Bulletin of the Seismological Society of America, 91, 3, pp. 594–603, June 2001
`
`Improving Global Seismic Event Locations Using
`Source-Receiver Reciprocity
`
`by Peter M. Shearer
`
`Abstract The leading source of error in seismic event locations is travel-time
`perturbations caused by three-dimensional Earth structure. The reciprocity of travel
`times between sources and receivers provides a method for testing the effectiveness
`of empirical methods for improving event locations that rely on nearby calibration
`events of known location. We apply this approach to travel-time residuals obtained
`by Engdahl et al. (1998) for almost 100,000 teleseismic events. By analyzing the
`residual patterns at thousands of seismic stations of known location, we characterize
`the spatial coherence of station/event mislocation vectors. We find that, on average,
`calibration events are likely to improve locations only if they are located within 100–
`150 km of the target events. For 84 events of known location, we find that applying
`source-receiver reciprocity can significantly reduce location errors by correcting for
`the teleseismic residual pattern observed at stations close to the target events. These
`results have implications for efforts to improve event locations for nuclear explosion
`monitoring purposes.
`
`Introduction
`
`Improving seismic event locations is an important part
`of research to support nuclear test verification efforts. A goal
`of the programs to monitor the Comprehensive Nuclear-
`Test-Ban Treaty (CTBT) is to achieve high-confidence, ab-
`solute location uncertainties of less than 1000 km2 (National
`Research Council, 1997). Errors in absolute event location
`in the routine location methods using reference one-dimen-
`sional velocity models are typically dominated by the bias-
`ing effects of three-dimensional structure. Two main ap-
`proaches have been applied to account for 3D structure, both
`in teleseismic and regional event location problems. In the
`first, improved velocity models of the crust and mantle are
`developed that more correctly predict the seismic travel
`times used by the location algorithm. This includes models
`of crustal thickness variations, upper mantle Pn velocities,
`and full 3D mantle tomography models. For example, Lie-
`nert (1997) demonstrated that a locally determined velocity
`model for regional phases in the western United States could
`improve the location accuracy of explosions at the Nuclear
`Test Site (NTS) in Nevada. Smith and Ekstro¨m (1996)
`showed that the rms location errors for 108 global events of
`known location could be improved by using a 3D mantle
`model. Although this approach has achieved some success,
`global velocity models are still too smooth to fully account
`for the sharp local velocity changes that in many cases may
`dominate the location errors.
`An alternative method is to apply empirical travel-time
`corrections based on the residuals observed for calibration
`
`events of known locations. Because travel times to nearby
`events are likely to have similar patterns of residuals, their
`locations can be improved by using these station corrections,
`even if the details of the underlying 3D velocity structure
`remain unknown. This approach would be straightforward
`if the ground truth events were in exactly the same places
`as the target events. However, in practice this is rarely the
`case, so considerable effort has gone into devising ways to
`interpolate the residuals between calibration events to create
`station correction surfaces that can be used to locate events
`at arbitrary locations (e.g., Cogbill and Steck, 1997; Schultz
`et al., 1998). A fundamental difficulty of this approach is
`the sparse coverage of calibration events in many parts of
`the world.
`In principle, due to reciprocity of travel times between
`sources and receivers, the residuals observed at seismic sta-
`tions (that of course have known locations) from distant
`events provide information that could be used to improve
`the locations of nearby events as measured by distant sta-
`tions. In this article, we experiment with this approach to
`characterize how rapidly mislocation vectors change with
`position and to test whether source-receiver reciprocity can
`significantly improve global event locations. We use the re-
`cent teleseismic relocation effort of Engdahl et al. (1998) for
`nearly 100,000 events from 1964–1995 as a starting point,
`although the same approach could also be applied to regional
`or local event data. To test the accuracy of our locations, we
`examine the reference events tabulated by Smith and Ek-
`stro¨m (1996).
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`We find that the scatter in computed station mislocation
`vectors is comparable to that seen in the Smith and Ekstro¨m
`(1996) test events, suggesting that station locations can serve
`as a proxy for calibration events. Station mislocation vectors
`typically change rapidly over short scales; the correlation
`distance of station mislocation vectors is less than ⬃150 km,
`suggesting that calibration events are only useful for im-
`proving teleseismic event locations if they are located within
`150 km of the target event. For 84 of the reference events,
`there is a suitable seismic station within this distance. For
`these events, median location errors are reduced compared
`to the original Engdahl et al. (1998) locations when travel-
`time corrections are applied based on source-receiver reci-
`procity.
