however, it appears that triggering occurs and short recurrence intervals are observed. In this paper we present an analysis of a rare data set of nearly repeating foreshocks with the hopes of determining the existence of a preseismic velocity change. 2. Data and Technique [9] We use for data nine foreshocks that occurred before the 20 January 2007, Odaesan, Korea, M w 4.6 earthquake [Kim et al., 2010]. The data set is rare and unique for our 2of16

3 Table 1. Origin Times for Nine Foreshocks and the Main Shock Event Number Date Time (h:min:s.s) Days Before Main Shock 1 17 Jan :12: Jan :20: Jan :04: Jan :33: Jan :18: Jan :36: Jan :25: Jan :06: Jan :55: Jan :56: purposes for five reasons. The first is that the events are nearly colocated as determined by high-precision correlation-based double-difference relocations [Kim et al., 2010]. The second is that the events exhibit similar waveforms, which means that they also share similar magnitudes, source time functions, and focal mechanisms. These two factors make it possible to perform velocity change measurements using the doublet method [Poupinet et al., 1984]. The third reason why these foreshocks are such a unique data set is that they all occur within 3 days of the main shock. This addresses the temporal sampling problem of repeating events. Table 1 shows that the eighth foreshock occurs 1.5 days before the main shock and that the ninth foreshock occurs about an hour before. This is extremely close in time to the main shock. The fourth reason is that these foreshocks occur in close proximity to the main shock with the nearest event being only 114 m away. Most of the time repeating events occur a significant distance away from the main shock hypocenter. If velocity changes were to occur in a region localized to the area surrounding the main shock hypocenter they may be missed by measurements far away. Therefore these nearby foreshocks present a unique opportunity to measure the existence of preseismic velocity changes at the depth of the main shock which is 9.4 km [Kim et al., 2010]. Another factor is that when a regional earthquake occurs often there is not a sufficiently close permanent regional station for these types of analysis. Frequently, it is only after the fact that a local temporary deployment is installed to capture the aftershocks. It is fortuitous, however, that the Odaesan earthquake sequence had a nearby regional station located only 8 km in epicentral distance away. This is the fifth reason why this is a unique data set. Figure 1. Map of study area with 20 January 2007 main shock hypocenter (star) with mechanism and broadband, short-period, and accelerograph stations operating in various networks in South Korea. Eight stations whose data are analyzed in this study are indicated by the station-source paths (straight black lines). Concentric circles are every 50 km radial distance. 3of16

