Time dependence of PKP(BC) PKP(DF) times: could this be an artifact of systematic earthquake mislocations?

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1 Physics of the Earth and Planetary Interiors 122 (2000) Time dependence of PKP(BC) PKP(DF) times: could this be an artifact of systematic earthquake mislocations? Xiaodong Song Department of Geology, University of Illinois, Urbana, IL 61801, USA Received 5 June 2000; received in revised form 11 September 2000; accepted 13 September 2000 Abstract Differential inner core rotation was first detected from time-dependent observations of differential travel times between PKP(DF) waves (which go through the inner core) and PKP(BC) waves (which turn at the bottom of the outer core) (Song and Richards, 1996). Criticisms concerning the reported detection have been raised, the most significant one being the possible bias from potential systematic earthquake mislocations. In this study, I examine this issue by comparing both differential AB BC and BC DF times between pairs of events with similar locations and waveforms. The procedure is very similar to the doublet technique proposed recently by Poupinet et al. (2000), who concluded that the time dependence of the BC DF times from the earthquakes in South Sandwich Islands recorded at College, Alaska observed by Song and Richards (1996) is an artifact of earthquake mislocations. Because the difference in ray parameters between AB (another branch of PKP, which turns at the mid-outer core) and BC is more than twice the difference between BC and DF, systematic mislocations have much larger effect on differential AB BC times than on differential BC DF times. My analysis of similar event pairs for the South Sandwich Islands to College, Alaska path shows a clear time-dependence of increasing BC DF times over time. The AB BC times of these same event pairs do not show any increasing trend, rather, they show a decreasing trend. The results rule out the possibility that the observed time dependence of the BC DF times is caused by earthquake mislocation, providing strong support for the differential inner core rotation Elsevier Science B.V. All rights reserved. Keywords: Earthquake mislocations; Time dependence; Differential inner core rotation 1. Introduction The initial evidence for a differential rotation of the inner core came from the observations that seismic travel times through the inner core along certain paths have changed over time (Song and Richards, 1996). In particular, the differential travel times between the PKP(DF) waves (which go through the inner core) and PKP(BC) waves (which turn at the bottom of the outer core) along the pathway from the South Sandwich Islands (SSI) earthquakes to College, Alaska station Tel.: ; fax: address: xsong@uiuc.edu (X. Song). (COL) were shown to increase steadily by about 0.12 s per decade from 1950s to 1990s (Song, 2000a). The most important source of errors in interpreting the observed temporal variation as evidence for inner core rotation is systematic event mislocation. Because global stations used to locate the earthquakes are not exactly the same in different years, the temporal variation could potentially be an artifact of the changes of the station distributions. One way to check the mislocation issue is to examine differential travel times between PKP(AB) (another branch of PKP, which turns at the mid-outer core) and PKP(BC). Because the difference in the ray parameters between AB and BC is more than twice the difference between BC and DF, /00/$ see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S (00)

2 222 X. Song / Physics of the Earth and Planetary Interiors 122 (2000) systematic mislocations have much larger effect on differential AB BC times than on differential BC DF times. If the SSI earthquakes are consistently mislocated closer than COL by 16 km per decade than their actual locations, the BC DF residuals will increase by 0.10 s per decade (enough to explain the observed BC DF temporal change), but the AB BC residuals will increase by 0.25 s per decade. In another scenario, if the SSI earthquakes are consistently mislocated shallower by 50 km per decade than their actual depths, the BC DF residuals will increase by 0.05 s per decade (not enough to explain the observed BC DF temporal change), but the AB BC residuals will increase by 0.20 s per decade. For the SSI-COL path, which shows apparent increases in BC DF residuals over time, no such pattern is apparent for the AB BC times we measured from the same data set, indicating that systematic event mislocations are unlikely to be the cause of the apparent temporal variation in the BC DF residuals (Song and Richards, 1996). Poupinet et al. (2000) visited this issue with a novel doublet technique, also involving AB BC times. A doublet is a pair of earthquakes from repeated ruptures at the same location which exhibits identical waveforms. Doublets can be often observed in local microseisms (e.g. Poupinet et al., 1984; Gillard et al., 1996; Li et al., 1998). The high similarity of the whole waveforms (including not only the main arrivals but also the signal-generated noise in the coda waves) is the key to ensure that the two events indeed occur at the same location have the same source mechanism, and sample the same Earth structure. Unfortunately, ideal doublets like those found in microseisms have not been found for the SSI-COL path, in spite of the tremendous effort undertaken by Li and Richards (1999). Three examples of true doublets were found by these authors, but the events have proved too small to permit accurate measurement of relative times for these low amplitude DF arrivals. Nonetheless, Poupinet et al. (2000) measured the difference d(bc DF) between the differential BC DF times of a pair of events and the difference d(ab BC) between the differential AB BC times of the same pair. They then assessed the effect of earthquake locations using the {d(bc DF), d(ab BC)} measurements. One of the critical problems in their analysis, as discussed in Song (2000b), is that the doublets they selected have large d(ab BC) values, indicating the event pairs are in fact far apart. In this case, the interpretation of {d(bc DF), d(ab BC)} measurements is sensitive to biases from the 1D reference Earth model used and heterogeneities in the mantle and the inner core, leading to their erroneous conclusion that the temporal variation in the BC DF times is caused by mislocation (Song, 2000b). In this study, I re-examine event pairs for the SSI-COL path. I use a procedure very similar to the doublet technique as outlined in Poupinet et al. (2000), but choose event pairs that best resemble doublets in terms of location and waveform similarities discussed in details below. 2. Analysis of event pairs for the SSI-COL path The best cluster of events in the SSI seismicity is around ( 56.2, 27.4 ) (Song, 2000a). Three limiting conditions are set in selecting each pair from this cluster of events so that they best resemble ideal doublets. (1) All the events are within 50 km from the Table 1 South Sandwich Islands events used in this study a Date Latitude ( ) Longitude ( ) Depth (km) M b a The event locations are from Engdahl et al. (1998) except the three events in 1958, 1959, and 1998 whose locations are from Earthquake Data Report.