`
`Data and Preliminary Processing
`
`Engdahl et al. (1998) (henceforth termed EHB) devoted
`considerable effort to produce a cleaner version of the phase
`data collected by the International Seismological Center
`(ISC) and to relocate nearly 100,000 events (1964–1995) us-
`ing an improved 1D velocity model, later arriving phases,
`ellipticity corrections, and azimuth independent patch cor-
`rections to account for station terms. The EHB locations are
`widely recognized as one of the best sets of teleseismic event
`locations. For 104 reference events (both explosions and
`earthquakes) from Smith and Ekstro¨m (1996), the EHB mis-
`location rms, average and median are 10.5 km, 9.0 km, and
`8.1 km, respectively. These numbers compare quite favor-
`ably to the best overall results (rms ⳱ 13.2 km) obtained
`by Smith and Ekstro¨m (1996) using a 3D Earth model and
`azimuthally varying station terms. At least some of the dif-
`ferences between the EHB and Smith and Ekstro¨m (1996)
`locations may be attributed to the inclusion of regional phase
`data in the EHB results (Smith and Ekstro¨m [1996] used data
`only at ranges greater than 30⬚).
`We use the EHB location residuals as a starting point
`for our relocation efforts. We first relocate the events using
`the L1 norm, source-specific station term (SSST) approach
`of Richards-Dinger and Shearer (2000). The L1 norm may
`have some advantages in earthquake location due to its ro-
`bustness with respect to outliers in the data (e.g., Kennett,
`1992; Shearer, 1997). However, the EHB data are sufficiently
`clean that it is unlikely that the L1-norm makes much dif-
`ference in this case compared to conventional least-squares
`approaches. To simplify our algorithm, we use only P, Pn,
`pP, pwP, S, Sn, and sS arrivals (no core phases) and weight
`all arrivals equally. We use the iasp91 (Kennett and Endahl,
`1991) velocity model. We compute SSST corrections using
`an iterative procedure based on the median station residuals
`from the 20 closest events to each target event (see Richards-
`Dinger and Shearer, 2000, for more details). This method
`should improve the relative location accuracy among nearby
`events but does nothing to improve the absolute location
`accuracy of event clusters.
`The SSST computed locations for 99,715 EHB events
`
`are available via anonymous ftp to mahi.ucsd.edu in the di-
`rectory /pub/EHB SSST. The SSST locations for 104 Smith
`and Ekstro¨m (1996) test events show a modest improvement
`over the original EHB locations; the mislocation rms, aver-
`age and median are 10.1 km, 8.4 km, and 7.5 km, respec-
`tively. In some regions the SSST locations appear to cluster
`more clearly into linear features than the EHB locations, but
`the improvement, if any, is generally very slight. A com-
`parison between the EHB locations and the SSST locations
`is shown in Figure 1 for earthquakes in the vicinity of the
`Mendocino Triple Junction off the coast of California and
`Oregon.
`
`Figure 1.
`Earthquakes near the Mendocino Triple
`Junction (offshore northern California and Oregon) as
`located by (top) Engdahl et al. (1998) and (bottom)
`the source-specific station term (SSST) method.
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`Source-Receiver Reciprocity and Station Relocation
`
`The reciprocity of travel times between sources and re-
`ceivers means that the travel time from a source to a receiver
`is identical to the travel time that would be measured if there
`were a source at the station and a receiver at the event (see
`Fig. 2). In practice, earthquakes or explosions are never lo-
`cated in exactly the same places as seismic stations. How-
`ever, if a station is located close enough to a target event,
`then the teleseismic residual pattern observed at the station
`should be correlated to the residual pattern seen at the event.
`In this case, seismic stations could serve as proxies for
`ground truth events. The potential advantage of this ap-
`proach is that there are data available for stations in many
`areas that are aseismic or currently lack ground truth events.
`If source-receiver reciprocity could be invoked, then these
`stations could be used to calibrate event locations in these
`areas.
