(1999) Epicenter estimation using erroneous crustal model(s) and skew regional networks

Ž .Physics of the Earth and Planetary Interiors 113 1999 303–319

ž /Epicenter estimation using erroneous crustal model s and skewregional networks

Rong-Song Jih )

Defense Threat Reduction Agency, 45045 AÕiation DriÕe, Dulles, VA 20166-7517, USA

Received 26 January 1998; received in revised form 5 October 1998; accepted 5 October 1998

Abstract

Ž .A simple, hybrid procedure is proposed for seismic location at regional distances when 1 the crustal model is notŽ . Ž .known, 2 the seismic network is not calibrated, and 3 the azimuthal coverage of recording stations is poor. Among all

parameters related to event location, the backazimuth estimated with a skew, large-aperture network appears to be the leastsensitive to the model error—under these difficult yet realistic conditions. This observation leads to a hypothesis thatepicenters could be better constrained through triangulation using backazimuths derived from two skew, large-aperturesubnetworks or arrays. If two subnetworks can be found such that the corresponding backazimuths are sufficiently apartŽ .say, they intersect at an angle of 208 or larger , the resulting absolute mislocation associated with the intersection point isoften less than 18 km, which is the permissible location accuracy as quoted in the Comprehensive Nuclear Test Ban TreatyŽ .CTBT . The origin time and source depth can then be obtained from a standard location procedure with the approximateepicenter held fixed. If the network cannot be partitioned to provide two ‘good’ backazimuths, then the conventional location

Ž .procedure which feeds on the phase picks altogether can still be used. The proposed algorithm is tested with three events:Ž . Ž . Ž .1 U.S. explosion Salmon of Oct. 22, 1964, 2 Kola explosion of Sept. 29, 1996, and 3 Pakistani event of April 28, 1991.The absolute location error associated with this hybrid method is typically comparable to or, in many cases, better than thatof the conventional method. Furthermore, this new approach also offers a measurable quantity which positively flags whenthe location is more likely to be good—even for regions that are not calibrated. These features could have importantimplications for the CTBT implementation as the proposed algorithm can readily be used in areas previously not well

Ž .studied as an ad hoc procedure on problem events while the International Monitoring System IMS stations are beingdeployed and calibrated gradually. For local seismic network operators, this algorithm could be an attractive alternative orsupplementary location procedure. q 1999 Elsevier Science B.V. All rights reserved.

Keywords: Seismic location; Adaptive method; Skew geometry; Unbiased azimuth estimation; Triangulation

1. Introduction

Seismic event location remains as one of the mostimportant discriminants for separating natural tec-

) Tel.: q1-703-325-2235; fax: q1-703-325-2166; e-mail:[email protected]

tonic and explosive events. Positive determination ofa seismic event as deep suffices to classify it as anearthquake, while if it can be established that theevent is shallow and if Ms–mb is small, then onemay classify the event as an explosion with a smallprobability of error. Approximately 80% of knownglobal earthquakes have focal depths greater than 50

0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0031-9201 99 00009-6

( )R.-S. JihrPhysics of the Earth and Planetary Interiors 113 1999 303–319304

km or are located more than 25 km at sea. Thus, thevast majority of earthquakes can potentially be iden-tified on the basis of location alone.

If the ground-truth location of a nearby seismicevent is known, the arrival readings at seismic sta-tions can be individually ‘calibrated’ to match thepredicted travel–time curves of some postulated ve-locity model. It has been long established that, withthe station corrections, locations of other seismicevents in the vicinity around the ground-truth eventcan be significantly improved. This is the standardapproach of ‘calibration’. In a special application ofthis technique, travel–time residuals are obtainedfrom a least-square location program which is runwith the depth constrained to the known ‘true’ value.When these residuals are used as travel–time correc-tions in the same program run depth-free, nearbyevents can be located with smaller errors in depth.An elaboration of this specific application has been

Ž .denoted the SRST Source-Region-Station-TimeŽ . Ž .technique by Veith 1975 see also Blandford, 1975 .

Alternatively, a postulated crustal velocity model canbe adjusted so that the estimated hypocenter wouldperfectly match the ground-truth event. Thus, thefine-tuned velocity model can be used to determinethe location of nearby events without the need ofestablishing residual corrections for individual sta-tions. Both the SRST and the model-tuning proce-dures require at least one ground-truth event.