3 Table 2 Event pairs used in this study (time lapse >10 years) X. Song / Physics of the Earth and Planetary Interiors 122 (2000) Event 0 Event 1 d(bc DF) (s) d(ab BC) (s) CC DF CC BC CC AB dt (years) reference location ( 56.2, 27.4, 100 km), except events in the 1950s, whose locations are poorly determined (Song, 2000a). (2) The difference between AB BC times of each pairs, d(ab BC), is <0.5 s. (3) Each pair is compared visually to ensure that the waveforms are as similar as possible; and only those pairs with cross-correlation coefficients >0.5 between the DFs (of each pair), the BCs, and the ABs are selected. All the seismograms considered are vertical components at COL and have been converted to the same worldwide standardized seismograph network (WWSSN) short-period instrument response. Table 1 lists all the events selected. The earthquake locations are from the catalog of events relocated by Engdahl et al. (1998) (EHB), except the two events in the 1950s and the event , whose locations are from the USGS Earthquake Data Report (EDR). Tables 2 and 3 list all the event pairs used in this study. Like Poupinet

4 224 X. Song / Physics of the Earth and Planetary Interiors 122 (2000) Table 3 Event pairs used in this study (time lapse <10 years) Event 0 Event 1 d(bc DF) (s) d(ab BC) (s) CC DF CC BC CC AB dt (years) et al. (2000), I found the differential time difference d(bc DF) of each pair by measuring the time shift d(df) between the DF phases of the pair and the time shift d(bc) between the BC phases, separately, using waveform cross-correlation. The d(ab BC) was found by applying the same procedure to the BC and AB phases of the pair. The cross-correlation coefficients between the DFs, the BCs, and ABs of each pair are listed in Tables 2 and 3. The {d(bc DF), d(ab BC)} measurements are compared with mislocation bands determined for mislocations up to 50 km for three different reference models (Fig. 1): IASP91 (Kennett and Engdahl, 1991), PREM (Dziewonski and Anderson, 1981), and PREM2 (Song and Helmberger, 1995). Similar to Poupinet et al. (2000), I construct the mislocation bands by calculating the predicted values of {d(bc DF), d(ab BC)} for the 1D reference models for event pairs between the reference source ( 56.2, 27.4, 100 km) and all sources located within a cylinder of 50 km in horizontal and radial directions surrounding the reference source (i.e. 100 km in diameter and height). If the DF travel times change with time, the measured points d(bc DF), d(ab BC) should fall outside the mislocation band. Fig. 1 shows that the measurements between pairs with time lapses >15 years are all above the mislocation bands, consistent with the time-dependence in the BC DF times. The measurements between pairs with time lapses <5 years are scattered around mislocation bands, indicating no noticeable time dependence in such short durations within the resolution limit of the mislocation bands. Note the mislocation band for IASP91 is significantly different from those for PREM and PREM2 at d(ab BC) > 0.4 s. This is one of the reasons that it is important to use event pairs with small d(ab BC) values; it is also one of the reasons that Poupinet et al. (2000) erred on their conclusion as discussed in Song (2000b). Given certain knowledge of the location difference of each event pair, the d(bc DF) and d(ab BC) measurements can be examined separately as a