`To examine source-receiver reciprocity in the EHB data
`set, we first relocate the stations to see if they move signifi-
`cantly compared to their known locations. Our starting point
`is the residuals for the SSST locations (see above). We fix
`the event locations and origin times and adjust the station
`locations to give the best L1-norm fit to the travel times. We
`consider only changes in the latitude and longitude of the
`stations; we do not permit depth variations. We use both P
`and S arrivals when available; many stations have only P
`picks. To even out the very nonuniform event coverage, we
`compute summary ray residuals based on 10⬚ bins in range
`and azimuth. One might object at this point by pointing out
`that because the true event locations are unknown, the station
`relocation procedure is not completely reciprocal to the
`event location procedure (which uses stations of known lo-
`cations). Biases in the event locations might thus feed back
`into the station locations. However, this will only occur if
`the residuals resulting from the event mislocations are sys-
`tematically different in one direction from the station com-
`pared to the opposite direction, creating a cos(h0 Ⳮ h) pat-
`tern in the residuals around the target station (where h is the
`event azimuth and h0 defines the direction of greatest posi-
`tive residual). Higher order terms, such as cos 2h and cos
`3h, in the residuals will not influence the location; it is only
`the degree-one component that has an effect. As we will see
`later, it appears that the strongest contributor to event mis-
`locations is near-source structure and that event mislocations
`are not correlated over large distances. In most cases, there-
`fore, there likely will not be a strong degree-one term in the
`residuals, and the biasing effects of event mislocation on our
`station relocation method will be minimized by averaging
`over a wide range of azimuths.
`We restrict our analysis to stations that recorded at least
`100 events, from at least 10 different summary-ray source
`bins, and with no more than a 90⬚ gap between summary ray
`azimuths. The resulting mislocation vectors for 3004 stations
`are plotted in Figure 3. The mislocation rms, average, and
`median are 8.2 km, 6.2 km, and 5.0 km, respectively (the 90
`
`Figure 2.
`Source-receiver reciprocity implies that
`the travel-time residual for a ray path from event E1
`to station S2 will be approximately the same as the
`residual from source E2 to station S1, provided the
`corresponding events and stations are sufficiently
`close together.
`
`and 95 percentiles are 11.3 and 14.1 km, respectively). These
`station location errors are 13%–33% less than the corre-
`sponding errors for the 104 calibration events in the SSST
`locations. The smaller errors in the station locations may be
`a result of (1) differences in the station distribution compared
`to the 104 calibration events, (2) the fixed depth of the sta-
`tions in the relocation procedure compared to the floating
`depths permitted in the event relocations, and/or (3) some of
`the residuals used in the station relocations being absorbed
`in event mislocations (see preceding paragraph). However,
`regardless of the exact size of the station mislocation vectors,
`it is instructive to to examine their directions and their degree
`of spatial coherence. This is illustrated in Figure 4, which
`shows the station mislocation vectors in detail across part of
`Europe.
`The station mislocation vectors are correlated among
`nearby stations but often exhibit sharp changes over very
`short length scales. For example, notice the group of four
`southward-pointing vectors in northwestern France (48⬚ N,
`3⬚ W) about 150 km west of a group of six eastward-pointing
`vectors (48⬚ N, 0⬚ E). Even greater incoherence in the station
`mislocation vectors can be seen across parts of Great Britain
`and Italy. The degree of spatial coherence of the mislocation
`vectors may be quantified by plotting the difference between
`pairs of mislocation vectors as a function of station spacing
`(Fig. 5). As one might expect, this plot shows considerable
`scatter. The globally averaged properties become clearer
`when the 50th (median) and 90th percentiles are plotted for
`10-km averaging bins in station separation. The mislocation
`vector difference is reduced as the station pairs become close
`together, but this effect only becomes significant for station
`separations of less than ⬃300 km. For comparison, the
`dashed lines in Figure 5 show the 50th and 90th percentiles
`of the lengths of the individual station mislocation vectors.
`When a calibration event is used to improve the location
`of a target event, a key question is how close the calibration
`event needs to be in order to significantly improve the target
`event location. We can address this question for teleseismic
`events on a global scale by using our station mislocation
`vectors as a proxy for event mislocation vectors. Thus, if we
`had travel-time data from a station of unknown location we
`could attempt to improve our initial estimate for the station
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`Figure 3. Mislocation vectors for 3004 global seismic stations as relocated using
`travel-time residuals to distant events (see text). The true station locations are shown
`as triangles; the lines are drawn in the direction of the relocated stations. The lengths
`of the vectors are highly exaggerated; for reference a 30-km mislocation vector is shown
`above the plot. Results are shown only for stations recording at least 100 events with
`no more than a 90⬚ azimuthal gap between events.
`
`location by subtracting the mislocation vector for a nearby
`reference station. Figure 5 shows that, on average, this will
`only lead to an improvement in the station location if the
`calibration station is within 100–150 km of the target station.