There are cases where no nearby event of knownlocation is available. Furthermore, there are caseswhere not only the crustal model is not well known,the seismic stations could be sparse or even spread ina very skew geometry. It is well known that a skewgeometry often gives very poor epicenter estimatewhen the conventional location method is used. Sec-tion 2 presents a procedure which is particularlysuitable for these disadvantageous situations. Thebasic idea is to decompose the recording network

Ž .into at least two subnetworks so that each subnet-work is comprised of stations spread over only oneside of the postulated epicenter. That is, each subnet-work should have a very large azimuthal gap andpreferably a large aperture as well. The locationsdetermined with these skew networks have hugeuncertainty ellipses; hence, these would be situationsto avoid in traditional location procedures. However,the proposed algorithm somehow turns these situa-

tions to advantages in location. This procedure isillustrated with two explosions with known locationas well as another event with well-constrained epi-center. A globally-averaged continental model,

Ž .IASP91 Kennett, 1991 , is arbitrarily chosen tomimic the situation where the true crustal structureof a region of interest may not be available, andseismic analysts would have to use a possibly erro-neous crustal model to start with.

2. Proposed location algorithm

Ž .1 Group the recording seismic stations into atleast two networks such that each network is on oneside of the preliminary location and has a lateralaperture as large as possible.

Ž .2 Relocate the event with each individual net-work. Since all stations are spread on one side, theerror ellipse is inevitably elongated. The major axisof the ellipse points to the same direction of the mostprobable backazimuth as observed from that hypo-thetical array.

Ž .3 If the two major axes intersect at an anglelarger than 208, accept the intersection point as thelocation.

Ž .4 Otherwise go back to Step 1 and re-group thestations. Usually this can be easily done by simplylooking at the map of all stations. If no two subnet-works can co-exist fulfilling the requirement of Step3, then use the conventional location algorithms withall phase arrivals lumped into one group in theinversion. Alternatively, use the mean location of thetwo epicenters determined in Step 3.

This algorithm calls for a few steps that may notbe regarded as favorite or appropriate in typicalseismic location procedures. It is generally desirableto have a network with an azimuthal gap as small aspossible—ideally the network should encircle theepicenter. In the proposed algorithm, however, sta-tions on only one side are deliberately sought. Thisskew geometry, in conjunction with travel–time ta-bles derived with a possibly erroneous crustal model,will inevitably lead to an incorrect epicenter. Never-theless, the major axis of the prolonged error ellipse,not the epicenter itself, represents the best backaz-imuth one can get, which is what to be used in thetriangulation. This is true only if the stations are on

( )R.-S. JihrPhysics of the Earth and Planetary Interiors 113 1999 303–319 305

one side and have a large aperture. Under theseconditions, the proposed algorithm turns the disad-vantages of skew network and erroneous crustalmodel into advantages in deriving the best estimate

Žof backazimuth. Other pieces of information such as.the location itself and the size of error ellipse are

tossed out, as they are not well constrained underŽthese same conditions. When two rays or backaz-

Table 1Relocation results using IASP91 model and various networks

a b c dNetwork 1 Network 2 Conventional Adaptive method DiagnosticU Ua 5 6.1 b 6 8.9 aqb 11.1 aab 28.3 7.0 14.66U Ua 5 6.1 c 9 12.4 aqc 7.4 aac 4292 3.6 0.12

a 5 6.1 d 7 7.3 aqd 11.9 aad 13.6 3.3 50.08U Ua 5 6.1 e 6 8.2 aqe 2.8 aae 22.3 3.3 12.45

U Ua 5 6.1 f 7 16.6 aq f 4.2 aaf 39.6 6.1 17.44a 5 6.1 g 8 41.4 aqg 7.8 aag 11.2 21.7 33.71a 5 6.1 h 4 48.5 aqh 9.1 aah 7.8 22.9 20.48a 5 6.1 i 4 24.5 aq i 9.5 aai 7.9 15.2 23.46

U Ub 6 8.9 c 9 12.4 bqc 4.6 bac 7.9 2.5 14.54b 6 8.9 d 7 7.3 bqd 5.4 bad 8.5 6.5 35.42b 6 8.9 e 6 8.2 bqe 2.6 bae 4.9 0.7 27.11b 6 8.9 f 7 16.6 bq f 6.4 baf 10.2 3.9 32.1b 6 8.9 g 8 41.4 bqg 9.4 bag 2.2 24.6 48.37b 6 8.9 h 4 48.5 bqh 3.4 bah 7.4 20.1 35.14