4 [10] Figure 1 displays the station map for the area. Station DGY of the Korea Meteorological Administration (KMA) is the station that is 8 km away. Many of the stations on the map did not have sufficiently good data to perform the velocity change analysis. We also looked at stations from the Korea Institute of Geology and Mineral Resources (KIGAM), and the Korea Institute of Nuclear Safety (KINS) in South Korea. It turns out that we need to have at least five of the nine foreshocks with good data at a station for our analysis. We present results for the S waves on the transverse components since the signal-to-noise ratio (SNR) was the strongest. The P waves and its coda were too weak on distant stations to obtain good results. The magnitudes of the foreshocks were relatively small ranging from 1.3 to 2.3 [Kim et al., 2010]. The waveforms were all filtered from 1 to 15 Hz. [11] Velocity changes are measured following the technique in Schaff and Beroza [2004]. It is a modification of the doublet technique in Poupinet et al. [1984]. The main difference is that we use time domain cross correlation instead of the cross spectral method because of its robustness. Subsample interpolation is done by fitting a quadratic to the five points surrounding the maximum. Delays are computed for a moving window at each sample in the waveform. The window lengths are 1 s. The velocity change is computed by fitting a line to the delays, dt, versus time in the waveform, t. The slope is equivalent to a constant velocity change in the volume through which the rays have traveled, dt = dv/v t, where v is the velocity and dv is the change in velocity [Poupinet et al., 1984]. [12] Instead of just measuring the delays relative to the first event as a master event, we make measurements for all possible pairs in the multiplet, dt ij, and use this redundancy to invert for the set of relative delays, t i, that are most consistent with the measurements [VanDecar and Crosson, 1990]. For example, in the case of four events: dt dt B t 13 1 CB C B dt 14 C B A t 2 t 3 t 4 C A ¼ dt 23 dt 24 dt 34 0 : C A The last row is added as a constraint for stability. The estimate delays, t i, are relative to the first event. This helps find the best fitting measurements for all the events as a cluster and minimize problems with the choice of the master event which may be less similar due to SNR or have bad data. 3. Results [13] Using the above described doublet method we show in Figure 2 six stations that had sufficiently good data to make velocity change measurements. The velocity changes are referenced to zero for the first event and plotted with event order for the nine foreshocks leading up to the main shock. Stations DGY, CHC, and JSB have measurements for all nine events. Stations SND and CHJ have measurements for seven of the nine events. Station WJU has five of the nine events. Stations YOW and SKC were also considered but were found to be unusable because they only had four events (see explanation in section 4). The magnitude of the velocity changes varies across the stations from 0.15% to 1%. A magnitude of 1% preseismic velocity change is extremely high considering the progression in the literature of placing a 0.1% upper bound on the existence of a precursory signal [e.g., Poupinet et al., 1984; Aster et al., 1990]. It is also high considering that coseismic changes are typically on the order of 3% for the S wave. The pattern of the velocity changes, however, is similar for the different stations at various azimuths. Events six and seven have unusually high values relative to the other events at all the stations where they are present. This suggests a near source effect either that common velocity changes are occurring in a small volume around the source or that some properties in the source characteristics of the foreshocks are the cause. [14] To test if the source characteristics of the foreshocks are influencing the measurements, we show in Figure 3 a scatterplot of the velocity change measurements with respect to source depth of the events. There is a strong positive correlation between these two parameters with five of the six stations showing correlation coefficients, r, of 0.9 or greater. The p values are all 0.01 or less indicating that these correlations are statistically significant at the 99% or more level. The red lines are least squares line fits to the data. Note that events 6 and 7 with the high values for the velocity changes also occur significantly deeper than the other events at 9.46 km. Thus it appears that the depths of the events are substantially affecting the velocity change measurements. [15] Figure 4 examines the locations of the events in greater detail in a depth cross section looking on to the fault. We note that all the events fall in approximately a 100 m square box. Some of the events are close separated by meters and can be considered true repeats, but the sequence taken as a whole is less than perfect repeating events. The average magnitude of the events is about 2 which for a 3 MPa stress drop has an estimated radius of 55 m. So these events do not all represent rerupture of the same overlapping fault surface. Events 6 and 7 are located close to each other at 9.46 km. Events 1 and 3 are about the same level and occur the shallowest about 100 m higher. The rest of the events occur at the 9.38 km level separated by only 3 m in depth. From visual inspection of DGY and CHC on Figure 2 it seems that the different depths of events 1 and 3 and 6 and 7 from the rest of the events are causing substantial variations in the velocity change measurements. Therefore for our next test we look at only events 2, 4, 5, 8, and 9 since they occur at the same depth within the errors of the relocation. [16] Figure 5 shows the velocity changes for the five events at a common depth of 9.38 km. The velocity changes are referenced to zero for event 2 and range from 0.02% to 0.5%. A general trend of velocity decrease leading up to the main shock is seen for most stations. This would be consistent with dilatancy theory where cracks are predicted to open up before an earthquake [e.g., Nur, 1972]. The measured temporal preseismic velocity change for these events, however, may be influenced again by the horizontal positions of the events. Figure 4 shows that there is a migration in time of the hypocenters across the fault to the southeast. If the temporal velocity change signal showed a trend but there was no migration of hypocenters for example if they occurred randomly we might be able to conclude that the temporal velocity change signal was real. 4of16