5 X. Song / Physics of the Earth and Planetary Interiors 122 (2000) Fig. 2. The measured BC DF time differences d(bc DF) between SSI event pairs are corrected for the differences in earthquake locations (Table 1) and the PREM model. The BC DF times show an increase of about 0.3 s over 30 years. Fig. 1. Comparisons between {d(bc DF), d(ab BC)} measurements (open circles) of similar event pairs and mislocation bands (lines). The event pairs (for the SSI-COL path) are listed in Tables 2 and 3. The mislocation bands are constructed by calculating the predicted values of {d(bc DF), d(ab BC)} for the 1D reference models for event pairs between the reference source ( 56.2, 27.4, 100 km) and all sources located within a cylinder of 50 km in horizontal and radial directions surrounding the reference source. The measurements between pairs with time lapses >15 years are all above the mislocation bands, consistent with the time-dependence of the BC DF times (top). The measurements between pairs with time lapses <5 years are scattered around mislocation bands, indicating no noticeable time dependence in such short durations (bottom). The increase in the BC DF times of about 0.1 s per decade on average is compatible with the previous direct measurements of BC DF times for the SSI-COL path (Song and Richards, 1996; Song, 2000a). Fig. 3 shows the measured AB BC time differences d(ab BC) after correcting for the earthquake locations (Table 1) and the PREM model. The data also function of the time duration between the two events. Fig. 2 shows the measured BC DF time differences d(bc DF) between the event pairs after correcting for the earthquake locations (Table 1) and the PREM model. The corrected BC DF time difference for each event pair is simply the measured BC DF time difference d(bc DF) minus the predicted difference between the BC DF times calculated using the given locations of the two earthquakes and the given earth model. The corrected d(bc DF) measurements clearly increase with the time lapses of the event pairs. Fig. 3. The measured AB BC time differences d(ab BC) between SSI event pairs are corrected for the differences in earthquake locations (Table 1) and the PREM model. The negative trend is opposite to the temporal trend in d(bc DF), suggesting that the temporal change in the BC DF times is not caused by event mislocations.

6 226 X. Song / Physics of the Earth and Planetary Interiors 122 (2000) Fig. 4. The measured d(bc DF) times are corrected for location differences using the corresponding d(ab BC) times divided by The factor 2.46 is the ratio of slowness differences between AB BC and BC DF for this path using PREM. show an intriguing temporal trend: a decrease of about 0.08 s in the AB BC times over a decade. Three possible causes of the negative trend are as follows. (1) The trend is real, perhaps reflecting a time-dependent structure in the bottom of the fluid outer core, which affects the BC arrivals. If the BC times are delayed steadily over time, both the d(bc DF) trend and the d(ab BC) trend can be explained within the error bars. This interpretation cannot be ruled out with the current data. The difficulty, however, lies on the physical mechanism that causes such a temporal change in the BC times, since the fluid outer core is generally considered to be homogeneous (Stevenson, 1987). (2) The d(ab BC) trend is a result of mantle biases which affect a few outliers disproportionally. (3) The d(ab BC) trend is caused by systematic event mislocation over time. The more recent events were mislocated further away from COL than they actually are. Fig. 5. Event pairs with similar AB BC times but increased BC DF times for the later events. The DF wave trains have been amplified by five times.

7 X. Song / Physics of the Earth and Planetary Interiors 122 (2000) Fig. 6. A SSI event pair with a smaller AB BC time but a larger BC DF time for the later event. The DF wave trains have been amplified by five times. In any case, the trend in d(ab BC) is opposite to the temporal trend in d(bc DF), suggesting that the temporal change in the BC DF times is not caused by event mislocations. Assuming that all the AB BC time differences d(ab BC) are the results of the differences in the hypocenter locations, the d(bc DF) times can be corrected for the location differences (Fig. 4). The conversion ratio from d(ab BC) to the corrections for d(bc DF) is 2.46 using PREM. The results using other reference models do not change significantly, because of our careful choice of using pairs with small d(ab BC) only. After the corrections, the temporal trend in the d(bc DF) times become more robust with a larger slope (Fig. 4). The temporal variation in the BC DF times is easily visible directly from certain seismograms. Fig. 5 shows overlays of pairs of seismograms with similar AB BC times but increased BC DF times for the later events. The similarity of the AB BC times reaffirms the similarity of the event locations. Thus, the noticeable changes in the BC DF times cannot be explained by location differences. Fig. 6 shows another event pair. The later event of the pair has a smaller AB BC time but a larger BC DF time. Clearly, the shift of the BC DF time is difficult to be explained by different locations because location differences (either in epicentral distances or in focal depths) would change BC DF times and AB BC times in the same direction. 3. Conclusion The doublet technique proposed by Poupinet et al. (2000) provides an excellent test on whether the observed temporal variation in BC DF times is an artifact of earthquake mislocations. My examination of the event pairs for the SSI-COL path suggests that it is not; the possibility that the observed temporal variation is caused by earthquake mislocations is ruled out. This conclusion is exactly opposite to the previous conclusion by Poupinet et al. (2000), whose erroneous conclusion was based on flawed data analysis as discussed in Song (2000b). The chief concern for detecting inner core rotation using differential BC DF times has been possible systematic event mislocations. We now have four independent lines of arguments against event mislocations being the cause for the observed temporal change along the SSI-COL path. The first three points in the following were discussed in Song (2000a). (1) The temporal trend at COL is robust, no matter what earthquake locations (EDR, EHB, or Joint Hypocenter Determination) are used. (2) Station distributions used to locate the SSI events do not show obvious shifts over time. (3) Data recorded at the Alaska Seismic Network within 8 years in 1990s show time dependence. There is no reason to believe any systematic change in station distributions and location procedures during the short period. (4) The pattern of increasing BC DF times over time at COL does not exist in the AB BC times, confirmed by this study. Acknowledgements I benefited from discussion with Paul Richards, Don Helmberger, Ken Creager, and Jay Bass. I thank Hanneke Paulssen for very helpful comments and Annie Souriau for preprints. Support for this research is provided by NSF grant EAR and NASA grant NAG

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