U Ub 6 8.9 i 4 24.5 bq i 8.3 bai 27.6 16.3 8.80c 9 12.4 d 7 7.3 cqd 5.5 cad 6.3 7.6 49.96

U Uc 9 12.4 e 6 8.2 cqe 2.0 cae 18.7 10.0 12.57U Uc 9 12.4 f 7 16.6 cq f 13.3 caf 11.7 14.4 17.56

c 9 12.4 g 8 41.4 cqg 2.7 cag 4.6 17.5 33.83c 9 12.4 h 4 48.5 cqh 7.6 cah 17.4 29.3 20.6c 9 12.4 i 4 24.5 cq i 5.2 cai 15.1 6.1 23.34d 7 7.3 e 6 8.2 dqe 5.6 dae 7.4 4.4 62.53d 7 7.3 f 7 16.6 dq f 5.9 daf 7.3 8.9 67.52d 7 7.3 g 8 41.4 dqg 6.7 dag 6.2 23.4 83.79d 7 7.3 h 4 48.5 dqh 4.0 dah 8.0 22.5 70.56d 7 7.3 i 4 24.5 dq i 12.4 dai 18.5 12.0 26.62

U Ue 6 8.2 f 7 16.6 eq f 3.5 eaf 81.4 12.3 4.99e 6 8.2 g 8 41.4 eqg 1.5 eag 4.9 17.0 21.26

U Ue 6 8.2 h 4 48.5 eqh 1.2 eah 15.4 28.3 8.03e 6 8.2 i 4 24.5 eq i 2.7 eai 3.1 9.1 35.91

U Uf 7 16.6 g 8 41.4 fqg 13.9 fag 18.2 15.5 16.27U Uf 7 16.6 h 4 48.5 fqh 11.0 fah 171.3 31.8 3.04

f 7 16.6 i 4 24.5 fq i 10.3 fai 13.4 4.8 40.9U Ug 8 41.4 h 4 48.5 gqh 7.0 gah 16.4 6.2 13.23

g 8 41.4 i 4 24.5 gq i 6.3 gai 3.9 29.2 57.17h 4 48.5 i 4 24.5 hq i 5.0 hai 1.8 17.7 43.94

a Ž . Ž‘a’ through ‘i’ represent different subnetworks selected from stations recorded Salmon in Jordan et al. 1966 see Fig. 1 for the subnetwork. Ž .‘h’ ; the integer is the number of stations in the subnetwork; the last figure is the absolute error in kilometers associated with the respective

subnetwork.bConventional location solution treating the combined network as a whole; the last figure is the absolute error in kilometers.c ŽSolution with the adaptive method, using the two subnetworks identified in columns 1 and 2; the first figure is the absolute error in

.kilometers associated with the adaptive solution; the second figure is the absolute error associated with the mean of two epicenter solutionsin columns 1 and 2—recommended when the two rays lead to an angle less than 208.d The angle of intersection. In general, if the angle is greater than 208, the adaptive method often performs much better than the conventionalmethod.


Fig. 1. Epicenters of Salmon explosion as determined with the first arrivals reported at four regional stations: WMO, FAY, FLO, and GRV,using travel–time tables of several one-dimensional continental models. The resulting epicenters are shown in blue stars, and the plus signrepresents the true location of Salmon explosion. Due to the poor azimuthal coverage of the stations, with a maximum gap of 3058, themislocations corresponding to six typical continental models vary from 31 to 54 km, which are not impressive at all. Nevertheless, all theelongated error ellipses point to almost the same direction. Two skew, large-aperture networks like the one tested here would suffice toprovide a ‘good’ epicenter estimate, provided the two rays used in triangulation are sufficiently apart.

.imuths are available for triangulation, it is wellknown in geodesy that the ideal situation is when thetwo rays are perpendicular to each other. This maybe difficult to achieve in reality, depending on theactual network configuration. Experience indicatesthat if the intersection angle is larger than 208, then

the result would generally be acceptable. If the inter-section angle is too small, that means the two net-works are virtually leading to backazimuths close toeach other, i.e., the two arrays are not providingadditional or independent information. Thus, the newalgorithm will not offer a location result any better