`Further, the average improvement in the station location is
`fairly modest (less than 30%) even at much closer station
`spacing. This is not to say that there are no regions where
`the station mislocation vectors show greater spatial coher-
`ence than the global average (presumably areas with rela-
`tively small local velocity perturbations). In these regions,
`calibration stations could be useful at distances greater than
`150 km. But there also exist regions where the mislocation
`vector coherence is less than the global average. Calibration
`stations in these areas would only be useful if they were
`extremely close to the target stations.
`Note that the observed residual patterns between indi-
`vidual stations may be correlated at station separations far
`greater than 150 km, due to velocity perturbations near the
`distant-source regions. It is only the degree-one part of the
`residual pattern that controls the station mislocation vectors.
`
`This part of the residual pattern appears to be dominated by
`local structures and can vary rapidly over minor changes in
`the station locations.
`Of course, the true locations of seismic stations are al-
`ready known so this analysis is useful only to the extent that
`it provides information relevant to the event location prob-
`lem. In the next section, we compare the station mislocation
`vectors to mislocation vectors for the 104 reference events
`and test to see if the event locations can be improved by
`using travel-time data from nearby stations.
`
`Using Source-Receiver Reciprocity to Improve
`Event Locations
`
`Figures 6–8 show mislocation vectors for our SSST re-
`locations of 104 reference events from Smith and Ekstro¨m
`(1996) compared to the station mislocation vectors discussed
`in the previous section. In some areas, the event mislocation
`vectors correlate with nearby station mislocation vectors.
`For example, in Figure 6, two events in the western United
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`Figure 4. A close-up of station mislocation vectors in Europe. The true station lo-
`cations are shown as triangles; the lines are drawn in the direction of the relocated
`stations. The lengths of the vectors are highly exaggerated; for reference a 30-km
`mislocation vector is shown above the plot. Results are shown only for stations re-
`cording at least 100 events with no more than a 90⬚ azimuthal gap between events.
`
`States (near 40⬚ N, 252⬚ E) are mislocated in the northeast
`direction, in approximate agreement with the mislocations
`of stations to the east and west of the events (stations to the
`south don’t agree as well). In Figure 7, two events near the
`Virgin Islands in the southeast Caribbean Sea (near 15⬚ N,
`298⬚ E) are mislocated to the southwest, in agreement with
`most (but not all) of the stations along the island arc. In
`Figure 8, two events between the Black and Caspian Seas
`(near 42⬚ N, 45⬚ E) are mislocated to the northwest, in agree-
`ment with the dominant mislocation trend of the nearby
`stations.
`
`In other areas, however, the event mislocation vectors
`disagree with the trend of nearby station vectors (or the sta-
`tion vectors may be so incoherent that no clear conclusion
`may be drawn). At least some of the discrepancies between
`event and station mislocation vectors may arise from the
`mismatch between the surface stations and earthquakes at
`depth. Also, the distribution of events around the stations
`will differ from the distribution of stations around the events,
`so one would not necessarily expect the mislocation vectors
`to be exactly the same.
`To more precisely apply source-receiver reciprocity in
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`Discussion
`
`Source-receiver reciprocity can be used to gain insight
`into the effectiveness of using ground truth calibration
`events to improve teleseismic event locations. Perhaps our
`most significant result is that station mislocation vectors
`change rapidly over fairly short distances, with a globally
`averaged correlation length of about 150 km. This has so-
`bering implications for the use of calibration events to im-
`prove teleseismic event location because source-receiver
`reciprocity implies that event mislocation vectors will be-
`have in a similar fashion. In most regions, calibration events
`at distances greater than 150 km probably will have little or
`no benefit in improving the location of a target event (and
`may worsen the location). Interpolation of correction sur-
`faces among calibration events will only be useful in tele-
`seismic event location if the calibration events are spaced
`closely enough that their mislocation vectors are spatially
`correlated.
`The coherence of the station mislocation vectors varies
`widely from region to region, but the observed coherence
`does not appear to be related in any simple way to the tec-
`tonics of the region. Some stable and tectonically active
`regions have station mislocation vectors that are coherent
`over large distances, whereas other examples have incoher-
`ent mislocation vectors. It is difficult to clearly assign origins
`to specific examples of the station mislocation vectors be-
`cause they could result from different causes (e.g., lateral
`velocity variations, dipping interfaces, and anisotropy) and
`the higher-degree components in the residual patterns, which
`might help to discriminate among these possibilities, do not
`contribute to the relocation vectors.