5 Figure 2. Velocity change measurements dv/v in percent as a function of event order for six stations. However, because the general trend of the velocity change signal coincides with the event order, we have to rule out the possibility that the measured velocity changes are not due to slight position differences. [17] Got and Coutant [1997] point out that less than perfect repeats can cause biases in velocity change measurements using the doublet technique. The maximum travel time delay, dt, between two events is when the relative position vector, dr, and the slowness vector, s, are parallel. The travel time delay varies as the cosine of the angle between the position vector and the slowness vector. For these nine foreshocks we have a priori information on the precise locations of the hypocenters from cross-correlationbased, double-difference relocations [Kim et al., 2010]. We can use this information to attempt to correct the delays for the known slight position differences. We do this by treating the events as a source array and inverting the differential times for the best fitting plane wave across the array described by the slowness vector according to the following equation: dt 12 x 1 x 2 y 1 y 2 z 1 z B dt 13 A ¼ x 1 x 3 y 1 y 3 z 1 z 3 s x B A s y A: s dt ij x i x j y i y j z i z z j The local coordinates of the hypocenters are given by x, y, and z. We perform a weighted least squares inversion using the square of the cross correlation coefficients as the weights. [18] The rationale for this approach is that since we know the positions of the events are not identical but separated by some distance, this will contribute to fluctuations in the delay measurements throughout the seismogram if the coda has a different azimuth and takeoff angles compared to the direct arrival. Therefore inverting for the best fitting slowness 5of16

6 Figure 3. Scatterplots of velocity change measurements dv/v versus depth of foreshocks. Crosscorrelation coefficients r are all positive and high, with low p values indicating 99% or higher statistical significance. Red lines are least squares line fits to the data. vector we can correct for these biases and assume that the residuals in the delay measurements that remain cannot be explained by a plane wave traveling across the source array. Then if any temporal signal in the velocity change measurements still exists we can infer that it is likely due to changes in the velocity of the medium and not position differences of the sources. [19] Following this procedure we show in Figure 6 the results of the slowness vector inversion as a function of time in the seismogram for station CHC. The mean cross correlation coefficients (CC) start out from 0.94 to 0.98 for the direct arrival and then gradually decrease throughout the coda to around 0.7 (Figure 6b). The slowness vector inversion for the direct arrival at zero time yields an expected S wave velocity of 3.6 km/s, an azimuth of 279, and a takeoff angle of 89 (Figures 6c 6e). The best fitting plane wave as a function of time in the seismogram shows slight fluctuations around the slowness vector of the direct arrival. This is consistent with results obtained by Dodge and Beroza [1997] who showed from studies using events as a source array that the dominant energy in the coda travels primarily in the same direction as the direct arrival. [20] Station DGY is only 8 km in epicentral distance from the events and has clear P wave arrivals along with coda which are shown in Figure 7a. The P wave comes in at 0.5 s and the S wave comes in at 2 s. The direct arrivals are relatively simple and have a short duration whereas the coda has much weaker SNR. This is reflected in the mean CC as a function of time in Figure 7b which is high around 0.95 for the direct arrivals and much lower for the coda. The inverted velocity for the direct P wave is 6.2 km/s at zero time (Figure 7c). This velocity persists until about 1.25 s where 6of16