Fig. 2. An illustration of the proposed location procedure. Shown on the top frame are the 7 stations which are grouped into 2 networks, ‘h’and ‘i’. Network ‘h’ consists of WMO, FAY, GRV, and FLO, while network ‘i’ consists of ATL, CPO, TASK, and FAY. The bottomframe shows the locations of Salmon using various networks and methods. Open circles are epicenters estimated with networks ‘h’ and ‘i’,which have an offset of 48 and 25 km, respectively. The dashed circle corresponds to the 1000 km2 uncertainty area as specified in the

Ž .CTBT. If the two networks are combined, the standard location routine gives a location which is 5 km away unfilled star . Applying theŽ .proposed location procedure to these two networks lead to an epicenter blue star which is 1.8 km from the ground truth location.


than what the conventional algorithm would do.Consequently, all stations should be lumped togetherin the location exercise in this case. Alternatively,one can use the mean location of the two epicentersdetermined with the two subnetworks. This is theprocedure used in the following testing cases. Notethat only the absolute location error is addressedhere. The formal error ellipse associated with the

solution resulted from this adaptive method is asubject for future study.

2.1. Example 1: relocation of Salmon explosion641022

Salmon, an underground nuclear explosion inMississippi, was seismically recorded throughout

Ž .Fig. 3. The Russian Federation conducted a large 350-ton chemical explosion in Kola Peninsula at 060546.2 h, on September 29, 1996.Ž .The ground-truth location 67.6758N, 33.7288E, shown in cross was announced for calibration purpose. This figure shows the locations

derived with seven one-dimensional continental models using 9 phase arrivals reported by stations in Finland and northern Scandinavia. Dueto the poor azimuthal coverage of the stations, with a maximum gap of 2588, the mislocations corresponding to six typical continentalmodels vary from 1 to 37 km. All the elongated error ellipses point to almost the same direction, which is 788 clockwise from North. Twoskew, large-aperture networks like the one tested here would suffice to provide a ‘good’ epicenter estimate, i.e., with the bias due to ‘modelerror’ significantly reduced, provided that the two rays used in triangulation are sufficiently apart.


North America and at some teleseismic stations. The5-kt explosion was detonated at 1600 h UT onOctober 22, 1964, at a depth of 828.1 m. Theepicenter is 31808X31.57Y N, 89834X11.8Y W, in theTaut salt dome in Hattiesburg, Southern Mississippi.Extensive studies have been conducted for this eventto validate crustal profiles toward different directionsŽJordan et al., 1966; Springer, 1966; Warren et al.,

.1966 . In the following discussion, IASP91 modelŽ .Kennett, 1991 will be deliberately used to test therobustness of the proposed algorithm. No stationcorrection will be applied to this crustal model,which is basically a worldwide average.

Ž .Jordan et al. 1966 published phase picksrecorded at 143 stations for Salmon explosion. Thirtyarrivals from stations within 108 are used in thefollowing tests. The stations are partitioned into ninegroups which are labeled ‘a’ through ‘i’. Selectingtwo subnetworks at one time, there are 36 possiblecombinations in total. Table 1 summarizes the results

Žof 36 tests of using individual subnetworks columns.1 and 2 , standard method with two subnetworksŽ .combined column 3 , as well as the triangulation

Ž .result using two backazimuths column 4 . Columns1 and 2 have three entities: the network identifica-tion, number of stations in the network, and the

Fig. 4. Same as Fig. 3 except for a different network. Eight phase picks were used in this location exercise. All the resulting elongated errorellipses point to almost the same direction, 1098 clockwise from North.


Ž .mislocation in km associated with this network.Column 3 is self-explanatory: the number representsthe mislocation measured in kilometers associatedwith the corresponding combined network. Column 4has two numbers. The first number is the mislocationof the proposed location method based on the trian-gulation. The second number is the mislocation cor-responding to the mean location of two epicentersestimated with two subnetworks listed in columns 1and 2. The intersection angle of the two correspond-

Žing major axes is labeled as the diagnostic measured.in degrees; column 5 . An asterisk in columns 4 and

5 indicates that the diagnostic is less than 208, andthe mean location is used. It is clear that wheneverthe intersection angle is larger than 208 or so, theresulting epicenter has an absolute error less than 18km, a radius corresponding to the 1000 km2 confi-dence region as specified in the CTBT. If the inter-section angle is less than 208, the two backazimuthsare close to each other, and the location would be offŽ .see lines marked with an asterisk . In these cases,the epicenters derived from the standard locationalgorithm should be used. Some of the subnetworkscould give very good epicenter without the need ofusing triangulation. However, the triangulation stepprovides a quantitative measure as when the locationcould be reliable, using the intersection angle as adiagnostic. Out of the 36 tests listed in Table 1, 32have a location error within 18 km when this hybridmethod is used.