`In regions where calibration events are missing, sparse,
`or poorly recorded, seismic stations could be used as sub-
`stitutes for calibration events. These could be existing or
`archived stations, or new station deployments specifically
`designed for this purpose. All that is necessary is for these
`stations to record travel times at a range of event azimuths
`and ranges that are comparable to the station distribution
`used to locate the nearby events of interest. Because stations
`are restricted to the near surface, reciprocity will be achieved
`most closely for shallow events, namely, those that will be
`of greatest interest for CTBT monitoring purposes. In areas
`of little or no natural seismicity, it may be cheaper and po-
`litically easier to field temporary station deployments than
`to arrange for calibration explosions. Of course, it would be
`necessary to leave the stations for a long enough period to
`record events at a wide range of azimuths. The most direct
`application of source-receiver reciprocity would be to set off
`explosions close to permanent seismic stations that one
`wishes to calibrate while deploying portable stations across
`wide regions to record the explosions. These temporary sta-
`tions would only have to record arrival times from a single
`explosion at each permanent station to obtain the travel-time
`corrections necessary to accurately locate (shallow) events
`near the portable station using the permanent network data.
`
`Figure 5.
`The difference in global station mislo-
`cation vector pairs plotted as a function of the distance
`between the true station locations. The solid lines
`show the 50th and 90th percentiles of the data, as
`binned in 10-km increments. The dashed lines show
`the 50th and 90th percentiles of the individual station
`mislocation vector lengths. Results are shown only
`for stations recording at least 100 events with no more
`than a 90⬚ azimuthal gap between events.
`
`the case of target events with nearby stations, we attempted
`to improve the event locations by using the following pro-
`cedure. We used only those target events for which there
`were nearby stations within 150 km, restricting our reloca-
`tions to 84 of the reference events (experiments with using
`smaller station-event range cutoffs drastically reduced the
`number of available events while apparently not yielding
`significantly improved results). For these stations, we then
`searched for distant events within 10⬚ of a distant station that
`recorded the target event. Next, we computed the median
`residual for that distant station to apply as a correction in
`locating the target event. While we only relocated 84 events
`using this method, it was necessary to have access to resid-
`uals from most of the other events in the EHB data set in
`order to compute all of these path corrections.
`The corrected reference event mislocation vectors are
`plotted as dashed lines in Figures 6–8 for comparison to the
`original SSST mislocation vectors (solid lines). In the ma-
`jority of cases, the errors in the locations are reduced, al-
`though in a few examples, the errors are increased. For the
`84 events, the original EHB mislocation rms, average, and
`median were 11.3 km, 9.8 km, and 8.8 km, respectively. The
`SSST mislocation rms, average, and median were 10.8 km,
`9.0 km, and 7.7 km. Following relocation using source-
`receiver reciprocity to the teleseismic residual patterns at
`nearby stations, these numbers were reduced to 9.1 km, 7.8
`km, and 6.6 km. The improvement compared to the SSST
`locations is fairly modest (about 15%), but consistent with
`the suggestion of Figure 5 that large improvement in loca-
`tions will be achieved only if the station/event spacing is
`much smaller than 150 km.
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`Figure 6. A close-up of station mislocation vectors (thin lines) in the western United
`States, compared to event mislocation vectors for reference events (thick lines). The
`SSST station mislocation vectors are shown as the solid thick lines; the mislocation
`vectors following application of corrections based on source-receiver reciprocity are
`shown as the dashed thick lines. The lengths of the vectors are highly exaggerated; for
`reference a 30-km mislocation vector is shown above the plot. Results are shown only
`for stations recording at least 100 events with no more than a 90⬚ azimuthal gap between
`events.
`
`In principle, the effect of source-receiver reciprocity is
`naturally accounted for in tomographic inversions for three-
`dimensional Earth structure. However, as Smith and Ek-
`stro¨m (1996) have shown, these models are currently of lim-
`ited effectiveness in improving event locations. Our results
`suggest that the scale length of the heterogeneity that dom-
`inates teleseismic event mislocations is much smaller than
`the typical resolution (1000–2000 km) of current global to-
`mographic models. Regional tomographic models can of
`course provide better resolution but are not yet available in
`many areas.