7 Figure 4. On-fault view depth cross section of nine foreshocks annotated with event order. the moving window of length 1 s starts to be dominated by the large amplitude S wave arrival at 2 s (time on the x axis is relative to the beginning of the window). Then the inverted velocity drops for the next 3 s out to 4.25 s to values that are expected for the S wave. The red horizontal line is the predicted S wave velocity based on a Vp/Vs ratio of and matches quite well with the observed. The slowness vector in the inversion is unconstrained, but nevertheless, we see it is able to capture realistic P and S wave velocities with this source array. However, at 5 s the unconstrained velocity reaches unphysical values of 10 km/s. We note that this peak coincides with a valley in the mean CC values on Figure 7b so erroneous data may be the cause. The azimuth for the direct P wave is 82 like expected at zero time and the takeoff angle is 41. These values are fairly stable for the first 3 s, but show greater variability compared to the direct arrivals afterward which may be real or due to a decrease in coherence after 3 s. [21] Figure 8 demonstrates for station DGY how this procedure affects the velocity change measurements. In Figure 8a the original delay measurements versus time in the seismogram are shown for the nine events. Events 6 and 7 show a strong decreasing trend for the S wave revealed by the line fits leading to the strong positive measured velocity change of about 1%. Significant fluctuations are also observed in the delay times. Figure 8b displays the delays as a function of time in the seismogram corrected by the best fitting plane wave from the slowness vector inversion at each sample in Figure 7. It can be seen that the significant fluctuations in the delays have been substantially muted. The trends of the magenta line fits for the S wave have also flattened so that they are close to zero leading to much smaller variations in the velocity change measurements from the slopes. [22] Figure 9 displays that original velocity change measurement in blue for the six station that were shown on Figure 2. Also on Figure 9, the plane wave corrected velocity change measurements for each station are shown in red. The corrections for station DGY from Figure 8 indeed produce very small variations in the velocity change measurements that are flat and stable leading up to the main shock. This is the case for the other stations as well. Thus, there seems to be no apparent preseismic velocity change for this earthquake within the measurement resolution at these stations after correcting for possible biases due to known position differences. [23] The best that we can do is place an upper bound on the existence of any preseismic velocity change. We estimate an upper bound as the range in the measurements (maximum minus minimum) divided by two. This value includes all the scatter in the measurements and represents the number as plus or minus an amount above a zero base line reference. We interpret the upper bound to reflect the measurement precision of the technique assuming there is no velocity change and place a limit on the maximum possible velocity change if one exists. The upper bound on the preseismic velocity change measurements ranges from 0.01% at station SND to 0.08% at stations JSB and WJU (Figure 9). We also calculate the improvement in measurement precision from the upper bound of the original measurements in blue divided by the upper bound for the corrected measurements in red. The measurement precision is improved by up 7of16

8 Figure 5. Same as Figure 2 but considering only events at a common depth of 9.38 km for events 2, 4, 5, 8, and 9 to remove any influence on the velocity change measurements due to depth. Values are referenced to zero for event 2. to a factor of ten or an order of magnitude at stations DGY and CHJ and 8.2 at station SND (Figure 9). 4. Discussion [24] It is encouraging that the measurement precision for velocity changes for less than perfect repeats can be substantially improved by up to an order of magnitude, extending the usefulness of the doublet method to many more events, which holds promise for greatly increasing the temporal and spatial resolution in the preseismic period. We now discuss considerations and limitations of the plane wave correction procedure. It is known that the resolving power of the slowness vector depends on the geometry of the source array [e.g., Dodge and Beroza, 1997]. For example, consider the case where several events occur on a line in two dimensions. In this situation slowness vectors that travel parallel to the line are well resolved which correspond to stations off the ends of the array. On the other hand, stations that are perpendicular to the line have slowness vectors that are poorly resolved and weakly constrained. This is because slight errors in the positions of the events or the differential time measurements can cause large variability in the inverted slowness vector. It can even occur where the slowness vector flips in exactly the opposite direction from the true direction or in terms of azimuth a 180 change. [25] An example of this is seen for station CHJ in Figure 10. The azimuth of the direct arrival is at 210 in Figure 10d. The events in the source array occur on a vertical plane with a strike of 115. This means that station CHJ is oriented nearly perpendicular to the source array (95 ). In 8of16

9 Figure 6. (a) Waveforms for S wave and 10 s of its coda on the transverse component superposed for the nine foreshocks at station CHC (Figure 1). (b) Mean cross-correlation coefficient (CC) for a moving window of length 1 for each of the nine events. Inverted slowness vector for the plane wave correction as a function of time in the seismogram decomposed into (c) velocity, (d) azimuth, and (e) takeoff angle. Figure 10d the azimuth versus time remains close to the direct arrival up to 2 s. Then it drops sharply down to 45 for the remainder of the record except for flipping back briefly to the 210 value at 7.5 and 9.25 s. The difference in azimuth is 165 which is close to the 180 change illustrated above. The data appear pretty clean with the waveforms being very similar to the eye in Figure 10a and the mean CC values being very high throughout the coda. Therefore the most likely explanation for this behavior is not due to data problems but due to the resolving power of the source array because the station is nearly perpendicular to the strike of the fault. The true azimuth, then, is most likely not 45 but is closer to 210. The reason the inversion finds a value of 45 is probably due to errors in the determined locations of the events and measured delay times. [26] The effect that this behavior has on the plane wave corrections for the velocity change measurements is most likely minor. The inversion of the slowness vector finds the best fitting solution in a least squares sense given inconsistent data. The fact that the resolving power of the source array is not as strong perpendicular to the fault as compared to parallel to the strike means that the data can be fit nearly equally well by an azimuth of 210 as it can by 45. Therefore the residuals will be nearly the same for a true direction closer to 210. It is the residuals for the delays that we plot in Figure 8b and subsequently fit the lines to and determine the velocity changes from the slopes. Since the residuals have not changed much the velocity change measurements also will not change much. 9of16