Fig. 1 illustrates several major features that con-stitute the corner stones of this proposed algorithm.The testing network, labeled ‘h’, comprises of four

Ž .stations WMO, FAY, GRV, and FLO spread on thenorthwestern quadrant of the event, with a maximumazimuthal gap of 3058. When the first P arrivals ofthese four stations are fed into the standard location

Žroutine, six different continental models labeled ‘I’,.‘J’, ‘B’, ‘D’, ‘L’, and ‘K’ in Fig. 1 lead to locations

that are off from 31.6 to 53.9 km. Obviously theselocations are very poor, due to the sparse, skewgeometry of the network plus the erroneous crustalmodel. Nevertheless, the uncertainty ellipses associ-ated with these six crustal models consistently alignedalong a backazimuth between 147.678 and 148.958.

Fig. 2 shows the testing result using the IASP91model as well as networks ‘h’ and ‘i’. The configu-ration of the networks and the location of Salmon areshown in the top frame of Fig. 2. Both networks ‘h’and ‘i’ have essentially a linear configuration. Theground-truth location of Salmon event is shown in aplus sign. The two epicenters estimated with net-works ‘h’ and ‘i’ are shown as open circles, respec-tively, which are outside the 18 km permissible

Žlocation accuracy as specified in the CTBT the.dashed circle . The two major axes as determined by

the two networks intersect at an angle of 43.948, andŽ .the resulting intersection point blue star is only 1.8

km away from the ground-truth location. If the con-ventional method is applied to the network with all

Table 2Comparisons of various epicentral estimates of 960929

a bE8 N8 Error No. Velocity model Remark

33.728 67.675 0.0 0 NrA Ground truth32.539 67.573 51.8 16 IASP91 PIDC REB32.499 67.550 54.1 11 IASP91 PIDC33.948 67.717 10.4 11 IASP91 this study, ‘a’q ‘b’34.105 67.696 16.2 11 IASP91 this study, ‘b’q ‘c’33.900 67.600 11.1 17 ? Norwegian NDC

Ž .33.252 67.677 20.2 14 ? Finnish NDC Helsinki bulletinŽ .33.851 67.592 10.6 20 ? Finnish NDC Bergen solution

33.757 67.701 3.2 7 Baltic Shield PIDC REV, P onlyŽ .33.586 67.718 7.7 11 Baltic Shield Bondar and Ryaboy 1997´

Ž .33.641 67.725 6.7 34 Baltic Shield PIDC CEB IMSqNDC phases

a The absolute error in kilometers.b Number of stations used.


Ž .seven stations combined, the location unfilled staris 5.0 km off. In this case, certainly the result ofconventional approach is not bad either. What theadaptive method would offer is a measurable quan-tity, namely the intersection angle, which tells uswhether we should use the triangulation result or use

Ž .the mean location without triangulation .

Several earlier location studies have experimentedwith the Salmon data with various conditions. Tomake the comparison meaningful, only those withoutstation corrections are quoted here. Based on 45stations at distances between 1.58 and 178, Herrin

Ž .and Taggart 1966 derived a location 13.2 km off.Ž .Rivers et al. 1981 used arrival times and backaz-

Fig. 5. Locating the Kola calibration explosion with the proposed adaptive method using two networks, ‘a’ and ‘b’, as shown in Figs. 3 and4, respectively. Network ‘a’ comprised of 8 stations and 9 picks: FINES, KAF, KJN, OUL, SDF, ARCES, KEV, and KTK1. The locationŽ .in open circle is 37.3 km off. Network ‘b’ comprised of 7 stations and 8 picks: HFS, NORES, ARCES, KEV, KTK1, SPIT, and SPAO,

Ž .and the absolute location error is 33.2 km. Combining all picksrstations together leads to an epicenter unfilled star which is 24.9 km awayŽ . Žfrom the ground-truth spot shown in cross in the center . Triangulating the two ‘backazimuths’ determined with networks ‘a’ and ‘b’ see

. Ž . 2Figs. 3 and 4 leads to an epicenter 10.4 km away blue star , which is within the radius of 17.84 km covering the 1000 km locationaccuracy called for by the CTBT. The two rays intersect at an angle of 32.58, indicating that the location result with the adaptive method isreliable.