`
`Our study examined both regional (e.g., Pn and Sn)
`and teleseismic phase data from the EHB data set. We also
`experimented with using only teleseismic arrivals at source-
`receiver ranges greater than 30⬚ in hopes of minimizing lo-
`cation biases associated with the strong velocity heteroge-
`neities in the crust and uppermost mantle. However, in this
`case the average location accuracy was reduced somewhat
`compared to the results obtained when the entire data set
`was used. The station mislocation vectors exhibited similar
`behavior to that shown in this article; on average the mis-
`location vectors were correlated only for station separations
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`Figure 7. A close-up of station mislocation vectors (thin lines) in eastern North
`America, compared to event mislocation vectors for reference events (thick lines). The
`SSST station mislocation vectors are shown as the solid thick lines; the mislocation
`vectors following application of corrections based on source-receiver reciprocity are
`shown as the dashed thick lines. The lengths of the vectors are highly exaggerated; for
`reference a 30-km mislocation vector is shown above the plot. Results are shown only
`for stations recording at least 100 events with no more than a 90⬚ azimuthal gap between
`events.
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`Figure 8. A close-up of station mislocation vectors (thin lines) in part of Eurasia,
`compared to event mislocation vectors for reference events (thick lines). The SSST
`station mislocation vectors are shown as the solid thick lines; the mislocation vectors
`following application of corrections based on source-receiver reciprocity are shown as
`the dashed thick lines. The lengths of the vectors are highly exaggerated; for reference
`a 30-km mislocation vector is shown above the plot. Results are shown only for stations
`recording at least 100 events with no more than a 90⬚ azimuthal gap between events.
`
`less than ⬃150 km. Thus, it does not appear that the range
`of applicability of calibration events can be extended by us-
`ing data only at longer source-receiver distances.
`Our analysis was focused on teleseismic locations, but
`many of the same concepts could be applied to purely re-
`gional location problems for smaller events, an increasing
`focus for CTBT monitoring efforts. The principles of source-
`receiver reciprocity apply at all length scales.
`
`Acknowledgments
`
`We thank Bob Engdahl for sending the EHB locations and residuals.
`Keith McLaughlin and Lee Steck provided detailed and constructive re-
`views. This research was supported by DTRA grant DSWA01-98-1-0005.
`
`References
`
`Cogbill, A., and L. Steck (1997). Use of propagation path corrections to
`improve regional event locations in western China, (Fall Meeting Sup-
`plement), EOS 78, no. 46, F445.
`
`Engdahl, E. R., R. van der Hilst, and R. Buland (1998). Global teleseismic
`earthquake location with improved travel times and procedures for
`depth determination, Bull. Seism. Soc. Am. 88, 722–743.
`Kennett, B. L. N. (1992). Locating oceanic earthquakes: the influence of
`regional models and location criteria, Geophys. J. Int. 108, 848–854.
`Kennett, B. L. N., and E. R. Engdahl (1991). Travel times for global earth-
`quake location and phase identification, Geophys. J. Int. 105, 429–
`465.
`Lienert, B. R. (1997). Assessment of earthquake location accuracy and
`confidence region estimates using known nuclear tests, Bull. Seism.
`Soc. Am. 87, 1150–1157.
`National Research Council (1997). Research Required to Support Compre-
`hensive Nuclear-Test-Ban Treaty Monitoring, National Academy
`Press, Washington, D.C.
`Richards-Dinger, K. B., and P. M. Shearer (2000). Earthquake locations in
`southern California obtained using source-specific station terms, J.
`Geophys. Res. 105, 10,939–10,960.
`Schultz, C., S. Myers, J. Hipp, and C. Young (1998). Nonstationary bay-
`esian kriging: a predictive technique to generate spatial corrections
`for seismic detection, location, and identification, Bull. Seism. Soc.
`Am. 88, 1275–1288.
`
`PGS Exhibit 2046
`WesternGeco v. PGS (IPR2015-00313)
`
`

`
`Improving Global Seismic Event Locations Using Source-Receiver Reciprocity
`
`603
`
`Shearer, P. M. (1997). Improving local earthquake locations using the L1
`norm and waveform cross-correlation: application to the Whittier Nar-
`rows, California, aftershock sequence, J. Geophys. Res. 102, 8269–
`8283.
`Smith, G. P., and G. Ekstro¨m (1996). Improving teleseismic events loca-
`tions using a three-dimensional Earth model, Bull. Seism. Soc. Am.
`86, 788–796.
`
`Institute of Geophysics and Planetary Physics
`Scripps Institution of Oceanography
`University of California, San Diego
`La Jolla, California 92093-0225
`pshearer@ucsd.edu
`(P.M.S.)
`
`Manuscript received 30 August 2000.
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`PGS Exhibit 2046
`WesternGeco v. PGS (IPR2015-00313)