10 Figure 7. (a e) Same as Figure 6 except for station DGY and it includes the P wave and its coda on the vertical component. Horizontal red line in Figure 7c is theoretical S wave velocity based on a Vp/Vs ratio of [27] Because the azimuth is poorly constrained it affects the other components of the slowness vector. Peaks and valleys in the azimuth on Figure 10d are strongly correlated with peaks in the velocity and takeoff angle. The velocity is unconstrained and reaches an unphysical 20 km/s at 1 s. This is because it corresponds to a change in azimuth and increase in takeoff angle to 140. The steeper takeoff angle means the projection of the relative position vector has a greater distance on the slowness vector and so a higher velocity is required for fixed differential times. Again, since the data show extremely high coherence at 1 s (Figures 10a and 10b) the explanation is most likely the same that the resolving power of the source array for the slowness vector at this station is poor and weakly constrained. Since these occur in isolated instances and the line fits are made for many data points that are weighted by the coherence we expect the influence on the velocity change measurements is minor. [28] In some sense we do not care about the resolving power of the source array because if the resolving power is poor then the plane wave correction is not as necessary. The resolving power of the source array depends on the geometry of the events. It is greatest where the x, y, and z dimensions are the greatest and weakest where they are the smallest. Therefore if the events are true repeats that are located exactly at a point it is impossible to constrain the plane wave traveling from the events to the station, because any plane wave will fit the data. But the case where we have true repeats is the ideal situation for making velocity change measurements in the first place because all unwanted path effects and position differences are removed. So if the events are separated in space the plane wave correction benefits, but 10 of 16

11 Figure 8. (a) Delay as a function of time in the seismogram for a 1 s moving window at station DGY. Delays are referenced to the first event, which is all zero for all times. The other eight events are plotted in multiples of 10 at the origin on the y axis in descending order. Events 6 and 7 are plotted at 50 ms and 60 ms, respectively. Magenta lines show portion of S wave and coda that is fit by least squares. The slopes of these lines correspond to the velocity change measurement. Bottom trace shows the waveforms superposed. (b) The same delays as in Figure 8a but corrected by finding the best fitting plane wave described by the slowness vector in Figures 7c 7e. if they are not the plane wave correction does not hurt, and it does not matter so much what the true slowness vector is. [29] Some further comments on the effect of location errors on our technique. The correlation measurements have associated measurement errors which are minimized in the inversion. The locations of the events have associated errors which are model errors in the inversion setup. The exact effect of these errors will depend on the characteristics of the errors themselves, the particular source array geometry and direction of the station. As we saw with the flipping of the azimuth in Figure 10d the most likely reason for this is because the dimension of the array in the perpendicular direction is small compared to the location errors and so resolving a plane wave traveling in that direction can be affected more by location errors. However, for a plane wave traveling along the array the dimensions of the array in that direction are much greater than the location errors and so the plane wave fit is not affected as much. The location errors for these foreshocks range from 6.9 m to 16.0 m (horizontal) and 11.3 m to 19.0 m (vertical) [see Kim et al., 2010, Table 2]. The along strike and depth dimensions of the source array are about 100 m on a side. This is nearly an order of magnitude greater than the locations errors, so we would expect the plane wave fit in these directions to be much better. It is these large separations of 100 m that cause the large biases in the velocity change measurements up to 1%. The fact that we are able to explain most of these biases with a simple plane wave fit indicates that the locations are sufficiently good enough to perform the correction. The more events in the source array the less effect the individual errors will have as well. [30] Another factor to consider in making the plane wave corrections is the discovery that there is a certain number of minimum events for various geometries of the source array. For example the minimum number of events required for exactly colocated events is two. The residuals in this case from any plane wave fit will reflect purely temporal changes and not artifacts from position differences. However, if these two events are separated by any amount and not exactly colocated at a point, then there is some slowness vector that will fit the delays between the events exactly and the residuals will artificially be zero. In this 1-D case where the events occur on a line the minimum number of events required for the plane wave correction is three as is illustrated in Figure 11a. Here the three events occur on a line with the delays in milliseconds next to them. There is no plane wave that can be fit to explain all the delays. For example, an S wave traveling at 3.5 km/s traveling from the east to the west would be able to explain the delays for the far left event and far right event but not for the middle event. Therefore the residuals after the plane wave correction could be expected to reflect temporal variations, which is what we want. If, however, these events with the same three delays were separated in 2-D space forming a plane as in Figure 11b there will be some slowness vector that will fit the delays exactly as illustrated. Notice that the 0.33 km/s velocity of the slowness vector is artificially low in this case (Figure 11b). 11 of 16