imuths measured at 12 LRSM stations, and theirlocations had an absolute error ranging from 37.6 kmto a few hundred kilometers. Comparing to theseearlier results, it is true that using the conventionallocation algorithm, all 36 configurations of seismicnetwork as shown in Table 1 already give very goodresults, with the largest mislocation being 13.9 km

Ž .only case ‘fqg’ in Table 1 . The problem with the

conventional location procedure is that the user usu-ally does not have any clue as when the mislocationwould be small. The so-called uncertainty error el-lipse does not account for the location bias due tomodel error. The proposed hybrid method does notalways offer a location better than that derived fromthe standard method. It provides, however, a measur-able quantity which tells the user if the triangulation

Fig. 6. Same as Fig. 5 except the network ‘a’ is replaced with network ‘c’ which is comprised of 11 phase picks: FINES, KAF, HFS,NORES, KJN, OUL, SDF, ARCES, ARCES, KEV, and KTK1. Using IASP91 model and the network ‘c’, the epicenter is 55.5 km off.

Ž .Combining all picksrstations of networks ‘b’ and ‘c’ leads to an epicenter unfilled star which is 24.9 km away from the ground-truth spotŽ .shown in cross in the center . Triangulating the two ‘backazimuths’ determined with networks ‘b’ and ‘c’ leads to an epicenter 16.2 km

Ž .away blue star , which is still within the 17.84 km CTBT-permissible error. The two rays intersect at an angle of 30.18, indicating that thelocation result with the adaptive method is reliable.


Ž .can be used for a location within 18 km , or theŽmean location should be used with a location accu-

.racy comparable to that of standard approach .

2.2. Example 2: relocation of Kola explosion 960929

ŽAt 060546.2 h, September 29, 1996, a large 350.tons chemical explosion was carried out in central

Kola Peninsula, Russia, in an underground shaft ofKirovskiy mine in the Khibini Massif. The exact

Žlocation of this event 67.6758N, 33.7288E, shown at

.the cross in Figs. 3 and 4 was announced. Table 2summarizes the location results obtained at the Pro-

Ž .totype International Data Center PIDC , FinnishŽ .National Data Center NDC , Norwegian NDC, and

DSWA. If many local stations are used, as the twoŽ .NDCs did in this case, or if a calibrated regional-Žized velocity model is available as it did in Bondar´

.and Ryaboy, 1997 , then the location determinationis not a major problem. The challenge rises when wehave neither. Using IASP91 model, the standardlocation algorithm gives an error around 50 km

Ž .Fig. 7. Reduced travel–time curves YsTyXr8 of first P arrival for zero-depth source. Eight continental crustal models shown are:Ž . Ž . Ž . Ž . Ž . Ž . Ž .IASP91 model green , model J yellow , model D blue , model G cyan , model K red , model L black , model H orange , and model

Ž .W gray . Except for the model W, which has a very thick crust, all the remaining are typical crustal models for stable continental regionsŽ .and have been tested for the event 960929 Fig. 8 .


Ž .Fig. 8. Comparison of the locations obtained with the conventional method yellow triangles against those derived with the adaptive methodŽ . Ž .red disks . The map is centered at the ground-truth location 67.6758N, 33.7288E with a radius of 50 km. The inner, dashed circle has a

2 Ž .radius of 17.84 km, which encloses an area of 1000 km . Using the conventional location algorithm and seven crustal models Fig. 7 , fourout of seven of the resulting epicenters fall outside the dashed circle. With the adaptive method, only two models lead to locations outsidethe circle. Also, five out of seven models give a location closer than that derived with the conventional algorithm. This comparisonsubstantiates that the proposed adaptive location algorithm provides a better epicenter estimate.

Ž .lines 2 and 3 of Table 2 . Note that the operationalconsiderations related to on-site inspections have

established a goal that remote treaty monitoringmethods routinely locate sources on land to within

Fig. 9. Pakistani seismologists suspected that a seismic event on April 28, 1991 could have been an explosion near the Indian test site whichŽ .is shown as an asterisk on the top. USGSrNEIC’s location cross of this event is far away from the border, however. Using IASP91 model

Ž . Ž .and 5 picks recorded at Pakistani MSSP Micro Seismic Study Programme stations DRP, THW, CEP, SAG, and NIL , the epicenterŽappears to be within Pakistani territory, 23.1 km from the PDE location. If 6 picks from another network of 4 stations HYB, BOM, KOD,

.SHI—not shown were used, the resulting epicenter is 33 km away from the PDE location. Combining the phase arrivals at these 9 stationsŽ . Ž .would lead to an epicenter unfilled star 12.3 km away from the PDE location. The adaptive method gives an epicenter blue star only 3.7

km away from the PDE location.


an area of 1000 km2 or less. This translates to aradius of 17.84 km. If the proposed hybrid triangula-tion method is used in this case, the absolute errorsdrop to within the permissible limit, even if an

Ž . Žerroneous model such as IASP91 is used Figs..5–8; see also Table 2, lines 4 and 5 .