12 Figure 9. Same as Figure 2 with original velocity change measurements shown in blue. Plane wave corrected measurements are shown in red. The upper bound on the preseismic velocity change is listed in the subplot titles and is taken to be the range of the maximum and minimum change divided by two. The factor of improvement in measurement precision is also listed as the upper bound of the original measurements in blue divided by the upper bound of the corrected in red. [31] For the general case of a plane in two dimensions for the source array the minimum number of events to use the plane wave correction is four so that the residuals will not artificially be zero because the slowness vector can be fit exactly. By the same reasoning, extrapolating to three dimensions for general geometries of the source array, the minimum number of events is five. Even though our nine events occur on a fault they do not occur exactly on a plane. These slight deviations from a plane make the source array geometry 3-D and require five events for our analysis. This was discovered when we tried to make the plane wave correction for stations YOW and SKC which had only four events. The velocities of the inverted slowness vector were unphysically low around 0.15 km/s. The explanation for this is presented in Figure 11b. [32] Our results are that we observe no apparent preseismic velocity change for this earthquake using these data. This does not mean that a preseismic velocity change does not exist, but it places limits on its existence. For our data we can place an upper bound on the magnitude of the change to range from 0.01% to 0.08%. We can compare to the field experiment in the SAFOD drill site at Parkfield [Niu et al., 2008] which was successful in measuring a preseismic velocity change for two earthquakes. Reasons why we may not have detected a change if one existed may be that it was too small, too short of duration, or occurred in a volume not sampled by the raypaths. 12 of 16

13 Figure 10. (a) Waveforms for S wave and 10 s of its coda on the transverse component superposed for the nine foreshocks at station CHJ (Figure 1). (b) Mean cross-correlation coefficient (CC) for a moving window of length 1 for each of the nine events. Inverted slowness vector for the plane wave correction as a function of time in the seismogram decomposed into (c) velocity, (d) azimuth, and (e) takeoff angle. [33] For Parkfield, the magnitude of the preseismic signal was about the same as the coseismic signal. But these measurements were taken in a borehole at 1 km depth and so they were not as large as the coseismic velocity changes typically observed due to strong shaking of unconsolidated sediments at the surface. Therefore we would not expect a preseismic signal measured by repeating events to be as large as the coseismic signal of about 3%. [34] The Parkfield experiment measured excursions in the delay times that occurred 10.6 h and 2.5 h before the M 3 and M 1 earthquakes, respectively. The raw data were sampled every 27 s. Manual stacks of the data were sampled every 45 min. Table 1 shows that while we have much improved temporal sampling for repeating events with event eight occurring 1.5 days before the main shock and event nine occurring about an hour before the main shock, it still does not compare to the temporal resolution of the Parkfield experiment. If a preseismic signal for the Odaesan earthquake had a duration of only a few hours, it could only be measured by the last foreshock and constrained by one data point. [35] For the case of Parkfield the M 3 event occurred 5 km away from the source and receiver and the M 1 event occurred 1.5 km away. In this case the hypocenter of the M w 4.6 Odaesan earthquake occurs much closer to the sources of the repeating foreshocks with the nearest being only 114 m away. The nearest station is 8 km away in epicentral distance and the focal depth of the main shock is 9.4 km. The other stations are more distant and may not 13 of 16