2.3. Example 3: relocation of Pakistani eÕent 910428

Seismologists at Pakistani Micro Seismic StudyŽ .Programme MSSP once suspected that a seismic

event on April 28, 1991, could have been an explo-sion near the Indian test site which is shown as anasterisk on the top of Figs. 9 and 10. They ap-proached the US Embassy in Pakistan for informa-

Ž .tion Turnbull, 1992 . USGSrNEIC’s PDE locationŽ .the cross in Fig. 9 of this event is far away fromthe border, however. Using IASP91 model and 5

Žpicks recorded at MSSP stations DRP, THW, CEP,.SAG, and NIL , the epicenter appears to be within

Pakistani territory, 23.1 km from the PDE locationŽ .Fig. 9 . If 6 picks from another network of 4

Ž .stations HYB, BOM, KOD, SHI—not shown wereused, the resulting epicenter is 33 km away from thePDE location. Combining the phase arrivals at these

Ž9 stations would lead to an epicenter unfilled star in.Fig. 9 12.3 km away from the PDE location. The

Žproposed adaptive method gives an epicenter blue.star only 3.7 km away from the PDE location. In

Fig. 10, the second network is replaced with that ofCEP, SAG, NIL, and NDI. Note that three of thesestations are part of the first network. The adaptivemethod gives a location 2.7 km from the PDE loca-tion. Combining these phase picks leads to a location3.4 km away from the PDE location. NEIC’s PDElocation was based on primarily teleseismic record-ings. The adaptive results in Figs. 9 and 10 stronglysuggest that the PDE location could have been verygood. If this is correct, it would imply that thecrustal structure of central northern Pakistan can

probably be approximated by a simple one-dimen-sional model—as far as location problem is con-cerned. The lesson learned from this instant is thatincorrect analysis of sparse seismic data can alarmcountries having political difficulties with theirneighbors. The United States should be ready toquickly respond to queries from third countries con-cerning ambiguous events. This problem can be re-duced through the implementation of ‘open seismicstations’ and encouraging development of analytical

Ž .expertise in explosion monitoring Turnbull, 1992 .Indeed, if we include the phase arrival from eitherthe station QUE, which is operated by the PakistaniMeteorological Department, or NDI, which is oper-ated by the Indian Meteorological Department, evenconventional location algorithms would have beenable to dismiss MSSP’s concern. MSSP plans toupgrade their seismic facility to include a new arraynear NIL, which is part of Pakistani contribution tothe CTBT IMS. Once this proposed Pari array isinstalled and operational, it is anticipated that eventslike 910428 can be easily located and identified withhigh confidence.

3. Discussion and conclusions

Quite a few investigators have examined the util-ity of including azimuth measurements as constraints

Ž .on location. Early studies by Julian 1973 , GjoystdalŽ . Ž .et al. 1973 , Shilen and Toksoz 1973 , considered¨

the use of azimuth estimates from arrays in locatingŽ .primarily teleseismic events. Smart 1978 used Lg

azimuth estimates to locate regional events. Rivers etŽ . Ž .al. 1981 extends the study of Smart 1978 to

incorporate the azimuths in a linearized inversionprocedure. However, their azimuth estimates wereobtained from three component stations and wereless accurate than those deduced from frequency–

Ž .wavenumber f–k processing of NORESS-type ar-

Fig. 10. Same as Fig. 9 except the second network is replaced with that of CEP, SAG, NIL, and NDI. Three of these stations are part of thefirst network. The adaptive method gives a location 2.7 km from the PDE location. Combining these phase picks lead to a location 3.4 kmaway from the PDE location. NEIC’s PDE location was based on primarily teleseismic recordings. The adaptive results in Fig. 9 and in thisfigure strongly suggest that the PDE location could have been very good. If this is correct, it would imply that the crustal structure of centralPakistan can probably be approximated by a simple one-dimensional model.


Ž .ray data. Thus, Rivers et al. 1981 concluded thattheir azimuth estimates were not very useful, while

Ž .Bratt and Bache 1988 illustrate that adding azimuthmeasurements obtained from array data do betterconstrain the location. The adaptive procedure testedhere appears to work exceptionally well because thetwo azimuth estimates required in locating the eventare accurately deduced from networks which canalso be considered as two arrays with extremelylarge apertures. For an array like this, the conven-tional frequency–wavenumber processing schemecannot be applied because the short-period wave-forms would be highly incoherent across the vastarea, whereas the long-period signals are not preciseenough. Furthermore, in many cases only the arrivalreadings are available and the f–k technique simplycannot be applied without waveform data.

Ž . Ž .Chang et al. 1983 , Chang 1985 correctlypointed out that station residuals are highly corre-

Žlated when an erroneous crustal model is used see.also discussion in Blandford, 1995 . The assumption

that all phase arrivals are uncorrelated as used inmany inversion routines is simply wrong. Chang andhis colleagues suggested to establish a covariancematrix of the residuals and to incorporate the covari-ance matrix into the location inversion. However, thecorrelation among station residuals is not just afunction of the inter-station distances, it is also afunction of the earth model. Even if we assume thatthe crust is truly one-dimensional, the larger thediscrepancy between the true and the postulatedcrustal models, the stronger the correlation amongstations on the same side from the epicenter. Theresidual covariance structure also depends on the

Ž .geometry relative to the source of each pair ofstations. For instance, assuming the crust of interest

Ž .is truly one dimensional yet unknown , stationsaround the epicenter with the same epicentral dis-tance but different azimuths will have extremelyhigh correlation in the residuals. These make theresidual covariance structure very difficult to berepresented as a function of the inter-station distancealone. This could be the reason why Chang’s ap-proach only provides a marginal improvement inlocating NTS events. The proposed hybrid approachappears to be able to get around this difficulty.

The proposed new location procedure consists ofa step of azimuth estimation, followed by a simple

triangulation step using the optimal azimuth esti-mates. This procedure is ‘adaptive’ in several senses:

Ž .1 The technique used in estimating the azimuthovercomes the difficulties in applying the f–k pro-cessing to large-aperture array and in the case oflacking waveform data.

Ž .2 The original network geometry may beseverely skew, yet the procedure can turn this disad-vantage into advantage to better constrain the az-imuth. In the case the network has too few stations towarrant an adequate partition of the network, theconventional location procedure can still be applied.

Ž .3 A good initial crustal model is not required,thus the prior calibration information may becomeless critical.

Ž .4 Different velocity models can be assigned tothe two subnetworks so as to best represent theunderlying geology and geophysics along differentpaths, if necessary.

Experience indicates that, using this staged trian-gulation approach, in most cases the resulting finallocation is relatively less sensitive to choice of theinitial velocity model. Thus, an obvious advantage ofthis adaptive location procedure is that perhaps thecalibration can be deferred to a later stage. Thiscould have a major implication for both the monitor-ing and implementation of the CTBT. This alsomeans that the procedure is transportable, at least inthe relative sense, to other regions of the globe.Experience also indicates that if the intersection an-gle is larger than 208, then the result would generallybe acceptable.

Only the absolute location error is addressed inthis paper. The formal error ellipse associated withthe solution resulted from this adaptive method is asubject for future study. However, if seismologistsare confident that an epicenter estimate is within 18km to the true location of a suspicious event, thenthe area to be inspected by the OSI team is about1000 km2, which is already acceptable according tothe CTBT. Thus, the formal statistical description ofthe error ellipse might be less important. As for other

Žpotential applications of this procedure such as rou-.tine generation of seismic bulletins , this procedure

offers a quantifiable measure as whether the locationderived with conventional location algorithms wouldbe reliable. Location precision associated with thisnew procedure can be quantified in a straightforward


manner with resampling techniques, such as MonteCarlo iterations or bootstraping.

Acknowledgements

The phase picks of Kola calibration event werefurnished by Istvan Bondar of Center for Monitoring´ ´Research. This research was conducted at the BasicResearch Program in Seismology, Defense ThreatReduction Agency. The views are those of the au-thor’s and do not represent the official policy of theDefense Department or the U.S. Government.

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(1999) Epicenter estimation using erroneous crustal model(s) and skew regional networks

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Transcript of (1999) Epicenter estimation using erroneous crustal model(s) and skew regional networks