14 Figure 11. Illustration of minimum number of events required in source array for different geometries. (a) Case of three events in a 1-D line with the delays in milliseconds annotated by each event. No slowness vector can explain all three delays, and so the residuals are expected to be temporal and not due to spatial differences. (b) Three events with the same delays but now in two dimensions forming a plane. In this case, a slowness vector shown by the arrow can fit the delays exactly with an artificially low velocity of 0.33 km/s. Any temporal signal in the delays will therefore be mapped into the spatial position differences and the residuals would be zero. Therefore, for this case it is necessary to have at minimum four events in two dimensions. have raypaths that would have sampled the volume of any possible preseismic velocity change. [36] We can also compare the upper bound for preseismic velocity changes determined in this study with other work using ambient noise temporal monitoring at Parkfield [Schaff, 2012]. For the ambient noise technique there is a tradeoff in the temporal resolution with the measurement precision depending on how many days are in the stack. However, we are also able to average over all the station/ component combinations giving 702 possible pairs which improves the measurement precision to help counteract this tradeoff with the desired goal of increased temporal resolution. From this work we consider a temporal resolution of 1 day stacks and we are able to measure a 95% confidence limit for an upper bound on preseismic velocity changes for the 2004 Parkfield earthquake to be %. This measurement precision is comparable to the 0.01% to 0.08% range found with the repeating foreshocks in this paper. The temporal resolutions are also similar with the repeating foreshocks being slightly better. For Parkfield the 13 borehole stations are closer, however, to the earthquake, all within 27 km of the main shock with the closest being 2.6 km away. 5. Conclusions [37] In summary, the main findings of this paper are listed below. Both vertical and horizontal separations as small as 100 m can significantly bias velocity change measurements using the doublet method. For some stations in our study such as DGY the biases were as high as 1%. Determining precise hypocenter locations for the repeating events, however, can allow for these biases to be minimized with a plane wave correction inverting for the best fitting slowness vector traveling across the source array. In order to apply this correction, it was discovered that it is necessary to have 5 or more events for the general case of most source array geometries in three dimensions. Fewer events are necessary in the ideal cases of a point, line, or plane. These corrections were demonstrated in this paper to improve measurement precision by up to an order of magnitude. This is good news because it extends the usefulness of the doublet technique to less than perfect repeats. This in turn increases the number of possible events that can be used, and offers potential to significantly increase temporal and spatial resolution in the preseismic period. [38] For the data presented here we observe no apparent preseismic velocity change before the 2007 Odaesan, Korea earthquake. The best we can do is place an upper bound ranging from 0.01% to 0.08%. This is quite low and comparable to the upper bound measured by ambient noise for the 2004 Parkfield earthquake which was % [Schaff, 2012]. These results come after a long history of searching for preseismic velocity changes and placing successively lower and lower limits on the upper bound as the techniques and data improved. In the early 1970s, premonitory changes in seismic wave velocity as large as 10 20% before earthquakes in Russia [Savarensky, 1968; Semenov, 1969], New 14 of 16

15 York [Aggarwal et al., 1973, 1975], and California [Whitcomb et al., 1973] were reported. Later studies of quarry blasts and man-made explosions, for which the location and origin time were known, showed no detectable changes in seismic velocity down to 1% for moderate earthquakes up to magnitude 5.4 [McEvilly and Johnson, 1974; Boore et al., 1975; Kanamori and Fuis, 1976; Bolt, 1977; Chou and Crosson, 1978]. Subsequent studies of repeating earthquakes appeared to confirm that velocity variations were nonexistent or at least very much smaller than found previously, on the order of 0.1% [Poupinet et al., 1984; Aster et al., 1990; Nadeau et al., 1994a, 1994b; Haase et al., 1995]. So as the measurement precision and techniques improved over time, the upper bound on possible preseismic velocity changes dropped by orders of magnitude from 10% to 1% to 0.1% and in this study as low as 0.01%. [39] Acknowledgments. 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